Sanrio Text Art

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⠀⠀⠀⠀⢠⠖⠲⣄⡀⠀⠀⠀⠀⡴⠒⠢⣀⣠⠤⠖⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠙⠒⠒⠒⢺⠃⢠⢤⡿⠤⣀⢀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠸⣄⣨⢿⡀⢀⡿⡄⢉⠆⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⡈⣠⠞⢦⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⡆⠀⠀⠀⠀ ⢀⡀⡧⠤⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠉⢩⠏⠉⠁⠀⠀ ⠀⠀⣳⡠⠄⠀⠀⠀⠀⠀⠀⢆⡰⠀⠀⠀⠀⠈⠀⢀⣀⡜⢯⠉⠐⢤⠀ ⠀⠈⠀⣱⢴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⡾⣄⠸⣋⣷⠀⡇ ⠀⠀⠀⠀⠀⣠⢽⡛⠙⣟⠛⢟⣻⡿⡻⠛⡯⡽⠒⣤⡿⣮⣇⠘⢋⠔⠁ ⠀⠀⠀⠀⡎⠀⠀⢘⠄⢸⠉⠉⠉⠉⠉⠉⢱⢰⠓⢩⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⡖⠂⢊⠀⣸⠤⠤⠤⠤⠤⠤⢼⠸⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣅⠇⠃⢁⣿⠉⡉⠉⢩⠒⡞⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⠯⠯⠭⠴⠧⠀⠀⣉⠤⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠦⠄⣀⣀⣀⡠⠤⠮⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠄⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀ ⠀⠀⠀⠀⢀⣀⠀⡊⣅⡕⠉⠑⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇ ⠀⠀⠀⠘⠀⢀⡑⠉⠉⠓⠠⡐⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑ ⠀⢠⠂⠈⠌⠀⠈⡆⠐⢧⠤⠋⠒⢁⡀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠐⢄⠀⠀⠀ ⠀⢘⠤⢀⠈⠒⠊⣄⣀⠜⠀⠀⠀⡠⠃⠁⠒⠂⠐⠊⠀⠉⠒⠒⢆⡀⠀⠱⡢⢄ ⠔⠁⠀⠈⠂⡤⠒⠁⠀⢀⠍⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠈⡄⠀⠀⢈⠮ ⠀⠀⠀⠀⡔⠀⠐⠒⠂⠁⢀⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠆⢸⠂⢀⡇⠀ ⠀⢀⡠⠪⠁⠀⠀⡰⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⣀⡀⠀⠈⠩⠠⣌⢀⣾⠃⠀ ⣎⠁⢀⠁⠀⠀⠈⢡⠀⠀⠈⡙⡉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣡⡾⣿⢿⠉⠀⠀ ⠙⠢⡀⠈⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠤⡾⠉⠁⢿⡜⡀⠀⠀ ⠀⠀⠀⠉⢉⠋⠐⠂⠐⠊⠁⠒⠀⠀⠀⠀⠐⠒⠈⠉⠐⡄⢡⡀⠀⢀⡴⠃⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠞⠛⠛⠛⠛⡟⣛⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠓⠦⣤⡀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠛⢿⣛⡶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⣿⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⣼⠏⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⣇⠀⣶⣷⡆⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠇⣼⡿⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⡞⢆⠙⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⢰⣿⡀⠀⢸⡿⠣⡀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠈⠓⢤⣀⡀⠀⢀⣠⠴⠋⠀⠹⣆⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⡾⠀⣿⣿⣇⠀⣹⠃⠀⠈⠑⠲⠤⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⣀⣀⠀⢻⡀⡀⠀⢿⡀⠀⠀⠀⠀⠀ ⢰⡇⢸⣿⣿⣿⠀⣿⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡆⢸⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⡆⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡴⢃⣾⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⠸⣿⡿⠀⡐⠹⠟⢷⣄⡀⢀⣀⣀⣀⣀⣀⣤⣴⣒⣒⣒⣒⣒⣒⣶⠚⠋⠉⠛⢧⣤⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠘⣇⠀⣿⡄⠦⠃⠀⠀⣾⡿⠋⠁⠀⠀⢈⣿⣟⠉⠉⠉⠁⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠙⣿⠀⠀⢸⠁⠀⠀⠀⠀⠀ ⠀⢻⡀⢹⡗⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠈⢇⠈⣷⣀⠀⠀⠈⠿⣦⡀⠀⠀⠀⢘⣿⣟⣳⣦⣤⣀⣀⣀⣀⣤⣷⣄⣀⣀⣠⣴⣿⣀⣠⣾⣃⣀⠀⡀⠀⠀⠀ ⠀⠀⠸⠗⠛⠛⠛⠉⠉⠉⠉⠉⠓⠒⠒⠋⠁⠀⠈⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠈⠉⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣉⣀⣴⣿⡿⠭⠿⠛⠛⠰⢿⡖⠛⠉⣉⣿⣷⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣶⣶⣶⣶⣾⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠃⠀⢱⡱⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠉⠁⠀⠈⠉⠉⠓⠵⢄⡑⡢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣤⣹⡶⢄⡀⠀ ⠀⠀⠀⡔⠁⠀⠀⠀⠞⠠⢄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠘⠌⠛⢦⣌⠐ ⠀⢀⠎⠀⠀⠀⠀⡸⡃⣤⠊⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⡄⠀⠈⠓ ⠀⡌⠀⠀⠀⠀⠀⣏⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⢰⠀⠀⠀⠀⠀⢀⡧⠒⠂⠈⠉⠉⠉⠀⠐⠒⠤⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⡈⠀⠀⠀⠀⠀⢸⡀⠀⢀⡄⠀⠀⠀⠀⢀⣀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⠽⠿⢯⠀⠀⠀⠀⠀⠀⠹⠟⢿⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⢰⡀⠀⠀⠀⠀⢸⠑⢢⣄⣀⡀⣉⣁⡀⢀⣀⡠⡴⢣⡀⠀⠀⠀⣠⠃⠀⠀ ⠀⠑⢄⣀⣀⡠⠃⠀⠈⠈⠢⢍⠟⠟⠛⢏⣡⠊⠀⠀⢻⠒⠐⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡜⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢎⠀⠈⠠⢒⡄⠈⠐⠊⠠⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠶⢶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡿⠁⠀⠀⢸⣏⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠀⠀⠀⠀⠘⣿⣆⠹⣿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠿⠖⠒⠒⠒⠒⠶⠶⠤⣤⣿⣿⡆⠹⣧⠉⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣿⣦⣆⡐⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣔⡢⣀⡉⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣥⣀⠀⢹⣿⢶⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡻⢷⣾⣧⡟⠀⠙⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⠉⠛⢿⣷⣤⡀⠀⠙⠳⣤ ⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠻⢿⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣆⠀⠀⠀⠀⠉⠻⣿⣆ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠐⢾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠖⠃⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⢁⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣥⠶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠦⣄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢀⣠⣴⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⢰⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢙⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⠛⠉⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⡷⣦⣤⣄⣀⡀⠀⢀⣤⣤⣤⣤⡄⠀⠀⣀⣀⣠⣤⡴⢾⡿⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⠇⠈⠳⣬⡉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⠛⢩⡼⠋⠀⠀⠀⠙⣷⣦⣀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠷⣤⣀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⢦⣀⣴⠏⠛⠟⠋⠁⠉⢷⣄⣠⣾⠋⠀⠀⠀⠀⠀⠀⢻⢹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⡆⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢠⠏⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡴⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣴⠛⠀⠀⠀⠈⠉⢍⡑⠒⢶⣄⠀⠀⠀⠉⠙⠒⠉⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⠒⢾⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠈⠛⢷⣄⠀⢀⣠⣴⡶⠿⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠏⠀⠀⠀⠀⠀⢻⣿⠿⠋⠁⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⠀⣤⣤⣤⣾⣿⣦⣤⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿⣠⣿⠋⠀⠀⠈⢻⣶⠶⠶⢶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢀⣽⡇⠀⠀⠀⠀⢨⣿⣄⠀⠀⠀⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠛⠛⢿⣤⣀⣀⣴⣿⣧⣽⠂⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣏⠀⠉⠁⠀⢠⣾⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⣀⣴⠟⠁⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⠶⠖⠛⢻⣿⠛⠛⠓⠲⠤⣤⠀⠀⠀ ⠀⠀⢀⣀⣼⣧⣤⣤⣤⡄⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠉⠉⠁⠸⣿⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠓⠒⠲⣿⣷⣤⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠄⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠿⢻⣧⠀⠀⠀⠉⠳⣦⡀⠀ ⠀⠀⠀⢠⠴⠞⢿⣧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⡿⠃⠀⠘⣿⢀⣀⣀⡀⠀⠈⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣧⡀⠀⠀⢽⠻⠉⢻⣿⠀⠀⠁⣿ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⡾⠟⠋⠁⣿⢸⠿⣦⡀⠘⢷⣤⣼⢿⡆⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⣩⣽⠿⠟⠻⣿⡿⠿⠿⢿⣿⠿⣿⡿⠿⢿⣿⠿⣿⡿⢿⣿⣭⣉⣡⣴⣶⣤⣀⢠⣿⣿⣞⣩⣷⡀⠀⠻⠷⠋⠁⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⣷⣄⠀⠀⠈⢿⣄⠀⠀⠉⠳⢦⣙⣷⠟⢁⡼⠋⠀⠀⣿⡌⢻⡏⠀⢀⣬⣿⣿⣿⠿⢿⣳⠾⣇⠀⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠹⣧⡀⠀⠘⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⡇⠀⣧⣾⣫⡿⠟⢻⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠉⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⡀⠀⣰⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣦⣄⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏⠉⠛⠛⠋⠀⠀⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⠀⢸⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⠄⢠⡞⠓⢶⠀⣼⢿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢾⣀⣸⠳⠴⠂⠀⡟⣾⠁⠀⠀⠀⠀⠀⠀⢀⡭⠿⢯⡉⠉⠙⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣁⣀⣰⣀⣿⣇⣿⡆⠐⢲⡄⠀⠀⠀⠸⢧⣤⣬⡛⠂⠀⣿⣤⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣭⣭⣭⣍⣍⣉⣐⣒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠑⢈⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢻⡟⠋⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡃⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⢀⣠⠤⠴⠦⢤⣀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⢧⡀⠀⠀⢸⠀⣰⢋⣴⠶⢦⣤⠤⣌⢻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡇⠀⢀⡴⠖⠲⢴⡃⠀⠀⠀⠀⢳⠖⠒⠚⠀⡇⢸⡀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣀⡟⠀⠀⠀⢀⡤⠖⠤⡀⢠⣏⡀⠀⠀⠀⢧⡀⠹⣄⡀⠀⣠⠏⣸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⣟⠀⠀⠀⣹⠀⠀⢳⡄⠀⠀⠀⠓⠤⣀⣉⣉⡤⠞⠋⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢿⡟⠁⠘⠦⠤⠴⠃⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀ ⠀⠀⠀⠀⢀⡼⠁⢸⡀⠀⠀⠀⠀⢸⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀ ⠀⠀⠀⢀⠞⠀⠀⠀⠳⢄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠘⡇ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⣇ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⡄⡽ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠏⠋⠀⣷⡇ ⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡾⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠠⣷⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠔⠋⠀⠀⠀⠀⠀⡼⠉⠀ ⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠈⠙⠒⠲⠤⠽⢦⣤⣀⡤⠤⢤⣤⣤⣀⣠⡤⠶⠚⠛⠓⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠎⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⣀⣰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣸⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣦⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣾⠛⢷⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠛⢿⣇⠀⣿⠟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠹⣷⠀⣼⠟⢛⣿⣶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠻⣶⡿⠿⠶⣿⠛⢿⡟⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠷⣾⠛⢿⠿⠟⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⣴⢿⡶⢾⡟⠳⣾⡋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣻⣶⡶⢻⣿⠶⣿⠷⣦⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣾⡇⠈⣿⢶⣼⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠛⠉⣿⣦⣾⡇⠀⣿⣤⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢷⠶⣷⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀ ⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⣼⠷⠶⠋⠈⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠈⡆⠸⣇⠀⠀⠀⠀⠀⠀⠈⠛⢦ ⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡧⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠈⠛⠛⠁⠀⡸⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠙⢿⡛⠛⢋⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠞⠁⠀⣀⣤⣀⠀⠀⠀⣰⣷⡾⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠉⠻⢷⣦⣄⣀⣀⠀⠀⣰⡟⠛⢷⣶⣶⢶⣾⡋⠀⠙⣷⡶⠟⠋⠁⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠉⠉⠙⢛⣿⣿⣄⣤⣾⠏⣠⡤⠿⣿⣶⡶⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⠟⠉⠉⠻⠏⠀⠀⠈⣿⠃⠀⡍⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶ ⣤⣤⣤⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠿⣄⠀⠀⠀⠀⠀⠀⣠⡟⢁⠀⠈⢀⣘⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⢸⢢⠹⠷⣤⣀⡀⣠⡼⠋⠈⡍⣰⠟⠉⠉⠻⠏⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣇⣘⢀⢀⠉⠃⠤⠌⣉⣉⠰⠀⠀⡇⠹⣄⠀⠀⠀⠀⠀⠀⢨⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠹⠟⠉⠙⢦⣀⡞⢂⣀⣀⡈⢐⣀⣀⣀⢛⡷⣤⣀⠀⣀⣴⠻⠈⢹⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣄⠀⠀⠀⠀⠀⠀⣸⡇⣿⠏⠁⠈⠙⡿⠋⠉⠙⢦⡸⢦⣬⡛⡛⠻⠀⠀⢀⣿⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠛⢦⣀⣀⣀⡤⠞⢻⡤⢽⣆⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⢀⠀⠀⠠⠀⣤⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠉⠋⠛⠂⠐⠁⠒⠆⠋⢷⣄⡀⠀⢀⣤⢾⠗⠈⢀⣀⣠⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣶⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣾⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠉⠲⣄⡀⠀⠀⠀⢀⡠⠤⠤⢤⡾⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠲⢤⡴⠋⠀⠀⠀⠀⠳⣀⠤⠤⢄⡀⠀⠀⢀⣼⠤⠤⠤⠿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠙⡄⠤⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢰⡄⠦⣷⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣄⠓⣨⠟⠉⠀⠈⠦⣀⣀⣀⡠⠞⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠳⡀⠀⠀⠀⠀⢀⡜⠉⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡍⠲⢄⡀⠀ ⠀⠀⠀⠀⠀⢀⠞⠀⠀⠉⠓⠒⠒⠊⠉⠀⠀⢀⣠⠤⠴⠒⠒⠒⠂⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠉⡷ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⠞⠁⢀⣴⡿⠋⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⣄⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⡴⠃⠀⣴⣿⣿⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢸⣿⣷⣄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⣸⠁⠀⣸⣿⡿⠘⣿⣄⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⣴⣿⡿⠹⣿⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣿⣯⣄⢀⣬⣿⠟⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣥⡄⢀⣭⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡀⠀⠈⡇⠀⠀⠙⢿⣿⣾⣿⣿⣶⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣿⣿⣿⣾⡿⠏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⢧⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⡈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⣞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⣳⣄⠀⢀⠤⠒⠈⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠤⡀⠀⠀⠀⣠⣞⡥⠚⢡⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⢠⠞⣱⠤⠀⠬⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠘⣤⡴⠞⠋⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢧⠀⠀⣿⡇⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⣤⣀⠀⢠⠋⠀⠀⠀⠀⢰⣣⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣼⡆⠀⠟⠀⠀⢸⠂⠀⠀⠀⠀⠀ ⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣶⠟⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⢰⢦⣤⠄⠀⠀⠀⠀⠀⣄⠀⠀⢰⣄⠀⠀⠀⡀⣤⣀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠘⢷⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣩⢺⣿⣿⣻⢹⡛⣟⣿⠇⢘⣟⢻⣿⣾⣿⣿⢽⢰⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠙⢲⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⠁⠀⠀⢸⣧⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠛⠒⠒⠒⠒⠒⠲⠼⢿⣧⠹⣆⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣤⣀⣈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣄⡈⠹⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⢾⣿⣏⠉⠳⢦⡀⠀ ⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⡟⠒⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠛⢷⣦⣀⠈⠓ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡼⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠉⠻⣷⣄ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇⠲⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠉ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠐⠚⠁⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠴⠒⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠢⢤⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣿⣶⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⠉⠀⠉⠛⠁⠀⠀⢀⣀⣄⠀⠀⠀⠀⠈⠙⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⠑⢢⣄⣀⠀⠀⠀⢈⣉⣁⣀⡀⠀⠀⠀⢀⣀⣤⡶⢷⣄⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢸⠉⠻⣍⠛⠶⣾⣿⣿⣿⣷⣶⠟⠟⢋⡵⠋⠀⠀⠙⣦⣄⡀⠀⢀⣀⠼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠦⣄⣀⣀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠈⠓⠦⡾⠉⠛⠉⠀⠙⢦⡴⢟⠀⠀⠀⠀⠀⢻⡇⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⠇⠀⢄⡀⠀⠀⠀⠀⠀⢧⡀⠀⢀⡴⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠴⡎⠀⠀⠀⠈⠩⡉⢱⣄⠀⠀⠈⠉⠉⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠿⠒⠒⠒⠒⠀⢒⣻⠷⠛⠋⠉⠉⠉⠉⠉⠛⠛⠷⠶⠿⠚⠛⠛⠛⠛⠻⠿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣤⣤⢤⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠛⠛⠲⣶⣴⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣰⡴⠞⠋⠉⠀⣰⡟⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣋⣡⡴⠶⠖⠀⠀⠀⠀⠐⠀⠀⠠⠄ ⡿⠋⠀⠀⢀⣀⣤⣇⠁⠃⠀⠀⠹⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣼⣿⡁⠐⣿⠶⠖⠲⣤⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠳⣿⣿⣧⣲⣏⠀⠀⠀⢸⡆⠀⢀⣾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠁⠀⠈⢿⡦⠤⠴⠞⠁⠐⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⠠⠄ ⣤⠶⢦⣀⠀⠀⠀⣼⠋⢩⡌⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢙⡆⠀⠚⢿⡶⠋⠙⠲⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣄⣠⠞⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣧⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡷⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⡀⠀⠀ ⣄⣀⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⢄⣀⣀⣀⣀⣀⣠⠤⠚⠋⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣄⡀⠀⠀⠀⢀⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣦⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠾⠛⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣠⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠙⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣼⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⡄⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢁⠀⠄⠠⠄⠀⣹⠀⠀⢀⣼⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠻⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠶⣀⣀⠤⠴⢀⡠⠞⠁⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⣀⣀⠀⠀⠀⣴⠃⠀⠀⠀⠀⣀⣀⡉⠉⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢀⣠⡼⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⡟⢦⡀⠀⠈⠙⠦⣄⡐⠚⠉⣀⡠⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠋⠈⠉⠙⠿⣇⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢸⡇⠈⠻⣦⣀⠀⠀⢈⣹⡶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠁⠀⠀⠀⠀⠀⣀⣤⠽⠛⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⡇⠀⠀⠀⢈⣽⠟⠉⠀⠀⠀⠀⠉⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡇⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⡇⠀⠀⡟⠀⠀⠀⠀⡠⠞⠉⠉⠈⠉⠳⢄⣠⠤⠤⢤⣀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡤⢴⣞⡟⠋⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠸⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠻⣆⣄⣠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣀⣀⣬⣿⠛⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠈⣧⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠑⠤⡀⢀⠔⠒⠲⡃⠀⠀⠀⠀⢡⠀⢠⣼⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡰⠈⠀⠈⢢⠐⠭⡀⠀⠈⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀ ⠂⠀⠈⣌⠙⡢⠀⠡⢀⠀⡀⠌⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠛⢌⢢⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⡰⠄⣀⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢗⢄⠀⠀ ⠀⠀⠀⡰⠁⠀⠒⠒⠊⠀⡀⠤⠀⠒⠒⠒⠒⠀⠤⠄⡀⠀⠀⠀⠀⠀⠈⠳⡈⠲ ⠀⠀⢰⠃⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠸⡀ ⠀⠀⡇⠀⠀⡰⠁⣰⡟⠉⠻⡆⠀⠀⠀⠀⠀⠀⢠⠞⠛⢶⣄⠈⠢⡀⠀⠀⠀⠁ ⠀⠀⡇⠀⡸⠀⣼⡟⢳⣄⣰⣧⠀⠀⠀⠀⠀⠀⢸⣀⣠⡾⠻⣧⠀⠰⡀⠀⠀⠀ ⠀⠀⡇⠀⡇⠀⠻⣧⣶⣯⣼⡟⠀⠀⠀⠀⠀⠀⠹⣧⣹⣷⣴⡾⠀⠀⡇⠀⠀⠀ ⠀⠀⠘⡄⢡⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠃⢠⠃⠀ ⠀⠀⠀⠘⢦⡑⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢴⠁⠀⠀ ⠀⠀⠀⠀⡀⡌⠚⠷⡔⠁⠀⠀⠁⠢⡀⠀⠠⠊⠀⠀⠈⢂⡠⠔⣷⠁⡟⠀⠀⠀ ⠀⠀⠀⢠⠊⠀⠀⡞⡄⠀⠀⠀⠀⠀⢱⠎⠀⠀⠀⠀⠀⢸⣳⠀⡿⠀⡇⠀⠀⠀ ⠀⠙⠁⠀⠀⢀⡗⠉⠈⠀⠀⠀⠀⢀⠌⠡⠀⠀⠀⠀⠀⠁⠈⢂⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⣇⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣟⣤⣤⣴⢴⣴⠸⡧⣤⣴⣖⢠⡄

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⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⠲⢶⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠦⣤⣄⠀⠀⠀ ⠀⠀⠀⠠⠄⣀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠉⢻⣄⠀ ⠀⠀⠀⣧⡤⠏⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀ ⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⠀⠀⠀⣿⢀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⣿⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⣿⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⠀⠉⠛⠛⠿⠷⠶⣶⡶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁ ⠀⠀⠀⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢿⡷⠒⠛⠋⠉⠉⠉⠉⠉⢉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠈⣦⣤⣤⠞⠁⠹⣜⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⣠⣀⠀⢸⡇⠀⣀⣠⣄⠈⠉⣽⠃⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀ ⣴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⠈⠛⠿⠗⠋⢹⠛⠛⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡟⠁⠀⠀⠀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⠀⣰⠒⣦⠀⠸⢴⣶⢦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢻⡄⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠙⠖⠋⠀⠀⣠⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢿⡀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⠀⠀⣀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀ ⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠶⠋⠉⠙⠻⠁⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠤⠖⠛⠋⠉⠀⠀⠀⠈⠉⠙⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀ ⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢰⠏⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠘⣆⠀⡀⢠⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⢀⣴⠿⠚⠛⠒⠶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣝⠿⠟⠃⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠇⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⢶⣤⣀⠀⠀⠉⠻⣧⣤⣤⣴⡦⣤⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⣨⠇⠀⠀⠀⠀⣀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠾⣥⣈⣙⣒⣒⣶⠿⠿⠿⢿⣿⡿⠷⠖⠒⠚⠋⣯⣤⣤⠴⠚⢿⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣸⡄⠀⠸⠯⠤⢶⡞⣿⣿⡟⠶⣤⣀⡀⠀⢈⡷⠀⠀⠀⣼⣶⠦⢤⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢙⣳⣶⢶⡞⠁⢻⡀⠀⠀⠀⠀⠉⠺⣍⣠⠴⠋⠀⠉⠉⠉⠁⠀⠀⡼⠃⢸⡆⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠙⣆⠀⠹⣄⣀⣀⣀⣠⣾⠃⠀⠀⣠⠴⠦⣄⠀⢀⡠⠊⠀⠀⢸⣇⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣆⠀⠀⠉⠉⠉⠀⠘⠦⣀⣰⠁⠀⠀⠘⡗⠉⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⠀⠀⢹⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣀⣼⣀⣀⣀⣀⣀⣠⠿⢦⡀⢸⡄⠀⠀⠀⣸⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠳⠷⣄⣀⣰⠷⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣰⠎⠀⠂⢁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⡀⠄⠁⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡀⠐⠀⡈⠠⠁⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠱⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⡡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣐⢣⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⢣⡙⠦⡙⠦⣙⠰⣃⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠻⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡑⠎⡔⢢⡑⢎⡡⢓⠬⡑⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⡑⢎⡜⡱⡘⢥⠚⡤⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣎⢷⣣⢻⢮⡻⣵⣻⣾⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢞⡷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢆⡍⠲⢌⠣⡜⡰⡉⢖⠱⣂⠭⡘⣅⠣⠎⡜⡡⢎⡌⡓⡌⢎⡱⡘⢤⡙⠜⡢⢅⠫⠜⣢⠑⡎⡔⣢⣵⣶⣿⡿⠟⡭⣮⣽⣾⢿⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣷⣌⠜⡱⢊⠵⣨⠑⡍⢎⠲⡡⢎⡱⢢⡙⡜⡰⡑⢎⠴⢱⡘⠦⣡⠙⡆⡜⣡⠓⣌⢣⡙⣤⣫⣴⣿⣿⠿⣛⣥⣽⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣛⣿⣿⣯⣖⡩⢒⡡⢍⡜⠬⣑⠱⣊⠔⡣⢜⡰⠱⣉⠎⡜⡡⢜⠢⣅⠳⣘⢰⣡⣯⣴⣷⣿⣿⠿⣟⣹⣦⣿⣿⠿⠋⠁⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣬⢛⣿⣿⣿⣷⣮⣶⣘⣦⢡⠓⡬⡘⢥⢢⡑⢣⠜⡘⠴⣑⣮⣵⣦⣷⣾⣿⣿⡿⢟⡻⣍⣶⣷⣿⣿⣿⣏⠀⠀⠀⠀⣼⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣍⣛⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⣏⣹⣔⣮⣷⣿⣿⣿⣿⣧⣳⣞⣿⣷⣦⣶⡾⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣭⣖⣦⣩⡍⢯⣙⣛⡛⣛⠻⡹⣍⣫⣕⣲⣬⣽⣶⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣯⣽⣽⣭⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⡿⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⡿⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠶⠦⢤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣤⡞⠋⠁⠀⠀⠀⠀⠀⠈⠙⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⡴⠶⡶⢦⢤⣤⣄⣀⣷⣞⣡⣤⣤⢾⣄⠀⠀⠀⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⣿⢡⢘⡐⠢⣶⣌⣿⣡⢺⡷⢦⣴⠌⢻⣦⡀⠀⠀⠀⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⣗⢢⠡⢌⣑⣢⣶⠛⣾⣟⠾⢦⣦⣍⢢⠰⣹⣗⠒⠒⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠧⠾⢚⣫⠷⠖⠚⠛⠛⠛⠓⠶⢭⣍⠛⠛⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢳⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡢⡝⢫⢬⠀⠀⠀⠮⠔⠢⠝⠀⠀⠀⢙⡰⣐⢒⣼⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⣄⣀⣀⣀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣉⣭⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢫⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⢦⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⢤⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠚⡅⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⠇⢀⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣠⣧⣤⠴⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠐⢲⠶⠶⠶⢿⡄⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀ ⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀ ⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀ ⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀ ⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣷⣾⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣶⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⣾⡿⠁⠀⠀⠀⢀⡴⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⡀⠀⠀⠈⢻⣷⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡟⠀⠀⣼⣿⠃⠀⠀⠀⠀⢸⡀⣄⣿⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣏⣠⣀⣧⠀⠀⠀⠈⣿⡄⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠏⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⣧⣿⣿⠁⠀⠀⠀⠀⣿⣦⣀⣀⣀⣀⣀⣼⣿⠆⠀⠀⢹⣿⢿⣻⠇⠀⠀⠀⠀⣽⣧⠀⠀⠀⠀⠀⠙⣧⣄⠀⠀⠀⠀ ⠀⢀⣾⡿⠃⠀⠀⠀⠀⣿⣧⡠⡤⠤⠤⠤⢄⡈⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠉⠉⢉⣄⡤⠤⠤⠤⣿⣇⠀⠀⠀⠀⠀⠀⢘⣷⡀⠀⠀⠀ ⠀⣾⡿⠁⠀⠀⠀⠀⠃⢻⣿⣄⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣨⡯⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⣻⣻⠀ ⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣀⣠⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣽⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇ ⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠻⠿⠿⠿⢿⣶⣶⣶⣶⣶⢶⢶⢶⠶⣶⣶⣶⣶⣶⣶⣾⠿⠿⠿⠟⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀ ⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡇⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁ ⠀⠀⠀⠙⠻⠿⣿⣶⣶⣶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣷⣶⣶⣾⠿⠿⠋⠁⠀⠀⠀

⣏⠽⣌⡳⣙⣎⢳⣙⣎⢳⣙⣎⢳⡙⣎⠳⣍⢎⢧⣹⣼⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢧⡙⢮⡱⢫⣜⢣⡝⣎⢳ ⡬⢳⣌⢳⡱⢎⡳⡜⣬⠳⡜⣬⢣⡝⣬⢳⣮⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⡝⢦⡙⢧⢎⡳⡜⣬⢣ ⡓⢧⠎⣇⠳⣍⠶⣹⢰⢫⡜⢦⢳⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣘⢧⡙⣎⢮⢱⡚⡴⢣ ⡝⡎⡽⣨⠳⣌⠳⡥⣋⠶⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢩⢖⡹⢌⢮⡱⢎⡵⢋ ⡱⣙⠴⢣⡹⢌⡳⢥⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⢋⠍⡙⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡍⠶⣉⠶⣉⠞⣢⢓⠮⡜⡭ ⢇⡇⡾⢁⢷⢉⡶⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠎⡰⢁⠎⢱⠈⣆⠰⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⡈⠷⡎⣁⠿⣀⠏⡶⡉⡶ ⢎⠖⣱⢋⢆⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠆⡡⠣⠜⡐⠪⢄⠣⢌⣶⣥⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠱⣌⠱⢎⡜⡸⠰⣅⠳ ⣮⣽⣢⣍⡎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢎⠰⣁⠣⡑⡌⡱⢈⡜⣸⡇⢎⠩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢌⡓⢎⠴⣑⠣⣌⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⠆⡱⣤⣽⣴⡠⡑⢢⢐⠢⡉⠆⣥⣿⣿⣿⡟⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣧⢚⡌⢲⢡⠚⣤⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠢⣿⢍⠢⡘⠥⡑⢌⠢⢥⣉⠾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣧⡘⢥⢊⢽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣢⣑⣌⡆⡱⢸⣲⣡⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡜⠤⢋⡌⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠜⣡⠒⡴⢙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⣥⣀⡰⠀⠀⢿⡃⢆⠓⡤⢋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠛⠟⠁⠀⠀⢸⡇⢎⡑⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢨⠒⣌⠲⢌⡱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢸⠣⢌⠒⡬⡐ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠱⡈⠶⢁⡸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢆⡙⢌⠣⡔ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠿⠿⠶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡔⡨⠔⣿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢐⣾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⣡⠢⡑⢎⣿⣯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠓⠾⣿⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠣⠣⡔⢡⠚⠤⣿⣯⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⡞⠉⠍⡙⢉⠋⡝⠙⠿⠷⠿ ⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⣠⠶⠟⠡⢈⠒⠠⣁⠒⡈⠜⡠⢃⠌ ⡀⠥⠈⠄⡁⢊⠐⡈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⣠⠔⠊⠳⡠⠌⢠⠁⠌⠡⢀⠱⢈⠢⠑⡌⡘ ⠐⠄⢃⠰⠐⡀⠂⠄⠡⢈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⢀⡀⠀⠀⠀⡠⠄⠒⠒⠠⠴⣾⣿⣿⣿⣶⣿⣾⣿⣿⢈⠱⡈⢆⢡⢊⠱⣀⠇ ⡀⠊⠄⡀⢂⠠⠁⠌⠐⠠⠐⢀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠘⢲⣠⠎⠀⠀⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⠸⡙⠃⣎⡐⠰⡈⠔⣈⠒⢤⢊ ⠠⡁⢂⡐⢀⠂⡌⡐⢈⡐⢰⣦⣌⡐⡠⢿⣿⠟⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡧⠟⠢⢌⡱⢈⠖⡨⠜⡤⢊ ⡀⢁⠆⢰⠈⢰⠀⡰⢁⠰⣿⣿⣿⣿⣷⣇⡆⠸⡈⢁⢆⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⡸⠱⢆⡸⡈⡎⢁⠷⣈⢁ ⠄⡃⢌⠢⠘⡄⠱⣀⠣⢸⣿⣿⣿⣿⣿⣿⠟⣣⣼⣾⣾⣿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡒⡱⠌⢦⠱⣌⢣⠚⡤⢋ ⢂⠱⡈⢆⠱⡈⠥⡐⠌⣿⣿⣿⣿⣿⣿⡠⠋⢀⡙⢳⠏⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡱⢨⡐⡱⢍⢢⠱⢌⠦⡙⠴⣩ ⠄⣃⠘⡄⢣⠐⡡⢊⢼⠿⢻⠛⢻⣿⣿⣷⣲⡌⣠⢏⡲⢸⠀⠈⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠅⣎⠓⡣⢄⣀⣀⣀⣀⠠⢴⡾⣑⢢⠢⡑⠴⣑⢊⠦⣙⢢⢣⡙⢦⢡ ⡐⠤⠑⡐⠢⠑⡄⢃⠰⡈⢌⡹⣌⢿⣿⣿⣿⣶⣧⣤⣷⣿⠀⠀⠀⠈⠓⠤⢀⣀⣀⣀⣀⣀⡠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠝⢲⠁⡏⠔⡌⢎⠲⡡⢎⠦⡑⢎⢆ ⢐⡢⠑⡨⢐⠡⢂⠅⣂⠑⠢⡐⢞⣾⠻⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢊⡅⣋⠴⣉⠜⣌⢣⡑⢎⡒⡍⢎⢆

⠀⠀⠀⠀⢀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⢻⣿⣿⣦⡀⠀⣀⠀⣶⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠉⠛⢛⠋⠉⠀⠀⠈⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣧⠗⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣤⣤⣤⣤⡀ ⠀⠀⢠⡾⠋⢀⠟⠀⠊⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⠛⠻⠿⠿⠿⠟ ⠀⢰⣿⠀⠰⠣⡀⠆⠣⡀⠈⠁⠀⠖⠀⠸⠇⢠⠊⠉⢆⠀⠀⠀⠀ ⠀⣿⢷⡀⠀⠀⠨⠶⠠⣝⠒⠢⠤⢀⣀⣀⣀⠄⠀⠀⠼⣦⠀⠀⠀ ⠐⣿⣇⠑⡄⠐⣄⠀⠁⠀⠢⠤⡀⠀⠀⣠⣃⢀⣠⠊⠤⢿⡀⠀⠀ ⠐⣿⡟⣆⡈⠲⢄⡁⠘⠤⣀⠡⣀⠀⠊⠀⠀⠑⠃⠘⠀⣼⠃⠀⠀ ⠀⠹⣇⣿⣧⠀⠀⠈⠒⠤⣀⣉⠛⠐⠂⠀⠚⠓⢃⣠⣾⡟⠀⠀⠀ ⠀⠀⠹⣿⣷⡆⡇⡀⠀⠀⠀⠀⠉⠁⠀⠈⣻⣿⣿⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣾⣷⡄⠀⠀⠀⢀⠀⣠⣾⣯⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣦⣤⣠⣨⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠲⣦ ⣰⠋⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⠀⠀⢸ ⢹⣦⡀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣾⣿⡶⣾⠀ ⠀⠉⠉⣿⡟⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⢿⣿⠀⠀ ⠀⠀⠀⢹⣷⠀⠀⠀⠉⠛⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⠀⣠⡤⠶⠶⢤⣤⡶⠚⠉⠙⠲⣦⣠⣤⣤⣤⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠞⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢰⠶⠀⠀⠀⣀⣇⣀⣀⣤⣤⣤⣼⣃⣀⡀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⣆⠀⠀⣠⣷⠶⠟⠛⠉⢉⣩⣭⣤⣤⣤⣌⡉⠉⠉⠛⠷⢶⣯⣀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢠⣿⡿⠋⢸⡏⠀⠀⠀⣘⣷⠟⠋⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠙⠻⢶⣤⡖⠀⠀⠙⣧⡹⣿⣦⣠⣤⣶⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠿⠿⣷⣶⣿⠟⠀⠀⠸⣷⣄⣠⣾⠟⠀⠀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⣀⣴⡿⣿⣞⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⣿⣿⣿⣿⡇⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣾⣿⣿⣿⣿⣷⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⢶⣶⣦⣄⡀⠉⢻⡏⢹⢹⣿⢋⣠⣤⣶⠶⠿⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⣤⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⣾⡿⠁⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠻⣧⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢀⣾⠏⠀⠈⢷⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡷⠃⠀⢸⣷⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⢿⡆⠀⠀⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⣾⡇⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⢸⡇⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⢹⣿⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⡛⠟⣷⠄⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⣾⠁⢀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠉⠋⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠻⠿⣷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤⣴⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠈⠙⢿⣦⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⠿⠷⠾⢿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⣀⣤⣶⠿⠛⠋⠙⠻⢿⣦⣄⡀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠟⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⠙⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⡉⠀⠠⠄⢥⣘⠐⠢⣄⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠏⠀⡗⠀⠀⠀⡀⠈⠻⣶⢨⡙⢧⡈⢙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢴⡟⠀⠰⠁⠐⠀⡁⠀⠀⠀⠘⣷⡜⣄⠃⠄⠈⣷⣄⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣃⣼⠀⢀⠈⢀⠀⡬⠐⣠⣄⣬⣿⠤⡋⠔⠓⢫⠉⣀⠠⢄⠠⢀⠀⡀⢀⠀⡀⠀⢀⠀⠀⠈⡉⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⣀⡴⠚⠛⠉⠀⠀⠈⠉⠙⢶⣄⠀⠀⠀⠀ ⠀⣹⢨⣿⡄⠀⠀⠂⡀⣤⣶⣿⢿⡛⣧⢣⡙⢬⡙⠦⡱⢌⠳⢌⠂⡄⢆⡡⢂⠆⠤⡑⢈⠐⡁⢂⠐⡠⠠⢤⡀⠈⠙⠳⠤⠤⠞⠋⢀⡤⠆⡙⢠⠉⠆⠒⠠⠀⠙⢳⣄⠀⠀ ⠀⣽⢠⡟⣿⣦⡄⣲⡿⠛⡍⢣⠯⡜⢢⢍⡙⣣⠜⣡⠓⣌⠣⠎⡜⡘⠦⡱⣉⢎⡱⣄⢃⠎⡰⢁⠎⠤⠑⢂⡉⢛⠲⠶⢶⣴⠾⠿⢛⣀⡦⠁⠀⠀⢀⠀⡀⠐⢂⡀⢹⣧⠀ ⠀⢼⡰⣟⢮⣽⠿⠋⠀⠰⠘⡂⢆⡉⠖⢮⣶⠡⡚⢤⢋⠤⣃⠓⡬⡘⠥⢓⠬⢆⡱⢌⢎⠲⣑⢊⡜⠢⢍⢢⡘⢤⠓⡌⢆⠤⢓⡘⢆⡼⣷⣠⢀⠂⠌⠐⠠⢁⠂⠌⣱⣿⡀ ⠀⠸⣷⣿⠿⠁⠀⠀⠀⠠⢁⠐⡂⢍⡘⢄⢢⠱⡌⠆⣍⠚⡤⢋⣔⣉⢆⣉⢆⠣⡜⣌⢎⡱⢊⠵⣨⢓⢮⡱⡘⡎⢵⡘⡌⢎⡱⣘⢦⡙⡿⣿⣆⡀⠀⠀⠀⠄⡈⢐⣸⣿⠀ ⠀⠀⢙⡿⢠⡀⠀⠀⡀⠄⠂⠡⠌⡐⢌⠢⠜⣠⠙⠬⡄⠳⢄⢣⠰⣈⠦⡐⢎⡱⠌⡔⡊⢖⡩⢆⡱⢊⢆⡱⡱⢚⠤⡓⡜⢢⠱⡌⢦⠑⣡⢫⢿⣧⠀⠀⢀⢀⡐⢦⡽⣿⡁ ⠀⠀⣾⠃⠈⠀⠀⠀⡐⠈⠄⡁⢒⣈⢦⣱⣎⣤⠙⢢⠜⡱⢊⠤⠓⡌⣒⢉⠦⡑⢩⠐⠥⠒⡤⠣⡜⠩⢎⢡⠱⣉⠖⡱⢌⣃⠧⡘⡌⠷⡀⢆⠉⣿⣦⣱⢬⡶⣏⢷⣹⣿⡅ ⠀⢰⡿⣀⠈⡁⠐⠰⢀⠡⠒⡐⢦⣾⣿⣿⣿⣿⣿⣆⢣⠑⠎⣬⣑⣴⣦⣷⣶⣥⣦⣉⣦⠱⣀⠓⡌⠱⡈⢆⠱⡈⠬⡑⡌⢤⢃⠱⡈⠆⡑⠤⠈⠘⢻⣯⣷⡻⣝⣮⣽⡿⠀ ⠀⢸⠇⠧⠀⠀⠌⢀⠂⠄⠡⢈⣿⣿⣿⣿⣿⣿⣿⡿⣤⣹⠟⠋⠁⠀⠀⣰⣤⣀⠈⠉⠛⠷⣮⡕⡨⠑⡜⢂⡳⢌⠲⣡⠜⣐⠊⢆⠱⣈⠐⠠⠀⠀⠈⣿⣷⣻⢽⣾⠿⠁⠀ ⢀⣾⢠⣶⠁⠂⠀⠀⠀⠈⠄⡁⠛⣿⣿⣿⣿⣿⣿⢻⡟⠀⠀⠀⡀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⣧⡵⣬⣷⣿⣿⣿⣷⣮⡄⣉⠂⡡⠄⡈⠐⠆⠀⠀⣿⣿⣽⡿⢋⠁⠀⠀ ⣻⡇⢾⣏⠀⠀⠐⠀⠀⠂⠀⠀⠑⠠⠉⠟⡛⢋⠔⣿⠁⠀⠀⣸⣥⣴⣿⣿⣿⣿⡛⢃⡀⠀⠀⠀⢸⣧⣹⣿⣿⣿⣿⣿⣿⣷⠀⠆⢡⠂⡁⠆⠄⠀⢰⣿⣿⡍⠀⠀⠀⠀⠀ ⢿⡇⣏⢿⣌⠐⡀⠀⠀⠀⠀⠈⠀⢁⠈⠐⡀⠂⠌⣿⣧⠀⠀⠿⣿⣿⠿⠛⢿⣿⣿⣿⡇⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⡏⠜⡀⢂⠔⠁⠠⠀⠂⣸⣿⠶⡀⠀⠀⠀⠀⠀ ⢸⡇⣟⢮⡻⣧⡔⣀⠂⡀⠀⠀⢀⠀⠠⠀⠀⠡⠈⢀⠹⢷⣦⣀⡈⠀⠀⠀⢀⡙⣻⠏⠀⠀⢀⣴⠿⢁⠊⡙⠿⠿⠿⠟⡡⠌⠐⡀⠆⠈⠄⠁⡀⢄⢼⣿⠁⠀⠀⠀⠀⠀⠀ ⠈⢿⣪⠷⣙⡖⡳⢆⣡⣐⠠⡀⠄⡀⢀⠀⠀⠐⠀⠀⠀⠂⠈⠙⠛⠿⢶⢶⢶⡶⣶⡶⢶⠿⠛⠋⠐⡀⠐⠠⠁⢈⠐⠁⡐⠀⠁⠀⠀⠄⠀⠠⣰⠎⣾⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣫⠗⣜⢧⣋⢦⡙⢦⡙⢦⡱⢌⠦⡑⡄⠢⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡀⠁⠀⠁⠀⠠⠁⠐⠀⠀⠁⠐⠠⡀⠀⠀⡀⠤⡰⠿⡱⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⢿⡜⣦⡙⢦⡙⢦⡙⢦⠳⣌⠶⡱⢎⠳⣜⡱⢌⢢⣁⢒⡰⣈⡔⣀⠂⡄⠂⡀⠄⡀⠄⠠⠀⢄⡀⠠⢐⠠⣀⠰⣀⢄⢣⢓⣧⠶⣩⠳⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠷⣿⣦⢹⡖⡹⢦⡙⣌⠳⣑⢎⠳⣌⠶⣩⠖⣬⢣⡓⣭⠹⣏⠳⢦⢣⡔⡲⢴⣊⢥⣉⢦⡜⣱⢊⡵⢢⣛⡜⣎⢧⡻⣜⡳⣍⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣵⣎⡳⣌⢣⠍⣎⠳⣌⢣⡑⢺⡤⢣⠝⣆⡛⣬⢓⡎⢧⡚⡵⢢⡍⢶⡩⢖⡹⢆⡯⣜⠳⣎⢾⣙⢮⡳⣝⣶⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠾⣷⣬⣷⣌⣦⣙⠦⡜⣣⠹⢤⡙⣤⢋⡜⣣⠹⡜⣣⠝⣲⡙⢮⡱⣋⠶⣩⢛⣬⠳⣎⣷⣿⡿⢏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠶⢿⢶⣿⣼⣥⣿⣼⣵⣮⣱⣎⣵⣣⣝⣮⣵⣯⣶⡿⣟⠻⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠉⠉⠙⠉⠋⠙⠉⠉⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⡗⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠉⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡤⠒⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀ ⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠙⢦⡀⢀⣰⠇⠀⠀⠀ ⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠁⣿⣿⣿⣀⣿⠃⠀⠀⠀⠀⠀⠀⠹⡉⠁⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡿⠇⠀⢀⣤⣄⣀⠉⠉⠑⡶⠦⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠉⠛⢿⢿⠿⠏⢁⡴⠛⠦⣀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⣷⣶⣧⡀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠓⠢⠤⠤⠚⠁⠀⠀⠀⣰⠓⢆⠀⠀⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⣄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡇⠈⢣⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠁⡇⠀⠀⣷⠶⠶⣤⡀⠀⠀⠀⢀⡤⢄⠀⠻⣿⣿⠏⠀⢸⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢣⠀⠀⠀⣀⣀⡀⠁⠀⢀⡀⠀⠓⣉⠀⠀⠠⣾⣿⣇⡜⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠈⢇⠀⢺⣿⣿⡟⠀⠀⠸⣍⢩⠟⠁⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⣌⣳⣄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⡴⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢲⣋⣀⣀⣀⡀⠈⠉⠉⠑⠒⣒⠚⠉⠉⠉⡤⢄⣀⠈⢳⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋⠀⠀⠀⠀⠹⣄⣀⢀⡤⠚⠉⠓⠦⣄⣀⣇⡀⠀⠉⠙⠦⠴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢈⡏⠀⠀⠀⠀⠀⠸⣅⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⢠⣤⣤⡄ ⢸⣿⣿⣿⢿⡿⣿⢿⡿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡿⣿⢿⡿⣿⢿⣿⣿⣿⡇ ⠀⢸⣿⡹⣎⡷⣝⣮⣷⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣾⣧⣻⡜⣷⢺⣽⡇⠀ ⠀⢸⣯⢷⡻⣼⣿⣟⣯⢳⢯⡝⣯⠝⡯⡝⡯⣝⡯⣽⢺⡽⣻⣷⣻⡼⣏⣾⡇⠀ ⠀⢸⣿⣣⣿⣿⣛⠾⣜⣻⢎⣿⠉⣶⠀⠀⣶⠉⡷⣭⢷⣫⢗⡿⣻⣷⣏⣾⡇⠀ ⠀⠈⠱⢿⣟⡧⣟⡽⣫⣞⣻⣼⣶⣉⠀⠀⣉⣶⣿⣼⣧⣛⡾⣵⢻⣷⡾⠏⠁⠀ ⠀⠀⠀⢸⣯⡗⣯⣞⡿⠏⠉⠉⠿⣿⡶⣶⣿⠿⠉⠉⠙⠿⣾⣱⢟⣾⡇⠀⠀⠀ ⠀⠀⠀⢸⣯⢟⣿⡏⠁⠀⠀⠀⠀⠉⠿⠿⠉⠀⠀⣀⣰⠶⢹⣿⢮⢿⡇⠀⠀⠀ ⠀⠀⠀⢸⣟⡯⣿⡇⣀⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠖⢰⣿⣏⣿⡇⠀⠀⠀ ⠀ ⠀⠀ ⠙⢿⣿⣇⠌⠁⠉⠀⠀⠀⣁⠉⠀⠀⠀⠉⠉⢀⣸⣿⡾⠋⠀⠀⠀ ⠀ ⠀⠀⠀⠀ ⠙⠛⣶⣾⣾⣾⣶⠒⠛⣶⠛⠒⣷⣶⣶⣾⠛⠋⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠛⣷⣾⠛⣤⣤⠛⣤⣤⣿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⣀⣠⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠛⠶⣤⣤⡴⠶⢶⣿⣟⣿⣻⣿⡋⠉⠁⠹⣇⠀⠀⠀ ⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣾⣿⣿⡿⣿⣷⣶⣶⣿⡄⠀⠀ ⠀⠀⠀⣿⡖⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠿⢿⣽⣷⣿⣿⣯⢿⡟⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣽⣾⢿⡅⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣨⣧⣀⡀ ⠘⠛⢻⡛⠃⣰⡏⠙⠉⠛⣦⠀⠀⠀⠀⢠⡞⠋⠙⠉⣷⢈⣡⣇⡀⠀ ⠀⠰⠾⣿⣳⡋⠀⠀⠀⠀⡿⠀⣞⣿⠆⢸⡄⠀⠀⠀⠈⢷⣽⠋⠉⠀ ⠀⠀⢠⡼⣷⣿⣷⠂⣠⡾⠁⠠⡀⣀⣀⡠⠿⣤⣴⣿⠟⢘⡏⠳⠀⠀ ⠀⠀⠀⠀⠙⠻⠷⠛⠛⠶⠶⠶⣤⣤⣤⠶⠶⠾⠛⠲⠖⠋⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡟⠀⠀⠉⠙⠻⢿⣿⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠟⠋⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣸⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⣠⣤⡀⢹⣿⣿⣿⣿⣿⣿⣿⠃⣤⣶⡄⠀⠀⠀⠘⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⡿⢠⣿⣿⣿⣿⣿⣿⣿⡀⢿⣿⡟⠀⠀⠀⢀⣿⣿⣿⣿⣧⠤⠤⠤⣤⣤⡀ ⠈⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣦⡀⠀⠀⠈⠉⢀⣾⣿⣿⡿⢿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣥⣣⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⠶⠛⠻⣿⣿⣿⣿⣽⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠶⣤⣄⣀⠀⠀⠀ ⠀⠀⠰⠟⠋⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣟⡛⠛⠛⠛⠛⠛⣛⣩⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣻⠋⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⠻⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠙⠻⠛⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⣀⣀⠀⠑⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣿⡿⣿⡇⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⣠⣿⣿⡿⠃⠀⡘⠀⠀ ⠀⠔⠉⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⢀⣠⣶⣿⢿⣯⢿⣇⠀⢸⠀⠀⠀ ⠂⠀⣴⣿⣷⣦⠀⠘⠒⠒⠒⠄⠠⠤⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣠⣴⣿⣟⡿⣾⣻⣽⣟⣿⡀⠈⡆⠀⠀ ⡀⠀⢿⣷⣯⣿⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠉⠓⠀⠀⣀⠠⠄⠒⠘⠉⠉⠉⠀⠀⣿⣿⣻⢷⣻⢿⣽⣻⣾⣽⣻⡆⠀⢰⠀⠀ ⠑⢀⠀⠀⠀⠙⢿⣾⡽⣯⡿⣽⣻⣟⡿⣯⡿⣿⢿⣿⣇⠀⠘⠉⠀⣀⣠⣤⣴⣶⣶⣿⡿⠟⠻⠛⠿⢿⣿⣯⣟⣷⣟⡾⣟⣧⠀⠸⡆⠀ ⠀⠀⠈⠁⢢⡀⠈⢿⣟⣷⢿⣻⣷⣻⢿⣽⣻⣽⢿⣞⣿⣦⣠⣶⣿⢿⣻⣽⣯⣟⣾⠁⢀⡀⠀⠀⢀⡀⢹⡿⣿⢿⣾⣿⣻⡟⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠑⠄⠀⠻⣯⡿⣷⢯⣟⣯⡿⣽⡾⣿⣽⣿⢿⣻⣽⡾⣟⣯⣷⣟⣾⢿⣄⡛⠃⠀⠀⠙⣃⣼⣿⢯⣿⣻⢿⣯⡀⠀⢊⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠙⣿⢯⣿⢯⣿⡽⣿⣽⣿⡿⣽⣻⣯⣷⢿⣻⠿⠋⠈⠉⠛⠻⢿⣷⣾⣿⣾⣿⠟⠋⠛⠷⣿⣯⣟⣷⡄⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⡀⠈⢻⣯⣿⣞⡿⣷⣿⣯⣟⣿⣳⡿⣾⠟⢁⣠⣤⡀⣀⠀⠀⠀⠈⠙⠞⠋⠀⠀⠀⣤⠶⣬⣿⣯⣟⣿⡀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠻⣷⣿⣻⣿⣟⣾⣽⡾⣯⡿⠁⢠⣿⣇⢈⣿⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⡿⣿⠈⢿⣟⣧⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⢠⣿⣯⣟⣾⣽⡟⠀⠀⢸⣏⣸⣿⣙⡿⠀⠀⠀⠀⢠⠴⢦⡀⠀⠹⣤⣼⣧⣿⠁⠈⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⣿⣳⡿⣽⣾⠁⠀⠀⠀⠻⢿⡿⠿⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠉⠛⠛⡁⡤⡀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⣿⡿⣽⣟⣿⡀⠀⡔⡸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠑⠀⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠹⣿⣻⢾⣻⣧⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠙⣿⣟⣯⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡤⠤⣄⠀⠀⠀⠀⠀⣠⠟⠀⠀⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠛⢿⣾⣽⢿⣦⣄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⢣⠀⠀⢳⢀⣀⣴⠊⠁⡠⠒⢦⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⢀⣀⠉⠛⠛⣿⣿⣷⣶⣤⣤⣼⢧⠀⠀⠀⡘⠀⢀⢾⣿⣿⣿⣿⠿⠳⠤⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⡇⠈⡽⢾⠿⠿⣯⢿⣽⣯⣿⠁⠀⠀⠀⡞⢣⠀⠀⠀⠙⣿⣿⣦⣤⠒⠲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠉⠀⠀⠀⣀⣀⣾⣿⡾⣇⠀⠀⠀⡰⠀⠀⢧⡀⠀⠀⢸⠀⠉⠙⠤⠼⠁⢀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢻⠀⠸⣅⢀⡏⠀⠀⠈⠒⠒⠋⠀⢀⠆⠀⠙⠒⠒⠁⢀⡰⠄⠀⠀⠴⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠉⠀⡠⠚⠐⠀⠀⠔⠊⠀⠀⠉⠒⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣟⡯⣟⣻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡹⠞⡩⠰⡑⡌⣡⢉⠳⢾⡽⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡽⢊⠴⢡⡑⠣⠜⡰⢄⡃⢎⠢⡝⣷⣳⡄⠀⠀⠀⢀⣤⢶⡻⡝⢯⠛⠮⠽⢽⣹⣞⣦⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⡟⡓⢪⡐⠣⢌⡑⠣⠜⡰⠘⣌⠱⣠⠙⣷⣻⠀⣡⣾⣻⠼⢋⠱⡘⢢⠙⣌⠱⢂⠆⡍⠺⣏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡟⣡⠙⡄⢎⡑⡊⠬⣑⠩⡔⢩⢄⠳⣀⢋⢳⣟⣾⢻⡜⠱⣈⠣⢅⡃⢣⠩⢄⢣⡉⠲⢌⡱⢘⢾⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⠣⡰⢉⡔⢊⡔⡉⢦⠡⡒⠬⣁⠎⢢⠅⠎⣜⡿⣼⢋⠔⡃⠦⣉⠦⡘⣡⠚⡐⢆⡡⢋⡔⠢⢍⡸⣞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⠇⡑⢆⠣⡘⢆⠢⢍⠢⠥⢡⠓⠤⡙⣂⠎⡑⣾⣽⡃⣌⠚⡌⡱⢐⢢⠱⢄⢣⢉⠦⡘⡡⢌⠓⠬⡐⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣳⠏⡜⢨⠑⡌⠦⣉⠦⡑⣊⠥⢊⡅⢓⠤⢊⡱⣟⡾⡐⢢⠱⡘⡰⢉⠆⡱⢊⠔⡊⠴⢡⡑⢊⡱⢊⠱⢸⣻⡀⠀⠀⣀⣄⡀⠀⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡘⣬⠂⠓⠸⡔⣂⠖⡡⠒⢬⢡⠘⡬⠌⡥⢸⣯⠷⢨⡑⢢⠱⢡⣞⡾⡕⡡⢎⢡⠓⢢⠜⡡⢆⠩⡌⢳⣽⠁⠀⠈⣟⣲⡵⣼⡳⣽⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠿⢼⠁⠀⠀⠀⢸⡔⡈⠖⣉⠆⢎⠒⡰⢩⠰⣉⠹⠌⡥⢌⡑⣊⠅⢎⢿⣝⢶⡈⢆⠹⡐⣊⠔⣊⠱⣸⡿⡞⠀⠀⠀⠘⢵⣫⡗⠗⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠀⠄⠀⠀⠀⢛⠄⣚⢤⣹⣤⢧⡷⣴⣭⢶⣱⢦⣵⣐⣪⡌⢆⠻⣭⣟⢦⢧⡱⣤⢯⣴⣿⠯⠋⠀⠀⠀⠀⠀⠀⣉⣁⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠁⠦⠊⠀⠀⢀⣸⢿⣹⠯⠓⠛⠚⠉⠉⠚⠋⠚⠛⠊⠛⠳⢟⣯⡶⣦⣉⢛⡚⢳⢙⡚⢻⣯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⣱⠀⠀⠀⠀⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣻⣶⡜⢄⠣⢎⠣⢯⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡣⠍⠦⢄⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣮⢑⢊⡱⢼⡷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣾⣻⢄⠹⣜⣿⡽⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣷⠊⡔⣊⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣸⠟⣧⠀⠀⠀⠀⣷⣻⠌⡒⣼⢷⠃⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡆⠀⠀⠀⢸⢾⣁⠎⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣳⢎⡽⣟⡼⠀⠀⠀⠀⢳⢯⣗⠡⣟⣿⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⡤⠀⢢⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⢸⣻⡸⡘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠚⠓⠁⠀⠀⠀⠀⠀⢻⣮⣧⡹⣞⣧⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⠐⠈⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⢿⡝⣑⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣝⠿⣼⢻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡾⣝⡾⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠯⢷⣫⡟⣞⠷⣶⢶⣤⣤⣤⣤⢤⣤⢤⣤⡤⣤⢤⡦⣖⣶⣻⣽⣳⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠖⠛⠒⠶⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⡀⠀⠀⣀⣀⠙⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣼⠇⢠⠋⠉⠙⢦⡴⠋⠀⠙⣆⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣿⣻⣷⣿⠀⠙⢄⡀⠀⠈⠃⠀⢀⡤⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣯⢷⣻⢷⣻⢾⣷⠀⢀⡴⠋⠁⠀⠀⠈⠉⠲⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣽⢯⡿⣽⢯⣟⣿⢿⡄⠻⣄⠀⠀⣸⢧⡀⠀⢀⡿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣽⢯⡿⣽⢯⣟⣾⠏⠈⢳⣀⠈⠑⠋⠁⠀⠉⠛⠉⣠⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣏⣿⡽⣯⢿⠟⠁⠀⠀⠀⠙⠳⢤⣤⣤⣤⣠⡶⠟⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⠿⣿⣻⣿⣽⣏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⢛⡿⠟⢾⣿⣿⣅⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠹⢮⣦⣿⣿⣏⢭⢻⡌⠑⢦⡀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⣀⣤⣶⠶⢶⠶⡶⠶⠶⣦⣤⣤⣀⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠏⠛⠛⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⣸⡟⡡⢆⡙⣆⠳⣌⢓⠳⣐⠦⡘⣍⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠘⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀ ⣿⡥⢣⠜⣣⡙⢆⡹⡘⢦⡙⢤⢣⡙⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⢻⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀ ⠘⢿⣦⣙⣤⣓⣌⣲⣉⢦⣙⢢⠣⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡇⠀⠀⢸⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣴⣤⣴⠄⠀⠀⠀⠀⠀⠀⡼⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣸⣿⣿⡄⠀⠀⠸⢮⡽⠗⠛⠀⠀⠀⠀⠀⠀⣰⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠘⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢞⢿⣿⣳⢯⡿⢃⣤⣶⣶⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⣤⣤⣤⡶⢞⠻⣉⢦⡱⢎⡜⢻⡟⣿⣴⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠈⢻⣇⠳⡘⢦⡘⠲⣌⢳⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⣀⣠⡶⢟⡡⢣⣙⣤⣭⣷⣤⡿⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠋⣵⣿⣗⢌⠲⣽⠏⠀⠀⠀⠀⠀⠀⠀⠙⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣿⢮⣵⣼⣧⣄⡀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡛⠛⠷⣤⣀⣠⡶⠟⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⢈⠱⡈⢜⢻⣅⣀⠀⢀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠉⠛⠳⢶⣄⡀⢀⣀⣤⡶⣿⢈⠆⣱⡶⢷⡿⢏⠩⠻⣶⠶⠛⠟⢳⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⢻⡘⢢⢉⣛⣿⢰⢈⠆⡅⣿⢶⡅⠎⣄⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣥⣦⠶⠟⠷⣬⣶⣽⠿⢛⠣⡑⣼⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣃⣒⣽⠋⣹⣦⠤⠖⠒⠀ ⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠋⢻⡄⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⡟⠋⠁⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣿⡄⠀⠀⣀⣸⣇⣀⠀⠀ ⠀⠀⢸⣇⠀⢀⣀⡀⠀⠀⣼⣷⡀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢈⣉⣁⡀⠀⠀⣩⡿⠋⠛⠛⠃ ⠀⠀⢀⣿⡿⠟⠋⠁⠀⠀⠸⠿⠃⠀⠀⠀⠀⠘⠿⠶⠋⠀⠀⢸⠟⣿⡿⣻⡀⣰⡟⠁⠀⠀⠀⠀ ⢠⠞⠋⠉⢿⣄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠻⣉⠿⠫⡽⣟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠷⣤⣤⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⢳⡈⢥⡥⢊⡅⢃⢎⢳⣤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⣼⠋⠙⠛⠛⣻⣟⡛⢛⣛⣿⡛⠟⠻⣶⡘⠁⢏⢔⢌⠒⡌⣲⣷⣓⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢁⣤⠤⣤⣴⢿⢃⠼⣬⡿⣧⠀⠀⢀⣨⢷⣄⡌⠁⡎⣶⠱⢜⣮⠵⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣷⢜⣹⢯⠜⠻⣦⡴⠛⠁⠀⠉⢹⣞⠔⠤⣣⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣤⢟⠎⢾⣎⠢⣀⢝⣷⣄⠀⠀⠀⣽⢛⡹⣿⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⢹⡌⢆⠸⣈⠹⡛⢶⢻⢿⠋⠛⠶⢞⣯⣥⡦⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢻⡿⠷⠾⠶⠷⢷⠾⠾⣯⣢⣀⣌⣷⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠛⠛⠷⢶⣦⣄⣀⣀⣤⣤⣤⣤⣴⣿⣿⣻⣟⣿⣾⠛⠉⠉⠉⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣸⣿⣟⣷⣿⣾⣯⣿⣤⣀⠀⠀⡀⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡾⣽⣿⣿⣿⣻⣟⡿⣿⣿⡿⣿⢿⣷⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣯⣿⣿⣷⢿⡾⣽⣿⣿⣿⣯⣟⣿⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠛⠛⣿⣿⢿⣻⣷⣿⠃⠀⠀⠀ ⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⣿⡀⠀⠀⠀ ⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡧⠤⠤⠄ ⠘⠛⠛⢻⡟⠛⠃⠀⠀⢀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⣠⣼⣷⠖⠂⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⣤⠤⣄⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠉⣿⠛⠛⠒⠀ ⠀⠀⠀⠀⣸⣷⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣯⣀⡀⠀⠀ ⠀⠀⠰⠛⠉⠉⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠈⠙⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⢦⣤⣤⣠⣄⣠⣀⣄⣠⣠⣤⣤⣤⡴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⡣⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠠⠊⠀⠉⠰⠀⠀⠀⢸⠇⠀⢠⠘⠁⠘⢢⡀⠀⠀⠀⠀⠀⠐⠒⢄⠀⣠⠼⠃⠀⡰⠊⠉⠀⢉⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠈⠙⠆⡰⠉⠁⢀⣤⢤⡄⠀⠀⠀⠈⠤⠁⠀⠀⣜⡁⡐⠁⠀⠀⠈⢂⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣠⠬⠵⠒⠒⣾⠖⣶⡧⣄⣀⠀⠀⠀⠀⠀⠀⣼⠀⠱⠀⠀⠀⠀⢀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⡯⣖⠺⣍⢻⡙⢯⡹⢜⣓⡒⠮⣍⡳⢤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⣳⢌⡇⡞⢥⡚⡼⢤⢋⡳⢦⣙⠳⣿⡀⣰⠇⠀⠀⠀⠀⠀⡠⠁⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠉⡄⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠾⠷⢼⣵⠮⠧⣷⣦⣭⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣊⠁⠀⠋⣒⡄⠀⠀⠘⠲⣄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢀⠏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡠⢎⠰⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⡤⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠸⢅⡈⢀⣈⡵⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⠶⢤⡀⢠⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⡄⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢱⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠁⠂⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡾⣧⣀⣸⡆⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀ ⠀⠀⠀⠀⠘⣆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⠖⠛⠓⣆⢠⠔⠃⠈⠢⠄ ⠀⠀⢀⡀⠀⠙⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣾⠀⠉⢊⢰⠋⠁ ⠀⣠⠆⠸⣄⠀⠈⠳⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠊⣴⠋⠀⠀⠀⠁⠀⠀ ⠘⠃⠄⢰⠄⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠊⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢸⡁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠅⣀⠼⠁⠳⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣾⠀⠐⠲⠀⡴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢈⠀⡀⢀⡀⡇⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠓⠶⣤⠴⠶⢶⡿⠁⣶⣽⣯⠉⠁⠹⡆⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡁⢼⣿⡏⠙⠻⣾⡛⢿⣆⠀⠀ ⠀⠀⠀⣻⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠷⣤⣼⣯⠟⣸⡟⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⢙⣆⣀⠀ ⢠⡶⢾⡶⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠚⢩⡏⠉⠁ ⠀⢀⣼⣷⠒⠀⠈⠋⠀⠀⠀⢶⡲⠀⠀⠀⠛⠁⠀⡈⣹⠛⠛⠀ ⠀⠀⢠⡼⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠷⠆⠀ ⠀⠀⠈⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀

⠀⠀⣰⣦⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣾⣿⣷⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡿⣷⣡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣷⣿⡧⡆⠀⠀⠀⠀⣔⣦⣜⢼⡿⣯⣂⣀⢴⣿⡿⢿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢿⣿⣿⣈⣟⡇⠀⢀⢠⣄⣷⠟⠻⠿⠛⠊⠉⠉⠚⢹⣿⣖⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠈⣾⣿⣿⣿⣏⡧⣢⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣾⣔⢄⡀⢀⣠⣲⣼⣷⣶⣿⣿⣾⣾⣿⣤⣒⢄⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣿⣟⣛⣿⣿⣾⡟⣶⣿⣾⣿⡿⡿⠇ ⠀⠀⠀⠣⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⠟⡻⢿⣿⣿⣿⡿⢿⣟⠻⠟⠃⠀⠀ ⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣏⡉⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠰⣿⣕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠩⢿⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⣟⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢉⡻⢿⣿⣿⣿⣿⣶⣶⣶⣶⡦⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢠⣦⣷⣿⣿⣿⣿⣿⣯⣟⡿⣿⢿⣷⡆⢀⣼⣿⣿⣻⣯⣿⣿⣿⣿⣾⣯⣔⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⣷⣿⣿⣟⣯⢿⣽⣿⣿⣿⣿⣿⣿⢯⣟⡿⣿⢿⣻⣾⣿⡿⣿⣻⣽⣷⣻⢿⣿⣿⣶⣅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣺⣾⠟⠉⠻⣿⣯⣿⣿⣿⣟⡷⣯⣟⣾⢿⣽⣻⣽⢿⣽⣻⢾⣽⡷⣿⣿⣿⣿⣟⣾⡿⠛⢿⣮⡢⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⠁⠀⠀⠀⢨⣿⣿⣿⣻⣞⣿⡽⣾⢯⣿⢾⣽⡾⣯⡷⣟⣯⡷⣿⣳⣯⢿⣿⣿⡁⠀⠀⠀⢻⣷⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡄⠀⠀⢠⣿⣿⣿⣾⣷⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣷⠀⠀⠀⢸⣿⢺⠀⠀⠀⠀⠀⠀⠀ ⠙⠹⣿⠶⢦⣼⣿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛⠿⣿⣇⣠⣴⣿⢟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡅⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡁⣿⡇⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣿⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣶⠿⠟⠋⠀⠀⠀⠀⠀⣼⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣻⣏⣀⣤⣄⣀⣀⣀⣀⣀⣀⣼⣿⣀⣀⣀⣀⣀⣀⣀⣠⣿⣟⡫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡃⠧⣉⠆⣃⠒⡄⢃⠆⡡⠒⡌⠰⢂⠅⡒⢌⠂⡆⢡⠒⡌⣐⠢⡁⠆⡅⠒⡌⡰⢨⠐⢢⠁⠖⡨⢐⠢⡑⢰⠈⡔⢢⢁⡒⢌⠰⢨⢐⠢⡁⠆⡅⡒⢌⠰⣈⠔⢢⠁⠖⡨⢐⠢⡑⢰⠈⡔⢢⢁⡒⢌⠰⢨⢐⠢⡁⠆⡅⡒⢌⠰⢂⠅⡒⢌⠂⡆⢡⠒⡌⣐⠢⡁⠆⡅⡒⢌⠰⢨⢐⠢⡁⢆⡡⠒⡌⠰⢂⠅⡒⢌⠂⡆⢡⠒⡌⣐⠢⡁⠆⡅⡒⢌⠰⢨⢐⠢⡁⠖⡨⢐⠢⡑⢰⠈⡔⢢⢁⡒⢌⠰⢨⢐⠢⡁⠆⡅⡒⢌⠰⣈⠔⢢⠁⠖⡨⢐⠢⡑⠰⣈⠒⠤ ⡡⢃⠆⡜⢠⠑⡈⢆⡘⢄⠣⢌⠱⡈⢆⠱⣈⠒⢌⠡⢊⠔⡠⢃⠜⡰⢈⠱⢠⠑⡂⢍⠂⡍⢢⠑⡌⢢⠑⢢⠑⡌⢂⠆⡘⢄⠃⠆⡌⢢⠑⡌⠰⣁⠊⡔⢠⠊⠤⡉⢆⠱⡈⢆⡑⠢⡉⠔⡡⢂⠜⡠⢃⠆⡌⢢⠑⡌⠰⣁⠊⡔⢡⠊⡔⣈⠒⡌⢡⠊⡔⢠⠃⡜⠰⢠⠑⡌⢢⠁⢎⡐⢡⠂⡔⠡⢌⠱⡈⢆⠱⣈⠒⢌⠡⢊⠔⡠⢃⠜⡰⢠⠑⡌⢢⠁⢎⡐⢡⠊⡔⢡⢂⡑⢢⠉⡔⢡⠂⡜⢠⠃⠆⡌⢢⠑⡌⠰⣁⠊⡔⢠⠊⠤⡉⢆⠱⡈⢆⠡⢃⠤⡉⠆ ⠥⡉⡜⢨⠁⢎⡐⢢⠘⡄⠣⢌⠢⡑⠌⡒⠤⣉⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡁⢎⠰⣈⠒⡌⢢⠑⡌⢢⠉⢆⠱⡈⢆⡘⠰⡈⠜⡨⢐⠡⢊⠔⡡⢂⠱⡈⢆⡉⢆⠱⡈⢆⡑⠢⢌⡑⢌⠢⡑⢌⠢⡑⠌⡒⢌⠢⡑⢌⠱⣀⠣⡘⢄⠣⡐⢄⠣⡘⢄⠣⡘⢄⠣⠌⡑⢢⠑⡌⢢⠉⢆⡘⢄⠣⢌⠱⡈⢆⠱⣈⠒⠤⣉⠢⡑⢌⠢⡑⢌⠢⢑⠢⡑⢌⠢⡉⢆⡘⢄⠣⡘⢄⠢⡘⢄⠣⡘⢄⠣⡘⠤⢉⠒⡌⢢⠑⡌⠱⣀⠣⡘⠤⡉⢆⠱⡈⢆⠱⡈⢆⠡⢂⠱⡈ ⢣⡑⢌⠢⡉⠔⡈⢆⠱⣈⠒⡄⢣⠘⠤⡑⠢⢄⠃⡜⢠⠑⡌⢂⠆⡑⠢⡑⢌⠢⡑⢄⠣⡐⢡⠊⠔⡂⢍⡐⢢⠑⠢⢌⡑⢌⠢⡑⢌⠢⡁⢎⠰⡁⢆⡑⠢⢌⠂⢆⡑⢢⠐⡡⢂⠌⢢⠑⡌⢢⠑⡄⢣⠘⡄⢢⠑⡌⠢⢄⠣⡐⢌⠢⡑⢌⠢⡑⢨⠐⡌⢢⠘⠤⡑⢢⠁⢆⠡⢊⠔⡈⢆⡘⢄⠢⡑⢌⠢⡐⢌⠒⠤⡑⡈⢆⠱⡈⢆⡘⢄⠣⡐⢌⠢⡑⠤⡘⢄⠢⡑⢌⠢⡑⢌⠂⡅⢢⠑⡄⠣⢌⠒⡌⠰⡈⠔⡡⢂⠱⣀⠣⡐⢌⠢⡑⠢⣁⠒⡌⢢⠁⡆⢡ ⢣⠜⡠⢃⠜⡠⠑⡌⠢⢄⠣⡘⢄⡉⠒⡌⠱⣈⠒⢌⠢⡑⢌⠢⡘⢄⠣⡘⠤⡑⢌⠢⡑⢌⠢⡉⢆⡑⢢⠘⠤⣉⠒⠤⡘⢄⠃⡜⢠⠃⡜⠠⢃⠜⡠⢌⡑⠢⡉⢆⡘⢄⠣⡐⢡⠊⡄⢣⠘⡄⢊⠔⡡⢊⠰⡁⢎⠰⡁⢎⠰⢁⠎⡰⢁⠎⡰⢁⠆⡱⢈⠆⣉⠒⢌⠂⡍⢢⠑⡌⢢⠑⠢⢌⠢⡑⢌⠢⡑⢌⠢⣉⠒⠤⡑⢌⢂⡑⠢⢌⠢⡑⢌⠢⡑⢄⠣⡘⢄⠣⡘⢄⠣⠘⡄⢣⠘⡄⠣⢌⡑⠢⡑⢨⠑⡌⢢⠑⡌⠒⠤⡑⢌⠢⡑⢨⠑⡄⢣⠘⡄⢣⠘⠄ ⢣⠜⡠⢃⠜⡠⢃⠌⡱⢈⠆⡑⠢⢌⠱⡈⢅⠢⣉⠢⠑⡌⢢⠑⡌⢢⠑⡄⠣⢌⢂⠱⡈⢆⠱⡈⠔⡈⢆⠩⡐⠤⡉⢆⠱⣈⠒⢌⠢⡑⢨⠑⡌⢢⠁⠆⡌⠱⡐⠢⢌⢂⠱⢈⠆⠱⣈⠢⢡⠘⡄⢊⠔⢡⢂⠱⡀⢆⡑⠢⡁⠎⠤⢑⠨⡐⢡⠊⡔⢡⠊⡔⢠⠉⢆⠱⡈⢆⠱⡈⢆⡉⠒⡌⠰⡁⢎⠰⡁⢎⠰⢠⢉⠒⢌⠂⠆⡌⡑⢢⠡⡘⢄⠣⠘⡄⢣⠘⡄⢣⠘⡠⢃⠱⡈⢆⠱⡈⢅⠢⢌⡑⢌⠢⡑⢌⠢⡑⢨⠑⢢⠁⢎⠰⡁⢆⠱⡈⢆⠱⢈⠆⡱⢈ ⢣⢊⠔⡡⢊⠔⡈⢆⠱⡈⢆⠡⢃⠌⢢⠑⡌⠒⠤⣁⠣⡘⢄⠣⠘⡄⠣⢌⡑⠢⢌⠢⡑⢌⢂⠱⡈⢔⡈⢆⡑⢢⠑⡌⠒⠤⣉⠢⡑⢌⠢⡑⢌⠂⡍⠒⢌⠡⢂⠱⡈⠢⡑⠌⡰⢁⠂⢆⠡⢒⡈⢆⡘⢄⠊⡔⢨⠐⡄⢣⠘⢄⠣⠌⣂⠑⠢⣁⠒⡄⢃⠜⡠⢉⠆⡱⢈⠆⡡⠘⠤⣈⠱⣈⠱⢈⠆⡡⠘⡄⢃⠆⡌⡘⠤⣉⠒⠤⡑⠢⡑⢌⠢⣁⠣⡘⢄⠣⠘⡄⢣⠐⡡⢂⠱⡈⢆⠱⣈⠒⠤⡘⢠⠃⡜⢠⠑⡌⢢⠉⢆⡉⠆⡱⢈⠆⡱⢈⠆⡘⢄⠊⡔⢂ ⢣⠊⡔⢡⠊⡔⢡⠊⡔⢡⠊⡔⢡⠊⡄⠣⢌⡑⠢⢄⠣⡘⠄⢣⠑⡌⢡⠂⡌⡑⠢⡑⢌⠢⢌⠢⡑⢢⠘⠤⡘⢄⠣⠌⡑⠢⢄⠃⡜⢠⠑⡌⢄⠣⣈⠱⢈⠆⡡⢂⠅⢣⠘⠤⡑⢌⣘⣤⣃⣦⣼⣤⣶⣬⣶⣬⣦⣵⣈⣆⣉⢆⡘⠰⢠⢉⠒⡄⢃⡘⢄⠊⡔⢡⠘⡠⢃⡘⠤⣉⠒⠤⡑⢠⠃⡌⢢⢁⠣⡘⢄⠊⡔⢡⠒⠤⡉⢆⠡⢃⠜⡠⢃⠄⢣⠘⡄⠣⡑⢌⠢⡑⢄⠃⢆⠱⣈⠒⠤⡉⢆⡑⠢⡑⢌⠢⡑⢌⠂⡍⠰⡈⢆⠱⡈⢆⡑⠌⢢⠑⡌⠒⡌⠄ ⢣⠱⡈⢆⠱⡈⢄⠣⢌⢂⠱⡈⢆⠱⣈⠑⠢⢌⠱⡈⢆⠱⡈⢆⠱⡈⢆⠱⢠⢁⠣⡘⢄⠣⢌⢂⡑⢢⠉⢆⠱⡈⢆⠱⣈⠱⡈⠒⡌⢂⠅⡒⢨⠐⡄⢊⠔⡨⢐⣡⣪⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣒⡌⢢⠘⡄⢣⠐⢢⠑⡄⢃⠔⠢⢄⢃⠒⢌⠰⡈⠔⡡⢈⠆⡡⢊⠔⡈⢆⡉⢆⠱⡈⢆⠡⢊⠔⡡⢊⠄⠣⢌⡑⠌⢢⠑⡌⢢⠉⢆⠡⢂⠜⡠⢑⠢⢌⡑⢌⠢⡑⠌⢢⠑⡌⡑⢌⠢⡑⢌⠰⡈⠜⡠⢃⠌⡱⢠⠉ ⢣⡑⢌⠢⡑⢌⠢⡑⠌⢢⠑⡌⢢⠁⢆⡉⠒⡌⢢⠑⡌⢂⠱⡈⢆⠱⡈⢆⠡⢊⠔⡡⢊⠔⡈⢆⡘⠤⢉⠂⢆⠱⠈⠆⡄⠣⠌⡑⢄⠣⠘⡄⢃⠜⣠⣧⣾⣷⣿⣿⣿⣿⣿⡿⠿⢛⠛⡍⢋⠍⡡⢁⠎⡰⠡⡉⢌⠩⣉⠛⡛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣦⣅⡊⢄⠣⡘⢄⡊⠱⣈⠢⢉⠢⡑⢌⠢⡑⠌⠤⠑⢢⠘⡐⠢⢌⢂⠱⡈⢆⠱⡈⢆⠱⡈⢌⡑⠢⢌⡘⢄⠣⡘⠤⢉⠢⡑⢌⠢⡑⢌⠒⠤⡘⢠⠑⡌⡘⢄⠣⡐⢡⠊⡔⢡⠊⡔⢡⠊⡔⢡⠊⡔⠡⠌ ⢣⠜⡠⢃⠜⡠⢂⠱⡈⢆⠱⡈⢆⡉⠆⡌⠱⡈⢆⠱⢈⠆⡱⢈⠆⡡⠒⡌⢢⠁⢎⠰⣁⠊⡔⠢⠌⢢⠁⠎⡄⢃⡉⢒⡈⢅⠊⡔⡈⢆⠱⣨⣶⣿⣿⣿⣿⡿⠟⡛⢩⠁⢆⠰⡁⢎⠰⡈⢆⡘⢄⠣⡘⢄⠣⠘⡄⠣⢄⠣⢌⡑⢌⠢⢄⠩⡙⠛⠿⣿⣿⣿⣿⣷⣼⡐⣢⣬⣵⣶⣷⣾⣶⣧⣬⣆⡡⢊⠔⡩⢄⠃⡌⡑⠢⠌⢢⠑⡈⢆⠱⡈⢆⡑⠢⢌⡑⠢⢌⠢⡑⢄⠣⢌⠢⡑⢌⢂⠱⡈⠜⡠⢑⠢⡑⠤⡑⢌⠢⢑⠢⡑⢌⢂⠱⡈⢆⠱⡈⠆⡱⢈⠅⡊ ⢣⠜⡠⢃⠜⣀⠃⢆⠱⡈⢆⡑⠢⡘⠰⣈⠱⡐⢌⠢⡁⢎⠰⡁⢎⡐⢡⠘⠤⣉⠢⡁⠆⡑⡈⢆⠩⢄⡉⠒⡌⢢⠘⠤⡘⢄⠣⣐⣡⣾⣿⣿⣿⡿⠟⡋⠥⡐⢡⠘⠤⣉⠢⢡⠘⡄⢃⠜⡠⠌⢂⠆⠱⣈⠢⢑⠨⡁⢆⠡⢂⠌⢢⠘⡄⢃⠔⣉⠒⡄⣉⠛⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣮⣔⢂⠱⢠⢁⠣⡘⠄⢣⠘⡄⢣⠘⠤⣈⠑⠢⢌⡑⠢⡑⢌⠢⡑⢌⠢⢑⡈⢆⠱⡈⢆⠱⡈⢆⡑⠢⡑⢌⠢⡁⢆⠱⣈⠢⡑⠰⡈⢆⠱⡈⠔⡡⢊⠔ ⢣⠎⡰⢁⠎⠤⢉⠢⡑⢌⠰⣀⠣⢌⠱⣀⠣⠘⡄⢣⠘⡄⢣⠘⠤⡘⠤⢉⠒⡠⠑⡌⢢⠑⢌⠰⡈⢆⣌⣱⣴⣷⣾⣷⣾⣶⣷⣾⣿⣿⡿⠟⢩⠐⡡⠘⠤⡑⢢⢉⠒⡠⢑⠂⠥⢘⠠⢊⠔⡈⠆⡌⢡⡐⢌⠢⡑⠌⡄⠣⢌⡘⠄⢣⠘⡄⢊⠔⡨⠐⠤⣉⠒⠌⡙⢿⣿⣿⣷⣆⠆⡄⠢⢌⡉⢛⠿⣿⣿⣿⣿⣦⡁⢎⠰⡈⠜⡠⢁⠆⡡⢊⠔⡠⢉⠒⠤⣈⠱⡐⢌⠢⡑⢌⠢⢡⠘⡄⢣⠘⡄⢣⠘⡄⢢⠑⡌⢢⠑⡌⢢⠑⠤⡑⢨⠑⡌⢢⠑⢌⠢⡑⠢⠌ ⢣⠜⡠⢃⠜⡠⠃⢆⠱⣈⠒⠤⡑⠌⡒⢠⢁⠣⡘⢄⠣⠘⡄⣉⠒⢌⠰⡁⢎⠰⢁⠆⡡⢊⢄⣣⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⢣⠐⡩⠄⢣⠐⣉⠒⢄⠃⡄⢣⠐⡡⢊⠔⡡⢊⠔⡨⢐⠡⡘⠤⡘⢄⠣⡘⠰⣈⠑⢢⠘⢌⠢⢡⠘⡄⢊⠔⣉⠒⡠⢉⠆⡑⢢⠘⣻⣿⣿⡷⡈⢅⠢⡘⢄⠊⡔⠹⢿⣿⣿⣿⣶⣥⠘⠤⡑⢌⠂⡅⢊⠤⡑⢌⡘⠰⣀⠣⡘⢄⠣⡘⢄⠃⢆⠱⡈⢆⠱⡈⢆⠱⢈⠆⡱⢈⠆⡱⢈⠆⣉⠒⢌⠢⡑⢌⠢⡘⢄⠣⢌⡑⠌ ⢣⠜⡠⢃⠜⡠⢉⠆⡡⢂⠍⡰⢈⠆⡑⠢⢌⠢⡑⢌⠢⡑⠰⢠⢉⠢⢡⠘⡠⢊⠔⡨⣰⣷⣿⣿⣿⡿⠛⢏⠡⢂⣵⣾⣿⣿⠟⢡⠊⡄⢣⠐⡩⠄⢣⠐⡌⢢⠘⡐⢢⠑⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠤⡉⢆⡉⠆⡑⢢⠡⡘⢄⠊⡔⢨⠐⡡⢊⠔⡁⢎⡐⢩⠋⠔⣁⠊⡔⢁⠎⡰⠈⡅⢢⠉⠿⣿⣿⣿⣿⣦⡘⠄⢣⠘⡄⢒⠨⡐⠌⡡⢂⠱⢈⠢⡑⠌⡂⢍⠢⡑⡈⢆⠢⢑⡈⢆⠡⢊⠄⢣⠘⢄⠣⡘⢠⠉⢆⠱⡈⢆⠱⡈⢆⡘⢄⠒⠌ ⢣⢊⠔⡡⢊⠔⡁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢎⠰⡁⠎⡰⢁⠃⠆⡌⢢⠁⢎⠐⡡⢊⣴⣿⣿⣿⠟⡩⢐⡉⢢⢑⣾⣿⣿⡟⢡⠊⡄⢣⠘⠄⢣⠐⡡⢂⠅⢢⠁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢆⡉⢆⡑⠢⢌⠢⡑⠢⡑⢌⠢⡑⢌⠢⡑⢄⠣⢌⡐⢢⠘⡄⢊⠔⡠⠃⢌⠢⢘⡀⢣⠘⡄⢊⠔⡠⠛⣿⣿⣿⣿⣷⣆⡡⠘⡄⠣⡐⢡⠂⡅⢊⠄⢣⠐⡡⠘⡄⢢⠑⡨⠄⡃⢆⡘⠄⠣⢌⡘⠄⡊⠔⣂⠑⡂⢍⢂⠱⡈⢄⠣⡘⠤⡘⢠⠉⠆ ⢣⠊⡔⢡⠊⠤⡑⢌⠢⡑⠌⢢⠑⡈⢆⠱⡈⢆⠱⡈⠔⡨⢘⠰⡈⠤⢉⠢⣑⣼⣿⣿⣿⠟⢡⠘⡠⢁⠆⡱⣾⣿⣿⢋⡑⢂⠱⡈⢆⠉⡜⠠⡑⢄⠣⡘⠤⣉⠢⡑⢌⠢⡑⠌⡄⢣⠘⡠⢃⠜⡠⢃⠜⡠⢃⠜⡠⠘⡄⢢⠑⢢⠑⡌⡑⢌⠢⡑⢌⠢⠑⡌⢢⠘⠤⡘⠄⡃⠜⡠⢊⠔⡉⣄⡃⢆⡘⡄⢊⠔⡡⢊⡐⢡⠐⡌⠻⣿⣿⣿⣿⣷⣤⣃⠜⡠⢃⠜⡠⢊⠄⢣⡐⢡⠘⡄⢣⠐⡡⠘⡄⢢⢉⠒⡄⢢⠑⡌⢒⠠⢃⡘⠄⡊⠔⡡⠊⡔⢡⢂⡑⢢⠉⠆ ⢣⠱⡈⢆⡉⠒⢌⠢⡑⢌⡘⢄⠣⡘⢄⠣⠘⡄⢢⠑⡌⠰⡁⠆⡑⢌⢢⣵⣿⣿⣿⠟⡡⠘⡄⢣⠐⡡⢘⠠⡙⢛⠃⢆⡘⠄⢣⠐⡌⠒⡄⢣⠘⡄⢣⠐⡡⢂⠱⣈⠢⡑⢌⠒⢌⠢⡑⢄⠣⢌⠰⡈⢆⡑⠌⢢⢁⠣⡘⠤⡉⢆⠱⢠⠑⡌⢒⠨⡐⢌⠱⣀⠣⢘⠰⣀⠣⠘⠤⡑⠌⡂⡵⣿⣿⣦⡒⢌⠢⡘⢄⠡⡘⢄⠣⠌⡑⠤⣉⠻⢿⣿⣿⣿⣿⣶⣧⣦⣵⣨⣘⣤⣘⣤⣣⣼⣤⣷⣶⣷⣾⣶⣾⣶⣮⣤⣧⣘⣄⢃⠒⢌⠢⡑⢌⠰⢡⠘⡄⢢⠘⠤⣉⠂ ⢣⡑⠌⠆⡌⠱⣈⠒⢌⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⢊⠰⢡⠘⠤⡑⣬⣾⣿⣿⠿⡁⢆⠡⢃⠌⣂⠱⣀⠃⢆⠱⡈⠜⡀⢆⡉⢂⠅⢢⠑⡌⢄⠣⡘⢄⠣⡐⢡⠒⠤⡑⢌⠂⡍⠢⡑⢌⠢⡑⢌⠢⢑⠂⡌⡘⢄⠊⡔⢡⢂⠱⡈⢆⠡⢊⠔⡈⢆⠡⢊⠔⡠⠑⡌⠒⠤⢡⢉⠒⢌⠢⠑⡌⠻⣿⣿⣿⣦⠑⡰⢈⠆⡱⢈⠆⡱⢈⠒⡄⠒⠤⡈⠝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣔⢁⠊⡔⢂⠥⢘⡀⢃⠒⠤⡁ ⢣⠜⡨⠑⡌⢡⠂⡜⢠⠃⡜⠠⢃⠜⡠⢃⠌⡒⠄⡃⢌⢂⠩⣰⣿⣿⣿⡿⠏⡑⠌⡄⠣⠌⢒⠠⡁⢆⠩⠄⡃⠜⡠⢑⠢⠘⡄⢊⠄⠣⢌⠢⡑⢌⠢⡑⢌⠢⡉⠔⡈⢆⠱⣈⠱⢈⠢⡑⢌⠢⡑⢌⠒⠤⡑⢌⠒⢌⠢⢌⠢⡑⡈⢆⠡⢊⠔⡈⢆⠡⢊⣴⣧⣬⣕⡈⠆⡌⡘⠄⣃⠱⡈⠥⡘⢿⣿⣿⣧⡐⢡⠊⡄⠣⢌⠰⢁⠎⠰⣉⢂⠱⣈⠑⢢⠐⠤⡈⢍⠩⡉⢍⠩⡉⢍⠩⢡⢁⠒⡄⠒⡄⢂⠆⡡⢊⠍⡙⠛⠿⢿⣿⣿⣿⣶⡈⢆⡘⠤⢘⠠⣉⠒⠄ ⢣⠜⡐⢣⠘⠤⡑⡈⢆⠱⣈⠱⡈⠒⡄⢃⠌⡰⠡⡘⢄⣊⣾⣿⣿⡿⢏⡑⢌⠰⠡⢌⡑⢌⠢⡑⢌⠰⡈⢆⠱⡈⠔⡡⢌⡑⠌⠢⢌⡑⠢⢡⠘⡠⠑⡌⠢⡑⢌⠢⡑⢌⠒⡄⠣⢌⠢⢑⠢⡑⢌⠢⣉⠒⢌⠢⣉⠢⢑⠢⡑⠤⡑⢌⠢⡁⢎⠰⣈⢲⣿⣿⣿⣿⣿⣿⣎⠰⡁⢎⡐⠢⡑⠤⠑⡌⢻⣿⣿⣧⠂⠥⡈⢅⠢⡑⠌⡌⢡⠐⡌⢒⠠⡉⠆⡉⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠡⢊⠔⡨⠑⡌⢢⠘⡄⠣⡘⠤⣉⠒⠌⡉⠿⣿⣿⣿⣶⡈⠔⡡⢒⠠⡉⠆ ⢣⠎⡰⢁⠎⡰⢠⠑⡌⠢⢄⠃⡌⡑⠌⢢⠘⡄⠱⣈⣶⣿⣿⣿⠟⡁⠆⡌⢢⢁⠃⠆⢌⠂⢆⠡⢊⢤⣕⡂⠥⡘⠤⠑⡂⠌⡌⡑⢂⠌⡑⢂⠱⣀⠣⡐⢡⠘⡄⢣⠘⡄⠣⢌⡑⠢⡑⢌⠒⢌⠢⡁⢆⡉⢢⠁⢆⠱⣈⠒⢌⠰⡈⠆⡑⠌⢢⠁⠆⣿⣿⣿⣿⣿⣿⣿⣿⡇⠜⡠⢌⡑⢄⠃⢣⠘⡌⢻⣿⣿⣇⠢⠑⡌⢂⠱⡈⠔⡡⢊⠄⡃⢆⠱⡈⠔⡈⢆⠱⡈⠔⡡⠌⡂⢅⠊⡔⠡⢊⠔⢡⠂⡅⢊⠔⢡⢂⠱⡀⢎⠰⡁⢆⡉⠿⣿⣿⣿⡆⢡⠊⡔⡁⠎ ⢣⠜⡠⢃⠜⡠⢁⠎⡰⢁⠎⠰⢠⠑⡌⠢⡑⣬⣷⣿⣿⣿⠟⡁⠒⢌⠒⡨⠐⡌⡘⢌⠂⡍⢄⠣⣾⣿⣿⡿⠐⡄⠣⡑⢌⠒⠤⡑⠌⢢⠑⡌⠒⠤⡑⡈⢆⠡⡘⢄⠣⣈⠑⠢⢌⡑⢌⠢⡘⢄⠣⡘⠤⡘⠤⣉⠢⡁⢆⡉⢢⠑⢌⠢⡑⢌⠂⡍⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡑⢢⠐⡌⡘⢄⠃⡌⠸⣿⣿⣿⡀⢣⠘⡄⢃⠜⡠⠑⡌⢢⠑⡌⢂⠱⡈⠔⡈⢆⡘⠤⡑⢢⠑⡌⢒⡈⠱⡈⢌⠢⡑⡈⢆⡘⢄⠊⠤⡑⡈⢆⠱⡀⢆⠱⡘⣿⣿⣿⡂⢅⠒⢌⠰ ⢣⠜⡠⢃⠜⡠⢃⠜⡀⠎⡰⢁⠆⡡⢂⣵⣾⣿⣿⣿⠟⣁⠢⢡⠉⢆⡘⠄⢣⠐⡡⢂⠱⡈⢆⣽⣿⣿⠏⡔⠡⢌⠱⠐⡌⡘⠰⡈⢜⣶⣿⣿⣷⣦⡑⠌⡄⢣⠘⢄⠒⠤⣉⠒⠤⡘⢄⠣⡘⠄⢣⠐⡡⢂⠱⠠⡑⢌⠰⡈⢆⠩⠄⡃⢌⠢⡑⢌⠢⡙⣿⣿⣿⣿⣿⣿⣿⠏⡐⢡⢂⠱⢠⠑⡌⢒⡈⢅⢻⣿⣿⡆⢡⢊⠰⠁⢆⠡⢃⠜⡠⢃⠜⡠⢃⠜⡨⢑⠢⠘⠤⡑⠢⢡⠘⠤⣈⠱⡈⢆⠱⢠⠑⠢⢌⠢⡉⢆⡑⢌⠂⢆⠱⡈⠔⡠⠹⣿⣿⡇⡌⡘⠄⡃ ⢣⢊⠔⡡⢊⠔⡡⢂⠱⡈⠔⡨⠐⣥⣾⣿⣿⡿⠟⣁⠒⡠⢑⢂⠩⢄⠢⢉⠢⡑⣄⣣⣦⣵⣼⣿⣿⣯⣴⣨⡑⢌⠢⡑⠤⣁⠣⢘⣾⣿⣿⣿⣿⣿⣿⡆⡘⢄⠣⢌⡘⠰⢠⠉⢆⠱⡈⠔⡡⢊⠄⢣⠐⡡⢊⡑⠌⢢⢁⠒⢌⠰⢡⠘⡄⠣⢌⠂⢆⡑⠬⠛⠿⠿⠿⡛⣍⣢⣵⣦⣮⣴⣥⣎⡄⢃⠔⡈⢾⣿⣿⡇⢣⢀⠣⡉⢄⠣⠌⣂⠱⢈⠆⡱⢈⠆⡑⢢⠡⣉⠒⢌⡑⠢⣉⠒⡄⢣⠘⡄⢃⠆⣉⠒⡌⢢⠑⠤⡘⢠⢉⠂⢆⠱⡈⠔⡉⣿⣿⣿⠠⡑⢌⡐ ⢣⠊⡔⢡⠊⡔⢠⠃⢢⠑⡌⣰⣿⣿⣿⡿⢋⡑⠌⠤⡑⢄⠣⣈⠒⣌⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣕⠢⠄⣃⢺⣿⣿⣿⣿⣿⣿⣿⣷⠈⢆⡘⠤⣈⠑⢢⠉⡔⠢⡑⢌⠰⡁⠎⡄⢣⠐⡡⢌⡘⢄⠊⣌⣦⠘⡄⢣⠘⡰⢈⠜⡠⠒⡌⠱⡈⢦⣷⣿⢿⣻⢯⣿⣽⣯⡿⣽⢿⣷⡈⠔⣹⣿⣿⣿⣦⡈⢆⠱⡈⠔⡡⢂⠱⣈⠢⢁⠎⡰⢁⠆⡱⢠⠉⠆⡌⠱⣀⠣⠘⡄⢣⠘⡄⢊⠄⢣⠘⠤⡉⢆⠑⠢⢌⡘⠄⡃⠜⡠⢡⣿⣿⡿⢠⠑⢢⠐ ⢣⠃⡜⢠⠃⠜⡠⢉⠆⣸⣴⣿⣿⣟⠓⡄⢃⠔⣈⠒⢌⡐⣢⣴⣿⣿⣿⣿⠿⢛⠋⡍⢩⠐⡄⢒⠨⢡⢉⠛⡻⢿⣿⣿⣿⣖⡠⢚⣿⣿⣿⣿⣿⣿⣿⣿⢺⠠⡘⠰⢠⠉⢆⠱⣀⠣⢌⢂⠱⣀⠣⠘⡄⢣⠐⢢⠐⡌⠌⣿⣿⣷⠌⡄⢣⠐⡡⢊⠔⡡⠌⡱⢸⣿⣟⣾⣯⣟⡿⣾⣳⣟⡿⣽⣯⣿⠇⣺⣿⣿⡿⣿⣿⣿⣦⣂⠱⡈⠔⡈⠆⠤⡑⠌⢢⠁⢎⠰⡁⢆⡉⠒⡌⡑⠤⣁⠣⡘⢄⠣⡘⢄⠚⠤⣉⠒⠌⠤⣉⠒⠤⡘⢠⠑⡌⠰⣱⣿⣿⡇⠥⢊⠄⡃ ⢣⡑⢌⠢⢉⠆⡱⠈⢦⣿⣿⣿⠛⡠⢃⡘⢄⠊⠤⡉⣦⣾⣿⣿⡿⠟⡩⠐⡌⢢⠑⢌⠢⡑⢌⠢⡑⠢⢌⠢⠑⡌⠹⢿⣿⣿⣷⡡⢻⣿⣿⣿⣿⣿⣿⠇⡊⠔⡡⠃⢆⠩⡐⢢⠐⢬⣿⣷⡂⢄⠣⣱⣼⣶⣿⣶⣧⣬⣶⣼⣿⣿⡜⡐⠢⡑⢄⠣⡘⢄⠊⡔⠡⢿⣿⣟⣿⣻⣽⣻⣽⣯⣿⡷⠿⢋⣼⣿⣿⡿⠃⡍⢻⣿⣿⣿⣦⣕⠨⡐⢩⠐⡌⡘⠤⢉⠂⢆⡑⠢⢌⠱⢠⠑⠢⢄⠣⡘⢄⠣⡘⠤⣉⠒⠤⡉⠜⡰⠠⡉⠔⡈⢆⠡⢌⣱⣿⣿⡿⡈⢆⠡⢊⠔ ⢣⠘⡄⠣⢌⠒⡠⢩⣿⣿⡿⠤⠃⡔⢡⠐⡌⡘⢤⣿⣿⣿⡿⠋⡔⢡⠂⡕⡈⠆⡩⢐⠢⠡⢌⠂⡅⢃⠆⡡⢃⠌⡱⢈⠽⣿⣿⣿⣤⣉⣛⡛⡛⢋⠅⡊⠔⡡⢂⠍⢢⠑⡄⢃⡘⢼⣿⣿⣧⣬⣾⣿⣿⠿⠛⠿⢿⣿⣿⡿⠟⢣⠘⢠⠃⠜⡠⠃⡔⣈⠒⣈⠱⡈⠍⠛⠛⡙⢋⠋⡍⢡⠂⣜⣬⣿⣿⣿⠟⡠⢃⠜⡠⠌⠻⢿⣿⣿⣷⣧⣂⠱⢠⠑⡌⢢⠉⡄⢢⠑⡈⢆⠡⢊⡑⢌⠰⣁⠊⡔⠡⢒⠠⡉⠔⡈⢆⠡⢂⠱⡈⠔⣈⣦⣿⣿⣿⡿⠡⡘⠄⠣⢌⠂ ⠣⠜⡠⢃⠌⢢⢱⣿⣿⡿⡐⠆⡱⢈⠂⡅⢢⢱⣿⣿⡿⠋⡄⢃⡘⠄⢣⠐⡡⠊⠔⡁⢆⠱⡈⠒⡌⢢⠘⢄⠣⡘⡐⠌⠤⠹⣿⣿⣿⣟⣿⣻⣿⣷⣮⡐⢡⠂⡅⢊⠔⡨⢐⠡⢌⢂⡙⠿⠿⠿⠿⢛⠡⢊⡑⠌⡂⠤⡐⠤⢉⠔⡈⢆⠉⢆⡑⢌⠰⣀⠣⠄⡃⠜⡈⣅⠣⠜⡠⢃⣜⣤⣿⣿⣿⣿⠿⢉⠰⢁⠆⡘⠤⣁⠃⢆⠩⠻⣿⣿⣿⣿⣶⣥⡘⡄⢣⠘⡄⢣⠘⡠⠃⠆⢌⠂⠥⣀⠣⡐⢡⠊⠔⡡⢊⠔⡈⢆⠡⢂⣱⣼⣿⣿⣿⡿⢏⠰⡁⢆⡉⠒⡌⢂ ⠍⢆⠱⡈⠜⡠⣾⣿⣿⢑⡋⠔⡁⢎⠰⡈⠆⡚⣿⡟⠱⢡⠘⠤⡘⠌⣂⠱⢠⠉⢆⠱⡈⢆⠡⢃⠜⡠⢉⠂⢆⡑⠌⡘⢄⠣⢼⣿⣿⣿⣞⣯⣷⣯⣿⣇⠢⢑⡈⢆⡘⢄⠣⡘⢠⠂⡜⢠⠃⡱⢈⠆⡑⢢⠘⠤⡑⢢⠡⣘⡄⣊⠔⡨⠘⡄⢒⠨⡐⠄⢎⠰⡁⢎⠰⣀⣦⣷⣾⣿⣿⣿⣿⠟⡋⢅⠊⡄⠣⢌⢂⡑⠢⢄⡉⢆⠡⢃⠤⢉⠛⠿⣿⣿⣿⣿⣶⣥⣜⣠⠑⠤⡉⠜⡠⢉⠒⠤⡑⢌⠢⡑⢌⠰⢡⢘⣰⣬⣾⣿⣿⣿⣿⡿⢋⠔⣈⠒⡌⠰⣈⠱⢀⠃ ⡍⢢⠑⡌⢢⠱⣿⣿⣟⠠⡜⢠⠑⡌⢂⠱⡈⠔⡠⠌⡑⢂⠩⡐⢄⠣⡐⢌⠂⡍⢢⠑⡌⢢⠑⡌⢢⠑⡌⡘⠤⡘⠤⠑⡌⠰⣈⣿⣿⣿⣟⣿⣯⣷⡿⢣⠘⠤⡘⠠⢌⠂⢆⡑⠢⡁⢆⠡⢊⠄⢣⠘⣄⣣⣼⣶⣵⣦⣿⣿⣿⣿⣷⣧⣵⡈⣌⢢⣱⣬⣦⣷⣾⣿⣿⣿⣿⣿⣿⠿⢛⠋⡄⢣⠘⡄⠣⢌⠑⡂⢆⡘⡐⠢⢌⢂⠱⣈⠢⡁⢎⡐⢢⢉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣧⣾⣴⣬⣦⣵⣼⣶⣿⣾⣿⣿⣿⣿⣿⡿⠛⡡⢂⠅⡊⢄⠣⡈⢅⠢⡘⠄⡃ ⣘⠢⡑⢄⠣⡘⣿⣿⣯⠐⡄⠣⡘⠄⡃⢆⠱⡈⠔⡡⠘⡄⢣⠘⡠⢂⠱⣈⠒⢌⠢⡑⢄⠣⡘⢄⠃⡌⠰⡁⢆⠱⡈⠱⡈⠥⢰⣿⣿⣿⠟⡛⢍⠩⡐⡁⠎⡰⢁⠣⢌⡘⠤⣈⠱⢈⠄⠣⢌⡘⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠩⡁⢆⡘⠄⢣⠘⡄⠣⡈⢅⠢⡑⢨⠐⠤⣁⠃⠆⡌⢒⠠⡑⢌⠰⡈⠆⡌⡘⠰⠠⢌⠩⡙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⡛⢋⠍⡰⢀⠣⡐⢡⠊⠔⡈⠆⡑⢨⠐⡡⢊⠔ ⢆⡱⢈⠆⢢⠁⣿⣿⣿⡖⣈⠑⢌⠢⢑⡈⠆⡱⢈⠔⡡⠘⡄⢢⠑⡌⠒⠤⣉⠢⡑⢌⠢⡑⢌⠢⡑⠌⡑⢌⡐⠢⣁⠣⡐⢡⣾⣿⣿⡟⢢⠘⡠⢃⠔⡡⢊⠔⣈⠒⡄⢢⠑⡄⠣⠌⣌⣑⣢⣼⣿⣿⡿⢋⠄⢢⠙⣿⣿⣿⡎⢡⠂⡌⢛⢿⣿⣿⣿⣯⡇⡙⠿⣿⣿⣿⣦⡑⢂⠌⡘⢄⠣⣈⠑⡌⢄⠃⡜⢠⢉⠒⠤⣉⠒⢌⠢⡑⠌⢢⠑⠌⡒⠤⣁⠣⡑⢌⠂⠥⣉⠒⡌⢒⠠⡐⢄⠢⡐⢄⠢⡐⢄⢊⡑⢢⠘⡄⢊⠔⡡⢂⡑⠢⢉⠢⠑⡌⠰⡁⢎⠰⠡⡈ ⢎⠰⡁⠎⡄⢣⠸⣿⣿⣷⡠⢉⠢⡘⠤⠘⠤⡑⡈⢆⠡⢃⠜⡠⢃⠌⡑⠢⢄⠣⠘⡄⢃⠜⡠⠑⡄⢣⠘⠤⡈⠥⢐⢂⣑⣾⣿⣿⣿⣁⣆⣱⣀⣣⣘⣤⣡⣎⣴⣬⣴⣧⣾⣶⣿⣿⣿⣿⣿⣿⣿⠋⡄⢣⠘⡄⢣⢸⣿⣿⣷⡀⢣⠘⢄⠢⣉⠻⣿⠿⡃⠜⡠⢉⠿⣿⣿⣿⣦⢘⠰⣈⠒⡠⢃⠌⢢⠑⢌⠢⢌⡘⠰⢠⢉⠢⡑⢌⡘⢄⠊⡔⠡⢒⠠⡑⠌⡂⢍⠒⡠⠑⡌⠢⡑⠌⢢⠑⢌⠢⡑⢌⠂⢆⡘⠄⢣⠘⡄⢊⠔⠡⡐⢡⠊⡔⠡⢌⠱⡈⢆⠡⢃⠔ ⡍⢆⠱⡈⠔⣂⠡⠻⣿⣿⣷⡈⢆⠑⡌⡑⢂⠱⡈⢄⠣⢌⠢⡑⢌⠢⣁⠣⢌⠢⡑⢌⠢⡘⠄⢣⠘⢄⠊⡔⢡⠘⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⢂⠣⡐⠢⣁⠒⡄⢾⣿⣿⣿⣷⣆⠡⢊⠰⢠⠁⢆⠱⢈⠆⠱⡈⠤⡙⢿⣿⣿⣷⣇⡰⢈⠔⡨⠘⡄⢊⠄⡃⠆⡌⡑⠢⢌⠢⢑⠢⢌⠢⡑⢌⠱⡈⢆⠱⡈⠔⡈⢆⠡⢃⠌⡑⠤⡉⢆⡘⠄⡃⠔⡨⠘⠤⢘⡈⠆⢒⡈⠆⡌⠱⡈⢆⠱⣈⠱⡈⢆⠱⡈⢆⠡⢊ ⡜⢢⠑⡌⠒⡄⢃⠅⠻⣿⣿⣿⣦⠘⡠⠘⡄⢃⡘⢄⠊⠤⡑⢨⠐⠢⢄⢃⠢⢡⠘⡠⢁⠆⡩⠐⡌⠢⣑⣨⣶⣿⣿⣿⣿⠟⡩⢉⠍⣙⣹⣫⣿⣿⣿⣿⣽⣭⣉⡍⣿⣿⣿⢀⠣⣾⣿⣿⠏⠰⡁⢆⠡⡑⢠⠡⢌⣿⣿⣿⢿⣿⣿⣷⣌⡆⡡⢊⠄⠣⠌⡌⡑⢌⠒⡐⢂⡙⢿⣿⣿⣷⡌⢢⢁⠣⡘⢄⠊⡔⠡⢂⠅⠣⢌⠢⡁⠎⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⠣⢌⠢⡁⢎⠰⣁⠒⠤⡈⢆⠱⡈⠔⡩⢐⠡⢂⠍⢢⠘⡰⢈⠱⡈⢆⠡⢂⠱⡈⢆⠡⡘⢄⠃⠆ ⢎⡅⢊⠔⡡⠘⡄⢊⠥⠙⢿⣿⣿⣷⣦⡑⢌⠢⠌⠤⣉⠒⠌⠤⣉⠒⡌⢄⠃⢆⠱⣀⠣⡘⣠⣣⣼⣷⣿⣿⣿⣿⠿⢋⠅⣊⢴⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢌⠢⠹⠟⡡⢊⡁⠒⡌⢢⠑⣂⠱⣾⣿⣿⡏⢌⠹⢿⣿⣿⣿⣿⣦⠌⡱⢈⠤⢑⡈⢆⡑⠢⠌⡌⢹⣿⣿⣿⣄⣎⣴⡡⢌⠒⢌⠡⢊⠌⡑⠢⡑⢌⠒⡌⢢⠑⡌⢄⠣⡘⠄⠣⢌⡑⠢⡑⢌⠢⡁⢆⡉⢆⠱⡈⢆⠱⡈⠔⡡⢊⠔⡈⢆⠱⣀⠃⢆⠱⡈⢆⠡⢂⠱⡈⢆⠱⡈⠜⡠ ⢎⡰⢉⠆⡡⢃⠜⡠⢊⠱⡈⡙⠿⣿⣿⣿⣷⣾⣬⣖⣠⣉⣜⡰⣀⣣⣌⣢⣩⣦⣶⣶⣷⣿⣿⣿⣿⡿⢟⡛⢩⠁⢎⠰⣨⣾⣿⣿⣿⠿⢛⠩⡁⢆⠰⢠⠉⡍⢛⣿⣿⣿⠙⡄⢃⠱⡈⠔⡡⠌⡑⢌⠰⡈⢤⣿⣿⣿⢏⠰⡈⢆⠢⠌⢛⠻⠟⡡⠒⢄⠣⢌⠂⡜⡀⢆⠱⡈⠔⡡⣾⣿⣿⣿⣿⣿⣿⣷⣎⠄⠣⢌⠢⢁⠣⢌⠢⡑⢌⠂⠥⡘⢄⠣⡘⢌⡑⠢⢌⡑⠌⢢⠑⡌⢢⠘⡠⢃⠜⡠⢃⠜⡠⠑⡌⢢⠑⡌⠒⠤⣉⠢⡑⢌⠢⣁⠃⢆⠱⡈⢆⠱⡈⠔ ⢎⠔⡡⢊⠔⢡⠊⠔⡁⢆⡑⢌⠰⣈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⠛⡋⢍⠰⢐⠢⠘⡄⠩⢄⣳⣿⣿⣿⢛⠡⢊⠄⡃⠜⡠⢃⠆⡱⢈⣼⣿⣿⡗⢊⠔⡡⢂⠱⡈⠔⡨⠐⡌⢢⠑⡈⠿⡟⢋⠄⡃⠔⢢⠑⡌⢢⠘⠤⡑⢌⢂⠒⡌⠒⠤⢑⠨⢄⠱⣈⣾⣿⣿⡟⡋⢍⡙⢿⣿⣿⣮⠑⡈⢆⠡⢊⠤⠑⡌⢢⠉⢆⠡⢊⠔⡡⢂⠌⡑⠢⢌⡘⢄⠣⡐⢡⠊⡔⠡⢊⠔⡈⢆⠡⢃⠜⡠⢃⠌⡑⠢⢄⠃⡜⢠⠃⠤⡉⢆⠱⡈⢄⠣⡘⠄ ⢎⠜⡠⢃⠜⡠⢉⠆⡑⠢⢌⠂⡅⢢⠉⢆⠱⡀⢆⠩⡉⢍⠩⢍⠩⡉⢍⡉⢆⠡⡘⠰⡈⢆⠱⡈⢆⠡⢊⡑⢨⢑⣾⣿⣿⠿⡑⡈⢆⠡⢊⣴⣿⣶⡄⢊⠔⢂⣿⣿⣿⠘⢢⠘⡄⢃⠆⠱⡈⠔⡡⠘⠤⡑⢌⠒⢌⠢⡘⠤⢉⠢⡘⢠⠁⢎⠰⡈⠆⡌⢒⠨⡑⢌⠢⡁⠎⣰⣿⣿⣿⠋⡔⢡⠂⡌⡘⢿⣿⣿⡆⠱⡈⢆⠡⢊⠡⢂⠅⡊⢄⠣⢌⠢⡑⢌⠢⣁⠃⢆⡘⠄⢣⠘⡄⠣⢌⠱⡈⢆⠱⡈⢆⠡⢊⠔⡡⢊⠔⡡⢊⠔⡈⢆⡉⢆⠱⡈⢆⠱⡈⢆⡑⠌ ⢎⢢⠑⡌⢢⠑⢢⠘⡄⢃⠆⡱⢈⠆⣉⠢⢡⠘⡄⢣⠘⡄⠣⢌⠢⢑⠢⠘⡄⠣⢌⡑⢌⠢⣁⠒⢌⠢⢡⠘⡄⣾⣿⣿⣏⠙⠤⢑⡈⠆⣱⣿⣿⡟⡈⢆⡘⢸⣿⣿⡷⢈⠅⡊⠔⡡⢊⠡⡘⠤⢡⢉⠒⠌⠤⣉⠢⡁⢆⠱⡈⠔⢡⠂⢍⠂⡅⢢⠑⡈⢆⠱⢈⠆⢢⠑⡌⠹⠿⣟⢃⠣⠌⣂⠱⢠⠑⢺⣿⣿⡇⢡⠘⡄⠣⢌⠢⡁⢎⠰⣈⠒⡌⢢⠁⢎⠰⢠⠉⢆⡘⢌⠢⡑⢨⠁⢎⡐⢡⠊⡔⢡⠊⡔⢡⠊⠔⡡⢊⠔⡡⢊⠔⢢⠘⡄⢣⠘⡠⢃⠜⡠⢂⠅ ⢎⠢⡑⢌⠢⡉⢄⠣⡘⢄⠊⡔⢢⠘⡠⢑⠢⢑⠨⠄⡃⢌⠡⢂⠱⡈⢆⠱⢈⠒⠤⡈⠆⠒⠤⡉⢢⠘⢄⠣⢰⣿⣿⣿⢉⠎⡰⢁⠢⡁⣿⣿⣿⡇⡘⢄⠢⣉⣿⣿⣷⢁⠊⡔⢡⠂⡅⢢⠑⡌⠢⢌⡘⢌⠒⡠⢁⠒⡌⠰⡈⠜⡠⢉⠆⡱⢈⠆⡱⢈⠆⡱⢈⠢⡁⠎⡐⢡⠊⡍⢂⠆⠱⡀⠎⡄⢩⢸⣿⣿⡇⠢⡑⢌⠒⡌⠰⡁⢎⠰⣀⠣⡘⠤⢉⠢⡑⢢⠉⠆⡌⢢⠑⡌⢢⠉⢆⡘⢄⠣⡘⠤⡑⡈⢆⡉⢆⠱⡈⢆⡑⢌⡘⠄⢣⠘⡄⢣⠐⡡⢊⠔⣁⠊ ⢎⡱⢈⠆⡱⢈⠆⡱⢈⠆⡱⢈⠆⡱⢀⠣⡘⢄⠣⡘⠰⡈⢆⠡⢂⠱⣀⠣⢌⡘⠤⡑⢌⡑⢢⠑⣂⠩⠄⣃⢚⣿⣿⣯⠘⢢⠑⡨⢐⠡⠌⣿⣿⣿⣔⠌⡰⢀⣿⣿⣿⡌⢒⡈⢆⡑⡈⢆⠱⣈⠑⠢⢌⠢⡑⢄⠣⡘⢄⠣⡘⠤⡑⢌⠢⡁⢆⡘⠄⢣⠐⡄⢃⠆⡱⢈⢴⣿⣧⠘⡄⢊⠅⢢⠑⡈⢆⣿⣿⣿⡃⠥⠘⡄⢊⠔⡡⠘⡄⠣⢄⠣⡐⢡⠊⡔⢡⠂⡍⠒⡌⢢⠑⢌⠂⡍⠰⣈⠢⡑⢄⠣⡐⢡⠂⡜⠠⢃⠜⡠⢌⠂⡜⡈⢆⠱⡈⢆⠱⣀⠣⠌⡄⢃ ⢎⡰⢁⠎⡰⠡⡘⢄⠣⡘⢄⠣⡘⢄⠃⢆⠱⡈⢆⠡⢃⠜⡠⢃⠜⡰⢀⠃⢆⡘⠰⡈⢆⡘⠄⠣⢄⠣⢘⡀⢎⣿⣿⣿⠈⢆⠱⣀⠣⢘⠰⡈⢿⣿⣿⣿⣶⣷⣾⣿⣿⣿⡄⠒⡄⢢⠑⢂⠒⠤⣉⠒⢌⢂⠱⡈⢆⠱⢈⢂⠱⢠⠑⠢⢡⠘⡄⢢⠉⡔⢨⠐⡡⡘⣤⣷⣾⣿⣿⣷⣌⢢⠘⡄⢃⢜⣼⣿⣿⡟⢄⠣⡑⢌⠢⡘⢄⠣⢌⠱⡈⠔⡡⢂⠱⡈⢆⠱⣈⠱⣀⠣⡘⢄⠣⢌⠱⢠⠑⡌⢢⠑⡌⢢⠑⡌⠱⡈⢆⠡⢂⠱⢠⠑⡌⢢⠑⣈⠒⡄⢣⠘⡄⢃ ⢎⡰⢁⠎⡰⢁⠒⡌⠰⡁⢎⡐⢡⠊⠜⡠⢃⠜⡠⢃⠌⢢⠑⡌⢢⠑⡌⡘⠤⣈⠱⡈⠔⡨⢌⡑⠢⡑⢂⠌⡂⢿⣿⣿⣏⠄⣃⠰⢈⠆⡡⢘⠠⣉⠻⠿⢿⡿⠿⠿⣿⣿⣿⡥⡘⢄⠊⠤⡉⢆⠰⡈⠆⡌⢢⠁⠎⡄⠣⢌⠢⡁⠎⡑⢢⠁⢆⠡⢊⢰⣡⣾⣶⣿⣿⣿⣿⠿⢿⣿⣿⣿⣶⣾⣾⣿⣿⣿⠟⠰⡈⠔⡡⠌⡂⢅⠊⡔⡈⢆⠱⡈⠔⡡⢂⠱⣈⠒⠤⡑⢠⠑⡌⢢⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⡑⢌⠢⡑⢌⠢⡁⢎⠰⡁⠎⡄⢣⠘⡄⠣⢌⠂ ⢎⡔⢡⠊⡔⢡⠊⡔⢡⠘⠤⡘⠤⡉⢆⠱⡈⢆⠱⡈⠜⡠⢃⠜⣀⠣⡐⢡⠒⡄⢣⠘⠤⡑⢂⠌⡑⢄⠣⡘⠰⡈⢿⣿⣿⣧⢀⠣⢌⢂⠱⡈⢒⠠⡑⢌⠢⡐⢡⢊⠹⢿⣿⣿⣧⣬⡘⠤⡑⠢⡁⢆⠱⣀⠣⡘⠰⡈⢅⠢⡑⢌⢢⣑⣢⣭⣦⣷⣿⣿⣿⣿⣿⠿⢛⠩⡐⢂⠆⡙⠻⢿⣿⣿⣿⡿⠟⡡⢊⠅⡘⠤⡑⢌⠰⣈⠒⠤⡑⢌⠢⡑⢌⠰⣁⠒⠤⣉⠒⢌⠢⡑⢌⠢⡑⢌⠢⡘⢄⠣⡘⠰⣈⠒⡄⠣⢌⢂⠱⡈⢆⠱⡈⢆⠱⣈⠒⢌⠢⢡⠘⡐⢢⠁ ⢎⡰⢁⠎⡰⢁⠒⡌⢢⠉⢆⡑⠢⡑⡈⢆⠱⡈⢆⠱⡈⠔⡡⢊⠤⡑⢌⠢⡑⢌⠂⡍⠒⢌⠢⡘⠰⡈⢆⠡⢃⠜⡈⢿⣿⣿⣷⣌⠢⢌⢂⠱⣈⠢⡁⢎⠠⡑⢂⠆⡡⢊⣿⣿⣿⣿⣿⣶⣥⣱⣈⣆⣡⢂⠆⡡⢃⠜⣀⢣⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⡋⢍⠰⡈⢆⠱⡈⢆⡘⢄⠃⢆⠢⡐⢄⠢⡑⢄⠣⡘⢄⠣⠌⡄⠣⢄⡉⠒⡌⢢⠑⡌⢢⠑⠤⣉⠒⠤⣉⠢⠑⡌⢢⠑⢌⠢⡑⢌⠢⡑⢌⠡⢂⠱⡈⢅⠢⢌⠢⡑⢌⠢⠑⡌⢒⠠⣉⠢⢑⠢⡑⢌⠢⡁ ⢎⠔⡡⢊⠔⡡⢊⠔⡡⢊⠔⡨⠑⠤⡑⢌⠢⡑⡈⢆⠱⡈⠔⡡⢒⡈⠆⡱⢈⠆⡱⢈⠱⡈⢆⠡⢃⠜⡠⢃⠌⡒⠨⢄⠛⣿⣿⣿⣷⣮⣤⣃⢤⡑⢨⠄⣣⣘⣤⣮⣴⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠢⢌⠰⡈⠿⠿⣻⣿⣿⣿⠁⢆⡘⠤⠑⡌⢂⠱⡈⢒⡐⠢⢌⠂⡍⢢⠑⢌⠢⡑⠌⡂⢆⠑⢢⠘⡰⢈⠅⠢⢌⠱⡈⢆⡘⢄⠣⡘⠰⢠⢉⠒⠤⣁⠣⡘⠤⢉⠂⢆⠱⣈⠒⢌⠢⡑⢌⠢⡑⠌⡒⢌⠢⢑⠢⣁⠣⡘⢄⠣⢄⠣⢌⢂⠱⡈⢆⠡ ⢎⠜⡠⢃⠜⡐⠌⡒⢄⠣⡘⠤⣉⠒⢌⠢⡑⠤⡑⢌⠢⡑⢌⠰⡁⢆⠱⣀⠣⡘⢄⠃⢆⠱⡈⢆⠡⢊⠔⡈⢆⠡⢃⠌⡒⠤⢙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢡⠊⡑⠢⠌⣉⠛⣿⣿⣿⣿⣧⣌⠱⡈⢆⠱⣈⣶⣿⣿⡿⢣⠍⠤⡘⢄⠣⠘⡄⢃⠜⡀⢆⡑⠢⡑⢨⠐⡌⢢⠑⡈⢆⠱⣈⠘⠤⡑⢄⠣⢌⠱⡈⢆⡑⠢⢌⠢⡑⢌⡑⠢⢌⡘⠰⣀⠣⡐⢡⠊⡜⢠⠃⡔⡈⢆⠱⡈⢆⠱⡈⢆⠱⡈⢆⠡⠒⠤⡑⢌⠢⡘⢄⠊⡔⡈⢆⡑⠢⡁ ⢎⢢⠑⡌⠒⡌⢢⠑⡌⢢⠑⠢⢄⡉⠆⡱⢀⠣⡘⢄⠣⢌⠢⡑⢌⠢⡑⠤⡑⢌⠢⣉⠢⡑⢌⠢⡑⢌⠢⡑⡈⢆⠡⢊⠔⡡⠊⡔⠠⢌⡉⢋⠛⡛⣛⢛⠛⢫⠉⡍⠰⢠⢉⠢⡑⢌⠱⡈⢄⠣⣈⠙⠿⣿⣿⣿⣿⣾⣾⣷⣿⣿⣿⠟⡡⢃⡘⠤⡁⠎⠰⢡⠘⡄⢊⠔⠢⢌⡑⢌⠢⡑⢌⠰⡈⠔⡈⠆⠤⣉⠒⢌⠢⡘⢄⠣⡘⢄⠢⡑⢢⠑⡌⠰⡈⢅⠢⢌⠱⢠⠑⡌⢢⠑⡌⢢⠑⠤⡑⢌⠢⡑⡈⢆⠱⡈⢆⠱⡈⢆⡉⠒⡌⢢⠑⢌⠢⡑⠤⡑⠢⢌⡑⠄ ⢎⠢⡑⡌⠱⣀⠣⡘⢄⠣⢌⡑⢢⠘⠤⡑⢌⠢⡑⠌⡒⢄⠣⡘⠄⡃⠜⡐⢌⠢⡑⢠⠑⡌⢢⠑⢌⠢⡑⠤⡑⠌⢢⠁⢎⡐⠡⢌⡑⠢⡘⢄⠣⡐⢄⡊⠜⡠⢃⠌⡑⠢⢌⠂⡅⢊⠤⠑⡌⠰⢠⢉⠒⡨⢙⠛⠿⠿⠿⠿⠟⢫⠑⡌⡐⠢⢌⢂⠱⣈⠑⢢⠡⡘⢄⢊⡑⠢⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠒⠤⣉⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢨⠑⡌⢢⠑⡌⢢⠁⢎⠰⡁⢎⠰⡁⢎⠰⡁⢎⡐⢡⠘⡄⢣⠘⡠⢃⠜⡠⢌⠱⡈⢆⡉⢢⠑⡌⢢⢁⠃⠆⡌⢂ ⢎⡱⠐⡬⠑⡠⢂⠱⣈⠒⠤⡘⠤⢉⠒⢌⠢⡑⢌⠢⡑⢌⠢⠑⡌⠰⢡⠘⡄⢣⠘⡄⢣⠘⡄⢊⠄⢣⠐⡡⠘⡌⢢⠉⠤⣈⠑⢢⢈⠱⡈⠆⡑⢌⠢⡘⠤⡑⠌⢢⢁⠃⢆⠱⠈⠆⡌⠡⢌⡑⠢⢌⠢⠑⡌⡘⢄⠣⡘⠤⡉⢆⠡⢂⠅⠣⢌⠂⠥⢠⠉⢆⠱⡈⢆⠢⢌⡑⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⢉⠒⠤⡑⡈⢆⠱⢈⠆⡑⢌⠢⡑⢌⠢⡑⠌⡄⢣⠘⠤⣉⠢⡑⠌⡄⢣⠘⡠⢃⠜⡠⠘⡄⢣⠘⡄⢣⠐⡡⢊⠔⡈⢆⡑⢢⠘⡄⢣⠘⡄⢊⠜⡰⢈⠆ ⢎⡐⢣⠰⡁⢆⠡⠒⠤⡉⢆⠱⡈⢆⡉⠆⡱⢈⠢⡑⢌⠢⣁⠣⢌⡑⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡘⢄⠣⡐⠥⡘⠤⣉⠒⠤⡉⠆⡌⢢⠑⡌⠰⡈⠔⡠⢃⠔⠩⡐⢌⡘⢄⢊⠱⡈⠔⡡⢂⠌⡡⢂⠅⢣⠐⡡⢊⠔⢡⢂⠱⡈⢆⠡⢊⠅⢢⠉⢆⠡⢊⠄⢣⠘⡄⢃⠆⡌⠱⡐⢌⠒⢌⠢⡑⢌⠢⡑⢌⡘⠤⡑⢌⠢⡑⢌⠢⡑⠌⡒⢌⠢⡑⢌⠒⢌⠂⡍⠰⢠⠑⡌⠒⡌⢢⠑⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⢣⠐⡡⢊⠔⢢⠘⡄⢣⠘⡄⢣⠘⡄⢊⠔⡡⠌ ⢎⠴⡁⢆⠱⡈⢆⡉⢆⠱⡈⢆⡑⠢⡘⠤⡑⢌⠢⡑⠌⡒⢠⠑⠢⢌⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⢑⠢⢄⡉⢆⠱⡈⠔⡡⢊⠔⡡⠘⠤⡑⠌⡌⠱⡈⠆⡌⠢⢌⠢⡑⢌⠰⡁⢎⠰⣁⠊⡄⢣⠐⡡⢊⠔⣈⠒⡨⠄⠣⢌⡘⠤⢉⠢⡑⢌⡘⢄⠣⡘⢄⠊⡔⢡⠘⠤⣉⠂⢆⡑⠢⡑⡈⢆⡘⠰⡈⢆⡑⢌⠢⡑⢌⠢⡑⠢⡑⢌⠂⡍⠢⡑⢌⡑⢢⠑⡨⠑⡄⢣⠘⡄⢣⠘⢄⠣⡘⢠⠃⡒⢌⠢⡑⢄⠣⡘⢄⠣⡘⠤⢑⠨⢄⠣⡘⢄⠊⡔⡈ ⢎⡔⢡⠊⡔⢡⠂⡜⢠⠃⡜⠠⢌⡑⢄⠣⡘⠤⡑⢌⠢⡑⢢⢉⠒⠤⡘⢠⠃⡌⢢⠑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠒⠤⡘⢄⠣⡘⠤⡑⢌⠢⢡⠉⢆⠱⡈⠔⡡⢘⠰⣈⠑⢢⠑⡌⢢⠑⡌⢢⠁⢆⠱⡈⢆⠱⣀⠣⡘⢄⠊⡔⣉⠒⠤⡘⢄⠃⢆⡑⠢⢌⠢⡑⠰⣈⠒⢌⠢⣉⠒⠤⣉⠢⢌⡑⠤⡑⠢⢌⠱⡐⠢⢌⠢⡑⢌⠢⡑⠌⡑⠰⣈⠒⡌⡑⢌⠢⡘⢄⠣⡐⢡⠘⡄⢣⠘⡄⡉⢆⠢⡑⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢄⠣⢌⠒⡌⢢⠑⡌⠒⠤⡁ ⠮⠔⡣⠜⡤⠃⡌⠰⡁⠜⣀⠃⠆⡌⢂⠱⣀⠃⡌⢂⡑⠌⡰⢈⠜⡠⢑⢂⠱⢈⠤⢉⠂⢆⠡⢂⡑⠌⡄⢃⠌⣂⠉⢆⠡⢊⡐⢡⢂⠱⢈⠢⡁⠎⡄⢃⠜⡠⠑⡌⢒⠠⣉⠂⠥⢘⡀⠣⠌⢂⡉⢢⠡⢘⠠⢃⠄⡃⢌⠢⢑⠰⠠⣉⠂⡅⢊⡘⠤⣈⠑⡂⠥⣈⠱⠠⣉⠂⡅⢂⠩⡐⠤⠑⡂⢌⠰⢁⠱⡈⢂⠅⣃⠢⢑⠨⠄⣃⠘⠤⣁⠣⠄⡃⠔⣁⠊⡔⢁⠊⡔⠡⢊⠔⡈⠆⡡⢂⠱⡈⠔⡡⢑⡈⠆⡡⢘⠠⡑⠨⢄⠃⡌⢂⠅⡊⠔⡨⠄⢃⠌⡑⠢⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠉⢳⡀⠀⠀⣀⡤⠴⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡽⢿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣼⠋⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢡⡾⣿⢷⣾⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣟⣿⡆⠀ ⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⣠⣿⣿⠧⠯⠟⠃⡇⣟⣇⣿⣿⣆⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣤⣤⣿⠇⠀ ⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⣯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣰⣿⢏⣿⣴⣿⣹⣷⣷⣿⣿⣧⣿⡏⣠⣴⣾⣿⢛⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢹⡆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢹⣇⢠⣿⣿⣧⣿⣿⣿⣿⣿⣶⣿⣏⣽⡟⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢿⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢠⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⣦⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⢸⡇⠀⢀⡴⠒⢦⣀⣠⠿⠗⠛⠛⠛⠛⠓⠲⠦⣄⡘⠦⣀⣀⣀⣴⠟⠁⠀⠙⣿⣿⣿⣿⣿⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀ ⠀⠘⣷⠀⢈⡷⣴⠚⣇⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⠉⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣴⡆⠠⣶⢘⣿⣿⣦⣿⢁⣸⣿⣿⣿⣿⣿⡟⣿⣇⣀⣼⣿⠀⠀ ⠀⠀⢹⣇⠸⣄⣈⣟⠉⣹⠀⣀⣤⣴⠶⠶⠶⠶⢦⣤⣀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢀⣾⠟⠙⠻⣷⣴⣴⣴⣿⡿⠿⢿⣿⣷⣵⠉⢏⣯⣿⣽⣷⣿⣿⣷⡿⠋⠀⠀ ⠀⠀⠀⣻⠎⠀⠀⠈⣩⣷⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⠸⣧⠀⠀⠀⠀⠀⢸⡏⡀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠙⢿⣄⠆⠘⠟⢿⡟⣿⡍⠁⠀⠀⠀⠀ ⠀⠀⣺⠏⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡙⢧⢻⠀⠀⠀⠀⠀⢸⡇⢿⣶⣤⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠘⣿⣿⣻⠀⠐⠛⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⣸⠃⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠸⣿⢀⣀⡞⢹⡆⡿⣃⣸⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⣿⠛⠀⢹⣷⠇⠄⢀⣢⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⣿⡄⠀⠀⣿⠀⠈⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠒⣿⠘⠲⠽⣿⡀⢧⡴⠃⠙⠁⣴⣲⡄⠀⠀⠘⢿⣿⠟⠤⡄⣸⣿⡀⣤⣾⡿⠃⠰⣿⠹⠶⢳⡆ ⠀⠀⠘⣷⡄⠀⣿⠀⣔⠒⢙⠿⠇⠀⠀⠀⢰⣚⡶⠀⠀⠀⢉⣵⠏⣀⣠⠶⣟⣻⣶⣿⣦⣤⣠⡬⠭⢴⡏⠀⠀⠀⠈⠓⠒⣷⣿⣿⣿⠿⠋⠀⠀⠀⠈⠻⠶⠛⠁ ⠀⠀⠀⠈⠙⢦⣜⣧⡈⠉⠉⠀⠀⠀⠀⠀⠀⠈⢻⣭⣍⣓⢿⣏⢰⢫⡴⠶⣭⡥⣤⡙⣿⢟⣵⣾⣿⣯⣽⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⣄⣤⡤⣌⠙⢛⡷⠲⠦⠤⠤⠤⢤⡤⠴⠚⠛⠉⠀⣷⡘⣮⢿⣧⡤⢤⣀⣨⣧⠯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠧⠿⠀⠀⠀⠀⠀⠀ ⠀⢿⣄⠈⠁⣰⡟⠀⢸⣧⡀⠀⠀⠀⣠⡾⠻⢦⣀⣀⣀⣼⢿⣿⣧⡄⠈⠀⠈⠙⢏⣺⡇⢸⣿⠟⠓⠲⡝⣿⣿⣿⠿⠿⢿⣏⢻⡄⠀⠀⠀⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠈⠛⠛⠋⠀⢠⡞⠉⢙⡷⠞⠛⠛⢦⢀⣴⠟⠛⢿⣧⠸⣧⣉⡥⠦⠀⣀⣀⣀⡇⠀⣘⡇⠀⠀⠀⢹⠈⡟⠀⠀⠀⠀⠹⣆⢿⣦⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⣀⣠⣄⣀⣠⣿⠀⡴⠋⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⢹⡆⣿⠉⣳⠂⣴⣿⠉⣹⢤⣾⡏⠀⠀⠀⢀⣾⠀⣇⠀⠀⠀⠀⠀⠛⢸⡿⣷⠀⠻⠿⢛⣿⣿⡆⠀⠀ ⢠⡟⠁⠀⠀⢈⡟⢿⠀⠀⠀⠀⠀⠀⠀⣸⠸⣧⠀⠀⠀⢸⡇⢹⡇⡞⣯⠽⣼⢦⣇⠤⢯⢷⣄⣀⣠⡾⠁⠀⠙⢦⡀⠀⠀⠀⠀⢸⡇⣿⣷⣶⣶⣾⣿⣿⡇⠀⠀ ⢸⡇⠀⠀⠀⢸⡇⠈⠣⣄⡀⠀⣀⣤⠞⠁⠀⠉⠳⣤⣠⡿⠃⠈⣿⡀⢹⡙⢹⢹⡏⢒⡾⠀⠉⠹⣇⠀⠀⠀⠀⠀⠙⠓⠶⠤⠴⠟⢁⣿⢿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠙⠧⣤⣠⣼⣧⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⣧⠀⣇⢸⢸⡇⣾⠇⠀⠀⣴⠟⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠹⣧⢸⠸⠿⢰⡟⠀⣠⡾⠋⠀⠀⠀⠀⣿⣹⠆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢹⣧⡖⣦⣿⣰⡟⠉⠀⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⣰⡿⠀⠀⠀⠀⣰⡟⠻⠥⠽⠚⢿⣷⣄⣀⠀⢀⣀⣾⠁⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠤⠞⠋⠀⠉⠓⠲⠚⠋⠀⠀⠀⠀⠰⣿⣼⣚⣒⣂⣄⣌⣿⡄⠉⠉⠉⠉⠙⠦⣄⣀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠂⠅⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠨⠨⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠁⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠨⡂⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⡂⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣤⢹⢾⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠝⣎⠻⡆⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠠⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠸⣣⢀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠾⢷⣶⣦⣄⡀⠀⠀⣠⣴⡾⠟⠛⠛⣟⠛⣿⡶⠀⠈⠐⠫⠶⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡍⠀⠀⠀⠀⠐⠈⠙⢿⣦⣾⡟⠁⠀⠀⠀⠀⠀⠈⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡿⠿⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡧⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠛⢿⣦⣄⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⢿⣇⢠⣶⣶⣶⣶⣤⣄⡀⠀⣿⡇⠀⢀⣠⣴⣾⠿⠿⢷⣦⣿⡇⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⣾⡿⠋⠁⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀ ⠙⠚⠵⠀⠀⠀⠈⠻⣿⡏⠄⠀⠀⠉⠛⢿⣶⣿⣃⣴⡿⠛⠉⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢹⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡏⠀⠀⠀ ⠀⣀⣠⡄⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⢶⣾⡟⠛⣿⡶⠶⠀⠀⠀⠀⠐⣿⣦⣄⠀⠀⠀⠀⠀⠛⢷⣦⣴⡿⠟⠻⠿⣶⣤⡀⢸⡇⣀⣴⣶⠿⠿⠿⣶⡄⠀⣠⣿⠏⠀⠀⠀ ⠈⠋⠁⠀⠀⢠⣿⠋⢸⣿⠀⠀⠀⠀⢀⣠⣾⠿⠿⠿⢷⣶⣤⣄⣀⡀⢀⣿⢏⢻⣧⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⢠⣽⣿⠿⢿⣿⣉⡀⠀⠀⠀⣽⡿⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡀⣸⣿⣤⣤⣴⣾⠟⠋⠁⠀⠀⠀⠀⢠⠉⢹⡿⢿⣿⣯⡀⢸⣿⠀⠀⠀⠀⠀⢠⣾⣿⡅⠀⠀⠀⣈⣽⣿⣦⣾⣿⣭⣀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⠟⣽⣿⡿⠁⠀⠀⣦⠀⠀⠀⠀⠀⠀⠘⢻⣿⣽⠻⣿⣿⡏⠀⠀⠀⠀⠠⣿⠇⠙⠿⠿⠿⠿⢻⣯⣵⡿⢳⣬⡝⠛⠿⠷⠿⠟⠉⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢿⣾⣿⠟⠀⠀⢀⣾⣿⣤⣆⠀⣸⡿⣷⣄⠄⠘⢿⣷⣧⡿⡿⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⠟⠁⠀⠀⣨⣿⠟⠈⢿⣎⣀⣿⠇⠈⢻⣷⡠⠀⠉⠻⣿⡀⠀⠀⠀⠀⠀⠈⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢤⡄⣿⡇⢻⣷⠌⣝⡿⢏⢰⣾⡗⣻⡗⢀⣤⢠⣿⠃⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣤⠀⢀⣀⠀⠀⣠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠰⠶⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣾⣿⣽⣷⣾⣭⣤⣿⣭⣿⣤⣽⣧⣿⣧⣾⣏⣼⡏⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠈⠛⠀⠘⠛⠃⠀⠛⠃⠀⠀⢀⣰⡿⠁⠀⠀⣠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⣶⣶⣤⣤⣤⣤⣦⣤⣴⣶⣶⠿⠛⠁⠀⠀⠀⠈⠺⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢿⡿⠿⠟⠿⣿⣿⣿⣿ ⣿⣿⣿⠋⣠⣤⣤⣉⠛⠛⢋⣉⡉⠀⠠⠀⠄⠀⢴⣶⣾⣆⠸⣿⣿⣿ ⣿⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⠁⠀⠀⢀⠀⠈⠉⠉⠀⢻⣿⣿ ⣿⣿⣿⠀⢩⣿⣿⣿⣿⣿⣿⣿⣧⣀⣈⣀⡀⠂⠈⠀⠀⠐⡀⢠⣿⣿ ⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⠂⠁⡀⢺⣿⣿ ⣿⣿⠁⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠗⠘⠿⢿ ⣧⣤⡄⢤⣼⠏⢰⣦⣶⣤⠙⣿⣿⣿⣿⡟⢡⣴⣦⣶⠈⡷⠞⠸⢿⣿ ⣿⣏⣁⠀⠌⣴⣿⣿⣿⣿⢀⣿⠡⠀⣹⡇⢻⣿⣿⣿⣷⡈⠂⣴⣶⣿ ⣿⣿⡟⢃⠸⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣄⠛⠿⣿⣿⡧⢰⣌⣿⣿ ⣿⣿⣿⣿⣦⣌⣉⣤⣤⣉⣉⣉⠛⠛⠛⣉⣉⣁⣤⣍⣩⣴⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣴⠒⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠒⠉⠁⠀⠠⠞⢀⣾⣿⡟⠛⢒⡒⢛⡲⠦⢄⣉⠑⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠋⣡⠖⠛⠳⣦⣀⠀⠀⠀⠀⣾⣿⣿⣠⣀⣀⣀⣉⠉⠙⠒⠪⠽⣶⣦⠤⣄⡉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡿⠉⣿⣵⣾⠁⠀⠀⠀⢈⣿⡆⠀⠀⣸⣿⡟⠀⠀⠀⠀⠉⠉⠉⠛⠲⣶⣄⡀⠀⠀⠐⠩⢝⣶⢤⣀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣯⠄⣼⣷⣼⣿⡟⠛⣷⣄⠀⠀⣾⣿⠇⡀⠐⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢏⠙⠓⠒⠦⣤⣌⣽⠎⣟⠦⣄⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢰⣏⡀⠀⣿⢿⡉⠘⡆⠀⣿⠏⠀⠘⣿⡏⠀⠁⠀⣟⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠉⠙⠻⣿⣿⢮⣷⣄⠈⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⠘⣿⣷⣴⣿⣥⠹⣴⣻⣿⡿⠀⠀⣠⣿⡆⠀⠀⣸⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄⠀⢻⣆⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⣿⠇⠙⠻⣿⣿⣿⣿⣷⣶⣾⠿⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠳⣄⠀⠀⠀⠀⠉⢻⣿⣯⣧⡀⢻⢷⡀⠀ ⠀⢀⣼⠁⠀⠀⠀⠀⠀⠪⢻⣶⣤⣀⣿⠟⠋⠀⠀⠉⠁⠀⠀⠀⢀⣺⣿⡉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠑⠀⠀⠀⠀⠀⠹⣿⣷⣳⡀⢲⢳⡀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⣀⣠⡤⢶⠾⠛⠋⠙⢻⡟⢿⣥⡶⢶⣄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢹⡇⢫⢳⠀⠁⠁ ⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠁⠀⠀⠛⠁⠀⠙⣷⠶⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣖⠂⠒⠒⠂⢀⣼⣧⠈⠏⡇⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⣴⠟⣡⡤⣄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣾⠿⣷⣶⣶⣶⣾⠶⢤⣄⠀⠀⠀⠀⠀⠀⢸⡟⢳⣦⣤⣶⣾⠟⠁⠀⠀⠃⠀⠀ ⠈⣿⣷⣶⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⡏⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⠚⠀⠀⠀⠠⢿⣀⣀⠾⡙⢯⣽⣿⢷⠀⠈⠓⣄⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣟⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣻⣶⣤⡄⠀⠀⢈⡻⣿⠷⣽⢿⡿⣯⠎⠀⠀⠀⠹⠀⠀⠀⣼⠟⠁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠘⣧⠹⡇⠘⢿⠛⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠶⣀⡀⠙⢿⣷⣶⠶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣻⣆⠀⠁⠀⠀⢀⡀⠀⠀⡳⣽⣽⣿⡟⠟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⡿⠉⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣄⡀⠀⠀⠀⠀⠀⠉⠛⠟⣿⣇⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣶⣀⣴⣶⠿⠋⠁⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⣤⣤⣄⣀⣠⣤⣙⣿⡟⠛⢿⣟⣛⣋⣛⣛⣛⣉⣙⣋⣭⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠋⠉⠉⠉⠉⠉⠉⣿⠟⢻⣇⠀⠟⠋⠉⠉⢿⣿⣄⣰⣄⡹⣟⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣶⣦⣀⣀⠀⣸⡿⠀⢸⡏⠀⣤⣤⣤⣶⣿⣿⣿⡀⠙⠷⣾⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡾⠉⠙⠙⠿⠏⠀⠀⢸⡇⠸⢿⠟⠛⠛⠛⣯⢹⣿⣄⡀⠙⢙⣿⣷⣬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣀⣀⣀⣠⣾⣿⡇⠘⢿⣷⣤⡟⠈⢻⣿⢿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⣿⣿⠿⠿⢿⣿⣇⡀⠈⠻⢿⣷⣶⣿⡏⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠋⣡⣴⣦⡀⠨⢿⣶⡶⢀⠈⡉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠾⣿⣿⣿⡷⠀⠀⢸⣿⡌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⢾⣿⣄⣙⡿⢿⣦⣥⣤⣾⣿⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠉⠀⢀⣿⣿⣷⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡐⢻⣦⣀⣄⣾⣿⡟⢹⢀⣯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠘⠛⠛⠛⠛⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠲⠄⠐⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠐⣶⣶⡶⡶⣖⠶⣒⢖⡒⡖⣒⢲⣒⠲⣦⡀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠐⠐⠐⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡿⣝⡳⣍⢞⡰⢂⠔⡘⢄⠣⢌⠒⡄⢿⣆⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⡐⢀⡀⢁⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣭⢳⡭⢦⡑⢌⠢⡑⠌⢒⠈⡔⠠⢂⠹⣇⠀⠀⢠⡁⡐⡈⢄⠢⢐⢀⠂⠰⢀⠌⡄⢰⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⢝⡲⢌⠢⡑⠄⢊⠄⡡⠄⠃⠄⢂⠹⡄⠀⣼⠀⠖⣈⠄⢢⠡⠌⡌⢥⢊⡴⢨⢟⡄⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡮⡕⣎⠱⡈⠌⡄⠊⠄⡘⠈⢀⠂⠀⢻⠀⠘⣯⣜⣤⣋⣦⡹⡜⣜⢮⡱⢎⡳⢚⢳⠣⣻⣶⢶⡖⠲⣒⠒⠀⠂⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢿⣼⣆⡷⣌⢰⢀⡁⠆⠰⢠⠀⠀⠀⡼⢷⣤⡌⠹⠷⢿⣧⣷⣿⣮⣧⡹⣎⢱⠉⡄⣩⣾⢹⠉⠏⢹⣿⡇⠀⡀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢻⣌⠣⠌⠠⠌⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠙⠛⠀⢃⠀⣻⠁⣸⣿⠻⢿⣿⡟⠀⠁⠀⠀⢨ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⠈⡁⠀⠐⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⡀⠄⠀⠀⡀⠄⠀⠀⠀⠀⠘⠁⠀⣿⣿⣿⣿⣿⣷⣾⢶⡶⠷⡿ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⠇⠠⢀⠁⠄⠐⢀⠐⠠⠁⢀⠠⢀⠠⠀⠄⠠⠀⠐⠈⡀⠄⢀⠐⠀⠈⠀⠀⠀⠀⠈⠹⠋⣽⣿⡗⡀⠀⠀⠒⣿ ⠀⠀⠀⠀⠀⠀⣠⠏⠀⢂⠁⠄⠊⡐⢀⠂⡈⠄⡁⢂⠠⢀⠄⠂⠌⣀⠂⠌⡐⠠⢈⠄⠂⡈⢀⠁⠀⡴⢲⡾⢄⢘⣿⣿⣿⠀⠀⠀⢠⢹ ⠀⠀⠀⠀⠀⣼⠇⡈⠆⠡⡈⡐⢡⢀⢂⣐⢄⣐⣠⣦⡴⠤⠦⠥⠦⠤⠤⠦⢤⣅⣂⡈⠔⠠⠀⠤⠼⠵⢏⡐⢦⡰⠘⣿⣿⠂⠀⠀⠀⣞ ⠀⠀⠀⠀⣼⠃⣰⠡⢌⢡⢐⡐⢢⡴⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣐⠀⠆⠄⠍⠛⢖⠀⠸⣿⠁⠀⠀⠀⣽ ⠀⠀⠀⢀⠇⡒⡰⢂⠌⡄⣶⠞⠩⣤⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣠⠎⠻⢆⡈⠠⠄⢂⠀⠀⠹⡇⠀⠀⡑⣺ ⠀⠀⠀⡐⠤⠱⡁⢎⢐⡞⠁⠑⣶⠿⡟⠉⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠙⠟⣷⡚⠈⠻⡆⠈⠼⠐⠀⠈⠾⠒⠙⠊⢛ ⠀⠀⠀⡇⢬⢑⡉⣦⡟⠀⠀⣸⣿⠒⢹⣾⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⣿⣷⡞⠀⣿⣇⠀⠀⢹⣧⠘⢠⢹⠀⠀⠀⠀⠀⢈ ⠀⠀⠰⡏⣼⢆⠻⣽⢁⡖⡘⡙⠻⢷⠿⠟⠁⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠈⠛⠿⢾⠟⣃⢃⠦⡌⢿⣎⢄⢺⠣⠀⠀⠀⠀⠨ ⠀⠀⠀⢿⣹⡎⡝⣿⠘⡯⠱⡌⠙⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠀⢰⡊⢦⢋⢮⡇⣸⡝⣢⢉⡾⠀⠀⠀⠀⢐ ⠀⠀⠀⠈⢷⣽⢢⢛⣆⠓⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⣀⣀⠟⠰⠀⠀⠀⠀⠀⠀⠘⠖⢺⣾⠛⣰⣏⠧⡱⣨⡗⡤⡤⠀⠀⠈ ⠀⠀⠀⠀⠈⠻⣿⡾⣽⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣼⣿⡽⠾⣷⣿⡇⣧⢡⣴⣴⣶ ⢤⠀⠀⠀⠀⠀⠈⠻⠷⣼⣻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣿⣿⢷⣿⣷⣿⣿⣿⠾⠿⠟⡛⠛ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠿⠿⠿⠿⠿⠾⠶⠶⠶⠶⢶⢶⠶⠶⠶⠾⠿⠻⠿⠿⢿⣿⣿⠋⠉⠀⠀⠌⢽⣿⣿⣿⠇⡌⡑⠈⠍ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⡁⠀⠀⠀⠀⠀⠀⠀⣤⠃⠀⢇⠀⠀⠀⠀⠀⠀⠂⢘⣛⡅⠀⠀⠀⠀⠀⠸⢿⣿⠯⠁⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⡂⠀⠀⣠⠋⠀⠀⠘⢷⢤⠴⣚⣡⠾⠚⠋⠀⠐⢆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡰⢸⠿⣽⣏⠿⣭⢯⡽⣭⢯⡽⣭⢯⡽⣭⢻⡝⣯⣛⢿⣧⡂⠄⠠⠀⠄⣀⠢⠐⡄⢢⠐⠠⡐⢤⢎⡴⣩⠖⡭⢎⡵⡩⢖⣤⣂⡔⠰⡈⠔⠠⢀⠀⠠⠀⢆⡐⢢⠐⠠⢀⠂⠄ ⠐⡠⢉⢿⣳⢯⣟⣧⡟⣼⢎⡷⣺⢵⣫⢞⡵⣫⢞⡵⣫⣏⡟⣿⡌⠠⢁⠂⠄⠢⢑⠨⡐⡈⢶⣫⢓⡎⢶⡱⣛⡼⢣⢞⣱⣋⢶⢫⢿⣦⡑⠌⢂⠠⠈⠄⡑⢂⡘⠄⣉⠐⡀⠊⠄ ⢀⠱⡈⠆⣿⢻⣞⣧⣟⡷⣏⡾⣱⢏⡾⣹⢞⡵⣫⠾⣵⢫⢾⣹⢿⣄⠂⠌⠠⠑⡨⠐⠤⣱⣿⠲⣍⡞⢧⡳⣍⠾⣙⢮⡕⣮⢋⡯⣞⡽⣷⠈⠄⡐⠀⠆⢠⠡⡐⢡⠂⡐⠠⡁⠂ ⠀⠆⠱⡈⠜⣿⣞⣷⣻⢾⣝⣳⡽⣎⢷⡹⣮⣝⣳⢻⣜⢯⡳⣏⠿⣿⣆⠈⠄⠱⡀⢍⠰⣿⢣⡟⣬⣝⣣⠷⣩⢯⡝⣞⡼⢣⡟⣼⢣⡟⣽⣮⠐⠠⠁⠌⡠⢂⠍⡄⠃⠄⠁⠄⡁ ⠈⡌⢡⠐⡌⠸⣿⡾⣽⣻⣞⣧⠿⣜⢯⣳⢳⣎⢷⣫⢞⡧⣟⡭⢿⣱⣿⣆⠈⡔⠨⠄⣽⣟⢧⣛⡖⣮⠵⣋⠷⣓⢾⡱⡞⣧⢻⡜⣷⡻⣽⣿⡃⠄⡁⠂⠔⡨⠐⡌⢡⠈⡐⠠⠐ ⠐⢌⠂⡜⠠⠁⠞⣿⣷⣻⣞⣾⢻⡽⣎⢷⣫⢞⣧⣛⢮⡳⣝⢾⡹⣖⢯⣿⡐⢠⠑⡌⣿⡾⡽⢮⣝⢶⣫⡝⣯⡝⣶⡹⣝⢮⣳⣻⣵⣻⡗⣿⡇⠐⠠⢁⢂⠡⢃⡘⠄⠂⠄⡁⢂ ⢈⠢⢁⠆⡡⠃⠄⡹⢿⣳⣟⡾⢯⣷⣛⢮⡳⣏⢶⡹⣎⢷⡹⣎⢷⡹⡞⡼⣷⡂⡌⠰⢹⣿⣟⣯⡞⣷⡭⣟⣶⣻⣵⣻⣭⢷⣯⢷⣞⣷⣻⣽⡇⢈⠐⡀⠂⡅⢢⠘⡄⢉⠐⡀⠂ ⠠⡑⢌⠢⠡⠌⠐⠠⢙⣿⢾⣽⣻⢶⣫⢷⡹⣎⢷⡹⣎⢷⣙⢮⣇⠟⣭⠳⣝⢳⢮⠱⡌⢿⣿⡾⣽⣳⢿⡽⣶⣻⣞⡷⣯⣟⣾⣯⢿⣞⣯⣿⡇⠀⠆⡀⢃⡘⢄⠡⠂⠌⡐⠠⢁ ⢀⠣⡘⠄⢇⠸⢀⠃⠄⡸⣿⣼⣻⢧⣟⡼⣣⢟⡼⣣⣛⡼⣛⡤⡜⢿⡠⢿⡘⣇⠟⣟⡻⣜⡻⢿⣿⣻⡿⣿⢧⡿⣼⣿⣧⣿⢻⡼⣿⢼⢧⣿⡃⡘⠠⢀⠇⢠⠘⡄⠛⢠⠀⢃⠄ ⠢⡑⢌⡘⢢⠁⠆⡈⢄⠡⢙⣿⣽⢯⡞⣵⢫⡞⡼⣱⢣⡞⣥⢳⡹⢶⡹⣲⠝⡮⣝⠶⡳⢼⣱⣋⢶⢫⢟⡻⣛⠿⡹⣍⠶⣩⢏⡷⣹⢾⣯⣿⢧⠀⢃⠄⢊⠄⢣⠌⡡⠂⠌⢂⡐ ⡡⡘⠤⠚⡄⢊⠤⠑⣂⠂⣉⠫⣿⡿⣜⢣⡳⣍⢳⣣⠗⣮⡕⣏⠾⣥⢳⡣⣟⡱⣎⢯⡝⢧⡳⣜⣣⠟⡮⢵⣋⠾⣱⡍⡾⡱⢎⡞⣥⣛⡼⢿⣌⡐⡈⠌⢂⠎⣡⠚⡄⠱⡈⠔⠠ ⡰⢡⡙⡜⡸⢄⠆⢣⢄⠣⢴⣿⠻⣵⢊⣧⢓⣮⠳⣥⣛⢦⢻⡜⣧⢫⢧⢳⣍⠷⣙⢮⠞⣧⢻⡜⡶⢫⣝⡳⢎⡻⣴⢹⡲⣝⢣⡞⢦⡽⣸⣛⠿⣷⣌⠘⡄⡚⢤⠓⡌⢡⠐⣉⠐ ⠁⢂⠡⢈⠡⠈⠌⠠⡈⣷⡿⢣⡟⡴⣫⠖⣏⢶⡛⢶⣩⢞⣣⡝⢮⣓⣏⡳⣎⢟⡹⣎⢿⣸⢣⡝⣞⡳⢮⡹⣭⢓⣧⠳⣽⡸⣣⣝⠳⡞⣥⢏⣟⡳⢿⣇⠈⡑⢊⠑⡈⠡⠉⢂⠉ ⠈⠄⠂⠄⢂⠡⢈⠰⣼⡟⣼⠳⣜⢧⣓⡻⣜⣣⣛⢧⡝⡮⣵⢚⡧⢏⡶⣹⣜⣫⠵⣎⡗⣮⠳⣝⣎⠷⣫⢵⣋⢾⡸⡝⣦⢳⣓⢮⡛⡽⣜⢯⡺⣝⢯⣻⣦⠐⢀⠂⠄⡁⠂⠄⠂ ⠠⢈⠂⡘⢀⠂⠤⣿⡿⣹⢖⡻⣜⡳⢎⡳⡵⢮⢵⡺⣜⢳⣎⢻⡜⢯⡜⡧⢞⡼⣹⠲⣝⢎⡟⡼⢼⡹⣱⢮⡝⡶⣭⢳⣣⢯⡜⣮⣝⡳⣝⢮⡳⡽⣎⢷⣻⣮⠠⢈⠐⠠⠁⠌⡀ ⠐⠀⠒⢀⠂⢌⡽⣣⢟⡼⣣⢟⡼⢭⡏⢷⣭⢳⣎⠷⣭⢳⣮⣷⣽⣧⠿⠙⠎⠓⠃⠛⠨⠉⠜⠙⢊⠑⠓⠚⠿⠾⣵⣯⣞⣧⣛⠶⣭⣳⠽⣎⡷⡽⣭⢷⡻⣿⣖⠠⠈⠄⡁⢂⠐ ⠤⠣⢜⡠⢌⡼⣳⡝⣮⢳⡝⣮⡝⣮⡝⣧⢞⣳⣮⡿⠟⠛⠉⠉⡀⢀⠀⠄⠀⠂⠐⠀⠂⠉⠀⢂⠠⠀⠌⠠⠀⠒⠀⠠⢉⠙⠛⢿⣶⣫⢿⣱⢯⡽⣞⣯⣽⣳⣿⡆⢡⠒⡰⠄⢆ ⠌⣑⠢⡘⢴⣫⢧⡻⣜⢧⣛⢶⡹⢶⣹⢮⡿⠟⣧⣔⡀⢄⣐⠀⠀⡀⠀⠠⠐⠀⠂⠀⠐⠀⡐⠀⠄⠂⠐⡀⠡⠐⠈⠠⣠⢬⠐⢦⣼⡿⢿⣽⡾⣝⣳⡽⣶⣻⣽⣷⠡⢊⠱⡈⢆ ⠘⡄⢣⠐⣹⡖⣯⢳⡽⢮⣝⣮⡽⣣⣿⠏⢻⣤⣼⣿⣿⣿⣿⣿⣦⠀⠠⠁⠀⠐⠀⠁⢀⠂⢀⠀⡀⠌⠀⠄⡐⠠⢸⣷⣿⣿⣿⣿⣿⣧⣷⡹⢿⣽⣳⣟⣳⡽⣾⣿⡑⢌⠱⡈⠆ ⠂⡜⢀⠣⣽⢞⣭⢷⣫⠷⣞⠶⣽⡿⢁⠐⢸⣻⣿⡟⣿⣧⢌⣿⣿⡄⠐⢀⠀⠁⠠⢈⠀⠄⠂⠀⠄⠂⠡⠐⠀⣁⣧⣿⣿⡤⣻⡟⣿⣿⡇⡐⢩⢿⣷⣞⣷⣻⢿⣾⠅⡊⠤⢑⡈ ⠁⢆⠡⢂⣿⢯⣟⣾⢳⣻⣭⢿⡿⢸⠀⠂⣿⣿⣿⣿⢛⣿⣿⣿⡿⡅⠈⡀⠄⡁⠂⠀⢄⢬⣠⡈⠠⠈⠄⡈⠄⠀⢋⣿⣿⣿⣿⢛⣿⣿⣷⠈⢆⢚⣿⣿⣞⡽⣯⣿⡃⠜⡠⢃⡐ ⠉⡔⡈⠆⢿⣿⣯⣞⣯⢷⣞⣿⠇⡈⠔⠠⢹⠹⣿⣿⣾⣿⣿⠟⢃⠠⠐⠀⠄⡐⠠⢁⠈⠻⠗⢃⠠⢁⠐⠠⢈⠁⡂⠜⢻⣿⣿⣿⣿⡿⠛⡨⢐⡌⣿⣷⢯⣟⣿⣿⡇⡘⠤⣁⠂ ⠌⡰⢈⠜⡨⣿⣷⣟⡾⣯⣞⣿⡰⢁⠎⡱⢢⠱⣌⠫⢍⡉⠡⢈⠄⢂⡐⡈⢔⠺⣷⣮⣼⣦⣼⣤⣶⣼⣿⠂⡁⢆⠡⢌⠢⡘⢍⢫⢋⡜⣣⢕⡢⢜⣽⣿⣟⣾⣿⡏⠔⡡⢒⠠⠡ ⠐⡡⢌⠢⡑⠼⢿⣿⣽⣳⢯⣿⣧⠘⣬⢱⡋⠷⣌⠳⡌⡔⡡⢊⢌⡰⢠⠑⡌⡐⢻⣯⡳⢭⣏⡳⣽⡟⢢⡐⣡⠊⠴⣈⠦⡱⢌⡲⡩⢖⡱⢪⣜⢣⣿⣿⣿⣿⠟⢠⡑⠄⢣⠈⡅ ⡌⢰⠈⠒⣤⠘⡎⣿⣿⣯⡟⣾⣿⣵⡌⢣⡞⢱⡎⣵⠘⣴⠑⢪⡔⢢⠑⠊⣴⠉⣦⢹⣿⣧⣿⣿⠋⡔⢣⠒⢡⡎⣵⡌⣶⢱⣮⢱⠓⣿⣾⢱⣾⣿⣿⣿⣿⠉⢢⠁⢰⠈⡆⢱⠀ ⢀⠣⡘⠰⣀⠒⡰⠄⢛⢿⣿⣯⣿⣷⣽⡺⣜⣧⡻⣴⢫⡖⣝⣦⣓⢮⡱⣍⢦⡹⢤⠳⣼⡙⣧⢎⣝⡲⣍⣎⢷⡸⣥⡻⣜⣳⢮⣏⢷⣳⢮⣷⣿⣿⡿⢛⡡⢊⠔⡨⢆⠱⣈⠆⡱ ⣌⠱⣌⠓⡬⡑⢆⡉⠂⠀⠈⢙⠻⠿⣿⣿⣿⣽⣟⣷⣯⣛⡷⢾⣹⢮⢷⣛⣮⡽⢯⡷⣞⡽⣎⣟⣮⠷⣏⡾⢧⣟⣳⣻⣝⣻⣾⣽⣿⣿⡿⠟⠋⢁⠀⠤⠑⡊⢌⠱⣈⡑⢢⢉⠒ ⠈⠃⠌⡉⠔⠉⡐⠄⡡⢈⠡⢀⠀⡀⠀⠈⠉⢻⡻⠿⠿⡿⢿⠿⢾⠿⡾⢷⣭⠿⣭⠷⡽⣯⡽⢮⡽⡿⢿⢾⠷⣾⠻⡟⣟⣛⣛⡏⠥⠀⠀⠄⠠⢀⢌⡰⢡⠘⡄⠣⢄⠘⢄⠊⠌ ⠠⢁⠂⡐⢈⠐⡀⠓⠴⣆⡒⡄⢢⠐⡁⠂⡁⠀⠛⢯⣗⡹⢎⡽⢮⡹⣭⠳⣎⢟⣼⡟⠀⠈⢿⣧⣏⢵⡫⢮⣝⢲⢫⡝⣳⡼⠋⢁⠀⢄⠡⢎⡱⣬⠦⠓⠤⢃⠬⡑⢢⠡⢌⡘⠤ ⠐⡀⢂⠐⡀⠆⠠⠁⠂⠌⡉⠙⠣⠹⢤⡡⠄⡁⠂⢀⠉⠛⠷⣾⣧⣛⡴⡻⣜⣾⡿⠀⢀⠀⠈⢻⣯⣎⠷⡳⢮⣭⡷⠞⢋⠀⠰⢠⣘⡴⢋⠮⡑⢦⠮⡑⢎⢖⠲⡱⢎⡓⢮⡜⢧ ⠶⣡⠖⠮⣔⢣⢳⡘⣤⠳⣌⢓⡣⢓⠦⣱⠣⣌⠱⢀⠀⠂⡀⠀⠉⠛⠿⠷⠯⢷⠃⠀⠠⠀⠀⠀⠿⠿⠾⠟⠋⠁⡀⠐⡀⠎⣱⠢⣗⣩⣯⣷⣍⡫⣴⢉⢮⡌⣛⣴⣧⣙⠣⣜⢢ ⡳⢤⡛⡜⣌⢣⠎⡵⢢⠗⣌⢎⡱⢍⡲⢥⠳⡌⠆⡀⠄⠐⠀⠀⠁⠠⠀⠠⠀⠀⠀⠐⠀⠀⠁⠄⠀⡀⠄⠀⢀⠂⠠⢁⡐⢘⣺⢟⣻⣿⣿⣿⣿⣿⣶⣿⣶⢞⢯⠻⡼⣛⠷⣭⢶ ⡝⢣⢳⡹⣌⠳⢎⠲⡍⡞⣜⣊⠶⡱⡘⢆⡣⢍⡐⠠⢀⠈⢀⠈⠀⠀⠄⢀⠀⠂⠁⠀⡀⠁⢀⠠⠀⠀⠀⠠⠀⠀⠂⠄⠒⡠⢼⠊⡖⣿⣿⣿⣿⣿⣿⣿⣿⡍⢎⢳⣱⣍⢞⣰⣣

⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⣿⡇⣿⣿⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠀⠀⠀⠐⠒⠲⠤⣄⡀⠀⠀⢀⣀⣤⣶⣿⡿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣹⣿⡆⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣟⣿⣯⣷⣿⣿⣿⣿⡿⠋⢀⠠⠤⠤⢤⣀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠟⠋⢠⠔⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⠀⠈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠉⠉⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡶⠖⠒⠉⠙⠲⢤⣀⣸⣟⡀ ⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡽⠃ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘⡧⠐⣦⡀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢳⡀⠀⠀⢸⢧⠀⠀⠉⠉⠁⡀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣀⠀⠀⠈⢃⡠⠤⣾⠈⠂⠀⠀⣀⣰⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠹⠿⠁⠀⠀⠀⢀⠀⢠⠇⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠸⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠸⠓⢼⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠖⠚⠁⠂⠚⠀⠐⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⢛⡿⢤⣤⢤⣤⣤⡤⠶⠖⠒⢯⡉⠉⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠜⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠒⠋⠉⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢰⠀⠀⣤⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⢸⠀⠸⠻⠋⡟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣀⣀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣀⣀⣈⣫⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⣀⣀⣀⡠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠉⠋⠻⣄⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠳⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⠤⠶⠋⠙⠳⣆⣀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⢶⣦⣄⠀⢀⣀⣤⣤⣤⣤⣼⠟⠁⢀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⡀⠀⠙⠿⠛⠉⠉⠀⠀⠀⠈⠀⠀⣿⣿⣦⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢰⣦⠀⠀⠀⣠⡀⠀⠀⠻⠋⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠈⠉⠀⠀⠘⣻⣏⣀⡀⣀⣤⣤⣄⣼⡟⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠀⠀⠀⠛⠉⠉⣩⣿⡿⣟⢿⣻⣿⣷⣄⣤⣶⡿⠿⠛⠋⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣄⣀⡀⣀⣽⡿⠿⠻⢷⣦⣤⣤⣼⣿⢯⡳⣝⢮⡵⣚⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠟⠉⠉⠉⠉⠛⠛⣿⡟⠉⠀⠀⠀⠀⣿⡟⢻⣿⣏⢷⡹⣎⣷⣿⣿⣾⣿⣿⣶⣦⣄⣀⣠⣤⣤⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⣤⡾⠏⠀⣾⣿⢎⡷⣹⢾⣿⣧⣿⣿⢻⡭⢯⡝⣿⣿⣿⢻⣝⣻⢻⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠉⠀⠀⠀⢹⣿⡞⣵⢫⡞⡽⣻⣿⣏⢷⣚⢧⣛⠶⣿⣿⣷⣮⢧⣛⢞⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣿⣾⡿⠿⠻⣿⣮⣓⣯⣼⣿⣿⣯⣿⡟⣮⣝⣾⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣯⡽⣭⢳⡝⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣿⡿⠟⠋⠀⢹⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣄⣠⣤⣤⣀ ⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⢿⣿⠋⠉⠉⠉⠁ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀ ⣠⣤⣤⣶⣾⣿⣿⠶⠶⠆⠀⠀⠀⠀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣴⠟⠁⠀⠀⠀⠀⠘⠻⣿⡿⠿⠟⠿⠖⠀ ⠙⠉⠁⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣦⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⢿⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠛⠋⠉⠉⠻⣿⣄⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣤⣀⣴⣾⠟⠁⠀⠀⠈⠙⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠟⠉⠉⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠈⠙⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡾⠟⠉⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠿⢷⣦⣀⣀⣀⣀⣀⣀⣀⣄⣤⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⡛⠛⠛⢛⣛⣛⣿⣿⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⣶⣤⣤⣤⣤⣶⣿⣿⣉⠩⡙⢛⠛⢫⠩⣉⣽⣿⣿⣷⣶⣶⣶⣶⣾⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢆⠢⢍⡹⡉⢏⣽⣿⢋⡙⠻⠿⡶⣷⢾⡷⠿⢛⠋⡍⢿⣿⣤⡩⢘⡐⢢⢡⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣥⣮⣴⣷⣿⠿⠷⣦⣥⣭⣦⣵⣤⣦⣦⣥⣭⣼⣴⠾⠟⠻⢿⣷⣾⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⢀⣴⡿⠛⠛⣻⣿⣶⣶⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡄⣰⣿⡿⠇⠐⣻⡟⠋⠁⢠⣶⠀⠀⠈⢿⣿⣶⣶⣤⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠛⠛⠻⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⢸⣟⠀⠀⠀⠈⠻⠷⣦⣴⠿⠁⠹⣯⠉⠛⠿⣿⡿⠛⠻⣿⣦⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠛⠛⠛⠛⠛⠛⠛⠷⢶⣤⣄⡀⠀⠀⠀⣿⠇⠀⠀⠀⠙⠧⣀⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⣾⠟⠀⢀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣀⣄⣀⡈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡲⣌⢧⡛⢷⡄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⢹⣷⣶⣶⣶⠶⠶⠿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣮⣒⠹⠚⠁⣀⡀⣀⣽⡷⠖⠲⣤⣸⡇⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢶⣾⣿⣻⢟⣯⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⡖⢯⣛⠳⡶⣄⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣻⣧⣿⣿⣿⣟⣿⣿⣦⣤⣄⣀⣀⣈⣉⣳⣌⣻⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣛⣿⣛⣿⣿⠈⠉⢉⣩⣿⡿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣟⣿⣟⣿⣿⣿⣶⣾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣻⠿⣿⣿⣿⡿⢟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠈⠀⠀⠀⠀⠀ ⢀⠀⠁⢀⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⣴⣾⡟⠛⠀⠐⠀⠀⠀⠀⠀ ⢸⠀⢰⣿⣿⡆⠀⠁⠒⠈⠀⢀⣤⠶⠚⠛⣻⡳⡆⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⣶⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀ ⠈⠄⠀⠉⢻⣿⣷⣶⣤⣤⡶⣫⣤⡴⠶⠛⠋⠀⣷⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠤⡟⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣀⣤⣾⣿⣹⠛⢻⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣹⣿⣅⣽⣿⣿⣿⣟⣿⣟⣻⣿⣶⠟⢁⣴⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠴⠧⠃⠠⠀⠀⠀⠀⠀ ⠀⢸⠀⢘⢿⣙⡿⣿⣿⣿⣿⣀⠈⡉⣉⣉⣡⣴⣾⣿⡿⠋⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⡆⠀⠀⢶⡆⣸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠡⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⢰⣰⣠⣾⡿⠿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⠉⠛⠛⠿⠟⠉⠀⠀⠀⢀⡼⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠙⠿⠏⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⣿⣿⣿⣿⣇⠀⢀⣉⠉⠀⠀⠀⢀⠛⠚⢀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⡈⠓⠀⠀⢀⣀⢸⡙⢲⠁⠀⠀⠀⢀⣠⡾⠋⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⣴⠲⣤⣤⣿⣿⣿⣿⣶⣤⣼⠋⠀⠉⢿⣁⣠⣤⣶⣾⣿⣿⣿⡞⠙⡆⠀⣠⠀⠘⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟⠲⠛⣛⣻⣿⣿⡿⠿⢿⣻⡀⢀⣀⣾⢿⣿⣿⣿⣟⣧⠈⠒⠽⠛⠓⡞⢩⠇⠀⢀⣤⢤⣤⠀⠐⡄ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⣸⣥⣹⣷⢿⣧⣀⠈⢳⣞⣟⢹⡿⢻⣏⣿⡟⢛⣿⡳⣦⣤⣀⣴⣻⡯⠤⠤⡞⠀⢘⢻⡗⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠻⠿⣿⣿⣿⡟⢻⠛⣿⠛⡿⠻⡟⣿⢣⢃⢿⡿⠻⡟⢻⡟⢿⢿⣿⡿⠁⠘⣤⠤⠽⣦⣟⠼⠁⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠿⣿⣷⣿⣶⣿⢾⣿⣾⡷⣾⣿⣼⣿⣿⢾⣷⣾⣷⣾⣿⡟⠁⠀⢰⢁⡀⠾⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣷⣴⣿⣿⣧⣼⣮⣿⣿⣿⣦⣿⡟⠋⠉⠀⠀⢠⠀⠘⣾⢣⣼⠋⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣉⠁⠀⠠⠐⠈⠀⠂⠀⠀⠁⠁⠀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣰⣾⣿⢟⡻⢿⣿⣿⣛⣭⣿⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⣟⣿⣿⣿⡿⠟⠿⠭⠿⠚⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠈⠉⠛⢿⣿⠛⠉⠁⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡇⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠘⣿⣿⣿⣿⣿⣿⣷⣀⣀⣤⣤⣀⣀⣾⣿⣿⣿⣿⣿⣿⠇⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠤⠖⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠲⡔⠓⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢸⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⠉⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣸⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣏⣤⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠿⣶⣶⣾⣿⣯⡏⠙⠻⣿⣿⣿⣿⣿⣿⠟⠋⠙⣿⣿⣷⣶⣶⠿⢿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⣿⣿⣧⣀⣠⣿⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⠋⠀⠀⢠⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠃⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠳⣆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣖⡷⠃⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⠴⠂⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠃⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠁⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⢛⠋⠁⠀⠀⠁⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠂⠀⠄⠀⠀⠀⠈⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠳⡞⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀

⢀⠂⠴⣃⡄⣆⠐⣀⠂⡐⣀⠂⡐⣀⠂⡐⣀⠂⡐⣀⠂⡐⡀⢂⡐⢠⢌⡐⢧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⡀⠀⠄⡀⠄⠠⢀⠠⠀⠄ ⢆⢈⠤⣱⢻⣜⠶⡁⢦⡑⢄⢂⠡⠐⡠⠁⡄⢂⢱⡀⢦⠁⡰⠡⣌⢢⢉⠂⠌⠆⠀⠀⠁⢀⠈⠀⠀⠁⠀⠈⠀⠀⠁⠀⠁⠀⠁⠀⠀⠠⠀⠀⠂⠀⢀⠀⠌⠀⠄⠂⢁⠠⠐⠈⠆ ⣏⢾⣠⢯⡟⣾⡹⣞⠧⢁⡂⠄⣂⠡⢤⠥⠆⢂⡄⠹⡖⡼⡐⡅⡸⢦⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⠐⠈⠠⢀⠂⠁⠄ ⢾⣹⢮⡷⡽⣳⣟⡼⣫⣀⠐⡆⢩⡐⢪⢷⡼⣄⢯⡇⡧⣍⠼⠁⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⢀⠡⠀⠂⡁⠂ ⡏⢾⢧⢿⡱⣽⢮⣷⢳⣭⢛⡶⣍⠓⣨⢷⠛⣼⠘⡖⣃⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠀⠀⠀⠄⡀⠀⠌⢀⠂⠄⡈⠐⡀⠁ ⡜⢮⣛⢮⣟⡑⢯⣹⡳⢎⡏⠶⠆⠀⣿⠋⠘⡀⠙⢰⠋⠁⡈⠐⢀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠄⢀⠀⢂⠠⠁⠂⠄⠂⡐⠀⡁⠠⠁ ⠭⢘⡽⣋⡈⢁⠋⠀⡏⢾⠆⠀⢀⡴⠃⢀⠂⠐⠈⡀⠄⠂⠐⠈⡀⠐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠂⡁⢈⠀⠄⠂⡀⠂⡁⠐⠠⢀⠡⢀⠁⠂ ⠀⡀⢿⡹⠁⠂⣿⠀⠁⠀⠀⠔⢏⣀⡐⠠⠈⡤⠛⠙⡄⢈⠠⠁⠠⠁⢂⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⡈⠄⡈⠄⠁⠄⠂⡀⠂⢁⠀⠂⠄⢁⠂⠄⠂⠠⠈⠄ ⠀⡀⢿⣣⠠⠃⠀⡀⠀⢠⠃⣼⠟⠀⢻⡤⠼⠃⠀⠀⢻⢠⠤⠼⠤⠤⠤⠤⠄⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣿⣀⣘⣠⣀⡠⢀⠀⠃⠄⠃⢀⠃⠄⠘⠠⠘⠀⡀⠄⠃⠄⢃⠀ ⠀⠄⠘⡇⢡⠆⠀⢠⠤⠛⢢⠯⣴⠦⠀⢇⠀⠀⠀⠀⠸⡄⠀⠀⠀⡌⠉⠉⠰⠒⠒⠒⣺⣿⣻⣷⣊⡉⠁⢡⠀⠀⠀⢀⢄⠀⠊⡩⢍⣉⣑⠚⠒⡤⢆⡁⠐⠠⠁⡀⠂⠌⢀⠂⠄ ⠀⠌⢇⢰⡟⢰⠀⢸⣀⣰⠁⠀⠈⣇⣠⠏⠀⠀⠀⠀⠀⠘⡄⢀⡠⡇⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⣻⣽⣦⣾⣆⠀⠀⡇⢠⠓⠚⠁⠀⠉⠀⠱⢤⡈⠑⠺⡄⢁⠐⢀⠡⠐⠀⠄⠂ ⠀⢂⢸⠉⣠⠘⠀⢸⠀⢞⣦⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⡷⠁⠀⠀⠀⠀⠀⠙⠛⠛⢷⡿⣽⣿⣯⡿⠀⠀⠱⢜⠆⠀⠀⠀⠀⠀⠀⠀⣵⣿⢀⣵⡀⢈⠠⠀⢂⠁⠌⡐ ⠀⢂⠀⡾⠃⠘⢠⠈⣆⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⡏⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⣾⠃⠀⠐⡲⠋⢆⣀⠀⠀⠀⠀⢰⣿⢿⣏⠁⠀⡇⠠⢀⠁⠂⠌⢂⡱ ⢀⠂⠄⡁⠘⠀⡘⡀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠠⠧⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⠀⡸⠁⠀⠀⠈⠓⠒⢣⣀⡿⣷⣾⣧⡤⠜⡇⢀⠂⡈⠰⡁⢆⡒ ⠠⢈⠐⢀⠂⢀⠂⠁⢸⠀⠀⠀⠀⢰⣶⡀⠀⠀⣶⡆⠀⠀⡸⡠⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡃⠉⠃⢠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠟⠂⡇⢀⠐⠠⠑⣌⠢⠜ ⠐⠠⠈⡄⠚⡄⣈⠕⠊⢇⠀⠀⠀⠀⠛⠀⠀⠀⢀⠀⢀⡔⠁⠀⢀⡧⠀⢀⣴⠀⠀⠀⣀⠀⠀⠠⣤⡀⢀⡸⠉⢸⠀⠘⠋⠀⡀⠀⠀⢀⣤⠀⠀⠀⠀⡇⠀⡃⠄⡈⠰⢡⠂⡉⠌ ⠈⡁⠒⢀⠡⢈⠀⣀⣠⡜⢇⡀⠀⠀⠀⠀⠀⣀⣠⣶⢟⠒⠒⠒⠓⣺⢖⡈⠀⠀⠀⠘⠽⠀⠀⠀⠀⢁⡴⠋⠫⠚⡄⠀⠀⠀⠟⠃⠀⠸⠟⠃⠀⠀⠀⣇⠀⢂⠡⠐⡁⠢⠐⡐⠈ ⠀⠄⡑⠠⠌⡐⢨⠀⠀⠀⡜⢉⠗⣶⣶⣖⠉⣡⣿⣿⠀⠳⡀⠀⠀⠁⠀⠉⠒⠦⢤⡤⠧⣤⡤⢖⠚⠁⠀⠀⠀⠀⠘⢄⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⢡⠂⡁⠤⠑⠠⠄⢃ ⢈⡐⠈⡔⠐⣈⠰⠀⠀⠀⢠⠃⢠⣿⣸⡿⣿⣻⢧⣼⡇⢀⠜⠢⠀⠀⠀⠀⢸⠀⠈⣷⣤⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡽⣦⡤⠤⢤⡀⠀⠀⣀⠴⠁⠀⠀⢌⡖⠰⣆⠷⡌⠐⢂ ⠠⣀⠣⢆⠡⣰⢺⠄⠀⢰⠉⠓⢼⡿⣽⣻⢷⣯⣿⡽⣟⠧⠤⠜⠀⠀⠀⠀⣸⣄⣤⡻⣿⣂⣄⣼⡆⠀⠀⠀⠀⠀⠀⠘⣠⢯⠐⡡⠚⠹⣝⠹⡀⠀⠀⠀⠀⣆⡷⢦⠌⡉⠄⣑⠂ ⠇⣄⡂⢌⢳⡭⣾⠃⠈⠀⠉⠉⡿⠋⠀⠙⣿⠉⢀⠙⣿⠐⠒⠚⠘⠃⠙⢚⣿⠋⡀⢠⠃⠀⡈⢿⣿⠀⠈⠉⠉⠉⠉⢹⣇⠴⠳⣄⡵⠿⡈⣆⡗⠒⠒⠢⢤⣟⣞⣧⠿⣜⢧⢏⡇ ⢤⣬⢳⣎⢷⡝⠁⠀⠀⠀⠀⠘⡇⡌⠀⡃⡇⠈⠀⢃⢹⠀⠀⠀⠀⠀⠀⠈⡏⠰⠀⢸⢰⠀⠰⠘⣿⠀⠀⠀⠀⠀⠀⡎⡎⡄⢠⢘⡀⠀⢱⠋⡆⠀⠀⠀⠀⠙⢾⢮⣟⡼⣫⣞⡴ ⠓⠚⠓⠚⠏⠀⠀⠀⠀⠀⠀⠀⢡⠰⣀⠇⠷⠰⣀⠏⡌⠀⠀⠀⠀⠀⠀⠀⢣⠱⣀⢈⡆⢄⣠⢣⠋⠀⠀⠀⠀⠀⠀⠓⢃⢇⡜⣠⢃⣠⠸⠒⠃⠀⠀⠀⠀⠀⠈⢟⠈⠙⠁⠋⠘ ⠀⣀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠊⠈⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠉⠲⠕⠃⠈⠉⠀⠉⠀⠀⠀⠈⢹⢠⢀⠤⡀⠤ ⠐⠈⡇⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠛⣤⠊⣦⠙⢰ ⠖⠡⠐⠤⠩⣿⣿⢹⣿⠍⠭⠩⠍⠩⠍⠍⠩⠍⠩⠍⠭⠩⠉⠭⠩⠍⠭⠭⠭⠭⠭⠭⠥⠥⠬⠥⠬⠤⠥⠤⠡⠌⠤⠥⠥⠬⠌⠵⠢⠤⠬⠴⠤⢿⣿⠢⢿⣿⠃⠒⠁⠚⠄⠃⠃ ⠀⠀⠀⠀⠀⣿⡇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣧⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣿⣦⣸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⡿⣿⠿⠆⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠶⠒⠚⠒⠒⠒⠒⠲⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⡪⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠀⠶⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⢦⡄⠀ ⠀⠀ ⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⣸⠁⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⣤⠴⠒⢺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡀⣈⢝⠁⠀⠀⠀⠀⣀⡰⠤⣄⠔⠀⠀⠀⠀⠄⠲⠚⠋⠀⠄⠀⠀⣧⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠚⠉⢹⠉⠀⠈⠐⠲⠲⠶⠶⠴⠒⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠉⠉⠒⠦⠤⢀⠀⠀⢀⢀⣀⠤⠚⠁⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢡⡏⠀⠀⢰⠀⠀⠀⡇⢠⣤⠀⠀⠀⠀⠀⢠⡔⠀⠈⠉⠉⢲⠀⠀⠀⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⢧⡀⠀⢰⠀⠀⠀⣳⠞⠉⠹⡄⠀⠀⠀⢸⡀⠀⠀⢀⠖⢯⠀⣀⠴⠞⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⣀⣀⣀⣀⣀⣠⠴⠖⠁⠀⠀⠀⠀⠈⠛⠦⣌⣀⡀⡸⠁⠀⠀⠀⠧⠤⡤⠤⠤⠙⣍⠙⠉⠀⠘⣇⠁⠀⠀⡀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⢸⡷⣄⣀⡰⣟⣯⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣶⣄⠀⠀⠀⠀⠀⠀⢺⠙⢋⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠙⠐⣠⠀⢛⣷⡀⠀⠀⠀⠀⠈⠛⠉⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠁⢡⡌⠁⢰⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠇⠌⠋⠠⣌⠁⢢⢀⣇⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠰⢀⡳⠡⠀⢞⢆⠻⢏⠡⢀⠖⡆⢉⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⡗⣈⠋⣀⠲⢋⣾⡟⢉⢂⡘⠅⡂⠜⣵⡀⠘⣻⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢨⡔⡇⠬⣽⡿⠐⢠⠁⢢⠌⣁⠢⣿⣿⡇⢤⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣟⠠⡙⢕⢣⣿⣏⠂⠰⠈⣀⠆⣄⣽⣿⣟⣿⠀⠘⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠐⢭⣂⣹⣼⣿⣌⡐⣁⡒⣬⣾⠟⢛⡉⠄⡁⢒⠈⣷⣄⡀⠀⠀ ⠀⠀⠀⡀⠘⢧⠊⢴⠟⠉⠉⠹⣟⢛⠓⣋⠙⢠⠈⠤⠐⠠⠅⠂⠔⠠⠚⠻⣦⡀ ⢀⣶⠋⠉⠉⢒⡾⡏⣀⣤⡀⠀⢹⡆⢁⠠⠁⢆⠌⡐⡁⠇⣈⠘⡈⡑⡈⠂⡜⡗ ⢸⣧⠀⠠⣶⠚⢇⠸⡅⠈⠀⠀⢸⠝⠠⡁⠜⠢⡘⠜⠠⠉⢌⡰⠀⠔⢈⠡⢠⢈ ⠀⢻⡄⠀⠀⢀⡼⠋⠙⡒⠶⢚⢋⢠⣵⠴⠓⠓⠊⠉⠉⠉⠉⠁⠛⠢⣄⠑⢂⠠ ⠀⠀⠙⢲⠖⠋⠠⣁⠊⡔⢩⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠈⢶⡈⠀ ⠀⠀⠀⣿⠁⠃⠒⣀⣲⡼⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠇⠀⠀⡇⣠ ⠀⠀⠀⢻⣌⣴⠠⣐⡿⠀⢰⣿⣿⡄⠀⠀⠀⣠⠖⢦⠀⠀⠀⠀⠀⠀⠀⣜⡵⡃ ⠀⠀⠀⠘⢿⣿⣿⡿⠟⠠⣄⣿⣿⠃⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⢀⣼⡿⠛⠀ ⠀⠀⠀⠀⠈⢻⠋⠀⢠⠊⠉⠻⡉⠑⠢⢄⠀⠀⠀⠑⢀⣀⡠⢴⡺⣯⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⣦⣀⡼⣴⠖⠂⣸⠀⠀⠈⢳⢒⡆⠉⠹⡄⢠⣐⣴⡿⡁⠀⣀⡤ ⠀⠀⠀⢠⠏⢸⠀⣠⡟⢪⠓⠛⠋⠘⠷⠂⣸⠖⠓⠒⠁⠉⠉⣼⡿⠃⠈⠺⣄⠀ ⠀⠀⠀⢸⡀⠸⣳⡄⡀⠎⠀⠀⢰⠆⢀⡼⢇⠀⠀⠀⣤⠖⠉⠁⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠈⠓⠚⠁⠱⣄⠈⠻⠂⣀⡴⠛⠁⠸⡖⢲⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⢸⠱⣤⠤⠀⠈⡯⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠉⠑⠦⡒⠒⠒⠒⠒⣤⣾⣷⣮⠉⢦⠀⠀⠀ ⠀⠀⠀⡠⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣯⣷⣿⣿⣮⣦⡀⠀ ⠀⠀⡜⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⢟⣾⣿⣿⡇⠀ ⠀⡸⠀⠀⠃⠀⠀⠀⡠⠒⠲⡄⠀⠀⠀⠈⠁⠀⠈⠛⣏⠀⠀ ⠠⡧⠤⢄⣀⠀⠀⠘⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⡠⢽⠤⠀ ⠀⢣⠀⠀⠰⣌⠀⠀⠀⣴⣷⠈⠇⠀⠀⠀⢳⣶⡍⠒⡗⠢⠀ ⠀⡸⡤⠒⠂⠙⣦⡀⠀⢿⣿⠀⠀⠀⣀⡀⠈⠛⠁⣴⣥⡀⠀ ⠀⠀⠘⢦⡠⠊⠈⢻⣦⡀⠀⠀⠀⠀⢁⣁⣀⣤⡞⠀⠀⠘⡆ ⠀⠀⠠⠎⠈⠒⢤⢄⣹⣿⣿⣿⢿⣿⣿⣿⣿⣿⠏⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⡴⠁⠰⣿⣿⣿⣯⣿⣿⡿⣓⡞⣷⣀⣀⡠⠊⠀ ⠀⠀⠀⠀⡜⠒⠒⠢⣿⢮⠽⣭⢳⡹⡜⣧⢻⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⢀⣤⢯⡻⣜⢧⣛⡝⡶⣫⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⠤⢤⣾⢟⡼⣣⡝⡮⣝⣳⣷⡿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⣏⡶⣣⢻⣻⡏⠯⠥⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠫⠍⠭⠅⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣾⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⣠⣤⡟⠻⠾⣏⣤⡀⠀⠀⢀⣤⡀⠀⠀⣀⣧⡄⠻⠛⣁⣤⡀⠀⠀⢀⣤⣄⠀⠀⣨⣿⣷⣽⡿⢿⣤⣄⠀⠀⢀⣠⡀⠀⠀⠀ ⠹⣿⣶⣾⡿⠿⣿⣶⣶⡿⠿⣿⣶⣶⡿⠿⣿⣾⣶⡿⠿⢿⣶⣾⡿⠿⣿⣾⣶⡿⠿⣿⣶⣶⡿⠿⢿⣿⣶⡿⠿⢿⣶⣶⣿⠿⢿⣶⣶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠛⣟⢻⣶⣦⣀⡀⠀⢀⣤⣴⡿⠿⢻⡉⣿⣷⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⣿⣿⠿⠇⠀⠀⠀⢀⠀⢼⣿⠛⢿⠶⢶⡍⣹⣿⣿⣿⣿⣍⣵⠖⣮⠛⣿⣇⣤⣀⠀⠀⠀⠀⠿⢿⣿⡿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⡟⢻⣿⣤⣜⠳⠜⣿⣿⣿⣧⣼⣿⡟⠁⠒⢉⠠⣿⡏⠙⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⣼⣇⡘⣿⣠⣿⣤⣴⣿⣿⣿⣿⣟⣿⣿⣤⣤⣬⣤⣽⡟⣤⣿⣄⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣀⣸⣿⣿⣿⡿⣙⣿⣿⣿⣿⣿⣏⡉⠉⠉⣹⣿⣿⣿⣿⡟⠋⠐⣿⡏⢿⣿⣀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿⣷⣶⡾⠿⢹⣿⠀⣿⡇⠀⢰⣿⡇⢹⡿⢛⣿⣿⣤⣿⡇⠀⢸⣿⡇⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⠛⠀⠀⠈⠉⢿⣇⣠⣼⣿⣿⣟⡁⠀⠀⣙⣿⣿⣇⣀⣼⣯⠁⠀⠀⠀⠘⠛⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣼⣾⠿⠿⠿⢿⣿⣿⣿⣶⣾⣿⣿⣿⠿⠿⠿⣿⣶⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣾⣿⠉⠀⠀⠀⠈⠉⣿⣿⣸⣿⣿⡟⠋⠀⠀⠀⢉⣹⣿⣇⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠇⠀⠀⢠⣦⣤⣾⠿⠁⣿⡇⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢸⣿⡇⣀⣠⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⠂⣿⡇⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣦⣼⣿⡇⠙⠛⠉⠛⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠛⠛⠟⠀⠀⣿⣇⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⣿⣿⢿⡿⠿⣿⣿⡟⠿⢿⣿⡿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣶⣶⣄⠀⠀⠀⠀⢾⣿⣿⣿⣯⣚⣿⣿⣇⣀⣺⣿⣇⣀⣻⣿⣿⣿⣿⣿⠽⠇⠀⠀⠀⣿⡿⢿⣷⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣟⣛⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠀⠿⠿⠿⠈⠿⠿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⣶⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢶⣶⣦⣴⣷⣶⣶⣆⣴⣷⢶⣶⣦⣤⣶⢶⢶⣦⣠⣾⣶⢶⣦⣠⣾⣶⣶⣦⣤⣼⣶⣶⣶⣤⣼⣿⣶⣶⣤⣼⡿⣶⣶⣄⣴⣶⣶⣶⣴ ⠀⠀⠹⠿⠿⠏⠁⠈⠿⠟⠉⠀⠈⠿⠟⠋⠀⠈⠿⠿⠛⠁⢨⣿⠿⠋⠁⠀⠹⠿⠋⠁⠀⠹⠿⢟⠁⠀⠉⠿⠟⠁⠁⠉⠿⠿⠭⠀⠉⢿ ⠀⠀⠀⡐⠂⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡶⢿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⠀⠀⠈⠁⡔⢲⡄⠈⠀⠈ ⠀⠀⠀⢠⣦⣀⡀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠈⠻⣄⣴⠟⠀⠀⠀⠀⠐⠀⠀⠀⠈⠳⣌⣡⡿⠁⠐⠒⢤⠤⠀⣁⣤⣧⡀⠀⠀ ⠀⠀⢸⡿⢿⠋⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠬⠀⠀⠀⢠⡤⠀⠀⠀⠠⠄⠀⠀⠈⠩⠄⠀⠀⠀⠀⠤⠸⣏⠻⣿⣷⠀⠀ ⠀⠀⠈⠻⠶⣾⠏⠀⠀⠀⠀⢠⠦⠀⠀⠀⠀⠤⠀⠀⠀⢠⠄⠀⠀⠀⠀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠀⡤⠀⠘⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠤⠀⢀⡄⠘⠠⣠⣶⣤⡀⠀⠀⠀⡀⠘⠤⠄⠀⠀⠀⠠⠄⢀⣄⢠⣾⣻⣶⡄⠀⠀⠌⢀⣤⠀⠣⠄⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠻⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢿⣍⡉⣼⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠟⠁⠀⠀⠀⠀⠀⠀⣠⣶⣻⣦⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣴⣿⣿⢶⡄⠀⠀⠀⠀ ⠙⣟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣌⣯⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⣹⡿⠃⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢛⣛⣛⣛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡙⠛⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⣡⡴⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣦⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣶⣬⣙⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿ ⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠈⢻⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿ ⣿⣿⠟⣡⣾⣿⣿⠿⠟⠰⢿⣿⡟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⢼⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹ ⡿⢡⣾⣿⠟⣉⣤⣶⣶⣶⣦⡙⢇⠀⢀⣿⣿⣿⢻⡿⠿⠿⢉⣿⣿⣿⡿⢻⠿⣿⠝⣠⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼ ⢡⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⡌⡿⠟⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⣿⡿⠟⢋⣡⣾⣿⣿⣷⣬⣙⠻⠿⣿⣿⣿⣿⠿⠛⣡⣾⣿ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣾⣿⡿⠿⠿⢋⣴⡄⢶⣦⣁⢠⡀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣶⣶⣿⣿⣿⣿ ⣧⠙⢿⣿⣿⣿⣿⣿⣿⠿⠛⣡⡶⠆⠐⠲⠀⣶⣠⣿⣿⠇⣌⠻⢿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣦⣭⣭⣭⣭⣥⣴⣾⣿⢋⣴⡿⢿⡟⢸⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⢁⣴⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢿⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣿⣶⣴⣄⠻⣿⣿⣿⣿⣿⠿⠟⠋⣡⣴⣌⣉⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣙⡛⣛⣉⣴⣦⣌⠹⠿⠷⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣴⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⣀⣤⡸⣽⣀⠀⠀⣐⡽⣷⣄⣠⣴⣛⡉⠀⡁⣸⣇⠀⠀⠀ ⠀⣞⢉⡻⠤⣤⣙⢿⠿⠏⠛⠛⠻⠛⠟⠿⣿⣗⡋⣻⣍⠑⠢⠄ ⢰⡀⣾⣼⣿⠟⠋⠀⣤⡄⠀⠀⠀⠀⢀⣀⠈⠘⢿⣿⣮⣷⡂⣼ ⠈⢷⣼⡟⠃⠀⢀⣤⣟⠃⣀⣾⣇⡀⠸⠿⡀⠀⠀⠹⣿⠟⢀⡮ ⠀⠀⣽⡇⠀⠀⠈⣙⡭⠤⠼⢯⡭⣅⣀⡓⠞⠃⠀⠀⠀⣾⡟⠁ ⠀⠀⣿⠁⢀⡴⠋⠁⠀⠀⠀⠈⠳⠶⠿⣏⣷⣦⠀⠀⠀⣟⠁⠀ ⠀⠀⢻⡀⣼⠃⢠⣤⡄⠀⠀⠀⠀⠀⢀⣀⢿⣭⣧⠀⢀⡎⠀⠀ ⠀⠀⠈⣷⣿⣥⡈⠋⠁⠀⢴⣶⠄⠀⠸⠿⠀⠐⣟⣀⣼⠀⠀⠀ ⠀⠀⡼⠇⣄⢭⠻⠦⠖⠒⠲⣤⡀⠀⠀⢀⣨⡿⠟⠉⠀⠀⠀⠀ ⠀⢀⣇⠘⢟⣿⣿⣦⣤⣄⣀⣸⡿⠟⠛⠛⢇⠀⠀⠀⠀⠀⠀⠀ ⣸⡞⢻⣤⠈⠉⡋⣿⣿⣿⠂⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀ ⡏⠃⢸⣭⢣⣀⣾⠿⣯⡯⣥⣀⣀⢠⠖⠚⣷⣶⠶⡾⡄⠀⠀⠀ ⢧⣤⣼⡟⠀⠙⣿⠃⠀⢣⡀⠀⠀⠀⠀⢀⣹⡿⡠⢠⣗⠀⠀⠀ ⠈⠛⠛⠢⠤⠤⣿⣦⠀⢀⡇⠀⣀⢠⣠⣼⠇⠉⠁⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⠾⢯⠵⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⢿⣶⣄⣴⣿⠟⠋⠁⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⢳⡽⣎⡟⣾⣻⣯⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣶⣿⡿⢿⣿⣶⣶⣦⣤⣠⣤⣶⣾⣿⠿⠿⠟⢻⡿⣧⢟⣳⣿⣾⣷⣿⣿⡿⣷⣶⣄⣤⣶⣿⢿⡿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⣿⡿⣵⣫⢿⣿⢧⣿⣟⡳⣟⣧⣛⣿⣿⣿⣼⢏⣾⢳⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣶⢫⣟⣻⣿⣿⣯⢳⣛⡶⣛⣾⣿⣟⣿⡿⣎⣯⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣼⡿⣼⣣⣿⣿⣿⣟⣿⣣⣿⣿⣿⣿⣿⢿⣸⣻⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠙⠛⠛⠉⢿⣾⣳⢭⣯⣷⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡷⠶⠿⠛⠓ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠉⠉⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⠀⠀⠀⢠⣤⣿⣷⣤⣦⣤⡄ ⠀⠀⠀⠀⢿⣧⠀⢀⡀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⠀⢀⢁⣿⡇⠀⠀⠀⠀ ⢠⣴⣶⡾⢿⣿⡟⠛⠛⠀⠀⠀⠀⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣼⣿⣀⡀⠀⠀⠀ ⠈⠁⠀⠀⠀⢻⣧⡀⢀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣧⣮⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⡿⠋⠙⠛⡿⠷⠀ ⠀⠀⠀⢀⣤⣶⢿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠙⠋⠀⠀⠙⢿⣦⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠁⠀⠈⠉⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣾⡿⠿⠛⠉⢿⣯⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⢀⣬⣽⣿⣿⣿⣿⣿⣿⣾⡾⢿⠿⠿⠿⠟⠛⠛⣿⡿⢯⢿⣿⣄⠀⠀⠈⢻⣷⡄⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣟⠋⠁⣠⣿⣿⡹⡽⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⢽⡺⣟⣿⣆⠀⠀⠅⠻⣿⣄⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠘⢿⣷⣰⣿⣿⣼⣷⣟⣾⣻⣷⣤⣤⣀⣤⣤⣾⣿⢏⣷⣯⣷⣭⣿⣿⣧⣠⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⠇⠀⠀⠀⣠⣿⠿⠛⠉⠉⠉⠛⢿⣷⡽⣏⣿⣛⣯⢿⣹⣺⣿⠿⠛⠉⠉⠉⠙⠻⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣶⢻⣼⢳⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣳⡽⣺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢻⣜⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⣻⢼⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣏⡾⣭⠷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⢀⡀⡄⣤⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣆⡀⠂⠀⠂⠀⠐⣢⣾⡿⠓⠂⠒⠒⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠉⠉⠙⠻⠿⣷⣶⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠉⠛⠿⢷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⡿⠁⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠶⠆⠀⣰⡆⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⢀⣴⣶⠿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣤⣀⠀ ⢰⣿⣿⠌⠁⠈⠽⣷⣶⣶⣤⣄⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇ ⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠿⣟⢛⡻⣷⣤⠀⠀⠀⣸⡟⠀⠀⠙⢿⣿⣿⣿⣿⠇ ⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠵⢈⣿⡆⠀⣠⣿⠃⠀⠀⠀⠈⠙⠛⠛⠁⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣰⣿⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣶⣶⣴⣤⣤⣶⡿⠟⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠳⢶⣤⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣯⡟⠁⣠⡶⠛⠉⠉⠉⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡏⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢉⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⠶⠶⢶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠉⠉⠉⠛⠳⢶⣄ ⣠⡾⠋⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈ ⠋⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀ ⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡒⣶⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀ ⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⢀⠐⣶⠶⠾⡇⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠈⠻⠿⡏⠀⠄⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠈⢁⡴⠛⢻⡄⠀⠙⠓⠛⠓⠛⠀⠀⠀⠀⠘⠤⣤⣴⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠉⠛⠓⢶⡾⠁⠀⢸⡷⠦⠤⠤⠤⠤⠤⢶⠶⠶⠶⠻⣟⠉⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢐⡄⢹⡆⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠷⠶⠶⠶⠶⠖⠛⠛⠛⡟⠛⠛⣟⠛⠛⠛⢛⠛⢻⣅⢀⣴⠿⠻⠾⠷⠶⡶⠶⠶⠶⡶⠿⠿⠷⠶⠶⠶⠶⠿ ⠻⠶⢤⣤⣤⡴⠾⢫⠁⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⠀⢩⠉⠁⠀⢰⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⢻⣦⣤⣶⣶⣶⣦⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡴⠖⠦⡤⣤⣤⣤⠤⢄⣀⣠⣤⣴⣶ ⠀⠀⠀⣰⣿⢍⠲⡐⢆⠦⡡⢍⠥⡋⣍⢛⠻⠿⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠯⠀⠀ ⠀⠀⢿⡟⡇⢎⡱⣉⢎⠒⡱⠊⠆⡑⠠⢈⠐⢠⠀⡌⣉⠻⢷⣦⣤⡶⢶⣶⠟⠉⠙⢻⣦⠀⠀⢀⣀⣀⣴⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣠⣾⠗⡩⢂⠱⢀⠊⠄⡁⠌⡐⠤⣁⢆⡚⢤⠓⡴⢡⢋⠦⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣶⡿⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢋⠁⢂⠡⡀⢆⠰⣈⠒⣌⠲⣉⠖⡡⢎⡜⢢⡙⡔⢣⠎⡜⣿⣧⠀⠀⢀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣈⣤⣎⡤⢃⡜⢬⠱⣌⠳⡌⠳⡌⢎⡱⢊⡜⣡⠚⣌⢣⠚⣼⣿⠁⠀⠀⠈⠀⠂⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀ ⣾⣿⣿⣿⡧⡘⢆⠳⣌⠲⣉⠳⡘⢦⡑⢣⠜⡤⢋⠤⢣⡙⠴⣻⣦⣀⣀⣤⠀⠀⠀⢀⣿⠟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣭⣟⣧ ⣿⣿⣿⣿⢣⠙⡌⢣⡌⠓⣬⢱⠉⡖⡌⢣⠚⣰⠉⡎⢱⡌⢳⢰⠉⡏⡝⢻⣷⣤⣴⣾⠋⣠⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⢏⢎⡱⣉⠦⣙⢢⡑⢎⡱⢢⡙⣌⠲⣄⠫⢜⡡⢚⠤⣃⣿⣶⣷⡅⠊⠍⠹⣷⡢⢄⠫⣽⣧⢀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿ ⢦⡑⢎⡜⢢⠱⣌⠲⡡⢆⡙⢦⡑⢣⠜⡤⢓⠬⡑⢎⠴⣉⠖⣹⣿⣿⡿⣷⠁⡌⠰⣹⣿⣌⠳⣸⣿⣥⣋⠧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⣙⠢⡜⣡⠓⡤⢣⡑⢎⣱⣷⣾⠿⣾⣴⣋⠖⡩⢎⢲⠡⢎⢽⣿⡿⣽⡿⡐⣌⠳⣘⣿⡇⡗⣸⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣴⠷⠶⠶⡿⠀⠀⠀⠀⠀⠀⠀⠘⠄ ⡓⢬⠱⡘⢤⢋⡔⢣⠜⣌⢲⣏⠀⠀⢀⣿⢻⡙⠴⣉⠦⡙⠠⢈⠙⡛⢟⡡⢓⡌⠳⣌⣿⡗⠤⣹⡟⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡙⢆⣣⠙⣆⠣⡜⣡⠚⡤⢣⡙⡻⠿⣛⢣⠣⡜⡱⢈⠂⢄⡑⢢⠱⡘⢦⡑⢣⠜⡱⣸⣿⠛⢀⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠷⢶⣤⣀ ⣿⣶⣦⣋⣴⡓⡜⢤⢋⡴⢣⠱⣡⠓⣌⠲⡑⠌⠠⡁⢌⠢⡜⣡⣇⡙⢦⡙⣌⢎⣵⣿⠏⠐⣾⡟⠀⠀⠀⠀⠔⠀⠀⠀⠀⣠⣔⠪⠽⠿⣦⠀⠀⠀⠀⠀⠀⢀⣀⣿⡅⠀⠀⠉⠻ ⡭⣙⢛⠻⢟⠿⣿⣷⣾⣶⣧⣯⣴⣍⣆⣑⣠⢈⣅⢢⣷⣿⠿⢟⠻⠿⢿⣾⣶⣿⠛⢁⢠⣿⣿⠁⠐⠀⠁⠀⠀⠀⢀⣴⡿⠓⠁⠀⠀⠀⣿⣦⣴⣶⣶⠿⠿⠛⠛⢻⣧⠀⠀⠀⠀ ⡲⣡⢎⠳⡌⢖⠲⣄⠫⣍⠩⡍⠍⠛⠛⠛⡛⠿⢿⣿⠏⢦⡙⣌⢣⡙⢆⣿⡟⢀⢂⣴⣿⣟⠛⠿⠶⠷⠶⠶⢶⣶⣿⠏⠀⠀⠀⠀⠀⣸⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠀⠀⠀

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣶⣤⣄⣤⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⣠⣴⣶⣾⣿⣷⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⡝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢯⣛⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣞⡱⢣⣞⣹⣿⡿⠋⠛⠛⠋⠁⠉⠛⠛⠛⠻⣿⣿⣛⠦⡝⢦⣹⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⣍⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⢿⡝⣦⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⢻⡏⠁⠀⢀⣀⡀⣠⣾⣿⣶⣦⣤⣶⣿⣷⡀⠀⠀⠀⠈⢻⣿⠛⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣽⢿⣮⣍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣶⢿⣧⣀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣇⣿⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣿⣿⣿⣿⣿⡄ ⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡁⠀⠙⠿⣿⣿⣿⣯⡻⠿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⠈⢛⣷⣤⠀⠀⠉⠉⠉⠁⠀⠀⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡀⠴⠛⠉⠀⠀⠀⠠⣶⡶⠀⠀⠀⠙⠟⢋⠠⢀⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣦⣤⣤⣠⣀⣄⣀⣀⣀⣠⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣯⢯⣽⣹⣿⣿⣿⣿⣿⣜⣿⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣫⣿⣿⣿⣿⣿⡷⠞⠀⠉⢡⣴⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢺⣷⣿⣟⣻⣽⣿⣿⣿⣿⡆⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⢾⣿⣿⣿⣿⣶⣶⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⢸⣿⡿⠈⠛⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀ ⠀⠀⢸⠀⠀⠈⠉⠲⣄⣀⡤⠤⢤⣀⣎⣁⠀⠉⠓⡄⠀⠹⡄⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣀⠆⠀⡇⠀⠀⠙ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢸⡉⢉⠎⠉⠉ ⠤⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣄⠫⠁ ⠈⠉⡁⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠛⠤ ⠠⠐⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢ ⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠉⠐⠒⠒⠒⠒⠒⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⢀⣘⠿⠀⠀⢠⣀⢄⡦⠀⣛⣐⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠣⠤⠘⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣷⣄⣤⣶⠾⠟⠛⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡶⠶⠶⢶⣤⣄⣀⣀⣠⣤⣤⣴⣶⣿⣿⣻⣞⣯⣟⣿⣏⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠁⠀⣼⣿⣳⣟⣾⣿⣿⣿⣿⣿⣶⣤⣶⣶⣾⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣳⢯⣿⢿⣿⣟⣾⣳⣟⣿⣿⣽⢯⣟⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡿⠾⠟⢻⣿⣞⣷⣿⣿⣿⣿⣻⣞⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣯⣟⣷⣯⡿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⠶⠶⠒⠂ ⠀⠀⠀⢀⣿⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠐⠚⠛⠛⣿⡏⠉⠁⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠘⣻⡟⠛⠓⠂⠀ ⠀⠀⠀⢀⣸⣷⡤⠆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⣏⣉⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣁⠀⠀⠀⠀ ⠀⠀⠀⠋⠉⠙⢷⣄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⣿⣭⣽⡛⠖⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⡀⠀⠀⠀⠈⢻⣦⠀⠀ ⠀⠀⠀⠀⠚⠁⠀⠀⢀⣨⣽⠿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣶⣶⠶⣶⣾⣿⣿⡋⠁⠙⢷⡄⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⠛⠉⠀⣰⣿⡿⣽⣻⣷⣄⠀⠀⠀⠀⢀⣴⣿⢿⡽⣿⣷⡀⠀⠈⢻⣦⠀⣠⡿⠃⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠙⢷⣤⣰⣿⡿⣽⣳⢯⣟⡿⣿⣶⣶⣿⡿⣟⣯⢿⣽⣳⢿⣷⡀⢀⣠⣽⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠁⠀⠀⠀⢩⣿⡿⣽⣳⢯⣟⡾⣽⣳⣟⣾⣳⢿⡽⣞⡿⣾⡽⣯⢿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣄⠀⠀⠀⣼⣿⣻⢷⣯⣟⡾⣽⣳⣟⣾⣳⢯⡿⣽⢯⣟⣷⣻⣽⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⡿⣽⣻⢾⣽⣻⢷⣻⣞⡷⣯⢿⡽⣯⣟⣾⣳⣟⣾⣳⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣯⣟⣾⣽⣯⣷⣯⣟⣯⣿⣽⣳⣟⣾⣳⣟⣾⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠙⠙⢛⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⡾⠻⢶⣤⣤⣤⣤⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡶⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣦⠽⢶⣚⡟⣖⣒⠶⢯⣴⣠⣤⠶⠶⢆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣰⠿⣫⡵⣞⡿⣯⢷⣻⡽⣯⣟⡿⣶⣏⠀⠀⠀⠀⢏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣖⣀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣴⠋⠉⠉⠛⢲⣴⡤⠾⣥⣻⣳⢿⣽⣻⡽⣯⣷⣿⣷⣯⣟⡳⣻⣀⡀⠀⣀⡼⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠀⠀⠀⠀⠉⠻⣶⡀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠀⡰⠃⠀⠀⠀⠀⣯⠀⠀⠀⠈⠀⠈⠛⠙⣳⡿⣭⡶⣶⢮⣿⣎⡽⡏⣋⡘⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢀⡟⠀⠀⠀⠀⠀⠘⠀⣤⡄⠀⢀⡀⠀⢀⣿⡼⣟⣿⣻⢿⡼⣿⠟⠛⠛⠛⢠⡀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠬⣇⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠢⣾⣽⣻⡽⣾⣿⢿⢷⣽⣤⣀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⢌⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣷⣻⡽⣿⢧⣾⣳⢷⡝⣆⢶⡶⢿⣄⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⢠⡖⠛⢻⣄⡀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠟⢻⡽⣾⡽⣯⢧⣿⣯⣟⡷⣞⡆ ⠀⠀⣀⣺⣧⡀⣴⣾⣏⡴⠋⡼⠋⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠳⣇⡀⢀⡀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣷⢿⣿⣿⢿⡾⣽⣺⠇ ⢠⣼⠋⢀⣄⣉⣯⣷⣿⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⠉⠩⣿⠒⠦⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡻⢞⢯⣻⡽⠋⠀ ⡠⢨⠷⠶⢤⠾⣻⣭⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⠀⠀⠀ ⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡋⠹⡍⠉⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀⣀⣸⣃⣀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠲⣤⡀⠀⠀⠠⣇⢘⣳⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠉⢳⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠈⠁⠀⣼⠒⠀⠊ ⢽⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠉⢷⡀⠀⢠⣟⠊⠭⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⢀⣀⣀⡏⠀⠀⠀ ⡸⣆⠀⠀⠀⡼⠃⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢿⠀⣸⠃⠀⠀⠀⢈⢿⠦⠖⠢⢄⡤⠒⠋⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠟⠛⠛⠦⠀ ⠐⠿⣄⠀⢸⡇⠀⠈⢿⡿⠀⠀⠀⠀⠀⢴⠒⡄⠀⠀⠀⠀⠙⠉⠀⠀⣼⡔⠃⠀⠀⠀⠀⠰⡈⠀⢀⠠⡀⠄⠠⠄⠰⢈⣧⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡾⢏⡀⠀⠀⠀⠀ ⠀⠈⠛⠧⣌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣉⡠⠀⠀⠀⠀⠀⢀⡠⡞⠛⠁⠀⠀⠀⠀⠠⣡⠷⠲⣦⠑⡠⢉⠂⣼⡶⠛⠁⢸⠋⠈⢷⡶⣦⡴⠶⠒⠊⠙⠃⠁⠀⠀⠙⢶⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠷⢤⣤⣤⣀⣠⣀⡤⠔⠢⣄⠴⠊⠙⠲⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠈⠳⣆⠀⢀⣼⡄⠀⠀⢾⠁⠀⣿⡽⣷⢻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⣃⡀⣠⢦⠶⠞⢤⡜⣱⢊⢧⡙⢧⡶⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣦⣀⣀⣠⣟⢿⣻⣟⡿⣶⣤⣳⠀⠀⣿⣹⣽⡾⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢸⣟⣿⣫⡃⠀⠀⠈⣿⠰⣋⢦⡙⢺⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⢐⡿⢨⣟⡷⣯⣟⡷⣯⣟⡿⣿⣻⣟⣯⢿⣖⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⣞⣧⣳⣤⣤⣴⣷⣦⣌⣐⣴⣾⣟⣶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⣹⢾⣽⣳⢯⣟⡷⣯⣟⣷⣻⣾⡽⠷⠾⠗⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⡞⢸⡟⣯⣿⣽⣯⡟⣾⣽⢻⣽⢻⡞⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠛⠛⢳⠛⢻⡟⠛⢻⠋⠉⠙⠉⠀⠀⠀⠀⠀⠀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠋⠙⠛⠛⠛⠾⠵⢯⠽⢷⠭⢿⡽⠟⠽⠶⠚⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⡤⡤⢴⠛⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⣄⣴⣄⣠⣀⣀⢀⡀⣀⡀⣀⣀⣠⣀⣀⣀⡰⠞⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠲⣲⡗⠒⠚⠓⠒⣞⠙⠋⠉⠀⠀⠀⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠁⠀⠉⠀⠹⣄⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣇⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠀⢀⣼⣤⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠳⣶⡶⠾⡷⣤⡤⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⢀⣀⣤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⣿⣷⣶⣤⣀⣀⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠉⠙⠻⠿⠿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠹⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⣀⣀⡀ ⣠⣤⣤⣾⣿⣷⣦⣤⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠿⠿⣿⣿⡟⠛⠛⠛ ⠉⠉⠉⠉⣿⣿⠉⠉⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣤⣿⣿⣅⣀⠀⠀ ⠀⠀⣀⣤⣿⣿⣷⡶⠆⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⢠⣶⡿⢷⣦⡀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠈⣻⣿⡟⠻⠿⠟⠀ ⠀⠀⠙⠉⠉⢻⣿⣦⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠛⠿⣿⡆⠀⠀ ⠀⠀⠀⠸⠿⠋⠁⠀⠈⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣻⣿⣦⠖⠋⠉⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠉⠉⠑⠒⠒⣿⡟⣯⣷⣿⣿⣿⣷⣶⣾⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣳⣟⡾⣿⣿⣽⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠙⠛⠓⠋⠛⠾⠻⣿⣻⣽⡟⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡡⢼⠶⠂⠀⠀ ⠀⠀⡤⠼⡧⠤⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠰⢼⠶⠄⠀⠀ ⠀⠀⠀⠤⢷⡒⠀⠀⠙⠁⠀⠀⠪⠯⠃⠀⠀⠀⠀⠀⣲⠷⠤⠀⠀⠀ ⠀⠀⠀⠀⣈⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀ ⢠⡶⣶⡾⠷⣶⢾⡿⢶⣶⠊⠉⠙⡖⠉⠉⢹⡿⣶⢶⡶⠶⣶⡶⢶⡆ ⢸⡧⣿⣿⢄⡟⠀⠀⠀⢀⣵⠲⣶⢿⣲⢶⡉⠀⠀⠀⢧⣹⣿⡷⢨⡇ ⢸⡗⡞⠓⠋⠀⠀⠀⢠⢿⠀⠉⢧⣿⣉⣾⣷⠀⠀⠀⠀⠑⠛⠛⣏⡇ ⢸⣏⡇⡀⠀⠀⠀⠀⠸⣯⠠⡄⢀⡀⢤⠙⣿⠀⠀⠀⠀⠀⣀⡀⣧⡇ ⢸⡇⣿⣟⠻⣄⠀⠀⠀⠿⣄⣀⣘⣀⣀⣼⠇⠀⠀⠀⣠⠟⣿⡼⢛⡇ ⢸⡇⣿⡿⢰⣸⣀⣀⣀⣀⣈⣑⣛⣚⣉⣀⣀⣀⣀⣀⣇⠺⣿⡟⢸⡇ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⣾⣤⡴⠶⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠈⠉⠙⠛⠛⠿⢷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣶⣷⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⠟⠻⠟⢻⠶⢏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠈⠉⠛⢿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⠀⠀⠀⠀⠀⠀⢩⣿⣏⠀⠀⠀⠀⠀⢣⡘⠿⠟⠁⠀⠀⠀⠀⢰⡏⠀⢀⣾⠟⠀⠀⠀⠀⠀⣰⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⣠⣀⣀⠸⠻⣍⡛⠧⢀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⢄⣾⠃⠀⢸⣿⣆⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣴⣿⠁⠙⠳⢤⡀⠀⢀⣬⣶⠿⠛⠻⣇⠀⠀⠀⣀⣠⡿⠟⠁⠀⠀⠀⠻⢿⣿⣶⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡿⠿⠿⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⢀⣹⣿⣟⡃⠀⠀⠀⠲⣿⣖⠚⠛⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣰⡾⠻⣿⣻⡟⠻⣄⠀⠀⢲⡏⡹⣧⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢡⡍⣿⡇⠃⢨⣿⡅⠀⠈⠙⢲⡏⠀⠁⢹⣷⠀⠀⠀⠈⠛⢻⣿⣶⣦⣤⣤⣤⣤⣴⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠋⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⣿⡄⠸⣿⣻⡿⠀⠀⠀⠘⢿⣦⣥⣼⡿⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠁⠀⢻⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠁⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣧⡐⠉⠩⠁⠀⣀⣬⠶⠖⢩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣍⣀⣄⣬⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⣹⠟⠷⠶⢶⣾⠛⠁⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠟⠋⠉⠻⢶⣤⣤⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⡔⠼⢠⡟⠀⠀⠀⣾⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠉⠉⠉⠉⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣷⡾⠟⠀⠀⠀⢸⣿⠠⠄⡀⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣀⡀⠀⠀⠀⣀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠕⠒⠉⡀⠄⠠⠐⠠⠀⡄⣄⡰⠔⠊⠉⠁⡀⠄⠠⠀⠄⡐⠀⢀⣀⠤⡔⢢⡝⣌⠣⣝⣢⠝⢊⡉⠱⠀⢆⡰⠐⢂⡈⠄⠐⠈⢀⡠⠔⠒⣉⠐⠂⠁⠀⠀⠀⠀⠀⠉⠐⠲⣍⠓⢦⡈⢣⡘⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠀⠀⠀⠀⠀⠐⠂⠐⠙⠓⠶⢤⣄⡀⢠⠏⠀⣴⠟⡤⢃⠎⡔⢣⠜⣢⠑⡎⠴⡡⢎⠴⡡⢎⠴⢱⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠠⠁⢀⠂⣡⣤⠵⠞⠉⠀⠀⠀⠀⠌⠐⠀⠄⢁⣈⡤⢔⢪⠱⡌⠳⣌⠧⠜⢊⠉⠤⠠⢘⠠⠄⢃⡉⠤⠂⠈⣀⣠⠔⢊⡉⠴⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢱⣧⠀⢧⢹⡀⠀⠀⠀⠀⢀⡶⠋⠀⢀⣤⠶⢟⡛⣛⢛⡛⢟⢻⣛⠶⣶⣤⣄⣀⠈⠁⠟⠀⣰⡟⡸⢰⡉⢞⡨⡑⢎⠴⡩⢜⡡⠱⡌⢦⠱⡌⡜⢢⡑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢀⣠⡥⠶⠞⠋⠁⠀⠀⠀⠀⠀⠠⠀⢂⣠⡤⠶⡚⢭⠡⢜⣨⡦⠳⠚⠉⡄⠘⢈⠤⠈⢒⠉⠠⠐⠈⣀⡤⠤⢒⠩⠡⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠸⡆⢹⣆⠘⣆⢳⠀⠀⠀⣰⠏⠀⢠⡼⢋⠦⡙⢦⠱⡌⢦⡙⣌⠲⣌⢣⢓⠺⠾⣭⣟⡶⣤⣰⡟⡰⢡⠣⡜⢢⡑⠭⣘⢢⡑⢎⡔⢣⠜⢢⡑⢒⡌⠥⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠒⠋⠁⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣴⣦⣉⠦⢘⣡⡼⠶⠛⠋⠁⡀⢂⡡⠁⠐⡈⠅⠐⠈⣁⡤⠴⠒⢋⠡⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠉⠓⠦⡄⠀⢻⡈⣼⡆⠸⡌⣇⠀⢰⡏⠀⣰⢏⠲⣉⠖⡩⢆⠳⡘⢦⠱⡌⡓⡌⢦⡉⢎⡱⢢⢍⡛⡛⣍⠲⣡⢃⠳⣌⠣⡜⡱⢌⠆⣍⠲⡨⢅⠎⡅⢎⠥⡘⢆⡱ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⣀⣠⡴⠾⠛⠉⠉⠈⠀⠀⠉⠉⠉⠛⠻⢿⣿⣤⡀⢀⣠⠴⠒⣀⠥⠀⠈⢁⣠⠴⠒⠋⠡⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢷⢈⢳⡀⢱⡘⡆⢸⡇⠐⣏⢎⡱⢌⢎⡱⢊⠵⣉⢆⠳⣌⠱⡘⢦⠙⢦⡑⢣⠎⡴⠱⣌⠱⢢⢍⠲⣄⠳⡘⠴⣉⠎⡔⢣⡑⠎⡜⢌⠲⢌⡱⠌⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⣴⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠈⠻⣿⣆⠐⠈⠁⡀⠤⠒⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⣇⠈⣷⠀⢧⢹⡸⣇⠈⣷⣈⠖⡩⢆⡱⣉⠖⡡⢎⡱⢌⢣⡙⠦⣙⢢⡙⢢⡙⡔⢣⢌⢣⢃⢎⡱⢂⠧⡙⢦⠑⡎⡜⡡⢜⡘⢬⢘⡂⠧⢰⠩⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠘⣿⣆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣇⢛⣇⠈⣆⢳⣻⡀⠹⣦⠙⡔⢣⠒⡥⢊⡕⢪⠔⡩⢆⡱⢣⠜⣢⠙⣆⠱⣌⠣⢎⠦⣉⠲⣬⣕⡬⡑⣊⠱⡘⠤⠓⡬⢘⠢⣅⠚⡌⢥⢊⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢹⡄⠞⡆⠸⡄⢏⢷⠀⠹⣎⠜⣡⢋⠴⢣⠜⡡⢎⡱⢊⡔⢣⠚⡤⢋⡔⢣⢌⠳⣌⠲⣡⡿⠁⠈⠙⣷⣌⡷⠛⣷⡉⠴⡉⠖⡤⢋⠜⡰⢢⠡ ⠻⣦⣄⡀⢀⣠⡴⠛⠉⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠤⠴⠶⠶⠦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⡈⢻⡀⢱⡘⡎⢧⡀⠙⣞⠤⣋⠜⣢⠙⡔⢣⠜⡡⢎⠥⣋⠔⡣⢜⡡⢎⡱⣤⣷⣬⣹⣆⠀⠂⢸⣿⠀⣼⡟⣐⢣⡉⢞⢠⢋⠬⡑⢆⠣ ⠐⠠⡈⠙⠛⠷⠦⡴⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡆⢰⣶⣤⣰⡿⠋⠀⠀⠀⠀⠀⠀⠤⣄⠈⠉⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣇⠐⣳⠀⢧⢸⡄⠳⣄⠈⠳⣌⠞⡤⢋⡜⡡⢎⡱⢊⠖⡡⢎⡱⢊⡔⢣⢒⡙⢦⣄⣉⠛⣷⣤⣽⠧⠞⡭⢰⠡⢆⡙⢢⢃⢎⠲⣉⢎⡱ ⢿⣤⣡⡈⠄⠠⢀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣠⣾⡟⠉⠀⠀⠀⢠⠙⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢻⣦⣶⡶⢶⡆⠤⣄⡀⠀⠀⢧⠀⠘⣦⠹⣧⠈⣆⢧⠀⠘⢦⡀⠈⠻⣔⠣⡜⡱⢊⠴⣉⢎⡱⢊⡔⢣⠜⣡⠎⡜⡡⢎⡍⣛⠹⣂⠦⡙⡜⡰⢃⡍⠦⡙⠦⣉⢎⡱⢌⠲⡐ ⠀⠉⠙⠛⢶⣥⣤⣄⣠⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡼⠁⠀⠀⠀⠀⢠⣼⡿⠁⠀⠀⠀⠀⠀⢸⡇⢸⠂⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠲⣄⠉⠛⠲⢮⣇⡀⠱⡜⣞⡆⠸⡌⢧⠀⠀⠙⠢⣄⠈⠛⢦⣱⢉⠖⣡⠎⡔⢣⠜⣡⠚⡤⢋⠴⡑⢎⠴⡡⢓⡌⢲⠱⡌⡱⢃⡜⣡⢃⠳⢌⡒⠬⠌⡥⣹ ⠠⠀⠂⠉⠀⠀⢀⣠⠽⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠁⡃⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠐⣧⢸⡂⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣿⠂⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⢷⣷⡈⠽⡄⢱⡸⡆⠀⠀⠀⠈⠳⢤⡀⠉⠻⢼⣄⠫⡜⡡⢎⠥⣋⠴⣉⠖⡩⢎⡒⢥⠣⡜⣡⠚⡴⢡⠣⡜⢤⡉⢞⡰⢌⢃⢣⢲⡝ ⣧⡀⠀⠠⠒⠊⠉⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠐⡀⠀⣠⣶⠿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⡡⠀⠀⠀⠀⠀⠀⠀⣴⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⠀⠀⠈⠹⣿⡆⢹⡀⢣⠹⡄⠀⠀⠀⠀⠀⠉⠳⢦⣀⠈⠳⠮⣕⣊⠖⣡⠚⡤⢋⡔⢣⠜⣢⠓⡜⢤⢋⡔⢣⢓⡘⠦⣉⠖⡰⢊⢌⠲⡝⠀ ⢹⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⣱⡿⠉⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⣿⠈⣷⡀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠞⡽⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠙⣿⡀⢷⠈⣇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣄⣈⠉⠛⠦⣽⣐⠣⡜⣡⠚⣄⢋⡜⢂⢣⡘⣡⣦⡟⣶⡡⢊⡱⢌⢪⡽⠁⠀ ⠌⣻⣿⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠀⠀⠀⠀⠀⣎⢹⣆⠀⢀⣠⣤⣴⣶⠿⠶⠾⠷⠲⠶⠾⠿⠷⠦⠤⣤⣄⣀⣾⠁⣾⡏⠇⠀⠀⠀⠀⠀⡠⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠎⣇⠘⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⡙⣶⢤⣀⠉⠛⠶⣥⣍⡲⢌⠢⣍⢢⠒⣉⢧⢻⡜⢷⣥⣒⢬⡿⠁⠀⡸ ⠒⡄⢿⣷⡄⢀⣀⡤⠖⠊⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⢹⣠⣼⣷⣿⡿⠷⠶⠚⠚⠛⠛⠛⠛⠙⠓⠒⠒⠦⠤⢤⣀⣈⠙⠛⠿⢾⣄⡀⠀⠀⠀⣸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠐⠸⡆⠹⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢧⠘⣦⠉⠳⣆⠀⣀⠈⠉⠳⠷⣴⣌⡘⣤⠟⣠⡟⠶⣤⣭⠟⠀⠀⡔⠀ ⢱⠈⡆⣿⣿⠉⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀⣰⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠷⣆⡀⠈⠹⠷⣆⣶⠇⣾⠀⠀⠀⠀⠀⠀⢀⣰⠰⢿⣿⣶⣁⢹⠀⢷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⡇⢿⡆⠀⢹⡆⠈⠹⣷⣶⣀⠀⠈⠹⢉⣰⣏⣰⣱⣾⠏⠀⣀⡿⠀⠀ ⣇⠎⡰⢘⣿⣆⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡈⠙⠲⣇⡀⠀⠀⠀⠤⠖⠋⠠⢀⡴⠈⠉⠻⢿⣇⠘⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⡈⡞⣆⠀⢳⡄⠀⠽⣄⠉⠙⠒⠶⢤⣅⣀⠀⠁⠀⣠⡴⠋⠀⡀⠠ ⣎⡳⡈⠥⡘⣿⡄⠀⠀⠀⠀⠀⠀⠹⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡙⢦⣤⡴⠞⠋⠠⣱⠟⠀⠘⣄⡀⠈⣿⡇⠘⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⠱⡸⡄⠀⢳⡀⠀⠈⠙⠺⣥⡢⠀⠀⠉⠉⠛⣉⡭⠖⠋⢁⣠⣶ ⢿⡵⢣⢑⢢⣹⣷⡆⢀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⣶⣄⢡⣶⠏⠀⠀⠀⠀⠉⠃⠈⢿⡄⢳⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣇⢡⠸⡆⠈⢳⡀⠀⠀⠀⠀⠉⠓⠦⠴⠚⠉⢀⣠⢄⣶⡿⠟⠁ 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⠜⠠⠁⣌⠰⠘⠊⠁⠀⠀⠠⠄⠄⠒⠀⠉⣀⠤⠂⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠞⠁⠀⠄⡁⠂⠐⠀⢀⡆⠳⢡⢆⡛⣤⢋⣊⣁⠂⣉⠻⢾⠿⠳⡜⢦⡹⣙⢿⡋⣡⣾⣿⡿⣞⣿⣽⣇⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣴⣾⠿⣭⢯⣵⡋⣰⣦⠿⣙⠲⢦⣨⣷⠿⣾⣿⣷⣧⠾⣥⣪⢟⣯ ⡌⢂⠩⠀⠐⠀⠂⠁⠀⠄⡀⢀⣄⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⡰⠏⡀⠄⡈⡐⠠⠄⠂⡐⢈⠀⢂⣵⠲⡽⣭⣳⡜⡴⢪⢥⠛⣦⠛⠛⠺⢧⣳⢍⡞⣻⡿⣝⣶⣽⢿⣯⣿⡿⢟⡿⠀⠀⠀⠀⠀⢀⣰⢏⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣰⠏⣼⢯⡟⣳⡏⣶⠟⣩⡵⢯⣬⣙⣇⠻⢧⣟⣿⣹⣏⢛⣿⢞⣹⣯⠧ ⠠⠀⠀⠈⢀⠠⠐⢈⣠⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⢬⣘⡡⢉⠡⠐⠠⢁⠠⠁⢀⠂⠌⡀⠿⣶⣛⡶⣹⠖⣭⢓⢮⡹⣔⠲⣍⢳⢦⡹⣎⣾⡋⠻⠿⡼⢾⣿⡿⠋⠘⠁⠀⠀⠀⠀⢀⣤⢟⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⢀⠂⢀⣼⣃⡼⠟⠻⡿⢿⣞⣡⣞⣧⡽⣞⣭⣵⡾⢟⡹⣿⣉⣿⡿⣯⣵⣯⣟⣛⣛ ⢦⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⣴⠋⡄⠀⠄⡀⠄⠡⡔⢀⠂⡁⢂⣤⣦⠙⢦⡈⠐⠄⠂⠌⡉⠛⠳⣏⠶⣩⢖⡱⢎⡳⣌⠳⣮⡵⢋⠡⡙⠳⠖⣋⡾⢋⠁⠀⠀⠀⠀⠀⣠⡴⡛⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡡⠁⢌⠠⠀⣽⢻⡶⣶⢖⣻⢟⡿⡷⡼⣻⠵⠚⣉⣡⠤⢖⡿⣞⢵⣫⣵⡾⢿⣭⣚⣬⣧⣭ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠒⠚⠉⣉⣡⡤⢾⡿⠁⡼⢀⣬⣔⣼⣦⡄⠙⠃⢄⠁⢾⣿⣽⣷⠈⣉⠡⢈⠌⡲⠜⢁⠂⢌⡻⢔⡫⣜⢣⣕⣮⠟⢁⣠⡤⢶⣶⠞⠛⠉⠈⢀⡀⣀⣤⣄⣴⣞⣋⣴⣉⣥⣄⣠⣄⣤⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡐⠠⢁⠂⠄⣡⠻⣶⣟⣖⡺⣇⡞⢾⣿⣜⣧⣞⣋⣷⡿⢿⣛⣿⣻⣽⣿⠽⠾⠛⠛⠉⠁⠀⠀ ⠀⠀⠀⠹⣆⣠⠤⠤⠒⠂⠉⠈⡀⠀⠀⠀⣀⣤⠴⠋⢡⠞⣷⣿⡿⣀⠄⣿⣛⠾⣧⣿⡇⡜⡰⠬⠃⠌⡙⠛⡉⣰⣉⠦⡆⢯⡱⣚⢬⡚⣬⢣⢏⣲⡽⠫⢉⡤⢦⣬⣥⣶⣿⣯⠶⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠈⠉⠀⠈⠁⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠶⠶⠦⣼⣥⣤⣂⣄⡁⠂⠬⠞⠁⠀⠈⠻⢵⡶⣽⣻⣶⣬⣿⣷⣯⢿⠶⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠄⠈⠀⠀⠁⠄⢒⡩⠴⢒⡛⠛⠛⡞⢟⣣⠓⠠⠙⣯⡟⣶⡟⠠⡘⢣⣙⠚⣤⣰⢡⡔⣡⢎⢳⡙⢦⡓⡷⣮⣕⡾⠶⠟⣻⣤⣴⢯⡷⢾⠛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡙⠛⠲⠶⠦⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠲⣉⣍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣦⣄⣀⣠⣴⣾⣿⡿⠿⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⡱⢢⢍⠻⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣾⣿⢣⢋⠴⣃⣎⣱⢎⣿⣧⣀⣀⠀⠀⠀⢀⣀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠋⠉⠉⠙⠛⠛⠿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⣿⡟⢥⢚⣲⣿⢛⣻⣿⡿⢟⡻⠿⣿⣶⣿⠿⡟⢻⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡤⢃⠾⣷⣳⣿⡏⡜⢢⡑⡣⢜⣿⣷⣧⢸⡡⢎⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⡉⢖⡩⣽⣿⡜⣌⠣⡜⡱⢊⣿⡿⢻⣧⡑⢎⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠻⣿⣦⣣⣱⣵⣿⣿⣷⠿⣣⠙⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣠⠘⢧⣀⣿⣿⠟⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⡿⠟⠁⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣾⣿⣿⡄ ⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⣿⣿⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⣀⣿⣿⣄⣄⣀⡀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⣷⣾⠃⠀⣀⠀⠘⢛⣿⣿⠿⠿⢿⠇⠀ ⢀⣤⣤⣶⣿⣿⣷⠶⠶⠶⠆⠀⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⠁⢠⡟⣿⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀ ⠙⠿⠛⠋⠉⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠏⠀⠀⠀⠀⠀⠀⢰⡾⢛⡙⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⡟⣿⠹⠶⠿⣹⣿⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⣨⣿⣿⣶⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡿⢘⣾⣶⡆⢰⣿⠟⠻⠟⠃⠀ ⠀⠀⠀⠠⣿⣿⠟⠻⣿⣦⡀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣾⢿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣾⠃⡀⠛⢛⢁⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣁⠀⠀⠀⠀⣸⣿⡀⠀⠁⠈⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⣼⠃⣐⣴⡿⠿⠿⠇⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠛⠻⠿⣿⣷⣶⣾⡿⠉⠀⠀⠀⠀⠀⢸⣿⣤⣴⣦⣶⣶⣶⣾⣿⣿⡿⢟⣿⢱⡏⣸⡿⠋⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⣹⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠉⠉⣉⣾⢏⠐⡀⢻⣷⣸⣧⡿⠀⣿⡇⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⢀⣠⣴⣿⠿⠿⣶⡶⠿⡛⢍⠎⢠⠐⠠⢹⣧⠉⠛⠛⠻⢿⣤⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⡿⢟⡩⠐⡈⠰⢠⠜⢮⡁⠂⠌⢤⢚⠣⣌⣿⣷⣦⣤⣤⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⢋⠄⣉⠙⣛⣿⡿⠶⣶⣶⣥⣮⣥⣴⣬⣶⣶⣿⠟⡛⢩⢿⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⠁⠚⡌⣶⠋⠁⢠⢱⢢⣵⠂⠀⠂⡔⢣⠒⠂⡌⣿⠐⢣⡎⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⠠⣀⠜⣀⠛⠡⡈⢴⡈⢄⠚⠁⡄⢣⡌⠰⢈⠡⢂⡱⢦⡐⠂⡀⢃⡜⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣾⣦⣤⣌⣠⣙⢢⠙⡠⢀⠡⠘⠥⢊⠅⢂⠐⠌⠲⣡⣑⣂⣰⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠙⠛⠿⠿⠿⢿⣷⣶⣶⣷⣶⣾⣶⣿⣿⠿⠿⠿⠿⠟⠛⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⢶⣦⣤⣤⣤⣤⣤⣤⣤⣾⣿⣦⣤⣤⣤⣤⣤⣤⣤⣶⠶⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡖⣌⠲⡩⢌⡥⡙⣌⠖⣹⣿⢢⡙⢬⠡⡝⢬⡑⢎⠴⣹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣿⣶⣝⣰⢃⠖⡱⢌⣮⣽⣿⣦⡙⢦⡙⡜⢢⣹⣼⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⡿⠿⠿⠻⠿⢿⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠉⠉⠛⢷⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡶⠾⠻⠶⣶⣄⡀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠙⢿⣦⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣠⣄⡈⢿⣿⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠈⣿⡀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⢠⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀⠀⠀⠀ ⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠙⠻⠷⠶⠶⠶⠶⠟⠋⠁⠀⠙⣷⠀⠀⠀ ⠀⠀⠙⣷⣤⣀⡀⠀⠀⣀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢸⡇⠀⢹⡇⠀⠀ ⠀⠀⢸⡏⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⠀⣸⡇⠀⠀ ⠀⠀⢸⡇⠀⣰⡆⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⣰⣿⣁⠀⠀ ⠀⠀⠈⣿⡀⠙⠃⠙⠁⠀⠀⣤⣄⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣾⠟⠉⢻⣧⣀ ⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣴⡟⣁⣠⣤⡶⠾⢿⣯⠀⠀⠀⢀⣽⠟ ⠀⠀⠀⠀⣾⠟⠻⠷⣦⣤⣤⣤⣤⣴⡶⠶⠶⠛⠛⠉⠉⠀⠀⠀⣀⣹⣷⣀⣠⡿⠋⠀ ⠀⠀⠀⣰⡿⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀ ⠀⠀⠀⠻⣷⣤⣀⠀⢠⣿⡤⠴⠖⠚⠋⠉⢁⣀⣤⠤⠴⢾⡿⠙⠛⠋⠙⠿⠟⣿⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⣿⣯⣠⠤⠶⠒⠛⠉⠉⠁⠀⣀⣀⣼⡇⠀⠀⠀⠀⠀⢀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣀⣀⣠⣤⣴⡶⠾⢿⡿⠋⠙⣷⣄⠀⠀⢀⣠⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⢛⣉⠉⠁⣠⣄⣠⡿⠁⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠟⠻⠷⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣆⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⡾⠋⠉⠉⠻⣦⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣤⣤⣹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣧⣿⠋⠉⠙⢿⡿⠛⠛⠷⣦⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣧⠀⠀⠀⣸⠿⣦⠀⠀⣻⡆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⠀⢠⣿⠁⠀⠀ ⠀⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣧⣤⡄⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀ ⠀⠰⠶⠾⣿⣿⣿⣿⣿⣿⣷⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣠⣾⣿⣿⣿⣿⣿⣿⠷⠶⠄⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⠹⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠀⠀⠠⠶⠛⠻⢿⣿⣿⡀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⠻⠶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⢿⣿⠿⠷⠶⢶⣶⣶⣶⣶⣶⡶⠾⠿⣿⡿⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⡿⠋⠁⢠⡿⠁⠀⣠⣶⣿⣄⣤⣦⣠⣶⣦⣄⠀⠘⣿⡄⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⡟⣿⣯⣤⡀⢠⡿⠁⠀⠀⠁⠈⠉⠉⢻⠟⠙⠋⠀⠈⠀⠀⠘⣿⡀⣀⣤⣽⣿⢷⣆⠀⠀⠀ ⠀⢀⣾⣿⠸⣿⣿⣿⣿⣿⡧⠤⠤⡤⠤⠤⠤⣤⠤⠤⢤⠤⠤⠤⣤⠤⠤⣼⣿⣿⣿⣿⣿⢌⣿⣧⠀⠀ ⠀⣾⣿⣿⣧⣙⠿⠿⣿⣿⣳⣀⣤⣃⣄⣀⣄⣃⣀⣠⣐⣠⣀⣀⣘⣀⣀⣺⣿⠿⠿⠟⢋⣼⣿⣿⡧⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠷⡿⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠉⣿⢸⣶⣿⣿⣿⣿⣿⣿⡀ ⢸⡟⢻⣿⡿⢿⣿⣿⣼⣇⠀⠀⠀⢠⡀⠀⠀⠙⣿⡿⠉⠀⠀⢀⡄⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⡟⢿⡀ ⠀⠀⠠⠏⠀⠀⢹⡿⠛⣿⣤⣶⣾⣿⣿⣶⣦⣴⣿⣷⣦⣴⣶⣿⣿⣶⣦⣴⣿⠛⣿⡇⠹⣿⢹⡇⠈⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠃⠀⠀⠈⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠙⠻⣷⣤⣶⡶⣶⣶⣦⣶⠟⠻⣿⠋⠉⢻⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢀⠠⣄⣀⣀⠀⠘⠣⢄⣴⠿⣷⣤⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠠⠀⠀⢒⠃⡃⠀⠀⠀⡀⠀⠀⢠⠙⠛⠟⠩⠹⣿⠀⠀⠀⡀⠎⠣⢀⠀ ⠀⠀⠀⠀⠀⢀⣀⣷⣈⡉⠉⠀⠑⠬⠤⠔⠊⠙⠴⠦⠔⠉⠉⢶⣶⣶⣇⣀⠀⠀⠑⢀⣀⡏⠀ ⠀⢀⠀⠀⠀⣙⣛⣿⣛⡛⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣄⠀⠀⠀⣛⣻⣿⣛⡃⠀⠀⠀⠀⠀⠀ ⢰⡝⢤⠀⠀⢉⣭⣿⣯⡥⠉⠉⢪⠻⠃⠀⡔⠀⠀⠛⠛⡊⠉⠉⣭⣽⣯⣭⡁⠀⠀⠀⠀⠀⠀ ⠈⠁⠁⠀⠀⢈⣽⡿⠿⢷⣤⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⣦⣿⡿⠿⣿⣅⠀⠀⠀⡀⣀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⣾⡍⣿⡿⠿⠿⣿⣿⣿⡿⠿⠟⠛⠛⢹⡇⠀⠀⠀⣿⠂⠀⠰⠇⢷⠁ ⠀⡤⠀⠠⡀⠈⢿⣄⠀⠘⣿⡟⢀⡀⢀⡀⢻⣏⠛⠿⣶⣶⣶⡿⠁⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⡁⠀⠈⣻⣦⣤⣿⡇⠘⢃⡺⠁⠸⠿⣶⣶⣶⣶⣶⡶⡷⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠈⠀⠀⢰⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⣾⣤⣤⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡉⠉⠉⠛⢻⡿⢻⣟⠛⠛⠋⠉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣶⡶⠟⠁⠀⠻⢷⣶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⣀⡤⢤⡄⡀⠀⠀ ⠀⠀⠀⠈⢠⠞⠉⠓⡶⠄⠀⠀⠀⢠⠏⠀⢀⢹⠅⠀⠀⢷⠀⠄⠀ ⠀⠀⢀⠀⢼⠀⢀⠁⠀⡀⠀⡀⠀⢸⠀⠐⢵⠉⠉⢳⡚⠛⢳⠀⠀ ⠀⠀⠀⠀⠘⡁⠀⢀⠁⠂⡀⠀⠂⠉⠛⢛⠛⠦⣤⠾⠜⢀⡾⡀⠃ ⠀⠀⠐⢠⠃⠡⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⠀⠀⠛⠒⠋⣀⢄⠃ ⠀⠀⠠⢬⣧⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠍⠉ ⠀⠀⠀⢀⣿⡴⠒⠘⠛⠀⠀⠀⠐⠒⡄⠀⠀⠉⠈⠯⢀⣜⡏⠉⠀ ⠀⠀⠀⠀⣀⡵⢾⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⡴⠋⠙⠂⠀ ⠀⠀⠀⡾⢭⣱⢀⡭⠟⡶⢶⠶⠤⠤⠤⠴⠶⣾⠻⢭⡀⠀⠀⠀⠀ ⢀⣠⠎⢀⠐⠞⣝⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠉⠒⢦⠀⠀ ⠸⣌⣧⣛⣙⡼⢡⠏⡀⠀⢀⠀⡀⠀⢀⠀⡀⡀⢀⠙⡀⠀⣩⠀⠀ ⠀⠀⠀⣎⣘⣦⡼⠒⠈⠀⠁⠈⠈⠀⠁⠁⠈⠀⠁⡒⢣⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⢄⠄⣀⢀⡀⠀⠀⢀⢀⢀⢠⠨⡰⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⣀⣄⣀⠥⣀⣀⣀⠠⠴⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣶⣾⠉⠉⠉⠉⣷⣶⣾⡏⠉⠉⠉⠉⠉⣷⣶⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⠀⣀⣸⣿⣇⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⡟⠛⠛⠛⠻⣤⡟⠛⠛⠛⢻⣤⣤⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⡇⠀⠀⠀⢸⣿⠋⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠿⠿⣿⣇⣀⣀⣀⣸⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣧⣤⠀⠀⠀⣤⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣤⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⡏⢹⣷⣶⣾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⣶⣾⣿⣧⣤⠀⠀⠀⠀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⣦⣼⣿⣷⡆⠀⠀ ⢐⣿⣿⢿⣿⡟⠉⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠉⢹⣿⣯⣿⣿⡇ ⠀⠁⠈⢸⣿⣇⣀⣀⡀⠀⠀⠿⠿⠿⠇⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⢠⣀⣀⣼⣿⡇⠈⠈⠀ ⠀⠀⣶⣾⣿⣿⣿⠛⠃⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠋⠈⠛⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠛⣿⣿⣿⣷⡆⠀⠀ ⠀⠀⠙⠛⠁⣙⣿⣿⣆⣀⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣀⣸⣿⡟⠋⠈⠛⠃⠀⠀ ⠀⠀⠀⠀⠀⠿⠿⠑⠿⠿⠿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣄⣴⠶⠶⣦⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠶⠟⠉⠀⠀⠉⠀⠀⠀⠈⠉⠙⠛⠛⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡿⠀⠀⠀⠀⠐⣴⣄⣀⣤⣤⣠⣴⣦⣤⡾⠂⠀⠀⠈⠙⠗⠠⣶⠶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣭⡽⢀⠈⡉⢥⡴⠀⣀⣤⣤⡀⠄⠀⠀⠀⣴⠾⣠⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣧⣙⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⠀⢀⣾⠏⡱⢈⠿⣆⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⢀⣄⣾⠋⡔⢦⡟⣦⡿⣤⣀⣀⣀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⡀⢀⣶⠷⠶⠛⠉⠉⠉⠋⠉⢿⣥⡘⣘⣿⡍⠰⣁⢻⣋⠝⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠙⢮⣥⣼⣿⠿⢊⢥⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣤⣮⣴⠟⢹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⣿⣉⠀⠀⢦⣤⡤⠀⠀⠀⣀⣀⠀⠀⠀⢰⣄⡴⠀⠀⢠⣿⠀⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣏⣀⡆⠄⠂⠀⠀⠀⠘⠯⠽⠃⠀⠀⠀⡀⡐⠤⣠⣼⠇⠀⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⡀⠀⣹⡿⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠻⣅⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠛⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣥⢿⡀⢀⣴⠶⣿⣻⡟⠛⠃⠘⠛⠻⣟⢿⠶⢦⡀⢀⡿⠘⠋⠀⠀⠀⠀⢀⣴⠶⢦⡀⠀⠀⠙⠶⠶⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠉⠀⠀⢉⣷⠶⠶⣥⡴⢾⡉⠀⠀⠘⣻⣏⠁⠀⠀⠀⠀⠀⠀⠘⢧⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣦⣀⣠⣼⣧⣀⠀⠀⠀⣸⣧⣄⣀⣴⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡛⠉⠀⠀⠙⢷⣠⡟⠉⠀⠉⠉⢤⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⣿⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠘⡗⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣿⡀⠀⠀⠀⢀⣾⠙⣧⠀⠀⠀⠀⢠⣏⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢦⣤⡴⠟⠳⠾⠛⠷⢦⣴⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣔⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠘⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣕⡂⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣟⣻⠶⣦⣤ ⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋ ⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣶⣶⣶⣮⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠓⠀⠐⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⡌⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠛⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣴⠏⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣟⣿⠀⠀⠀⣠⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣰⠟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠻⢿⣿⣿⣿⣿⡼⠿⠃⠀⠀⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠟⠉⠠⢲⣄⠀⠀⠀⠀⠻⣿⣿⣿⣿⢂⡄⢀⡀⡙⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⢲⣴⣾⣿⣶⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣿⣿⣿⡿⡅⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠙⢿⣟⣻⣿⣿⣿⡿⠿⠟⠛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⢀⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⣿⣿⠀⢀⣨⣼⣇⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⡟⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠻⠿⠟⠋⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⣿⣿⠾⠋⠉⠀⢙⣷⣉⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠰⠟⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣏⣻⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠁⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⢈⣾⠃⠁⠀⠀⠀⣰⣿⣶⠶⣶⣤⣄⡐⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⠰⡄⠀⡀⢀⣴⣿⣧⣀⠀⠀⢀⣾⣻⠆⠀⢰⡟⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠳⢶⣟⢻⣿⣟⣿⣾⣿⣿⣶⣾⢃⠀⠀⠀⣦⡄⣠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠈⠉⢿⣰⠀⠀⠀⠁⠠⠈⣰⣟⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⡶ ⠀⠀⠀⠀⣠⡾⠋⠁⠈⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⡶⠶⠿⠛⠛⠛⠉⠉⠀⠀⠀ ⠀⠀⠀⣼⢫⠀⠀⠀⠀⠀⠠⢻⣟⣳⡶⠶⢦⣤⣄⣀⡀⠀⠀⠘⣿⣿⣿⡏⠀⣼⣿⣯⣭⣭⣽⣿⣿⣿⠟⢻⣷⠶⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠇⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠂⠀⠀⠉⠉⠛⠂⠀⢿⣜⣿⠀⢠⣿⣿⠉⠀⠀⠀⠀⠐⠛⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣾⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣶⣴⣤⣤⣄⣠⣀⣀⣀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡙⣛⣲⠶⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠿⣀⣤⣶⠶⠾⠟⠛⠛⠛⠛⠛⠛⠻⠷⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠾⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢓⣤⣤⣴⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⠶⠞⠋⠁⠀⠀⡀⢀⣾⠃⠀⠀⢠⡷⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⢀⠃⢸⡏⠀⠀⠀⣼⢶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⢻⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡀⣤⣀⡀⠉⠛⠛⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢻⣿⣿⢿⡇⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣈⢉⠹⡆⠀⠀⠀⠀⠘⠷⠶⠚⠓⢶⡴⠛⠀⠀⠀⠀⠀⠈⠛⠿⠛⠀⠀⠀⠀⢸⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣀⠀⠀⠀ ⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡉⣉⢍⣻⢲⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀ ⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠙⠿⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠾⠿⠧⠼⢣⡈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆ ⠀⠀⠀⠀⠙⠛⠿⠶⠶⠶⠶⠿⠛⠋⠁⠁⠀⠀⠀⠀⠀⠉⠉⠙⣻⣶⠶⠶⠦⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣥⡶⠶⠛⠛⠋⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⡉⠉⣹⣿⣂⠀⠄⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠼⠀⠀⠀⠀⠄⣿⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠛⠉⠉⠙⠻⠷⢤⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⣀⣀⠀⣀⣤⡴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⢾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢠⣴⠿⠶⢤⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⢺⣧⠀⠀⠈⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠈⠁⠀⠀⢰⡏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠋⠒⠚⠶⢤⣄⣀⣀⣀⣀⣀⣘⣻⣶⣦⣤⣄⣴⡶⢟⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣏⠿⣩⢗⡹⢎⡷⡹⢎⡳⣝⣎⢳⣙⣎⢳⣙⢎⡳⣙⢎⡳⣙⢎⡳⣙⢎⡳⡝⣎⡳⣙⣎⡳⣙⣎⢳⡭⢋⠁⠀⠀⠀⢀⠒⡰⢀⣂⣴⣠⣆⣐⣌⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠿⠿⠿⠻⢟⠿⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡐⢢⠒⡄⢃⠆ ⢮⡛⡵⢮⡹⢞⡲⣝⢫⡵⣚⡬⢇⡳⣜⢧⣺⣼⣷⣿⣿⣿⣿⣾⣷⣿⣾⣵⣭⣶⣱⣋⠶⣩⢳⡜⠣⢀⠃⠖⠤⡀⣄⠚⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣄⣤⣴⣾⣿⣿⣿⡿⢿⢛⣫⢍⠶⡒⢭⡚⢥⡋⠮⣍⢷⣬⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡸⢐⠒⡌⢂⠇ ⢧⣛⢼⢣⡝⢮⠵⣎⡳⣜⡵⣚⣭⠳⣭⣾⣿⣿⣿⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣿⣿⣿⣷⣶⣤⣾⣿⣿⠟⠋⠉⠀⠉⠉⠙⠻⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⡘⢦⢩⢒⡍⢦⡙⢦⣙⠲⡌⠶⣱⢆⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠴⢁⠎⡰⠌⢢⠘ ⡳⢎⡞⡵⣚⡭⢞⡲⢵⣊⠶⡳⢬⣳⣿⣿⣿⢋⡴⢍⢎⡱⢎⣙⠦⡒⠴⡂⣍⣩⣙⣛⣻⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠉⠀⠈⠉⢻⣿⣿⣿⣌⣥⣮⣼⣤⣽⣢⡌⠳⣌⠳⣌⢯⠢⢿⣿⣿⣷⢶⣦⣄⣀⣀⣀⣠⣴⣶⡋⠔⡡⢢⢁⠎⡰⠌⢢⠡ ⡽⣩⢞⣱⢣⢞⡣⢏⡳⡜⣭⢳⢣⣿⣿⣿⢃⢇⡚⢬⢊⠖⡩⢆⠳⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠨⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⢷⡈⢎⠳⡹⣿⣿⣿⡳⣎⠿⣹⣛⢯⡻⡵⢫⣷⡌⠔⡡⢂⠜⡠⢃⠆⡡ ⣳⢱⡎⢧⡛⣬⡝⣭⢳⣙⢦⣋⣾⣿⣿⡟⡌⢦⡙⢆⡫⢜⡱⢊⣿⣿⣿⣿⠟⠋⠉⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠀⠈⠹⣿⣿⣿⣎⢱⢋⡵⢡⣿⣿⣿⡷⣭⣛⣥⣛⢮⡳⣝⡳⣎⢿⣄⠣⡘⢢⠑⡌⢢⢁ ⢧⢳⡹⣣⢝⡦⡝⢶⡩⢞⡬⢧⣿⣿⣿⡑⣎⡣⣜⠼⣐⣣⣲⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣆⡹⢰⠃⣽⣿⣿⣷⡓⢾⠴⣫⢞⡵⣋⢶⡹⣎⢿⣆⢑⠂⡉⠴⡁⢎ ⣏⢶⡹⡲⢭⠶⣹⢣⡝⣣⢞⣱⣿⣿⣿⢰⢣⣱⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣹⢫⡞⣵⢫⡞⡽⣎⢷⡹⣎⠿⣎⠀⡘⠔⠁⡈ ⢞⢦⣛⠵⣋⠾⣥⢫⡼⣱⡚⣼⣿⣿⡟⣬⣾⣿⣿⡿⠛⠉⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢟⡍⢦⡱⢌⡭⣛⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠻⢿⣿⣿⣿⣿⡜⣧⡝⣮⢳⣹⢳⢎⡷⣹⡜⢯⣻⡆⠀⠢⠱⣈ ⣏⠞⣜⣣⢏⡳⣜⢣⡞⣥⢛⣼⣿⣿⡯⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢏⡕⣣⠚⢦⡙⡬⢜⡩⢶⡙⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡜⣶⡹⢎⡷⣭⢳⣫⢞⡵⣚⢧⣳⢻⡔⠢⣀⠡ ⢮⡝⡺⣔⢫⠵⣎⠗⣎⢧⢫⣼⣿⣿⣧⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢣⠚⡴⢡⠛⡴⣉⠖⣩⠜⣆⠻⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣞⣥⡟⣭⠶⣭⢳⣣⢟⡼⣹⠮⣵⢫⣞⠐⡄⢃ ⢧⢼⢡⣉⢼⡹⣈⢿⡸⡌⣧⢸⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠡⢏⠹⣠⠏⡸⢤⢁⡼⢁⠼⣀⢏⣠⢉⡹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣧⡿⣸⢹⡌⣧⣉⡼⢡⣇⢿⡸⣇⡏⠸⡈⠄ ⣏⠮⢧⡹⢆⡷⣩⠖⣧⡛⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣃⢏⠼⣑⠦⣩⡑⢎⡼⣰⣭⣶⣵⣮⣴⣃⠎⢻⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡵⣫⠞⡵⣎⠷⣋⡞⣎⢷⡙⢢⠑⡬⠘ ⢮⣹⢣⡝⢮⡱⣇⡻⢴⡙⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢎⠼⣘⡌⢖⣡⠚⣍⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣂⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣦⣴⡀⢀⠀⠀⠀⢹⣿⣿⣿⣳⣯⡷⠾⠯⠷⠿⢞⣋⡔⢡⢊⠔⡡ ⢧⢣⣛⣜⢣⠗⣮⠹⣖⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⣿⣿⣿⢃⢮⠱⡡⢎⠣⢆⡛⣼⣿⣿⡟⣡⠒⣼⣿⣿⣿⣿⡿⢟⡛⣛⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣸⣿⣿⡇⠀⠀⠈⠀⠈⠉⠀⠀⠈⠉⠐⠊⠴⠁ ⣫⢧⡓⢮⡹⢞⡥⣛⢦⣹⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣌⢣⠳⣌⠛⣤⠣⣿⣿⣿⣧⠑⣽⣿⣿⣿⠟⣡⠚⣔⠣⢥⠳⣌⢳⣙⢿⣿⣿⣿⡿⢛⡭⢩⠬⡱⢬⢌⡍⣛⢿⣿⣿⣿⣦⠀⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⡵⢪⣝⢣⡝⣺⠴⣋⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠁⣻⣿⣿⣿⠰⡌⡖⣣⢬⠹⢤⢓⡜⣿⣿⣿⣿⣿⣿⣿⠧⠞⡥⣋⠦⡛⣌⠳⡌⠶⢬⡊⢿⣿⣿⣿⠠⣍⢣⢚⡱⢊⠶⣘⠴⣊⠽⣿⣿⣿⡆⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⣝⢣⣎⠗⣮⣱⢋⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡆⡱⢎⡴⢊⡝⣢⠣⡜⣌⢛⠿⣿⣿⣿⣿⢈⠧⣓⡌⢖⡱⢌⡳⢸⡡⢇⡛⢼⣿⣿⣿⣿⣶⣍⢲⢡⢏⡲⢡⢎⡱⣊⢽⣿⣿⣿⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢳⢎⡻⣔⢣⢏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣕⠌⣲⠩⡜⡰⡍⡜⣌⢓⣊⣼⣿⣿⣿⡌⢎⡱⡘⡜⢢⡙⡔⣣⠱⢣⡙⣾⣿⣿⣿⢿⣿⣿⣧⠣⢎⢲⠱⣊⡕⢎⣼⣿⣿⡟⠀⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⢧⣋⠶⣍⠞⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣧⣵⣥⣾⣶⣾⣿⣿⣿⣿⣿⣿⣷⣌⠱⣙⠬⢣⡙⢦⢡⣫⢝⣼⣿⣿⣿⢇⢊⣿⣿⣿⠱⡩⢎⡱⠎⡜⢢⣿⣿⣿⡧⠀⠀⠉⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢞⢦⣋⠾⣌⣿⣿⣿⠟⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢿⣿⣿⣿⣶⣍⣊⡕⣚⣍⣮⣵⣿⣿⣿⣿⣷⣮⣿⣿⣿⠏⡵⢡⠳⢬⡳⢭⣿⣿⣿⡟⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠶⣩⠳⡼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠿⠿⠿⣟⠻⢥⢋⡴⢩⢎⠧⣵⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣎⢳⡍⢷⡩⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⣿⣿⣿⣯⡔⣩⢓⡫⢱⣌⡚⡤⢋⢴⡣⣩⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴ ⣎⢳⠺⣥⢛⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⣙⠴⢃⠦⡱⢊⣝⣥⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⢀⣀⣠⣤⣶⢿⣹ ⢮⡍⡗⣎⠧⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢻⡟⡿⢿⣏⢿⡱⣏⢾⡱ ⡳⢎⡽⣌⢳⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⡿⠿⠛⠋⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡳⡽⣙⢧⣞⣣⢟⡼⣣⣛ ⣝⠺⡴⣙⢎⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢳⡝⣭⢖⣮⢳⣎⢷⣣⢏ ⢮⡝⡼⣩⠞⡼⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⣿⢏⡷⡹⢎⡾⣜⡳⣎⠷⣎⢯ ⡳⣜⢣⢧⡛⢶⣹⣿⣿⡿⠀⠀⠀⠀⠀⢺⣿⣿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⢰⣿⣿⣿⡿⣫⢞⡵⣫⢟⡼⢎⡷⣭⢻⡜⣧ ⡳⢎⣏⠶⣭⢓⣾⣿⣿⡃⠀⠀⠀⠀⠀⣹⣿⣿⠟⠻⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠆⠀⠀⠀⢻⣿⣿⣷⣙⢮⣓⢧⡻⣜⢯⡜⣶⢫⡞⡵ ⣝⠳⣎⡳⣬⢣⢿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⡿⣬⢳⡝⣮⢳⡝⣮⡝⢶⣫⢞⡽ ⢮⡝⢶⡙⢦⢏⣎⣿⣿⣿⣆⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⡟⠀⠀⠀⢀⣾⣿⣿⠿⣜⣳⢺⡱⣏⢾⡱⣞⢧⣛⢮⡳ ⡳⢎⡧⣝⢣⡞⢶⡘⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⢠⣾⣿⣿⡿⣛⡼⡲⢯⡵⢫⡞⣵⢫⣞⡹⣎⠷ ⡝⡮⢵⢎⡳⣜⣣⡝⢦⣹⣿⣿⣟⠀⠀⠀⠘⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⢀⠤⢀⠌⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⣠⣴⣿⣿⣿⢿⡱⣏⢶⣹⢳⠞⣽⣚⡵⡳⣎⠷⣭⣛ ⣳⢱⢺⡜⣣⠽⣩⢓⡮⡝⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⣏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣈⣀⣌⣤⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣿⣿⠁⠀⣿⣿⣿⣿⡻⣜⢧⡻⡜⣯⠞⡶⣭⣛⡵⣣⠟⡶⣭⣛ ⢧⢫⢳⠼⣡⢯⡱⣋⢶⡹⡹⣿⣿⣿⣦⡀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣿⢭⣳⡹⢎⡷⣹⠖⣯⢳⢧⡳⣭⣓⢯⣳⣓⢮ ⣏⢞⣣⢯⡱⢮⡱⣝⡲⢵⠳⣍⠿⣿⣿⣿⣷⣤⣀⠹⣿⣿⣿⣄⣤⣶⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣥⣶⣾⣿⣿⣿⠯⣞⡥⣏⡟⣼⢣⡟⣼⢣⡟⢶⣣⢟⣬⢳⣎⠷ ⡞⣬⣓⢮⡱⢧⡝⣬⠳⣍⡻⣌⠟⣜⠻⢿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠟⣸⣿⣿⣿⠿⣏⠷⣛⡼⢮⡵⡺⣵⢫⡞⣵⢫⡞⣧⡝⣾⡸⣳⢎⡟ ⣝⡲⣍⠶⣙⢧⡚⡵⣛⢬⣓⢮⡛⣜⢫⠶⣩⢝⡻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣴⣾⣷⣶⣤⣴⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠿⢿⣿⣿⣶⣦⣀⣰⣿⣿⣿⣟⣥⣾⣿⣿⣿⢭⡳⣭⢻⡱⣝⢶⡹⣵⣋⢧⡻⣜⢧⣛⢶⡹⣖⡝⣧⢻⡜ ⠚⠵⠎⢯⣙⣎⣗⢳⢭⠺⣜⢦⡝⣎⢧⣛⣼⠮⠷⠍⠛⠻⢿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠛⠿⡿⠋⠉⠉⠉⠙⠻⣿⣿⣤⣴⣶⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣶⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡹⣎⡗⡧⣏⢷⡹⣎⢷⢣⡞⢧⡻⣜⢧⣛⢮⡳⣭⢞⡼⣣⢟ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠛⠋⠉⠛⠻⣿⣿⣾⣿⣿⣶⣶⣶⣶⣶⣦⣤⣀⡀⠀⠠⢀⣤⣾⣿⣿⠿⠿⢿⡟⠉⠁⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣛⢯⢏⡷⣹⢣⡗⣳⢺⡵⢫⡞⣵⢫⡞⢧⣛⢧⡻⣜⢧⣛⢮⡵⣋⢮⡳⣝⢮ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠉⠁⠉⠻⠟⠉⣙⣙⣛⡿⢿⣿⣦⣰⣿⣿⣿⣭⣤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡮⣝⢮⢳⡭⣳⢞⡵⣫⢞⣧⢻⡜⣧⣛⢧⣛⢮⡳⣝⢮⡝⣶⡹⣝⢮⡳⣝⢮ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢿⣿⣷⣿⣿⣿⣿⣿⠟⣛⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡹⣎⡗⣳⡝⣮⢳⡝⡾⣬⢳⡝⡶⣹⠮⣝⢮⡳⣝⢮⡝⣶⢹⣎⠷⣹⢎⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢱⣺⣢⣶⣿⡿⠟⣛⢿⣷⣾⣴⢩⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣽⡳⣞⢵⡺⢵⣋⢾⡱⢧⡻⣜⡳⣭⢳⡝⣮⢳⡝⣮⡝⣮⢳⣎⡟⣵⢫⢞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣷⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡸⠤⢿⣧⣿⣧⢹⣢⢎⣿⣿⠟⢤⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣎⠷⣭⢳⡝⣮⡝⣧⢻⣜⡳⣭⢳⡝⣮⢳⡝⣶⡹⢎⡷⣚⡼⣣⢟⢮ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣷⣶⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠹⢢⢋⣽⣿⣶⣶⣿⣿⣦⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⣾⣿⡿⢡⣿⣿⣿⣭⣻⣜⣳⠺⣥⢻⣜⡳⢎⡷⢭⣳⡹⢎⡷⣹⢲⡝⣯⡜⣧⢳⡝⣮⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⢀⡏⣛⠻⢻⣿⣿⣦⡐⠀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣿⣿⣿⡿⣛⠻⢿⣿⣿⣉⠀⠀⠀⠀⣠⡀⠀⠀⣀⣀⣀⣠⣾⣿⣿⣿⣿⠿⣋⡕⢣⣿⣿⣿⣿⣿⣷⣧⢻⣜⡳⢮⡝⣯⠞⣧⢳⡝⣏⠶⣭⢳⡞⣵⢺⡵⣫⢞⡵⣫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⢨⠒⡥⢫⢖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀⣠⣼⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣀⣀⣨⣵⣾⣿⡟⡱⢌⠳⡌⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣆⠲⢤⡓⢤⡏⣼⣿⣿⡟⠛⣿⣿⣿⡯⠾⠽⠧⠿⠾⠽⠾⠷⠟⠞⠛⠓⠛⠚⢓⡛⠚⠓⠛⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠉⢻⣿⣿⣇⠹⣐⢣⣿⣿⣿⢏⢶⠩⣍⠲⢤⡙⠻⠿⣿⢿⣿⠿⡿⢿⣿⣿⣶⣿⣿⣿⣾⣿⣿⢿⣿⡿⠿⢟⡥⢚⣥⣋⡕⢢⢿⣿⣿⡏⡹⣉⠏⡥⢋⡝⡩⢇⠲⡔⠼⣿⣿⣿⡎⢦⡹⣚⣼⣿⣿⡿⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠈⣿⣿⣿⣧⣡⣿⣿⣿⢏⣎⢏⠳⣌⠓⠦⡍⡝⣒⠦⠲⣌⠲⣑⢎⡩⢝⠫⣍⠭⣋⠽⣉⠖⣌⠲⣌⠭⣇⣳⣿⠟⠻⣿⣦⢻⣿⣿⡧⣑⢎⡹⣐⢫⠔⡣⣍⠳⡸⣑⠺⣿⣿⣿⣦⣷⣿⣿⣿⠟⠁⢀⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠈⠻⣿⣿⣿⣿⣿⢏⡎⡴⢋⠵⡨⢝⠲⣉⠖⡱⢎⠳⣌⠳⡜⢢⠕⣎⠳⣌⠲⢥⢣⠣⢞⡌⠳⡌⢞⣣⢻⣷⣆⣠⣿⡗⢺⣿⣿⡷⢡⠚⣔⠣⢎⡚⡱⣌⠣⡕⢎⡱⠹⣿⣿⣿⣿⡿⠛⠁⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢈⣿⣿⣿⢏⡼⡰⢅⡏⢲⣉⢎⡱⡱⢊⡵⢊⡵⢌⠳⣌⠳⣘⠦⡓⡬⢓⡬⠲⡍⢶⡘⣣⠝⣢⠖⡱⢞⢛⡛⢥⢊⢽⣿⣿⣿⢡⠫⡔⢫⢬⠱⡱⣌⠳⡜⢪⠜⣵⠹⣿⣿⣷⡀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⢀⣾⣿⣿⢏⡞⡼⡑⢎⡜⣡⢚⡤⢣⡙⢦⣑⠣⣜⢪⡱⢌⡳⢌⡣⢕⡩⠖⣌⠳⡜⣢⢱⡡⠞⣤⢋⡜⣡⣎⡙⢆⡫⢜⣿⣿⣿⢠⢣⡙⢆⣣⢣⡱⣌⠳⣘⢣⡙⣌⢳⠹⣿⣿⣷⡄⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⣾⣿⣿⡏⢎⠴⢣⡙⡌⠞⡤⢓⡌⢣⡙⢆⢎⡱⡘⢦⠱⣉⢖⡡⢝⢢⡙⡜⣌⠳⣌⠱⢆⡹⣘⠔⣳⣿⠟⠛⣿⣎⡿⠸⣿⣿⣿⢂⠧⡙⢦⠱⣂⠳⣌⠣⡍⢦⡑⢎⡍⣳⠹⣿⣿⣷⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣟⣬⣉⢎⣵⣶⣿⣶⣭⡪⢜⡱⢪⠍⣆⠳⡙⣌⠣⡍⢦⡙⢎⠦⣹⡐⢎⠵⣈⠟⣌⠲⣉⢎⡹⣷⣄⣠⣾⡏⡟⢱⣿⣿⣿⡊⡵⣉⠮⣑⠎⣵⣈⣳⣘⠅⣎⣥⣾⣦⣧⣽⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⣿⡿⠟⠛⠻⢿⣿⣶⣷⣷⣾⣤⠳⡑⢎⡱⢌⣣⣜⣊⠵⣢⠹⣌⠎⣕⡚⣌⠳⣉⢦⠱⢭⣛⠛⡱⢚⡜⠰⣿⣿⣿⡑⢦⠱⡓⢪⣾⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⠀⠀⠈⠉⠀⠀⠀⠀⠈⢻⠛⠋⠛⢻⣿⣷⣿⣆⣿⣿⣿⣿⣿⣿⣆⣇⣈⣸⡀⢳⡈⢳⣈⡖⢹⣶⣾⣿⣶⣏⣈⣷⣿⣿⣿⣸⣈⣱⣾⣿⣿⡏⠁⠀⠀⠉⠋⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠿⣿⡿⠛⠉⠉⠙⢻⣿⡿⠿⢿⣿⣷⣜⣡⣌⣴⣿⣿⠿⠛⠿⢿⣿⡿⠟⠻⢿⣿⣿⣿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢻⣿⠟⠻⢿⡟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣶⣶⣶⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣷⣶⣿⣿⣷⣄⣠⣼⣿⣷⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣯⣀⢀⣠⣴⣤⡀⢀⣠⣾⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣿⡿⠟⠋⠛⠿⠿⣿⣿⣧⣄⣀⣤⣾⣦⡀⠀⣠⣾⣶⣦⣶⣦⡀⢀⢀⣤⡀⠀⠀⠀⣠⣦⣀⢀⣠⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⣿⡿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⢿⣿⣿⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡐⠒⢤⠙⡨⠑⡌⠹⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⠏⡐⢆⡒⠦⠤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡡⠜⠰⢡⢉⠆⡱⢐⠩⠰⠡⠌⠹⢿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣶⣶⣾⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⡡⢊⠜⡠⠜⡠⢃⠜⠢⡅⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠊⠔⣉⠆⠣⢌⠢⡑⣌⠢⢅⠣⣉⠒⠤⣈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⠩⠰⠌⡔⢡⠊⡔⢡⢂⡱⢈⡱⠌⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠒⠡⠢⠱⠌⡒⠤⡉⢆⠡⣊⠔⢢⡐⠤⣉⢉⢩⠙⣉⣋⡙⢋⡙⣉⢋⠍⣉⠡⢡⠐⡄⢂⡉⣉⠉⡍⡙⣉⢋⢋⡙⣉⢋⠍⣉⢩⠐⡄⠒⡌⢢⣉⠱⢌⠰⠁⠚⠐⠃⠂⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠿⠿⠿⣶⣦⣄⣀⠀⢀⣀⣀⣀⣀⣀⣀⣰⣿⣟⣿⣻⢿⣷⣤⣾⠿⠟⠋⠉⠙⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠉⠙⠻⠿⠟⠛⠛⠛⠛⠛⣻⣿⣟⣾⣳⣯⣟⣾⣿⡆⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣞⡷⣿⡿⣿⣿⡿⣿⣿⣶⣤⣴⣶⣾⣿⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⢿⣿⣿⣿⣟⡿⣧⣟⡿⣿⣿⣻⣟⡿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣯⣟⣾⣿⣿⣯⣟⡷⣯⢿⣿⣿⣿⡾⣽⣻⡷⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠻⠿⠿⢿⣿⣿⣿⢿⣻⢷⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣯⣿⣽⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⠀⠀⠀⠀ ⢀⣀⣀⣸⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣿⡶⠶⠶⠦ ⠉⠉⠉⠉⣿⡏⠉⠁⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⣹⣧⣤⡄⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠒⣾⡿⠶⢦⣤⠀ ⠀⠀⠚⠋⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⢠⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⣾⣿⣄⡀⠀⠀⠀ ⠀⠀⠀⣠⡴⠟⠋⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠁⠀⠉⠛⠓⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠻⠷⣶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢱⠖⢋⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢁⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠘⣦⣾⣄⣀⡴⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡐⢀⠀ ⠀⠀⡀⠀⡀⣿⣿⣿⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠐ ⠶⠶⠶⠷⠾⠛⢁⣿⡱⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣼⣿⠟⠉⣿⣶⢮⣽⣷⢶⣦⡄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠀ ⣄⣀⣀⣀⣠⣴⠿⠣⠑⠈⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢾⣿⣿⢯⣿⡽⣦⣤⡄⠀⡠⠴⢟⣿⣶⢻⡼⣝⡲⡐⢄⠠⠀⠄⠠⠐⠠⢈⠔⡁⠆⡁ ⠉⠉⠉⠉⠁⠈⠀⠀⠀⠁⠂⠀⠀⢀⠀⡁⢀⠀⠀⠀⠀⠀⠈⡜⣫⣷⣿⣾⣻⣵⣻⡿⣿⣟⣼⣟⣿⢯⣏⢿⡱⢣⠍⠂⢀⠁⠈⠄⡁⠆⣁⠢⠐⢂⠡ ⠀⠀⢀⠠⠁⠒⠈⠄⠀⠀⠀⠀⠀⠂⠠⠐⠠⢀⠠⣀⣄⣠⡤⠞⠋⠙⠿⢿⣉⣿⡟⠛⠿⣽⠿⡟⢏⠳⠊⠵⠈⡁⠠⢈⠀⠠⢈⡐⠰⠈⢄⢂⠩⠐⢂ ⡀⠂⠌⠠⣀⢂⠐⡀⠠⠀⡀⠀⠀⠠⢀⠂⠄⡈⠄⢻⡿⠋⠁⠀⠀⠀⠀⠈⠙⠻⠃⠀⠀⠙⢦⣁⠈⠀⡀⢀⠀⡁⠂⠈⠐⠠⢈⠁⠆⠒⡈⢌⡐⢂⠌ ⡰⠐⡌⡰⢀⠆⡒⢠⢁⡐⣀⠂⡌⡐⠤⢈⠐⢠⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⣦⢁⡐⡀⠆⠤⢁⠂⠌⡐⠠⢈⠄⠱⡐⢂⠔⡡⢊ ⠀⠁⠢⠡⣉⠒⡉⢆⠒⡴⢠⠃⡔⢁⠊⠄⡈⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⠀⢸⣇⠰⡈⠜⡠⢃⠜⡠⢁⢃⠢⠌⡐⠠⠁⠌⡐⠂ ⠀⠀⠀⠐⠀⠀⠡⠈⠊⡔⢡⠊⡔⠂⠌⡐⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣿⠤⠑⢌⠰⠁⠎⡐⢁⠂⠐⠀⠄⠀⠁⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠡⢀⠁⠂⠔⡠⢀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⡀⠆⠤⡉⠔⡈⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠸⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⡿⠇⠀⢈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠑⢴⣷⡄⠀⠀⢿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣠⡿⣷⣶⣤⣤⣤⡄⠀⠀⣠⡤⠤⠴⠶⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠶⣾⣿⣆⣬⣿⠇⠈⠉⠉⠉⠛⠛⠛⠛⠛⢇⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⢿⣀⢆⣼⣿⠛⠛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⡑⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⡏⢛⣾⣽⠚⠁⠊⣿⣧⡿⠚⠭⣒⠢⠤⢄⣀⣀⣀⡀⠀⠀⢳⣄⣀⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠌⢂⠁⡈⠐⡈⠔⡠⢁⠂ ⠀⠀⠀⠀⠀⠂⠐⢈⠓⠛⠘⠣⣎⡔⠃⠐⠀⢁⣾⣧⡀⠀⠀⠉⠒⠂⠤⢤⣀⠉⠉⠉⠉⣁⣼⡯⢅⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠌⡱⢈⢆⡑⢢⠌ ⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠐⠁⠀⠀⠆⠰⢺⢽⣻⣿⣷⣶⣶⣾⣄⠀⠀⠀⠉⠈⠁⠉⣠⡿⡑⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠰⠈⡅⢊ ⡒⠀⠀⠀⠀⣀⠈⠀⠀⠈⣰⠣⠔⠀⡀⠰⣂⠀⢈⡐⠉⠊⠉⠙⡛⢿⣿⢶⣶⠶⡶⢚⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂ ⠷⠒⠀⠒⡴⠉⠀⢀⠐⢠⠹⣆⠀⠀⠑⠂⠉⠀⢞⠣⢀⡄⠒⠂⠃⠈⣻⣞⡟⢢⠑⡊⠔⠂⢖⡲⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡳⠦⢄⡀⣀⣀⡐⢢⠹⠖⠋⠀⠀⣈⢳⠶⡚⠷⠚⠟⠾⡜⢆⢀⣀⣾⣿⡟⢾⠣⣽⡾⣝⢯⠶⣙⠧⠓⠜⡳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⠷⡾⣜⣡⠀⣈⠀⠲⡹⢦⠲⡔⢮⢯⡓⠁⠠⢄⡞⣷⠾⣮⢿⡽⣿⣳⣟⢦⡳⣞⡿⣹⢾⡙⠈⠀⢀⠰⡔⢦⠤⠤⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⢢⢳⡑⢮⠱⢫⠜⠃⠴⢤⡀⠈⠉⠀⠺⠴⡼⢶⣧⣿⢯⢷⡳⢮⡙⠯⢷⠯⠷⠱⢎⠳⡅⠊⠈⠁⠉⢉⠓⠌⢂⠐⠠⠄⠄⠂⢀⠀⠃⠀⠀⠀⠀⠀⠀ ⠂⣆⠰⢢⣱⢢⠌⢈⠐⣶⡘⠄⠉⠙⢀⡔⣬⢳⣮⢧⢯⣶⣱⢯⣝⢯⡤⣀⠀⡀⢠⠸⡝⠋⠀⠐⡌⠉⢀⡀⢎⠀⠀⠀⠀⠀⠀⠌⣲⢡⠀⠀⠀⠀⠀ ⠓⠀⢀⡳⣏⠳⠈⠢⠙⢤⣠⡐⢢⡛⢦⠛⣎⠳⣌⢧⣤⣤⣀⠊⠚⠀⠀⢀⣀⢤⣁⠃⠙⠀⠀⢄⡠⣄⣤⣰⣄⢲⡘⠂⠀⠀⠀⡖⠩⢂⠀⠀⠀⠀⠀ ⣀⣤⣞⡵⡁⠃⠠⣌⣵⡂⢄⡉⣆⡙⡞⠷⢂⢡⡀⢈⡜⢧⣃⢆⣖⠲⠂⠀⠈⣀⣀⣀⣀⣀⡴⣫⠓⠈⠀⠀⠀⢩⣄⣀⡀⢶⠛⡞⠀⠀⠀⡀⠷⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⠀⠀⠁⠂⠁⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⠅⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⡄⠁⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠐⠀⠀⡀⠀⠄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠠⡈⠢⠈⡁⡉⠀⠀⠀⠈⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠐⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⡄⠠⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠂⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⡁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠁⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⣿⠿⠛⠉⠉⠉⠉⠻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠁⣠⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣿⣿⡿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡇⠀⠀⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⡿⠇⠀⠀⢹⣿⣿⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀ ⣸⣿⣿⡟⠈⠉⠉⠉⠁⠀⠀⠈⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⢀⣶⣦⣤⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀ ⣿⣿⡇⠀⢀⣴⣾⣿⣿⣿⣿⡿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇ ⣿⣿⣷⣰⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇ ⠹⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠀⠹⣿⣿⣿⣿⣄⠙⠛⠛⠋⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⣰⣿⣿⡇ ⠀⠀⠈⠻⣿⣿⣿⣷⣄⣀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⡇⠀⢀⣼⣿⣿⡟⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣦⣤⣤⣬⣿⠿⠿⢋⣴⣿⣿⣧⣶⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣆⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⠿⠿⠋⠉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣏⣿⣿⣿⠋⣈⣹⣿⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡃⢀⣿⣿⡿⠟⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠙⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣾⣿⣿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣷⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⡿⡟⠙⢏⠙⢦⢹⡍⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⢸⡀⢹⡀⠸⡄⢸⠀⡇⢸⣤⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠓⠳⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠸⣌⢳⡀⢳⡀⣧⣸⣠⣷⣼⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠙⣷⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⢧⣈⣦⣽⠶⣿⣫⣽⡷⠶⠾⠶⠿⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡥⢙⣯⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡛⠛⠲⠶⠦⠴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷ ⣤⠶⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠛⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠦⠤⠤⠤⠴⠖⠛⠋⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠳⡀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡏⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠃⠀⠀⠀⢻⠉⠙⠓⠒⠒⠒⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣿⠀⢀⣀⠠⢝⡚⠁⠀⠀⠀⠰⣦⣤⡶⠶⠾⠂⠀⠀⠀⣠⠔⠒⠒⠒⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠷⣦⣄⣀⠀⠀⠀⠀⣀⣠⣤⠖⠛⠉⠀⠀⠹⣧⡈⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠄⠀⢀⣰⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣦⣤⣌⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⡶⠾⣛⣩⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⢬⣭⡉⠉⠉⠛⢿⠿⠟⠛⣿⣿⡛⠛⠻⣿⣭⣤⣀⣛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⣿⠛⠚⠿⠷⢾⣷⡶⢋⡟⢿⡝⢷⡾⠛⠛⠛⣏⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣉⣹⠃⠀⠀⠀⠀⢠⣿⣉⣾⣀⣈⣿⣖⣹⡷⠀⠀⠸⣏⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃⠀⠀⠀⠀⠀⣀⡼⣛⡇⠉⡀⢉⡟⢧⣄⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⣀⡴⠞⢹⡟⠉⠛⣿⠙⠛⡟⠉⠉⣷⢤⣀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⠖⢾⡏⢹⡄⠀⢸⠃⠀⠀⣿⠀⠈⣇⠀⠀⡏⢀⡽⠛⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠽⣿⡷⠤⠾⢤⣤⢞⣿⡦⣤⠾⠤⠾⢷⣯⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣤⡼⠏⠛⠈⠛⠻⠦⠴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣴⣀⣤⡶⠶⠿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠶⠾⢷⣶⣤⣠⣤⣤⡶⣿⣿⢿⣽⣻⣿⡅⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠰⣿⣯⢿⣿⣿⣿⢿⣿⣶⣿⣿⣿⡦⠀⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⡿⢿⣯⡿⣾⣿⣿⣾⣽⣿⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣻⣾⠿⣦⠀⠀⠀ ⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣿⣆⣀⣀ ⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠈⠋⣿⠍⠀⠀ ⠐⠒⠻⣿⠛⠁⠀⠀⢸⣿⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⠟⠀⠀⠀⢘⣿⠷⠲⠄ ⠀⠀⣤⣽⣷⠒⠀⠀⠀⠁⠀⠀⠀⠀⠻⠭⠏⠀⠀⠀⠀⠀⠀⢀⣰⣾⢯⣄⣀⠀ ⠀⠀⠀⢀⣸⣷⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏⠉⠛⠛⢾⣍⠀ ⠀⠀⠀⠿⠉⢀⣨⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣶⡶⣿⣿⡿⣿⣄⠀⠀⢀⣿⠀ ⠀⠀⠀⢀⣴⣿⣿⣻⣿⢿⡱⢎⡿⣿⣟⣿⣻⣿⢏⡳⡹⢿⣿⡽⣿⣦⣤⠞⠃⠀ ⠀⠀⢠⣿⠁⠀⠙⢿⡟⡦⡝⢮⡜⣱⢫⢏⡽⣘⢮⡱⣍⡛⣿⣿⠿⠋⠋⠀⠀⠀ ⠀⠀⠨⣿⡀⠀⠀⣾⠻⣔⢫⢖⡹⢆⡏⡞⡴⣍⠶⡱⢎⡵⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢻⣿⡹⣌⡳⢎⡵⢫⡜⣱⠳⣌⡳⣍⡳⡜⡭⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠷⠻⠷⠿⠾⠷⠿⣿⠿⠾⠷⠿⠞⠟⠳⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠷⢶⠦⠶⢴⢦⡞⠻⢶⠦⠶⠴⢦⠶⠟⠁⠀

ᴮᵃᵈᶻᵗ⁻ᵐᵃʳᵘ ☠︎︎༒︎✞︎🕸𖤐 ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⣀⣤⣴⣶⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠛⠋⠉⠹⣿⣿⠏⠉⢻⣿⣿⡏⠉⠹⣿⣿⠏⠉⠙⠛⢻⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⣤⣤⣤⣴⣾⡿⠋⣉⠩⢿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠖⢋⠩⠙⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠙⠋⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠠⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⡀⠠⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢂⠐⢈⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⠐⠠⢁⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣢⣼⠿⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠙⠉⠙⠶⠮⣤⠾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 🇰‌🇺‌🇷‌🇴‌🇵‌🇮‌ ˚˖𓍢ִ໋🧚🏻₊˚ʚ 🪷 ₊˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡀⠈⣿⣿⠁⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢀⣿⡏⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⢀⣼⣿⣷⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⡆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡟⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠉⠛⠿⣿⣿⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⢀⣴⠟⢛⡛⢷⣆⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠟⠛⠉⠀⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⡇⠀⠈⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣦⡀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡘⣧⡀⠀⠖⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠐⠂⠈⢿⡄⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⡈⠙⠻⠛⠋⠀⢴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣆⠀⠀⠀⠀⣼⠇⣾⣿⠃⠀⠀ ⠀⢀⣤⣤⣼⣿⡟⢿⣿⣦⣀⠀⠀⠀⠈⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠀⠻⢷⣬⡴⠟⢋⣼⣿⡟⠀⠀⠀ ⠀⠸⣿⣿⠿⠟⠁⠀⠙⠿⣿⣿⣶⣤⣄⣀⡀⠙⢿⣿⣷⣄⠀⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣀⣀⡀⠀ ⣴⣾⣿⡿⠀⠀⠀⠀⠀⣠⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣭⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠘⠿⢿⣿⣿⠀ ⣿⣿⣅⠀⠀⠀⠀⠀⣴⣿⠟⠁⣼⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄ ⠈⢿⣿⣷⣄⠀⢀⣾⣿⠏⠀⢰⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠘⣿⣧⡀⠀⠀⠀⠀⠀⢙⣿⣿ ⠀⠀⠙⠿⣿⣿⣿⡿⢃⣠⣤⣿⣿⣿⣿⣿⣿⣶⡄⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡀⠹⣿⣧⠀⠀⠀⢀⣤⣿⣿⠏ ⠀⠀⠀⠀⢀⣿⣿⠁⣾⣿⠿⣿⣿⣿⣿⠃⠙⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠹⣿⣧⣶⣾⣿⡿⠛⠁⠀ ⠀⠀⠀⢰⣿⡿⣿⣿⣿⡿⠀⠈⠛⠛⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⡋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣷⣦⣄⡀⠀⠀⣀⣤⣶⣿⡿⠋⠀⠈⣿⣿⣆⢠⣴⣶⣦⣄⠀⢀⣴⣶⣦⣀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⠿⠛⡉⠀⠀⠀⠀⠈⠿⣿⣿⡿⠛⠿⣿⣿⣿⡿⠛⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ GᑌᗪETᗩᗰᗩ 🌙🐥🌼🌟🥟✧˚ ༘ ⋆｡♡˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣧⠀⠀⢀⣴⣿⡿⢿⣛⡛⢏⡛⣛⠻⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣠⣿⣤⣾⣿⡿⢯⡜⢥⠒⣍⠲⢥⠣⣝⢪⡑⡎⣝⡻⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡼⣠⠸⡜⢻⣀⠿⣀⢟⡸⢇⡿⢸⢠⠻⣜⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣽⣿⣛⣾⣧⠓⡜⡥⢊⡖⣻⣾⣳⡺⣌⢻⣐⢻⡞⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢧⣿⣿⣿⣿⣿⣿⡿⣙⣴⣍⣧⣘⠻⢿⣿⣿⠜⣢⠥⣻⡇⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡿⢣⡍⡖⡹⢣⣶⣿⣟⣛⣛⣿⣷⡧⣉⠦⣋⡔⢣⡹⣷⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢇⡣⢝⡰⢃⡇⢮⠹⡏⢟⡫⢻⠝⡰⢥⠓⢦⡙⢦⠱⣻⡄⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢊⠖⡣⡜⡱⣘⠆⡏⢼⢨⣑⢣⢚⡱⢊⡝⢢⡙⢆⡫⢔⠿⡶⢗⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣌⡏⠴⢣⡑⠮⡜⡜⢢⠧⣘⢆⠳⣌⢣⠜⣣⣿⡮⣑⠎⡎⡵⢪⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⣌⠳⣡⠝⡲⡑⢮⠱⣊⠕⣪⠱⡌⡖⣩⣶⣿⣷⣭⣚⠴⡱⣩⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡑⢎⡱⢆⡹⢔⡙⢦⡙⡴⢋⡴⢣⢱⣺⣽⣿⣻⢧⣿⡏⡖⡱⣂⢿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠟⠋⣿⣿⡘⡜⡰⢍⡲⢩⠜⡢⣕⢪⠱⣌⣣⣷⣿⢯⣝⣭⣿⣿⡝⢲⢡⢣⣿⡇⠈⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠉⠁⠀⠀⠀⣿⣿⢬⡱⣉⠖⣡⢇⢫⠔⡎⡬⢓⡴⣿⣿⣷⣾⡿⢟⡽⢤⡙⠦⣍⠶⣿⡇⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢧⡑⢎⡹⡐⡎⢎⠞⡴⢱⢃⠖⣹⠻⣿⡖⣩⠖⣘⠦⣙⠲⢬⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢷⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡟⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⡜⣡⢎⠣⢖⡩⢜⡡⠞⣌⠓⣎⠹⣄⢫⣽⣷⢡⡚⢥⠚⡴⣙⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡀⠀⠀⠀ ⠀⢠⣿⡿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⢹⡘⣔⣪⣙⣦⣽⣦⣽⣼⣬⣳⣌⣗⣼⣿⠟⣍⠧⡜⢪⣕⣮⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢶⡄⠀⠻⣿⣍⠀⠀ ⢴⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣭⣺⣵⣾⡿⠿⠛⠋⠉⠉⠉⠉⢉⣿⣿⡿⢿⣙⣺⣴⣷⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡋⢅⠊⡔⣻⠀⠀⠹⣿⡆⡀ ⠈⠘⣿⣷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣠⡤⣤⡤⠶⡛⢍⢢⣑⣌⣒⣤⠟⠀⠀⠀⣿⣏⡇ ⠀⠀⠈⢻⣿⣶⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⢡⢡⠂⡔⢰⠀⡆⠑⠘⠊⠉⠉⠉⠉⠀⠀⠀⠀⣴⣿⡇⠃ ⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⣶⣶⣶⣤⣤⣤⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠣⠘⠀⠊⠀⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣾⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣶⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⡾⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣶⣶⣾⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 𝖯𝗈ɕ𝗁ɑɕɕ𝗈 🍩.𖥔 ݁ ˖🐻 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣟⣿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⡿⠏⠁⠀⠀⢠⣴⣤⠀⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣾⣿⣷⣶⣤⠽⣿⣷⠭⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠋⠉⠉⠉⠈⠉⠛⠀⠀⠉⠀⠁⠀⢤⣄⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⣆⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟⠻⠿⣿⣦⣼⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⣼⣿⡟⠛⠉⠀⠀⠀⣠⣾⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠹⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⢿⣟⣻⣿⣟⢷⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣤⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⡆⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⡖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣌⠉⠁⠀⠀⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣈⣙⣻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠿⠟⠻⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣽⣿⡿⣿⣷⣿⡿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣷⡄⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣽⣿⢿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⢿⣹⣿⡿⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⢿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣷⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠳⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣯⠉⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⠿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠰⣿⣿⣿⣶⣶⣤⣴⣤⣤⣤⣤⣶⣶⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ redo(still by the og creator)⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣉⢉⡉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⢠⡴⠇ ⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⢸⠀⠀ ⠠⡏⠀⠈⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠙⠒⣦⠀⠀⠉⠉⠛⠒⠲⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⣀⣠⡤⠶⠖⠒⠒⠒⠒⠒⠶⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡤⠖⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⣿⡆⠀⠀⣾⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣛⡀⣤⣀⢩⡽⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣠⡴⢤⣀⠀⠈⠓⠛⠛⠚⠀⣀⡤⠞⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠈⠛⠦⣄⣀⣀⡤⠞⠉⠀⠀⠀⠀⢀⣠⣞⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⠃⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠘⡆⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡇⠀⠀⠉⣉⣽⠷⢦⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢿⣿⡿⣿⠀⠀⣿⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢷⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠯⡿⠟⠀⢠⡀⠀⠀⠀⠉⡟⠹⣆⣠⠇⣠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠳⢦⠤⣤⠶⣯⠀⠀⠀⢀⡞⠁⠀⠀⠙⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡳⢤⣀⡀⠀⠀⠀⠀⢸⠀⢿⠀⣸⠀⣀⣀⣸⣇⠀⠀⠀⢀⣟⣾⡻⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠺⠿⣭⡟⠛⠛⠛⠳⠤⣴⡋⠉⠉⠁⠀⡾⡟⠂⠀⠸⡿⠉⠛⠁⢀⣠⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⢳⣾⣥⢴⣾⣄⣀⡤⠞⠋⠉⠛⠲⠦⣟⣽⡟⠀⠀⢀⡇⠀⠰⣞⡉⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣼⠃⠘⠿⢾⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠦⠤⡾⠁⠀⠀⣸⠃⢀⡶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠷⠀⠀⢀⡼⣇⠀⠀⠀⣴⠞⠉⠉⠙⠓⠀⠀⠀⢹⣤⣤⠞⠃⣠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⣯⡞⠛⠦⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠤⠴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣠⡴⠟⣞⡄⠀⠀⢀⣧⠤⠀⠀⠀⠀⠀⢠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⡤⠿⠶⠦⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣶⣶⣶⣶⣶⣤⣀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀⣀⣠⣤⣶⣶⣶⣶⣦⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⣀⣙⣿⡿⠋⠛⠛⠋⠁⠈⠛⠛⠛⠻⣿⡟⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⣀⣼⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢿⡀⢀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢻⡏⠀⠀⢀⣀⡀⣠⣾⣿⣶⣦⣤⣶⣿⣶⡀⠀⠀⠀⠈⠛⣿⠛⢷⡀⠀⠀⠀ ⠀⠀⣀⡽⢷⣦⣉⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡏⠉⡽⣖⠾⣥⣀⠀⠀ ⣴⣿⣿⣿⣿⣇⣿⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣇⣿⣿⣿⣿⣷⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠙⠿⣿⣿⣿⣯⡛⠿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⣷⣤⠀⠀⠈⠉⠉⠁⠀⠀⣿⣿⣧⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠈⠉⣿⣿⣿⣿⣿⡀⠐⠛⠉⠀⠀⠀⠀⢖⡦⠀⠀⠀⠙⠛⠃⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⡏⣹⣯⣙⡏⢹⣿⣿⣿⡿⠿⡿⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⡯⢯⣽⢹⣿⣿⣿⣿⣇⡀⣳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⣿⣇⣀⣵⣾⣿⣿⣿⡷⠞⠀⠉⢡⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢯⢸⣷⣿⡛⣩⣽⣿⣿⣿⣷⡄⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠵⠾⣿⣍⣾⢾⣻⣿⣿⣿⣶⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡟⠈⠙⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⢻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠉⠉⠉⠙⠓⠲⢤⣀⡀⠀⣼⢧⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠬⠽⣶⣿⠦⣡⣞⣠⠴⠖⠶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⢀⣠⠶⠚⠋⠁⠀⠀⠀⠀⣀⣠⠤⠴⠒⢚⡿⣿⡋⣀⢦⣄⣠⣾ ⢀⣴⡾⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣾⠋⠁⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⢀⡴⠋⠀⡏⣷⣾⠟⠉⠁⠀ ⣾⠏⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⡀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⢀⣴⠟⠀⠀⣸⠃⢸⠙⣆⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣻⡿⠟⠛⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⠀⠀⢈⢻⣶⣶⡟⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣰⠏⠀⢸⡄⠸⡄⠀⠀ ⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⠟⠛⠛⢻⣇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⠏⠀⠀⣼⠀⠀⣷⠀⠀ ⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠙⢳⣶⣶⡟⠁⠀⠀⠀⢀⣼⠃⠀⠀⢀⡟⠀⠀⢹⠀⠀ ⠀⠀⠈⠙⠿⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡟⠁⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡴⠻⣇⠀⠀⠀⢠⡾⠁⠀⠀⠀⣼⠁⠀⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⣼⣿⠁⢀⡀⠸⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢷⡴⢋⣵⠋⠀⠀⠙⠳⢶⣶⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣆⠀⠀⠉⢳⠀⠀⠀⠀⠘⢷⠤⢤⣴⠆⠀⠀⠀⢾⣀⡗⢀⡴⢋⣴⠛⠛⠛⠛⠻⠶⠶⠶⠿⣧⡀⠀⢀⣼⠋⠀⠀⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⡶⠿⠿⢦⣄⣊⠀⠀⠀⠀⠀⠸⣦⡞⠁⠀⠀⠀⠀⢈⣭⡴⢋⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⠃⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣌⢿⣄⡀⠀⠈⠙⠛⠷⠦⣤⣄⣀⣀⠀⣠⡴⣦⠀⣠⣿⣯⣴⣯⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⣄⣠⣼⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡏⣾⣛⡿⣏⡀⠀⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣬⣩⠶⠋⣥⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣤⣤⣤⡄⠀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣾⠿⠿⠿⣷⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⣠⣦⣴⣾⡿⠿⠿⢿⣷⡀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠇⠀⠀⠀⠀⠈⠛⠻⣳⣆⣀⣤⣶⣶⣶⣶⣾⣿⡿⣛⢟⣻⢿⣷⣾⡿⠿⠛⠁⠀⠀⠀⠀⠐⢿⣿⡄⠀⠀ ⠀⠀⠀⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⢉⢉⣉⣿⢣⢞⡱⣚⡜⢮⣹⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠀⠀ ⠀⠀⠠⣿⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠂⢸⡿⢏⡞⢮⣵⣧⣽⣳⣦⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀ ⠀⠀⠀⣿⡟⠀⡀⠀⠀⠀⠀⣀⡠⠟⠀⠀⠀⠀⠀⠀⢸⡟⣧⢜⣻⣿⢸⣻⡿⢇⢧⣘⠧⣿⣄⣀⣠⣤⣤⣼⣧⣸⣿⠀⠀ ⠀⠀⠀⡻⣿⣇⠈⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡜⣮⢜⡻⣿⣿⡹⢎⠧⣝⣚⡾⣿⣿⣏⣧⠳⣬⠹⣿⣿⠀⠀ ⠀⠀⣲⣿⠯⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⢿⣽⣿⢿⣭⣞⣼⣟⣿⡟⢦⣿⣎⢳⡜⣣⢿⣿⠀⠀ ⠀⢠⣾⡿⢤⡞⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠛⠛⠛⢛⣿⣿⠟⡯⣜⢣⢞⣱⣿⣿⡆⠀ ⠀⢸⣿⣷⠏⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣻⣜⣬⣓⣾⡿⠁⣿⡇⠀ ⠀⢸⣿⡟⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠚⠋⠁⠀⠀⣿⡇⠀ ⠀⢘⣿⡇⠀⠀⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣿⣇⡀ ⣿⣿⣿⡷⠶⠶⠶⠗⠀⠀⠀⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡆⠀⠀⠀⠿⡶⠶⠶⢶⣿⣿⣿ ⠈⢙⣿⣧⢄⣀⣶⠀⠀⠀⠀⠛⠿⠟⠀⠀⠀⠀⠀⠀⢀⣴⢴⣤⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠀⠀⠀⠀⣧⣀⠀⣼⣿⠋⠁ ⣴⣿⣿⣿⣮⠉⠉⢀⣀⣀⠐⠐⠲⢦⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠦⢀⣀⡀⠉⠉⣿⣿⣿⣿⡆ ⠈⠉⠉⣿⣿⣦⡖⠻⠉⠀⠀⠀⠀⠀⣤⣼⠗⠶⢦⡀⠀⠀⠀⠀⠀⠀⣸⠷⠖⠶⣤⡄⠀⠀⠀⠈⠉⠓⢶⣴⣿⣿⠛⠋⠀ ⠀⠀⢸⣿⡿⠻⢿⣤⡈⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠛⡆⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠙⣷⡀⠀⠀⢀⣴⡿⠻⢷⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣐⡿⠀⠀⠀⠀⠀⠠⣸⠇⠀⠀⠀⠰⢿⣤⠀⠀⠀⠀⠀⠀⣷⣤⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠚⠛⣾⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⢀⣠⣼⡷⠖⠂⠀⠀⠀⠈⠓⢶⣿⣴⡀⢀⠀⢀⣺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠷⠾⠋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⠻⠾⠶⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣿⢻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⣿⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣿⢀⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠑⠲⠤⣤⡀⢤⠖⠋⠀⠀⠀⠀⠀⣿⣼⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠠⠀⠀⠀⠀⠀⠀⠀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⢰⢸⡇⣰⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣦⣴⣤⣦⣿⠿⠿⣿⣤⣴⣤⣦⣴⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣿⡿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⢿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠿⠿⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠿⠿⣶⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢿⣿⣶⣄⠀⠀⠀ ⠀⢀⣴⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣄⠀ ⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣸⣿⠀⠻⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣦⣤⣴⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⠀⠀⠂⠸⢿⣶⡶⠾⠟⠀⠀⠀⣤⣿⡟⠀⠀⠈⠛⢻⣶ ⠀⠀⠀⢀⣴⣿⡏⠁⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡿⠛⠋⠉⠉⠉⠉⠙⠛⠻⣿⣷⣶⣤⣷⣶⣄⡀⠀⢰⣾⣿⠋⠁⠀⠀⠀⠀⠈⠉ ⠀⠀⣠⣿⡿⠋⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠉⠙⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣼⡿⠋⠀⠀⠀⣠⣤⣴⣾⣿⠿⠿⠿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⢀⣠⣾⣿⠟⠋⠉⠁⠀⠀⠀⠈⠉⢻⣿⣿⠟⠉⠉⠙⠛⠛⢿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⣀⡀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⢠⣿⡇⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡁⠀⣠⣿⣿⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⡿⠋⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣷⣤⣴⣶⣾⣿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣦⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣏⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣹⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡸⠁⢰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠂⠄⠀⠁⠀⡲⠀⡠⠀⠀⠆⠘⠄⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠀⢠⠂⠐⡄⠢⡀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠘⠤⠠⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡛⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠎⠙⣯⠃⠀⠀⢀⠤⠐⠊⠉⠉⠉⠁⠒⠠⢀⠀⠀⠀⠀⢃⠀⠀⠁⠀ ⠀⠀⠀⠈⡧⢮⢛⢖⣴⣦⠀⠀⠀⠀⠀⠀⠀⣴⣦⡑⡀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠩⢀⠿⣸⣿⣿⠃⠀⠀⡀⡀⠀⠀⣿⣿⡇⡸⠄⣠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠁⠀⠀⡆⠀⠀⠀⢰⠒⠂⠀⠀⠀⠀⠜⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⡅⠀⠀⠀⡷⠂⠀⠄⠀⠠⢀⠀⠀⠐⠒⣡⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠈⠦⡀⠀⢠⠆⠘⡄⠀⠀⠔⠉⠀⠀⠀⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠄⠀⡐⠀⠉⠒⠂⠀⠀⠈⠒⠊⠀⢃⠀⠠⠂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡀⢀⠠

⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣷⣶⣷⣤⣤⡶⠖⡆⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣧⣄⡰⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⠯⢿⣗⢿⠏⡆⠀⠀⠀ ⠀⠀⢀⣿⠻⣿⣿⣿⡴⠛⠳⣕⣿⡃⠀⢀⡀ ⢀⣴⣾⣿⣶⣿⡿⢿⣶⠆⠀⢋⠉⠈⢉⠤⠂ ⢺⣿⣿⣿⣿⣿⣿⣃⡏⡁⠀⢸⣿⠀⢐⠈⠀ ⠀⣿⣿⣿⣿⣿⡿⢫⣾⡎⠁⠀⢹⠀⠀⠀⠀ ⠀⢹⣧⡍⡉⣉⣢⣿⣯⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠛⠷⠖⠛⠻⠿⠿⠿⠖⠊⠀⠀⠀⠀⠀

🪐✩°｡⋆⸜ 🎧✮🏹 𝒞𝒽𝒾𝒷𝒾𝓂𝒶𝓇𝓊 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣶⠿⢟⣛⡉⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⢟⣭⠶⠛⠉⠁⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣝⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⣿⢷⡟⠀⠀⠀⠀⠀⣤⡀⠀⠀⠹⣿⡷⠶⠿⠿⠿⠿⠿⠷⢶⣶⣦⣤⣀⣠⡾⣷⠏⠁⠈⠙⠛⠻⣶⣄⠀ ⠀⠀⣰⣿⢸⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠯⣹⢟⡾⢣⣶⠀⠀⠀⠀⠀⠐⣿⡇ ⠀⠀⣿⡟⡾⠀⣀⠀⠀⡀⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⣾⠃⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⢸⣟⡄⣀⣼⣟⠀⢠⣿⠂⢐⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⡆⠀⠀⠀⠀⢹⡇ ⠀⠈⠛⠛⠛⢿⣿⣿⠛⢻⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣸⣷⠀⢠⡀⠀⠘⣿ ⠀⠀⠀⠀⠀⣾⢯⡟⠀⠀⢿⣶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣶⡦⠙⠿⠟⢿⣦⣼⣿⣦⣴⡿ ⠀⠀⠀⠀⢸⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠀⠉⠉⠀ ⠀⠀⠀⠀⣿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⠀⣸⡏⣾⠁⠀⢀⣴⢞⣫⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣛⠶⣄⠀⠀⠀⠀⢹⣷⠀⠀⠀ ⣴⡾⠟⣛⣵⠇⠀⠀⣾⢧⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠸⡇⠀⠀⠀⠸⣿⣦⣀⡀ ⠹⣷⣏⡉⠀⠀⠀⠀⢻⡜⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⢣⡟⠀⠀⠀⠀⣨⣿⡿⠃ ⢀⣽⡿⡃⠀⠀⠀⢀⣠⣿⠮⣽⣟⠛⠉⠀⠀⠀⣶⠜⢿⠿⢳⣆⠀⠀⠀⠹⣿⣟⣛⣥⢞⣁⠀⠀⠀⠈⢻⣷⡄⠀ ⢼⣯⣤⣿⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⣠⣴⡿⠇⠀ ⠀⠀⣿⣧⣴⣤⣬⡻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⣁⣈⣻⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠟⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠙⠛⢻⣿⡿⠀⠀⠀⠀⠀⠀⠺⣿⡿⢿⣿⠟⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣻⣥⣄⠀⠀⠀⠀⢀⣄⣸⣷⡿⠃⠀⠿⠋⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡑⣿⡀⢻⣧⠀⠀⢰⣿⠁⣿⢹⣷⣶⡄⢠⣴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⢹⡇⠘⠛⠛⠋⠀⠀⠈⠻⠿⠋⣼⠇⠈⣿⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣾⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⣸⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠋⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ≽^•༚•🎀≼ 𝐌𝗒 𝗌ω𝖾𝖾𝗍 ρ𝗂α𐓣ⱺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⣦⣤⣴⠶⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⠿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠿⠶⠒⠲⢶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡷⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢶⣄⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀ ⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄ ⠘⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⢷⣤⡾⠋⠀⡄⠀⠀⠀⠀⠀⣄⡀⢀⣴⣦⣀⣀⣴⣄⠀⠀⡀⠀⠀⠀⠀⢠⠀⠙⢶⡟⠀ ⠀⣰⠏⠀⠀⢰⠇⠀⠀⣤⠤⢾⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⢷⣄⣀⠀⠀⠸⡆⠀⠈⢻⡄ ⠀⢿⡀⠀⣠⠏⠀⢀⣰⠇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠈⠹⣆⠀⠀⠻⣄⠀⢀⡇ ⠀⠈⠛⠛⢿⣆⡀⢻⣻⣦⡀⠛⠋⠀⠀⠀⣐⠿⢗⡀⠀⠀⠛⠋⢀⣴⠏⣙⣀⣴⡟⠛⠛⠁ ⠀⠀⠀⠀⠀⠉⠉⠙⢿⣬⣿⠦⣤⣀⡀⠀⠈⠓⠊⠁⠀⣀⣤⣶⣟⣡⣾⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡟⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠈⠻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣏⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠙⢳⣶⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⢶⡶⠋⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠋⠁⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠙⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛⠋⠛⣻⣟⡛⠉⠛⢛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠤⠟⠻⠦⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 𓍢ִ໋🌷͙֒₊˚*ੈ🎀⸝⸝🍓⋆ ᴡɪsʜ ᴍᴇ ᴍᴇʟʟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠛⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠸⣿⡀⠀ ⠀⣴⡾⠿⠷⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀ ⣼⡏⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⡠⠤⣿⠀⠀⠀⢸⣿⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⣞⠁⠰⣿⠀⠀⠀⢸⡟⠀ ⢿⡇⠀⠀⠀⡷⠄⡀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⡼⠁⠀⠜⡏⠀⠀⢠⣿⠁⠀ ⢸⣷⠀⠀⠀⢷⠀⠙⢦⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣈⠀⡀⢀⣾⠁⠀⢠⣾⠏⠀⠀ ⠀⢿⡇⠀⠀⠈⡆⠀⠈⠱⡄⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢐⡽⠃⠀⣠⣾⠋⠀⠀⠀ ⠀⠈⣿⣄⠀⠀⠈⢦⡀⠀⠻⡄⠀⠸⣿⠀⠀⠀⣀⣤⣤⣤⣴⣾⣿⣶⣿⣶⣶⣦⣤⣤⣿⡇⢀⠀⡠⠋⠀⣠⣼⡿⠁⠀⠀⠀⠀ ⠀⠀⠘⢿⣦⠀⠀⠈⠳⠠⠀⢦⡀⢀⣿⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣿⣄⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⣿⣦⣄⠀⠀⠁⠀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀ ⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⢰⡾⠟⠻⣧⠀⠀⠀⠀⠘⢿⣿⡿⠀⣠⠤⠒⢶⡀⠀⠀⢈⣿⡆ ⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⢀⣀⡀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠘⠿⣶⡾⠟⠀⢀⣀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠈⣧⢄⣰⣿⠏⠀ ⠀⠀⠘⠿⣷⣄⠀⠀⠀⣠⠖⠋⠁⠑⢦⡀⠉⠁⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠹⣦⣀⣤⠞⢋⣼⡟⠁⠀⠀ ⠀⠀⠀⠀⠘⢿⣦⡀⠰⠧⠀⠀⠀⠀⢀⣹⠄⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣶⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣦⣘⠒⢦⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣴⣶⠟⠁⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⡷⠶⠶⠶⠶⠶⠿⠛⠛⠋⠉⠁⣿⠃⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⢹⣷⣦⣀⣀⣀⣀⣀⣀⣀⣠⣤⡾⣿⣦⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⣸⡟⠈⠉⠉⠛⠛⠛⠛⠛⠉⠁⠀⠘⣿⠿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡾⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⢀⡈⢻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠠⣤⣤⣤⣤⣤⡄⠀⠀⢠⣿⠀⠀⣀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣿⡏⣿⡏⠀⠀⢀⣾⡷⠶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣶⡿⠁⠹⣷⣦⣴⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 𖦹 ׂ 𓈒🐇 ೀBᨵׁׅꪀׁׅBᨵׁׅꪀׁׅRꪱׁׅϐׁׅ֒ϐׁׅ֒ᨵׁׅꪀׁׅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⠘⣧⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⢤⣀⡀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣴⠷⢲⣦⠃⠀⠹⡷⠸⡆⠀⠀⡰⣫⠜⠉⠁⠴⢗⢀⡈⣻⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⣏⠆⣾⠉⠓⢠⡞⣷⣧⣙⣦⣴⠓⣛⣲⣤⣼⠒⢸⣯⣟⠃⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⣄⣹⣤⡤⠂⢷⣄⣩⡿⢾⣭⣛⣛⡻⠥⢽⢤⡸⠋⢹⡟⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠸⣆⠀⢰⠟⠉⠀⠀⠀⠺⣿⣇⠀⣨⣿⠉⠳⣼⡑⠀⠀⠀⠀⠀⠀⠀⠈⢸⡄⠀⠀ ⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠁⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀ ⢸⠁⠀⠀⠀⠀⠀⠀⡸⠀⣼⠃⠀⢤⣾⣿⣿⠀⠀⢀⣀⣄⣀⠀⠀⠀⢠⣶⣦⣤⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁ ⠘⢆⠀⠀⠀⠀⠀⠀⢱⣷⠋⣀⣀⡉⢻⡿⠟⠀⠀⠀⣴⣶⣦⠉⠀⢺⣼⣿⣿⠛⠀⠀⠀⠸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠸⡀⠀⠀⠀⠀⢀⡾⣯⠸⣇⣀⣙⡶⠖⠀⠀⠀⠀⣟⠁⣸⠀⠀⠀⠀⠋⠁⠤⠤⢤⡀⠀⢻⣱⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⠹⢦⣄⠀⢠⠞⠁⠘⢶⣄⡈⠀⠀⣀⣤⣄⡀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⠬⢉⣀⠼⠋⠷⡀⠀⢀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠙⠲⢼⡇⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⣀⠴⣃⣀⠤⠞⠋⠁⠀⠀⠀⠈⠓⠬⠧⣀⣠⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣼⠙⣏⠒⡲⠚⠋⠉⠙⠛⠓⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⡇⣠⣼⣾⣧⡅⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⢶⠋⠀⢻⣨⣏⣤⠇⠀⠀⠀⠲⣬⢅⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠹⡄⢀⠉⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⡀⢙⡀⢒⣂⢀⣀⣀⣾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡍⡇⢸⠏⣬⠉⠑⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣿⠀⣼⣥⣏⡘⡷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣛⣧⣿⠙⠚⡿⢿⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ <3@Pixi3_Ang3l

badtz-maru☠︎︎༒︎✞︎🕸𖤐 ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄⠀⠀⠀⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⣀⣤⣴⣶⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠛⠋⠉⠹⣿⣿⠏⠉⢻⣿⣿⡏⠉⠹⣿⣿⠏⠉⠙⠛⢻⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣤⣤⣤⣤⣴⣾⡿⠋⣉⠩⢿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠖⢋⠩⠙⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠙⠋⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣤⣤⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠠⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⡀⠠⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢂⠐⢈⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢀⠐⠠⢁⣼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣢⣼⠿⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠙⠉⠙⠶⠮⣤⠾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ kuropi˚˖𓍢ִ໋🧚🏻₊˚ʚ 🪷 ₊˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⣀⣴⣾⣿⠿⠿⠿⠿⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⢀⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡀⠈⣿⣿⠁⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⢀⣿⡏⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⢀⣼⣿⣷⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣿⡆⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡟⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠉⠛⠿⣿⣿⣶⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⢀⣴⠟⢛⡛⢷⣆⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠿⠟⠛⠉⠀⢿⣿⡄⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⢸⡇⠀⠈⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣦⡀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡘⣧⡀⠀⠖⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠐⠂⠈⢿⡄⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⡈⠙⠻⠛⠋⠀⢴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢻⣆⠀⠀⠀⠀⣼⠇⣾⣿⠃⠀⠀ ⠀⢀⣤⣤⣼⣿⡟⢿⣿⣦⣀⠀⠀⠀⠈⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠀⠻⢷⣬⡴⠟⢋⣼⣿⡟⠀⠀⠀ ⠀⠸⣿⣿⠿⠟⠁⠀⠙⠿⣿⣿⣶⣤⣄⣀⡀⠙⢿⣿⣷⣄⠀⠀⢀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣀⣀⡀⠀ ⣴⣾⣿⡿⠀⠀⠀⠀⠀⣠⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣭⣤⣤⣤⣴⣶⣶⣿⣿⡿⠟⠋⠘⠿⢿⣿⣿⠀ ⣿⣿⣅⠀⠀⠀⠀⠀⣴⣿⠟⠁⣼⣿⣿⣿⣿⣿⠉⠉⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄ ⠈⢿⣿⣷⣄⠀⢀⣾⣿⠏⠀⢰⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠘⣿⣧⡀⠀⠀⠀⠀⠀⢙⣿⣿ ⠀⠀⠙⠿⣿⣿⣿⡿⢃⣠⣤⣿⣿⣿⣿⣿⣿⣶⡄⢸⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡀⠹⣿⣧⠀⠀⠀⢀⣤⣿⣿⠏ ⠀⠀⠀⠀⢀⣿⣿⠁⣾⣿⠿⣿⣿⣿⣿⠃⠙⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠹⣿⣧⣶⣾⣿⡿⠛⠁⠀ ⠀⠀⠀⢰⣿⡿⣿⣿⣿⡿⠀⠈⠛⠛⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⡋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣿⣿⣿⣿⣿⣷⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣷⣦⣄⡀⠀⠀⣀⣤⣶⣿⡿⠋⠀⠈⣿⣿⣆⢠⣴⣶⣦⣄⠀⢀⣴⣶⣦⣀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⠿⠛⡉⠀⠀⠀⠀⠈⠿⣿⣿⡿⠛⠿⣿⣿⣿⡿⠛⠿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ gudetama🌙🐥🌼🌟🥟✧˚ ༘ ⋆｡♡˚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣧⠀⠀⢀⣴⣿⡿⢿⣛⡛⢏⡛⣛⠻⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣠⣿⣤⣾⣿⡿⢯⡜⢥⠒⣍⠲⢥⠣⣝⢪⡑⡎⣝⡻⣿⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡼⣠⠸⡜⢻⣀⠿⣀⢟⡸⢇⡿⢸⢠⠻⣜⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣽⣿⣛⣾⣧⠓⡜⡥⢊⡖⣻⣾⣳⡺⣌⢻⣐⢻⡞⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢧⣿⣿⣿⣿⣿⣿⡿⣙⣴⣍⣧⣘⠻⢿⣿⣿⠜⣢⠥⣻⡇⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡿⢣⡍⡖⡹⢣⣶⣿⣟⣛⣛⣿⣷⡧⣉⠦⣋⡔⢣⡹⣷⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢇⡣⢝⡰⢃⡇⢮⠹⡏⢟⡫⢻⠝⡰⢥⠓⢦⡙⢦⠱⣻⡄⠀⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢊⠖⡣⡜⡱⣘⠆⡏⢼⢨⣑⢣⢚⡱⢊⡝⢢⡙⢆⡫⢔⠿⡶⢗⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣌⡏⠴⢣⡑⠮⡜⡜⢢⠧⣘⢆⠳⣌⢣⠜⣣⣿⡮⣑⠎⡎⡵⢪⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⣌⠳⣡⠝⡲⡑⢮⠱⣊⠕⣪⠱⡌⡖⣩⣶⣿⣷⣭⣚⠴⡱⣩⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡑⢎⡱⢆⡹⢔⡙⢦⡙⡴⢋⡴⢣⢱⣺⣽⣿⣻⢧⣿⡏⡖⡱⣂⢿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠟⠋⣿⣿⡘⡜⡰⢍⡲⢩⠜⡢⣕⢪⠱⣌⣣⣷⣿⢯⣝⣭⣿⣿⡝⢲⢡⢣⣿⡇⠈⠙⠻⢿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠉⠁⠀⠀⠀⣿⣿⢬⡱⣉⠖⣡⢇⢫⠔⡎⡬⢓⡴⣿⣿⣷⣾⡿⢟⡽⢤⡙⠦⣍⠶⣿⡇⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢧⡑⢎⡹⡐⡎⢎⠞⡴⢱⢃⠖⣹⠻⣿⡖⣩⠖⣘⠦⣙⠲⢬⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢷⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡟⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⡜⣡⢎⠣⢖⡩⢜⡡⠞⣌⠓⣎⠹⣄⢫⣽⣷⢡⡚⢥⠚⡴⣙⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⡀⠀⠀⠀ ⠀⢠⣿⡿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⢹⡘⣔⣪⣙⣦⣽⣦⣽⣼⣬⣳⣌⣗⣼⣿⠟⣍⠧⡜⢪⣕⣮⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢶⡄⠀⠻⣿⣍⠀⠀ ⢴⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣭⣺⣵⣾⡿⠿⠛⠋⠉⠉⠉⠉⢉⣿⣿⡿⢿⣙⣺⣴⣷⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡋⢅⠊⡔⣻⠀⠀⠹⣿⡆⡀ ⠈⠘⣿⣷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣠⡤⣤⡤⠶⡛⢍⢢⣑⣌⣒⣤⠟⠀⠀⠀⣿⣏⡇ ⠀⠀⠈⢻⣿⣶⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⢡⢡⠂⡔⢰⠀⡆⠑⠘⠊⠉⠉⠉⠉⠀⠀⠀⠀⣴⣿⡇⠃ ⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⣶⣶⣶⣤⣤⣤⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠣⠘⠀⠊⠀⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣾⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣶⣤⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⡶⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⡾⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣶⣶⣾⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠟⠻⠿⣿⣦⣼⣿⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⣼⣿⡟⠛⠉⠀⠀⠀⣠⣾⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠹⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⢿⣟⣻⣿⣟⢷⣦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣤⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠻⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⡆⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⢸⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⡖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣟⢻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣦⣌⠉⠁⠀⠀⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣈⣙⣻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠿⠟⠻⠿⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣽⣿⡿⣿⣷⣿⡿⣟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣷⡄⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣽⣿⢿⣻⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⢿⣹⣿⡿⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⢿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣷⣿⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣶⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠳⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣯⠉⠛⠻⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⠿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠰⣿⣿⣿⣶⣶⣤⣴⣤⣤⣤⣤⣶⣶⣶⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣉⢉⡉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣶⠟⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠛⠙⠛⠛⠿⣷⣶⣶⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⣀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣯⣿⣻⢿⣿⣿⣿⣯⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠛⠿⢿⡿⣿⣿⣿⣿⣯⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣰⣄ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠾⠟⣿⣟⠛⠋⠉ ⢀⣤⣶⣶⣿⡷⠷⡶⠀⠀⠀⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠧⠀⠀⠀⣤⣿⣿⣶⣴⡄ ⠈⠉⠁⠀⠈⣿⣆⣀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⢀⢼⡶⣷⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⣿⠃⠉⠀⠀ ⠀⠀⠀⣶⡿⠿⣿⡍⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠛⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣻⣿⢿⣷⣦⣤⠀ ⠀⠀⠀⠁⠀⠀⣈⣿⣿⣟⢠⣴⣿⣿⢿⡿⣶⣄⠀⠀⠀⣠⣾⡿⣟⢿⡿⣶⡄⣀⣴⣿⠟⠁⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⢤⣾⡟⠃⠈⣙⣿⡿⠿⢾⣧⣛⢷⣻⡷⣠⣾⡿⣣⢟⡼⣳⣿⠟⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⣹⣯⡞⣵⠫⡟⣧⢹⢥⡻⡼⣿⣇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⣿⢣⡟⣼⢃⡟⣼⡹⣎⢷⡹⣝⣿⣇⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣼⡟⣮⢳⡝⣮⢣⡝⡶⣹⢎⡷⣹⢺⠼⣿⣷⣶⣿⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠉⠛⣿⣽⢎⡷⣹⢎⡷⢺⡵⢫⡞⣵⢋⣷⣿⡿⠛⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠽⣿⠀⠀⠀⠀⠈⠛⣿⣞⣵⣫⠎⢧⣛⢧⡻⢼⣯⣿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠈⠻⣷⣿⣎⠷⣭⢳⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⡠⡿⠛⢿⣿⣼⡿⠛⢿⣧⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⢤⠴⠞⠋⠀⠀⠀⠙⠏⠀⠀⠀⠙⠻⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⠾⠛⠉⠉⠉⠁⠈⠉⠉⠉⠛⠻⢶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⣽⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⢠⡿⠁⠀⠀⣰⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⠀⠀⠀⢿⡄⠈⢷⡄⠀⠀⠀ ⠀⠀⣰⡿⠁⠀⣾⠇⠀⠀⠀⢿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠸⣷⠀⠈⢻⣆⠀⠀ ⠀⣼⠏⠀⠀⠀⢿⡖⠒⠒⠶⣄⠀⠀⠀⠀⢰⣗⣠⣤⣤⣀⣺⡇⠀⣠⠶⠛⠛⠫⢵⠲⣴⡿⠀⠀⠀⠹⣧⠀ ⢰⡏⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⡇⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⣇⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢹⡆ ⢸⡇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣯⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣓⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢻⣆⡀⠀⠀⠀⠀⣠⡾⠏⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠋⠉⠉⠉⠁⠀⠙⢷⣄⡀⠀⠀⠀⢀⣠⡿⠀ ⠀⠀⠈⠛⠛⠞⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠻⠞⠛⠉⠀⠀

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣶⠟⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠙⠛⠛⠿⣷⣶⣶⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⣀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣯⣿⣻⢿⣿⣿⣿⣯⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠛⠿⢿⡿⣿⣿⣿⣿⣯⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣰⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠾⠟⣿⣟⠛⠋⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⡷⠷⡶⠀⠀⠀⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠧⠀⠀⠀⣤⣿⣿⣶⣴⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⣿⣆⣀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⢀⣼⡶⣷⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⣿⠃⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⣿⡍⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠛⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣻⣿⢿⣷⣦⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣈⣿⣿⣟⢠⣴⣿⣿⢿⡿⣶⣄⠀⠀⠀⣠⣾⡿⣟⢿⡿⣶⡄⣀⣴⣿⠟⠁⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡟⠃⠈⣙⣿⡿⠿⢾⣧⣛⢷⣻⣷⣠⣾⡿⣣⢟⡼⣳⣿⠟⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⣹⣯⡞⣵⢫⡟⣧⢻⢥⡻⡼⣿⣇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⣿⢣⡟⣼⢣⡟⣼⡹⣎⢷⡹⣝⣿⣇⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣼⡟⣮⢳⡝⣮⢳⡝⡶⣹⢎⡷⣹⢺⠼⣿⣷⣶⣿⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠉⠛⣿⣽⢎⡷⣹⢎⡷⢺⡵⢫⡞⣵⢋⣷⣿⡿⠛⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⠀⠀⠀⠀⠈⠻⣿⣞⣵⣫⢞⢧⣛⢧⡻⢼⣯⣿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⠻⣷⣿⣎⠷⣭⢳⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⣠⡿⠛⢿⣿⣼⡿⠛⢿⣧⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⢤⠴⠞⠋⠀⠀⠀⠙⠏⠀⠀⠀⠙⠻⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠠⠄⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⣾⠁⢹⡆⠀⠀⠀⠀⠀⠀⡴⢛⡛⢶⡀⠀⢰⠞⣛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣧⠀⢹⡄⢹⡄⢸⡇⠀⠀⢰⢫⢽⡞⣇⠻⠟⠘⠋⠉⠛⠀⠿⠗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⣉⠉⠳⣄⠀⠘⣦⠀⢿⡬⠧⠸⢧⣄⠀⠘⢮⣍⣴⢟⣷⠀⣀⠀⠀⠀⣀⢺⣞⠃⠀⠀⠀⠀⠀⢀⣠⡴⠶⣶⢲⡶⠶⡿⣽⠿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⠞⠋⠀⣰⣷⣤⣶⣶⠿⣧⣄⠘⣧⣤⣼⠇⠀⠀⠀⠀⣤⡙⣧⣀⣀⠀⢧⣐⣻⣄⡁⠻⠲⠟⢉⣼⣷⣶⣾⣿⣿⣿⣶⣿⣥⣀⣼⠋⠀⠀⠀⠈⠢⢄⣿⠳⣤⠤⠦⢤⣤ ⡤⠶⠶⣇⠰⣄⣼⠋⠉⡘⠘⠙⠀⣤⣽⡆⠘⣇⣏⠀⠆⢲⣔⡞⠘⢣⣿⡍⡿⢻⣍⠉⠘⠾⠟⢛⣛⣯⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠋⠰⡴⣶⠞⠃⣼⠀⠈⢷⡀⠀⠀ ⠀⠀⢠⣿⡀⠹⣇⠀⠸⠇⠶⠶⠟⠀⣸⣇⣴⠟⢻⣄⡛⠀⠘⠃⠀⣀⣾⠷⠛⠛⠛⠳⠦⣴⣞⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⢿⣹⣦⣄⡀⠀⢠⣴⣏⣀⣄⡘⡷⣦⠀ ⠀⠀⡟⣼⣷⣄⣟⣦⣄⡠⡞⡿⠀⠈⣫⡏⠀⠀⠐⢯⣥⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣼⠾⠋⠁⠈⢻⣅⡾⡀ ⠀⠀⣧⢻⣾⣿⢿⣷⡏⠀⠀⠀⠀⢀⢟⡇⠀⠀⠀⢠⡿⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⡟⠀⠀⠟⠳⠀⠀⢤⡄⠀⠀⢠⠶⡆⠀⢠⡆⠀⠀⠀⠙⣧⠀⠀⠀⠀⣿⡡⠃ ⠀⠀⠘⠳⠯⢵⡟⣿⣥⠦⠶⠶⠚⠛⢛⡇⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣀⣤⠶⠀⠀⣠⣾⣤⢾⡀⠀⠀⠀⠀⠀⠠⠞⢧⠀⠀⠀⠀⠁⠀⢘⣧⡀⠀⠀⢠⡟⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠻⣦⣀⠉⠉⠉⠉⠉⠀⢀⣠⠞⣩⠞⣯⣈⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢙⡶⣶⠛⠀⣀⠀⠀⢀⣼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢀⣤⢆⣰⠏⠛⠶⠤⠤⣤⣴⣿⠁⠀⣏⠀⠀⠉⠉⠀⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠛⠛⠋⠓⠒⠋⢡⡟⠉⣉⣉⣤⠾⡫⠇⠀⠀ ⠀⠀⣠⡴⠦⡤⠖⠒⠛⠋⠀⣌⠛⣦⠀⠀⢠⡶⣫⡴⠛⠁⠀⠀⣀⡾⣯⠉⠉⠻⢦⣴⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣀⡀⠀⠀⠀⠀⢠⡟⣋⣉⣉⡡⠔⠊⠀⠀⠀⠀ ⠀⣴⠋⢀⡀⠀⠀⠀⠀⠀⠀⠙⣧⣼⠧⣤⣴⣿⣭⣤⣀⣀⣀⣠⣾⣇⠹⢤⣀⡤⠀⠈⣾⢧⡉⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⢀⣴⢟⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⡇⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠞⠋⠀⠀⠀⠀⠀⠀⣨⣭⡿⠋⠀⠀⠀⠀⣀⣠⡏⠀⠈⠑⠢⠤⣉⡉⠛⠓⠶⠶⠶⠤⠤⠤⠤⠤⠶⢛⠵⠋⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀ ⠀⠙⠛⠻⣤⣀⠀⠀⠀⠀⠀⢨⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⣦⡀⠀⠀⠀⠰⣿⡏⠉⠛⠶⢤⣄⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣀⣲⡾⠷⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉ ⠀⠀⠀⠀⠛⢶⡂⠸⣿⡇⠀⣰⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⣤⡐⣧⡀⠀⠀⠀⠀⠈⠙⠶⢦⣄⠀⠀⠀⣀⣠⠶⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠬⣷⣠⡾⠷⠞⠻⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠢⠿⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡶⠟⠉⠁⠂⡀⠃⡀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠘⠒⠚⠛⠒⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠺⢛⡳⢜⡚⠞⡚⠟⠃⡿⢸⠧⢟⠳⠛⠛⢞⡃⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⣻⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢠⣿⡗⣿⣜⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠈⣿⣿⣶⣽⣾⣿⣧⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣴⣶⠿⠟⠛⠉⠉⠁⠀⠀⠉⠉⠛⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣄⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣟⡡⡜⢆⣿⠈⢉⡟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣏⠦⣕⢎⢣⡜⡓⣎⢜⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠿⢻⡱⢺⣀⣈⢏⡲⢸⡍⠈⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠏⠳⢣⠱⠃⠮⡜⡜⠒⠣⠞⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⠛⠿⢷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡜⢣⢮⠓⠺⡴⣱⠉⠉⢧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢈⣿⡿⠟⠿⣷⣦⣤⣀⣀⣀⡀⠀⠀⠀ ⢸⣿⠙⢳⡚⠦⣔⢣⣿⡷⣲⣿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⣿⠉⠙⣿⣿⣿⣿⣆⠀ ⠈⣿⣆⠞⡱⣍⠞⢲⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣼⣿⣶⣶⣿⡟⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣶⡿⠋⠀⠀⠈⠛⠛⣻⣿⠃ ⠀⢻⣿⣾⣷⣿⣷⣿⣿⣿⢛⡦⢣⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠙⢿⣿⣿⣇⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣼⣿⠿⠿⠛⠁⠀ ⢀⣾⡟⠁⠀⠀⠀⠈⠙⣿⡯⡜⣯⢞⣿⣧⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠘⣿⡜⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣦⣿⣿⢿⣷⣄⠀⠀⠈⠿⠟⠀⠀⠀⠀⣀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⠀⠀⠀⠀⢀⣿⠏⠉⠉⠁⠀⠀⠙⠿⣷⣦⣄⠀⠀⠀⠀⣰⣾⠟⠋⠁⠀⢀⣼⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⣶⣤⣄⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣶⣶⣿⣧⣀⠀⢀⣴⡾⠟⠈⠙⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣦⣤⣄⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠻⣦⣠⣶⣿⠿⠟⠻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠈⠉⠛⠿⣿⣾⣿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠙⣿⠉⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣠⣾⠟⣿⣶⠿⠿⣶⣄⣠⣤⣼⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⣾⡿⠁⠀⠀⠀⢻⣏⡁⠀⠈⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⣀⣠⣼⣷⡀⠀⠀⣰⣾⠟⣿⡄⠀⢸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⠶⠶⣿⠛⠛⠛⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣴⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡀⠀⠀⠀ ⠀⣀⣠⣤⣼⣿⣤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠶⠾⣿⡿⠿⠿⠷ ⠈⠉⠉⠉⢹⣿⠉⠉⠀⠀⠀⢰⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⣀⣬⣿⣷⡶⠄⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⢀⡴⠶⣦⡀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⣿⡿⠿⠷⠶⠀ ⠀⠀⠈⠉⠉⠉⢿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠿⣿⣏⣤⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡿⠛⠿⣶⡄⠀⠀ ⠀⠀⠀⠀⠿⠋⠁⠀⣈⣿⡏⠀⠀⣿⠟⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠿⠋⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠁⠁⢠⠤⣄⠀⢀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠄⠘⠷⠋⠈⠙⣷⢻⣇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠘⣿⡌⢻⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⡀⠀⣰⣦⣀⣴⡿⠂⠻⣷⣤⣤⣤⣶⡿⠃⠀⠀⠀⠸⣿⡿⠋⠉⠉⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠛⢿⣿⠹⣿⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢸⣿⣷⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋⠘⠿⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠛⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⠀⠀⣠⣿⣄⠀⠀⠀⠀⠀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣟⡿⢯⡟⣽⢫⡽⣍⠳⣍⠺⡰⢡⠒⣬⢶⡶⣌⣿⠿⠟⣿⡇⢢⠐⣸⠇⡐⠄ ⡿⣞⡽⣻⡜⣧⠻⡴⣩⠳⣌⢣⠱⠬⢲⢯⡟⣾⣽⣣⣀⡀⠘⡇⡡⢊⢸⠷⠚⠖ ⣿⣱⢻⠉⠉⠉⠁⠉⠒⠉⠀⠀⠀⠀⠰⣏⣿⣳⣯⢷⣏⡷⢳⣹⡹⣳⢸⢂⡉⠔ ⡷⣭⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣶⣳⢯⢿⣼⢫⡷⢧⣻⢱⡿⢀⠔⡈ ⡷⣩⢟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠳⠬⡟⢸⠖⠚⠒ ⡳⡕⣎⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⢾⠒⠓⡈ ⡳⢍⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣾⣀⠂⠄ ⡝⢪⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢿⠀⠃⠒ ⡙⢦⡉⢇⠀⡀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠠⠀⡘⢸⠒⠄⠀ ⡙⢦⠚⡭⢆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢂⠄⠁⢸⠀⠀⠀ ⡱⢊⠱⡄⢧⠛⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠔⠊⠣⡀⠀⢸⠁⠘⠀ ⡑⢎⠱⡈⢆⠱⣠⠋⠁⠄⠒⠒⠂⠁⠀⠈⠀⠀⠀⠀⠀⠡⠀⠀⢡⠀⢸⠀⠀⠀ ⡍⢆⠣⡜⣈⠆⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣇⠀⠀⠀⢄⠁⣀⠔⠀⢸⠀⡀⠀ ⣝⣎⢷⣘⣦⣹⣱⣄⣀⡀⣀⣀⣸⣤⣤⣴⣾⣿⣿⣿⣾⣿⣿⣻⡆⡀⢾⡀⢄⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠉⠉⠉⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠐⠺⠂⠁⠉⡀⠀⠀⠪⠉⠉⠻⠳⢦⣄⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠿⠀⢜⠆⠀⢀⠀⠀⠈⠠⠀⠀⠈⠐⠀⡒⠁⢄⠹⢿⡉⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠋⠀⠈⠀⠀⠀⢀⢅⠁⠁⡀⢈⠀⠨⠀⠂⠁⠠⢧⠰⠈⠁⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣞⠁⢀⠀⠀⠀⡅⠂⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠄⠊⠌⠀⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⢰⡟⠀⠁⠐⠀⠈⠀⡀⠉⡀⠀⠀⠀⠀⠀⢀⠀⠎⠘⠄⠀⠀⠀⠹⣧⠈⢿⣄⠀⠀⠀ ⠀⠀⣠⡟⠁⠀⣾⠁⠐⡐⢿⢓⠛⣯⠓⠀⠀⠀⠀⠀⡀⢂⠊⠑⢥⠸⢃⡏⠇⠀⠀⣿⡄⠀⠻⣦⡀⠀ ⠀⣸⠏⠀⠀⠀⢷⡀⠂⠀⣿⠐⠁⢲⢧⠂⣿⣨⠑⠠⣤⣓⠦⢬⠇⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀ ⢀⣿⠀⠀⠀⠀⠈⢿⣤⡀⣾⠀⠀⣿⠀⠀⠂⠀⠀⠂⠀⠡⠀⢨⠁⠀⢸⠄⠀⣠⡼⠃⠀⠀⠄⠀⢹⡇ ⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣷⣆⣹⣄⣀⣀⣀⣀⣀⣀⣒⣅⣀⣸⣇⣾⣿⡿⠉⠀⠀⠄⠀⠀⠀⢸⡇ ⠀⠹⣦⡀⠀⠀⠀⢀⣠⡾⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡟⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢻⡀⠀⠀ ⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒ ⠀⠀⠈⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀ ⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀ ⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⣶⣤⣴⡶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣆⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠻⠿⠿⠟⠛⠋⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣺⡿⠋⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⡀⢀⣰⣆⠀⠀⠀⠀⠀⠈⠻⣿⣦⢠⠏⠉⢳⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠿⠀⠙⠃⠀⠀⠀⠀⢿⣿⠇⠀⣀⠉⠀⠘⠇⠈⠙⠛⠷⣦⡄⠀⠀⠀⠀⠙⣿⢿⡀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣠⣿⡀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣿⣻⣷⠴⣒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⢿⣦⣀⣀⣀⣤⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠉⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⣾⠟⠋⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⠛⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣿⡏⠀⣾⣿⣧⠀⣿⣿⣀⠀⠀⣰⣿⠿⠛⠻⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠿⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡇⠉⠉⢿⣷⣄⠉⠛⠁⠀⠙⠛⠛⠳⢾⣿⡇⠀⣶⣶⡄⢻⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣶⣄⠀⢹⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠟⠃⢸⣧⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠹⣿⣷⣽⣟⣀⡐⠿⢀⡀⠀⠀⠀⢀⣀⠀⢿⣶⣤⣴⣿⡏⡀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣠⣴⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⡇⠀⠸⣷⣿⡟⠙⣻⣶⣾⣷⣿⣦⣷⣬⣩⣤⣼⡿⣯⣿⢻⣽⡟ ⠀⠀⠀⠀⠀⠀⣸⣿⡁⣀⣠⣤⣤⣴⡏⠁⠀⠀⢹⡟⢿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣶⡶⣾⣷⣶⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣹⣯⠙⠛⢻⣷⠧ ⠀⠀⠀⠀⠀⠘⣿⣿⠟⣻⠋⣠⣾⣿⣿⡴⠶⠚⠻⠧⣄⣩⠿⢿⣦⡀⠀⠀⠀⠀⠀⣾⠟⣿⡿⠛⠉⠁⢿⡇⣿⢻⡿⠉⠛⢹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠾⣻⡁⠀ ⠀⠀⠀⠀⠀⢠⣿⡟⠊⠁⠀⢿⡇⠈⠁⠀⡀⠀⠀⠀⠀⡻⠁⠀⠈⢿⡆⠀⠀⠀⠘⠋⣼⠟⠀⠀⣤⡀⠈⠀⠀⠀⠁⢀⣀⠀⠹⣧⠀⠀⠈⠉⠙⠛⠛⠋⠉⢹⣿⣿⣷⣾⣿⡁⠀ ⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⣿⠁⠀⠀⠘⠟⠀⣤⣺⡶⠋⠀⠀⠀⣸⡗⠀⠀⠀⠀⠰⣿⠀⠀⠈⠋⠉⢰⣦⣶⣶⡆⠛⠻⠂⠀⣿⠶⠶⠶⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣷ ⠀⠀⣀⣤⣼⣿⣯⣼⣤⣀⣀⣿⣧⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⣾⢿⣶⣤⣄⡀⠀⠀⠹⣷⣄⡀⠀⣠⣶⣆⣸⣿⣆⠀⠀⢀⣼⡿⠛⠿⣷⣌⢿⡆⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⢸ ⣴⠟⠛⠉⢀⣾⢛⡁⠹⣿⣥⡾⠻⢷⣶⣤⣤⣤⣴⠶⠾⠟⠛⢋⠀⠀⠈⢻⣿⠛⢷⣦⣤⣴⣿⡿⠈⢹⡾⠏⠸⣷⡝⠱⣶⡿⢫⣾⠛⣷⣼⣿⢸⣿⣶⣾⠿⠿⠟⠛⠛⠋⢀⣠⣾ ⣇⠀⠀⠀⠘⢿⣤⣙⣓⣒⠒⠲⠶⠶⠶⠶⠤⠤⠶⠴⠶⠶⠞⣛⣁⣠⣴⡿⠟⠀⠀⢹⣿⣷⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣸⣿⣶⣽⡾⣋⣾⣃⣀⣀⣠⣤⣤⣤⣶⡾⢿⠿⠋ ⠻⢷⣦⣀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⣀⣠⣴⣿⠟⢿⣦⣾⣧⣤⣄⣠⣀⣀⣀⣤⣍⣹⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⠿⠿⣿⣷⡶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⡶⠶⣶⠶⠿⢟⠛⠛⠉⠉⠁⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣐⣦⣥⣼⣶⢶⡶⣦⣬⣴⣀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠒⣵⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢰⣭⣅⣦⣵⡾⠟⡫⠍⢦⠱⡐⢆⠲⣁⠎⣩⠙⡛⢷⣦⣕⡀⡀⠀⢠⣪⠭⠯⠵⠚⠀⠀⢻⡡⡀⠀⠀ ⠀⠀⠀⠀⠠⣀⣿⣧⣿⠛⡥⠘⣆⠱⣉⠦⢡⠓⡬⢑⠢⣍⠰⠩⢜⠢⢌⡹⢻⣮⣢⠘⢜⣆⠀⠀⠀⠀⠀⠀⠉⠒⣅⠂ ⠀⠀⠀⢰⢹⣏⣽⡦⢡⢋⠴⣉⠤⢓⡰⢌⠣⢜⡰⢉⠲⢄⡋⡕⢊⡱⢊⠴⡁⠞⣷⣵⣼⣹⡀⠀⠀⠀⠀⢀⡴⡚⠕⠁ ⠀⠀⠀⠀⠱⣽⡟⣐⠣⣌⠲⢌⡒⠥⢒⠬⡑⠦⢌⠣⣑⠪⠔⣌⠣⡔⡩⢢⠍⡜⠤⢿⡟⣇⣤⣤⣶⣄⠀⡾⠘⠀⠀⠀ ⠀⠀⠀⠀⣖⣿⠰⢡⠒⡤⢓⠢⡜⢌⡃⠖⣉⠦⣉⠖⡡⢎⡑⢢⡑⠦⢱⠡⡚⢌⡜⢌⣿⣹⢈⢧⠣⠫⢓⡣⠃⠀⠀⠀ ⠀⠀⠀⢰⢸⡧⣉⠦⡙⢤⢃⠣⠜⢢⢡⢋⡔⠢⣅⠚⡰⢡⢊⠥⡘⡜⢢⠱⢡⠎⡰⢊⢼⣇⣿⡜⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⡇⢲⠰⣉⠆⢎⡡⢋⢆⠣⡒⠬⣑⢢⡙⡰⢃⣜⣦⠱⡘⢢⡍⠲⢌⡱⢊⢼⡏⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢺⡏⢆⠓⡤⢋⠆⡥⢋⠤⣣⣅⠓⣤⣿⢷⣵⣼⠞⠷⣧⣼⡿⢿⣅⣎⣴⢃⣾⡻⡏⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣸⡗⣌⠣⢒⡉⢖⡰⣉⢆⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⡍⢛⠛⣿⣿⢿⣕⣢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢻⡷⢨⠜⡡⢚⣤⢚⡟⠋⣱⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣸⣾⠟⢉⡽⢧⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢌⣾⢃⢇⢪⠱⣟⠉⠋⠁⠀⠈⠛⠁⠀⠀⠀⢠⣀⣀⡰⠆⠀⣀⣤⠞⠉⢻⡀⣻⠲⡼⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⣥⡟⢣⢊⡔⣊⡑⡛⠷⠶⠶⡶⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⡾⠋⠁⠀⠀⠀⠀⠻⣷⢞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢾⡗⣨⢑⠢⢜⢠⢒⣩⣜⣥⡷⠟⠋⠁⠀⠀⠀⠀⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⡼⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢬⣻⣷⢊⡱⢊⢦⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⣤⡾⢫⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⢸⣇⢎⡴⡿⠉⢷⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡋⣿⢻⠋⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠝⣿⡿⢯⡔⠘⢷⣀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢟⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⢻⣾⣽⣷⡞⡹⢛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠚⠋⠿⣶⣭⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢣⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⡀⠀⢀⡴⢏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠈⣸⠷⢾⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣧⣀⣀⣠⡴⡾⣏⠀⠀⠀⣠⣴⠃⠀⠀⢧⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠓⠂⠈⠈⠊⢓⣒⠚⠝⠋⠙⣒⠦⠖⢞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⡤⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠊⠃⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⡀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠁⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⠀⠌⣀⠄⡂⠄⠀⠀⠀⠀⠳⠀⠁⠀ ⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⡀⠍⠠⠀⠁⠁⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠐⢈⠤⠀⠀⠀⢨⠀⠐⠀ ⠀⠀⠀⢀⠉⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠈⠄⠀⡀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⠀⠈⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠁⠀⠂ ⠀⠀⠀⠄⠀⠈⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠌⠀⠀⠀⠄⠀⡀ ⠀⠀⠀⠀⠀⠂⠀⠀⠈⣈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⡠⢈⠊⠂⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⢎⡄⠀⠀⠀⠀⢀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠅⡂⡒⠡⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⡀⠀⠀⠀⡁⠀⠀⠀⠀⠉⠈⠊⠌⠘⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂ ⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡀ ⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⠔⠊⠑⠒⠄⣄⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⡀ ⠀⠀⠀⡀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠄⠤⠂⠂⠒⠂⠒⠐⠐⠐⠀⠂⠂⠈⠈⠀⠁⠈⠀⠈⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠒⠄⢀⡀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⢀⠀⠀⡀⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠠⣶⣿⣿⣷⡶⠀⠀⠀⣀⡴⣖⡦⡀⢀⣤⢤⡤⣀⠀ ⠀⠈⣿⣿⣿⠀⠀⠀⢰⢯⡽⣞⣵⡳⣟⢮⡗⣯⡽⡀ ⠀⠀⣿⣿⣿⠀⠀⠀⠸⣏⣾⢳⡞⣽⢞⡯⣞⣳⣽⠁ ⠀⢀⣿⣿⣿⠀⠀⠀⠀⠈⢺⡳⣏⣟⢾⣹⣳⡝⠂⠀ ⠀⠻⠿⠿⠿⠗⠀⠀⠀⠀⠀⠈⠙⢮⠯⠃⠉⠀⠀⠀ ⠀⠀⠀⢀⡄⣄⡀⢀⣀⣀⡜⠓⣄⠤⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠉⠉⠉⠩⣉⣀⣼⡒⠊⠁⡃⠀⠀⠀ ⠀⠀⠀⡝⠀⠀⠀⠀⠀⠐⠍⠵⢫⣧⡰⡔⠀⠀⠀⠀ ⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢁⣼⠤⠄⠀⠀ ⠀⠀⠨⣧⠀⠘⠃⠀⠀⡤⠄⠀⠙⠁⠀⣚⠒⠀⠀⠀ ⠀⠀⠠⠚⠹⢤⣀⣀⠀⠀⢀⣀⡤⠜⠉⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣴⣶⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⢡⡿⠛⠀⠘⠻⣿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⡷⠋⠀⠀⠀⠀⠀⠈⢿⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡸⣷⣾⣷⣦⣤⡀⣀⣀⣠⠤⢤⣄⣀⠀⠀⠀ ⢸⣿⡏⠆⠀⠀⠀⠀⣿⡇⢀⣼⡿⠁⠀⠀⠀⠙⢿⡟⢻⡿⠋⠀⠸⢿⣿⡟⢆⠀ ⠸⣿⣿⡀⠀⠀⠀⠀⠙⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠹⣷⣬⡆ ⠀⠻⣿⣷⣄⠀⠀⠀⣀⣠⢿⣇⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⡆⠀⠀⠀⠀⣹⣿⡇ ⠀⠀⠙⠿⣿⣿⣶⣿⣷⣶⣿⣿⣿⣦⣀⠀⠀⣀⣴⣿⣁⣼⡟⠀⠀⠀⢀⣿⣿⠇ ⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠁⠈⠛⠿⣿⣿⣿⣿⠋⠙⠛⠋⠀⠀⠀⠀⠈⠉⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢻⣿⣷⣄⠀⠀⠀⢀⣤⣤⣤⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣭⣛⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠛⠿⣿⣶⣾⡿⠛⠛⠛⠛⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠙⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣾⡿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠛⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠻⣷⡄⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⣶⠿⠿⣿⠏⢿⣆⣀⣀⣀⠀⠀⠀⢀⣿⠿⣿⡿⢷⣦⣼⣿⡆⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢿⣦⣾⡟⢀⣿⡿⠿⠿⠝⣷⠀⠀⠸⣿⡀⢻⣧⣴⡿⠏⣸⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣻⡿⣷⣤⣉⣹⣿⠿⠙⠷⠶⠶⠾⠋⠀⠀⠀⠹⢷⣮⣿⣷⣤⣶⣿⣷⣦⡀⠀⢀⣀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⡄⠀⠰⣟⠞⣁⣴⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣷⣍⠻⡾⣿⠀⠘⢿⣷⣿⣧⣤⣤⣄⣀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⠋⢀⣤⣿⣧⠈⢿⡆⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣠⡀⠀⠀⠉⠉⠛⠛⠛⠻⣿⣦⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⢸⣯⣰⣿⣁⣠⣿⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣧ ⠘⣿⣧⡀⠀⠀⠀⠀⠀⠻⣿⣏⠙⠛⢛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣾⡿⢿⣶⣶⣶⡿⢿⣧⣀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⣀⣀⣀⣤⣿⡏ ⠀⠈⣻⣿⠆⠀⠀⠀⠀⢀⡿⣿⢷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠶⠿⠿⠋⠀⠀⠀⠀⠀⠀⠈⢙⣻⠿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠿⠿⠿⠛⠉⠀ ⠀⣸⣿⠃⠀⠀⠀⠀⠀⣿⢱⠏⣸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣆⠈⠻⣷⣶⣶⡄⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⡾⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⣾⣿⠿⠿⣷⣦⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⣸⣿⡁⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣤⣰⣿⠁⠀⠸⣿⡀⠀⠀⠀⠀⠀⢾⣿⠟⠋⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠻⣷⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢉⣿⣿⠏⠀⣀⣤⣿⣧⣄⣀⠀⠀⠀⠘⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠶⠶⠟⣀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣾⠟⠁⠀⣾⡟⠉⠉⠉⢙⣿⣷⣶⣤⣴⣿⣧⣄⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣴⡿⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠃⠀⠀⠀⢿⣧⡀⠀⠀⣿⡟⠉⠉⠙⠋⠉⠉⢻⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣤⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣄⠀⠀⢀⣼⣿⠿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣷⣶⣤⣤⣤⣶⣶⣾⡿⠿⠛⠋⠁⠀⠀⠀⣶⣦⡄⠀⠀⠀⣀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢸⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠛⠛⠶⣦⣄⣠⣴⠾⠛⠛⠛⠳⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄⠀⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀ ⠀⣠⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀ ⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⢿⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣠⡿⠀ ⠈⠻⣶⡟⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣼⠷⣤⣤⣴⠾⠛⠷⠶⠶⠾⠛⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠉⢻⣿⠁⠀ ⠀⣸⡟⠀⠀⠀⠀⣾⠃⠀⠀⢰⣶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣷⣄⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠹⣧⠀ ⠀⣿⠀⠀⠀⢀⣼⠏⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡄⠀⠀⠘⣷⡄⠀⠀⠀⢹⡆ ⠀⢿⣄⣀⣠⡾⠋⠀⣤⣴⣿⠃⠀⢠⡞⠉⠳⡄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣴⠋⠙⢦⠀⠀⠈⢻⣶⠦⠀⠈⢿⣦⣀⣀⣾⠃ ⠀⠀⠉⠛⠹⣧⡀⠀⠉⡀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⢀⣠⡿⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⠿⢷⣄⣙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠲⠤⠤⠶⠂⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⣀⣼⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠙⠻⠶⠶⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⠶⠶⠟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⡋⠛⠻⢿⣿⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣾⡿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠇⣿⣿⣿⣿⠃⠀⢀⣤⣤⡈⣿⣿⣿⣿⣿⡏⣴⣶⡄⠀⠀⢹⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡶⠶⠶⢿⣿⣿⣿⡄⠀⠈⠻⠿⢃⣿⣿⣿⣿⣿⣧⡙⠛⠃⠀⢀⣼⣿⣿⡿⠛⠉⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣤⣤⣶⣿⣿⣏⠁⢹⣿⣿⣿⣶⣤⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣀⣤⠾⠻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠷⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠰⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣿⣿⣎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢨⡳⣜⡘⢦⢣⢣⡝⣬⢣⡝⣭⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⡷⣬⠝⣦⢋⠶⣘⢦⠳⡜⢦⣛⠼⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣷⡭⣟⡴⣋⡞⡭⢎⡳⣙⢦⢭⡓⣧⢛⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⠤⡑⢌⠰⠠⢌⠓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡽⣾⣱⢯⡼⣱⢋⡶⢭⣚⠶⣙⡖⣏⡞⣆⠀⠀⠀⠀⠀⠀⣼⢁⡒⢌⢢⠑⡌⠦⣙⢢⡙⡴⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡷⣯⢷⡹⣇⠯⣜⠳⡬⢏⡳⣜⣣⡝⡞⣧⠀⠀⠀⠀⢰⡏⢦⢘⡂⢎⡱⢌⡳⢄⢧⡚⡵⣲⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡽⣯⣟⣼⣛⡬⢏⡵⢫⣕⠺⡴⡹⡜⡭⣇⠀⠀⠀⡾⡜⢦⢣⡜⣱⢊⡵⣘⢎⠶⣹⡜⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡷⢯⡶⣏⡞⣭⢚⡵⢊⠷⣡⠓⣍⠖⡹⡆⠀⠀⢻⣝⣮⢳⢮⡕⣯⢶⡹⣎⣟⣶⣻⡽⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣟⣿⢣⡟⣤⠛⣤⢛⡤⣃⠟⣠⢛⠣⠻⢄⠀⢀⣿⣼⢿⣜⡿⣼⢧⣿⣻⡼⣧⡿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡞⣯⢞⡴⣉⠦⡓⠴⢡⠊⣁⠂⡔⢡⢂⠜⡠⢌⠛⠿⣾⣽⣯⢿⡾⠷⣛⢯⢻⡵⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡧⢏⠢⡑⢢⠑⡌⢢⠑⡤⢃⡜⡄⣋⠴⣁⠎⡜⠢⠔⢢⡐⠢⢄⠡⢂⠌⢣⠹⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⡉⢆⠱⡈⢆⡱⢌⡱⢊⡔⢣⠔⡱⢌⠲⣌⠚⡴⣉⠎⡥⣘⠱⢌⠒⡩⠘⡄⠳⡌⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⡔⢡⠊⡔⣉⠖⡌⢦⡑⢣⠜⣡⢎⡱⣊⠵⣈⢳⠰⣡⠚⡴⢡⠚⡌⢥⠃⡭⢘⡱⡜⡱⢆⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢅⡚⡌⢦⡙⡰⢡⡚⡌⢦⡙⢦⡙⢆⢎⡱⣌⢣⠝⣢⠛⣤⢋⠴⢣⡙⡜⣢⡙⠴⣉⠖⣭⢳⣙⠶⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⢋⢦⡱⢚⡤⢣⣃⠧⣜⡘⢦⡙⣦⣹⠮⠞⠒⠘⠂⠉⠐⠙⠒⠋⠞⠧⠾⣱⣦⡙⢧⣙⢮⡕⣳⢎⡿⣥⢻⡄⠀⠀⠀⠀ ⠀⠀⣸⢇⡏⢦⡓⣭⢒⠧⣎⢳⣬⠗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢮⣗⡾⣱⢏⡾⣱⣏⢷⡀⠀⠀⠀ ⠀⢀⣿⠸⣜⢣⡝⢦⣋⣾⣼⡋⠱⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣶⠋⣻⣧⡟⣵⣏⢾⡭⣇⠀⠀⠀ ⠀⢸⣯⢳⣎⠷⣸⢣⡷⠋⠀⢹⣿⠿⡟⠉⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢻⠿⣿⠁⠘⢿⣞⣞⣯⢞⡧⠀⠀⠀ ⠀⢸⣯⢗⣮⢻⡵⣻⠁⠀⠀⢸⣿⡏⢻⣷⣿⠇⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⡿⣿⣿⡏⢻⣿⠆⠀⠈⣷⢾⣭⣟⡷⠀⠀⠀ ⠀⠘⣿⢯⡞⣧⣛⡏⠀⠀⠀⠈⠻⢿⠿⠿⠋⠀⠀⠀⠀⣀⠀⠈⠛⠁⠀⢀⡄⠀⠀⠀⠉⠿⠿⡿⠋⠀⠀⠀⣻⣟⡾⣾⡇⠀⠀⠀ ⠀⠀⠹⣿⣽⣳⢯⣧⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠹⣟⡛⣟⡛⣻⠟⠀⠀⠀⠀⠀⠀⠀⠐⢀⢠⡴⢀⣿⢯⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣯⡿⣽⣆⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣤⠽⠋⠀⠀⠀⠀⠀⣀⣀⡀⠲⠞⣛⣤⣾⣟⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⢢⡍⢲⢰⣤⣤⢠⡄⠀⢠⠀⠀⠉⢡⡔⢠⢠⠐⡆⢲⠛⣭⢱⣬⣷⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠻⠿⣿⣶⣧⣶⣬⣒⣉⣎⣵⣮⣽⣻⡧⢶⣍⣎⣱⣈⣳⣦⣽⣶⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠠⢤⡐⢌⠢⣉⠜⡩⢥⢩⡝⠀⠙⣎⠭⢌⠥⡙⢄⠆⣤⡰⠆⠀⠀⠀⠀⣀⡠⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣀⠀⠀⠀⠉⠓⠧⣜⡬⡑⢦⡿⠀⠀⠀⠸⣯⠘⢦⣑⡮⠜⠋⠀⠀⢀⣴⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠈⠁⠉⠈⢳⡄⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⠀⠀⣶⣹⣤⡾⣦⣅⣀⠀⠀⡀⢖⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢺⠏⡜⢂⠏⠻⠄⣀⢀⣀⡠⣀ ⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠰⡀⢮⣔⣫⠶⡭⢖⡳⢭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⠀⠀⠈⣿⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⣿⡅⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⢸⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠽⠿⠷⠶⠤⣄⣀⣸⣧⡀⠀⠀⠂⠀⠀⢀⣀⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣤⡤⠤⠶⠷⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠉⠛⠋⠉⠛⠛⠛⠭⢭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⣖⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣺⠥⠒⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⢁⣼⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⢀⣠⡟⣹⠃⠀⠀⠀⠀⠀⠀⢦⣶⡶⢾⣖⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀ ⠀⠀⠀⠀⠀⠀⡀⢼⡟⣯⠞⢹⠀⠀⠀⠀⠤⠤⠇⢀⠁⠀⠀⠀⠘⢽⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠳ ⠀⠀⠀⣠⣤⣦⣟⣠⠞⠁⠀⢸⡄⠀⠀⠄⠀⠀⠀⠈⠙⢴⠂⠀⠀⠀⠀⠁⠀⠀⢇⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀ ⣤⣶⣿⣿⣿⣷⠟⠁⠀⠀⠀⠈⢳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⢏⢸⣧⣌⣤⣄⠀⠀⠀⢀⠀⠀⠀⠀⢀⣴⣾⣷⣶⣦⣤⣄⠀⠀⠀⠠⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀ ⡿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠿⠿⣷⡶⣷⡾⠿⠀⠀⠀⠀⠙⠉⠉⠋⠿⣿⣿⣧⡄⠀⠀⡀⠀⡷⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠢⣤⡠⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡄⢄⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠞⠀⠀⠀⡇⠀⡇⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⠀⠀⠀⠉⠳⣿⣿⣯⡷⣄⢰⣀⣄⠀⠀⠀⢨⠻⣾⠿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠗⢦⢰⠁⢠⢻⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠹⣦⡀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣟⣻⣷⣶⣴⣦⣤⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⢀⡏⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠻⣦⣤⣀⠀⡠⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠯⢿⣿⣿⣿⣿⣾⣶⣦⣤⣤⣀⣀⡀⠆⠀⠀⠀⠠⠴⣣⠤⠏⠹⡅⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠛⢿⡿⠿⣿⣿⡿⠲⠭⠴⠖⠋⠀⠀⠀⠀⢳⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢰⡆⢹⣛⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣿⣠⣐⣴⣿⠏⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⢈⣁⣀⣀⣉⡩⠭⠷⠗⠒⠒⠦⠤⠤⠤⠤⣀⣀⣳⣆⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⡘⣆⣠⣀⡀⣄⣤⣠⢀⠀⡀⢀⠀⠀⡄⣀⠀⢰⢷⠋⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢀⣿⣿⣿⣿⡿⠛⠛⠛⠛⠻⣿⣿⣿⣷⣿⣇⠈⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠘⡄⠃⠉⠁⠀⡼⠑⠓⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⣶⣾⣿⣿⣿⣷⣷⣿⣶⣥⣤⣤⣮⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠙⠛⠛⠛⠛⠛⠛⠙⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠲⠤⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠀⠒⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠛⠒⠒⠒⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠀⠈⠉⠙⠳⣦⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢻⡄⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠈⣿⢀⣴⠞⠋⠉⠀⠀⠈⠉⠛⢷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠟⠀⣿⡟⠁⣾⣿⣿⣷⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠹⢿⡿⠏⠀⠀⠀⠀⠀⠀⠈⣿⡀ ⠀⠀⠀⠀⣠⣶⠟⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⢀⣼⠟⠁⠀⠀⠙⠷⣤⣀⡀⠀⠀⣀⣠⡾⠛⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀ ⠀⠀⣾⠃⢀⡤⠄⠠⢄⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⠀⠀⡿⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⣀⣀⣠⣴⣾⠋⠁⠀⠀ ⠀⠀⣷⠀⠈⠓⠢⠔⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢻⡆⠀⠀⠀ ⠀⠀⠻⣧⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠑⢆⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⣠⣼⠿⠟⠻⢷⡆⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡅⠀⠀⢸⠀⠀⠀⣸⡏⠀⠀⠀ ⠀⢰⠏⠀⠀⠀⠀⣾⣧⣄⣀⠈⢳⣤⡤⠴⠶⠶⠟⠛⠛⠉⠁⠀⠑⠦⠴⠋⠀⢀⣴⡟⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⣨⡿⡟⣩⡛⡿⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠻⣦⣄⣀⣈⣿⡴⢹⣿⣿⣶⣾⣷⠉⠉⡟⠛⡿⠻⢶⣶⣶⣶⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⠿⣯⡉⣩⣃⠀⢀⣏⡻⠿⣏⣀⢀⠃⠀⡇⢀⣿⠁⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡟⠛⠁⠀⠈⠛⠋⣿⡇⣾⠏⠻⠾⠛⠙⣿⣤⣼⠀⢸⣇⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⣰⣿⣤⣿⡄⠀⠀⠀⠀⠉⢹⣯⣤⣤⣿⡄⢀⡀⢀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣤⣤⣤⠾⠋⠀⠀⠈⢷⣄⡀⠀⢀⣴⡟⠁⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡿⣍⢯⡝⣣⢏⡼⡽⢋⠩⣉⠻⣧⣝⡮⠗⡹⣮⡕⣫⢎⢧⡛⣬⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⢏⡽⣩⠝⣮⣱⢋⢮⣱⡿⢋⠙⣧⢋⡞⣥⢫⡜⣣⡝⢮⡝⣭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⢭⡝⣭⢚⡵⢫⡜⣣⡝⢮⡱⢫⣜⡱⣭⢚⡭⡝⡭⣭⠹⣍⠞⣥⢫⡜⣣⡝⣎⢧⡛⣬⠳⣍⠞⣥⣋⣎⢳⡍⡾⣩⢏⡽⣩⢞⡹⣜⡹⢎⡅⣪⠖⡥⢯⡹⣍⣏⢳⢭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⡝⣭⢫⣝⡣ ⡗⣎⡳⣜⠳⣎⠼⣁⠎⡱⢄⠣⠼⢋⡔⢡⠒⡌⡟⡴⣋⠮⣕⡣⢞⡼⡱⢎⡵⢣⢏⠶⣩⠞⡴⣋⢞⡴⢭⠺⡴⣓⠮⣖⠳⣎⢖⠧⢮⡱⢣⢮⡱⢣⢏⠶⣩⠞⡼⡱⢎⡵⣓⢮⡱⢣⢏⠶⣩⣛⠴⣣⡿⠞⠻⣁⣦⡑⠎⠓⡜⢦⡛⡼⡱⢎⡳⡜⣥⢳⡙⢦⢫⡜⢶⡩⢞⡬⣓⢮⡱⣓⢮⡱⣓⢮⡱⣋⠶⣙⢦⣛⠼⣣⠛⡡⢉⠳⣍⡳⢬⡳⣌⢏⢶⣩⠳⣜⡽⣸⠹⣆⣿⣿⣧⣚⢼⣢⣽⣶⣿⣬⣟⠴⣣⢎⡳⢼⡱⢣⢏⡖⣣⢏⣜⠲⣍⠯⣜⢣⢏⡝⢮⣱⢣⢎⡏⣎⢳⡜⡥⣇⠻⣔⢫⣜⠲⣍⠞⣬⠳⡼⡱ ⡟⡼⣱⢎⡻⢌⢋⠣⡘⢰⠈⣦⣑⣢⠘⡄⢣⢰⡛⡴⢫⣝⠲⣭⢓⠮⣝⡹⣜⢫⢞⡹⣱⢫⢳⣙⠮⣞⡱⢯⡱⡭⢞⣬⠳⣍⢮⡝⣣⠽⣙⠶⣙⢏⡞⣭⢣⡛⡵⢫⡝⣲⢹⢲⡙⣏⢞⡹⢳⡬⢳⡱⣇⣌⠡⠻⡿⢏⠨⡑⣈⢧⡙⡶⡹⣍⢳⡹⣜⢣⡛⡭⢇⣛⠮⡵⣋⢶⡹⢲⣍⠳⣎⢳⡹⢲⡹⣍⡻⢬⡳⣌⠷⡡⢇⣰⣅⠋⡔⡙⢦⠽⣸⢎⡳⢎⡽⢦⠳⣥⡛⣬⣿⢾⡽⣷⣿⣿⢿⣯⣟⣿⣟⢣⡇⢯⣙⠶⣩⠟⣜⢺⡱⢞⡜⡻⣜⡹⢎⡝⢮⡹⢣⣳⠹⣎⢳⢭⡓⡞⡵⢎⡻⣜⢣⡞⣹⢎⡻⣜⢳⣹⢓ ⣟⢲⢣⡎⡵⢊⢄⠣⡑⢌⢲⡿⣹⢻⣧⠜⡠⢃⡙⢾⡕⣎⡻⣔⢫⠞⣦⢓⡮⢳⢎⡳⡵⣋⢧⡝⣺⣴⣿⣶⣧⣽⣊⡶⣹⣼⣶⣩⢇⡏⢧⣛⡜⢮⣜⢲⢣⢽⣘⢧⣚⢥⢏⠶⡹⡜⢮⡱⢧⣹⢣⡳⣜⡛⢿⣇⠰⡈⣳⠴⣩⢖⡹⢖⣣⡝⡲⢵⣊⠧⣝⡜⣣⢎⣳⡱⢭⡲⣍⡳⢬⢳⢎⠧⣝⡣⢗⢮⠵⣋⡖⣿⡠⢑⠨⣷⣮⠷⣠⢡⢎⣳⢣⡞⣭⣓⢮⣙⣳⣦⣽⣦⣿⣯⣿⣿⣿⢾⣿⣞⡿⣿⣾⣵⣚⢧⣙⠮⣕⣫⢜⡣⡝⢮⠼⣱⢎⡵⢫⡜⡧⣝⡳⣬⠳⢮⡝⡲⢭⣳⡙⢮⠵⣎⢳⠼⡱⢮⡱⢎⡳⡜⡭ ⣏⢧⢫⣜⡱⣊⠄⢣⠘⣄⣚⠷⠿⢋⣅⠊⠴⡡⠘⡄⢿⡰⣓⠮⣍⡻⡔⣏⣞⡹⢮⣱⠳⣍⠶⡹⣜⣿⡖⣞⣬⣏⣿⢻⣾⣿⣻⣷⡎⣝⣣⠞⣜⣣⢎⣏⠞⣦⢋⡶⣩⠞⣮⢹⣱⠹⣎⠵⣋⢶⣙⠶⣣⡝⣎⠿⡶⢿⢇⣏⠳⣎⡝⡺⡴⣹⡙⣦⢋⡞⢦⡫⣕⢫⢖⣹⣒⢳⠼⣱⣋⡞⢮⡝⣲⢭⣋⢮⢳⡹⣜⡜⣻⠻⣿⣏⠁⢆⣵⢋⡞⣴⢣⣛⡴⢭⣒⢻⣿⣯⣻⣝⢯⣿⡿⣿⣏⡿⣞⡽⣿⣷⣯⣿⢿⠲⣍⠾⣘⢦⢏⡵⣋⢧⣛⠦⣏⡼⢣⣛⡼⣒⢧⢧⡛⢧⡚⣭⢓⣦⡽⠾⠷⣮⣝⢺⣙⠶⣍⡻⣔⠻⡜ ⡯⢎⡳⣬⠳⣍⠷⡶⢷⡟⡉⠦⠱⣈⢼⡿⣤⢡⣉⡴⣋⠶⣍⡳⢭⠶⣙⢶⣊⢷⣩⢖⣹⣼⠿⣟⢯⣛⢿⣮⣳⡽⣞⣯⣿⡷⣯⣿⡳⡜⢦⠻⡜⢦⣫⠜⣝⡲⣋⣖⢣⡻⣔⠳⣬⢓⡮⡹⣍⡞⣬⢳⠳⣜⣣⣛⠼⣣⠞⣬⢛⡴⣍⡳⣕⣣⡝⣲⢫⡜⢧⣓⢮⣙⢮⢲⣍⡞⣣⠗⡮⡜⡧⢞⡱⢮⣙⡎⢧⢳⠼⣸⢕⣫⢖⡹⣛⡟⣣⢏⡞⣬⡓⢧⢞⣣⡝⢦⢭⣽⣿⣻⢯⢷⣛⣿⣿⣾⣝⣾⣽⣿⣿⣿⣮⡳⣍⠞⣭⠞⣎⢶⣙⠶⣩⢞⡼⣜⡣⢗⣎⡳⣚⣦⡿⠖⠻⢶⣿⡋⠴⡑⠢⢌⢻⡞⣬⠳⣍⢶⣩⡛⡼ ⣏⡳⣝⡲⣹⢬⢳⡙⡞⣷⡈⢒⠱⣀⣾⡗⣣⢇⡳⡼⣱⣋⢞⡱⣏⠞⣭⠶⣩⢖⣣⢮⡙⣿⣿⣬⣇⣏⢞⣹⣿⣷⣟⡾⣿⣽⣿⣿⣿⣿⣿⣷⣭⠳⣬⢛⡬⢳⡱⢎⢧⢳⡜⣹⢆⡻⣔⠻⡴⣹⢬⣓⢻⡜⢦⣙⠮⣕⠻⣌⣳⣚⠴⣓⢮⢲⡍⢧⣣⢛⡼⣜⡲⢭⣚⠵⣪⡜⢧⣋⠷⡹⣜⢣⣛⢬⠳⣜⢫⢎⡳⣍⠞⣦⢫⠵⡳⣜⡱⢞⡼⣡⠻⣍⡞⢦⡝⢮⣾⣟⣾⣵⣛⣮⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣘⡏⢶⡛⡼⡲⢭⢞⡱⣋⠶⣱⢫⢞⡴⣋⢶⡏⠰⣈⠱⣈⠻⣧⣂⠱⡁⢎⣾⠟⣬⢛⣬⢳⢲⣙⠶ ⣶⣱⢎⡵⢣⢞⣣⡝⢮⣙⠟⡷⠾⣟⢣⡞⣱⢎⡳⡵⢣⡞⣭⢓⣎⠟⣦⢛⡵⣪⠵⣊⣷⣿⣿⣿⣿⣿⣿⠻⡵⢮⡝⣿⡿⣿⣿⡽⣾⢷⣯⣟⣿⣿⣦⢫⡜⢧⣫⠝⣎⡳⣜⣣⢞⡱⣎⠯⣕⡳⢎⣞⣱⢺⡱⢎⣽⣾⣿⣿⣿⣿⣿⣬⣳⢣⢞⡳⢬⢳⡱⢮⡱⢇⣏⢞⣱⢚⠧⣎⠳⣵⣊⣷⣼⣾⣿⢿⠿⠿⠿⠿⢿⣿⣟⣮⠵⣪⢕⡫⢖⡭⡳⣍⡞⢧⠞⣥⠿⣿⣿⢻⣿⣾⡿⣟⣿⢿⣷⣿⣿⣾⣿⣿⣿⡷⣩⢞⣣⠽⣱⠽⣩⢞⡱⣭⠞⠷⣋⢞⡲⣍⠞⣿⣄⠡⠒⡄⣿⣟⣿⡆⠽⠻⢿⣜⢣⡏⢶⣩⢶⡩⢞ ⢧⣭⢛⣮⣓⣎⣶⣩⢇⡏⣞⢭⣓⢎⡗⡺⡥⢏⡳⢭⡳⣙⢦⣛⣬⠻⡔⣏⠶⣣⢛⣼⣿⣿⣿⣿⣿⣟⣬⣏⣵⣧⣿⣿⠳⣭⣿⣿⣿⣿⣾⣿⢟⡻⣍⣳⢚⠧⣎⡻⣌⠷⡱⣎⢞⡱⢮⡝⢦⣹⢣⢞⡬⢧⣙⣿⣿⢿⣽⣿⣻⢾⣿⣿⣿⣯⣮⠱⣏⢮⡱⢣⣛⡼⣘⠮⡜⣭⣞⣼⣿⡾⢟⠛⡩⢁⠆⠢⠜⣠⠃⡜⢠⠻⣿⣿⣷⡍⣮⢕⡫⢶⣙⠶⡹⣎⣛⢦⡛⡼⣿⡿⣜⣿⣿⣿⣻⣿⣯⣿⡿⣿⣿⣿⣿⡿⡰⢏⣖⢫⡵⢫⡕⡮⡑⢦⣼⣐⡙⢮⡱⡹⢮⣱⢛⣿⠟⡠⢙⠛⡉⠔⡡⢃⠜⣿⡱⢮⣷⢫⢏⡟⣬ ⡳⢎⣽⣾⣿⣟⡫⢿⡿⣿⣜⢦⣋⢞⣜⠳⣭⢫⡝⣣⠽⣩⢖⣣⢎⣳⣽⣾⡧⣝⢺⣿⢯⣿⣿⣾⣟⣿⡿⣿⣿⢿⣿⣿⣙⢦⣿⣿⣳⣯⡿⣿⣮⠱⡞⡴⢫⣝⢲⣣⢝⡺⡱⣍⠮⡝⣦⢋⠷⣌⡳⣚⡜⣣⣿⣿⣻⣿⣻⢾⣽⣻⢾⡽⣿⣿⣿⣷⣾⣷⣿⣿⣷⡜⣭⢳⣽⣾⠟⡋⡅⠒⡌⢢⠑⡬⢈⢇⡱⢄⠓⡌⡡⠒⢌⢻⣿⣿⡔⣫⡜⢧⣚⡭⢳⡱⡭⢶⡙⢶⡙⢿⣿⢿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣿⣟⠲⡽⣩⢎⡗⢮⢳⡜⢿⣦⡝⠻⣣⣐⣶⢯⡱⢏⡖⢯⣿⠠⡑⡌⢢⢱⣾⣄⣮⣼⠯⣽⣿⣱⡯⣞⡹⢆ ⣟⣻⣿⣿⣻⣭⣿⣿⣷⣽⣿⡶⣩⠞⣬⠻⡴⢫⣜⢣⣻⡶⢿⣴⡿⢏⣳⣿⡱⢎⣻⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣽⣿⣯⡖⣿⣿⣯⣷⣟⡿⣿⣧⢹⡚⣵⢪⠳⡜⢮⣕⣳⣬⣷⣽⣰⣋⢷⣸⣱⢣⢞⣱⣿⣿⣟⡷⣯⣟⡾⣽⢯⡿⣽⣻⣿⣿⣯⣟⣾⡽⣿⡿⠶⠿⢋⠔⡨⠔⣈⠇⢬⡁⠞⡠⢃⠦⡐⢎⠰⣁⡒⢍⠂⢆⠻⣿⣿⠦⣝⢎⡶⣙⠧⡽⣱⢣⢏⠧⡝⢮⡹⢿⢯⢿⣿⣽⣿⣿⣿⣿⣽⣿⣋⡟⣴⢋⡾⡜⡭⢞⡜⣣⠞⣷⡽⢯⣙⢦⡳⢭⡓⢾⡩⢿⣆⣡⢘⣤⡿⢿⣿⣿⡌⣿⣟⣾⣵⣾⣷⢿⣿ ⣞⣿⣿⣷⢯⣿⢾⣯⣿⡿⣿⣿⡡⢟⡜⡳⣭⡓⢮⢇⣛⣿⡿⢿⡾⢟⣻⣿⣿⣎⣽⣿⣿⣿⣻⣟⣿⣿⡿⣿⣟⣾⣯⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣗⣣⡝⢶⣩⠳⣭⣷⣾⡟⠛⡛⠛⠛⡛⠻⠿⠿⣿⣾⣿⣿⡷⣯⣟⡷⣯⢿⡽⣯⣟⡷⣯⣿⣿⣿⣯⣷⣿⣿⠑⢬⠑⡌⢢⢑⠊⡔⢊⠔⡈⢆⠱⢌⢢⣱⡮⢗⡭⣹⣦⠉⢆⠡⣻⣿⣷⢚⡼⢲⡍⣗⣣⠝⣮⡹⣚⢭⣣⢝⡺⡜⢮⣍⡛⡟⢿⣿⣿⢿⠳⣜⡜⣎⢧⢳⡹⡜⣭⣾⣥⣟⡴⣙⢮⡱⢮⠵⣣⣛⡬⢳⢣⢏⡛⡯⣝⡜⣣⢻⣿⣼⣿⣾⢯⡱⢎⡝⠿⣾ ⢿⣿⣿⣿⡿⣯⣿⣿⣯⣿⣿⣿⣏⢞⡭⣓⠶⣹⡍⣎⣿⡯⢼⣿⠜⣳⣿⣿⣿⣗⠾⣿⣿⢿⣿⣯⣿⣿⢿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⡼⣓⠞⣴⡹⢎⣖⡛⣾⣿⠙⡤⠓⡌⡑⢣⠘⡑⢢⠒⡤⢈⢽⣿⣟⣷⣻⣾⣽⢯⣟⡷⣯⣟⣷⣻⣿⣿⣿⣷⣿⣿⡎⢰⠡⡘⢄⠣⡘⢄⠣⡘⠰⢌⠒⢬⣿⣱⢊⠷⡸⣅⠾⣏⠌⢆⡉⣿⣿⡧⣹⢣⢞⡱⣎⠽⣲⡱⢏⡶⣓⢮⣕⢫⡳⢬⡝⣺⢱⡚⣦⣯⣙⢦⡛⣜⡎⢧⣳⣽⡿⣏⣿⣿⣿⣿⣷⣿⣬⣓⢳⡬⢳⣍⡳⢎⣝⡲⢵⡚⣥⢻⣿⣿⡟⣱⢮⣱⢫⡜⣏⠶ ⣮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⢺⡱⣍⣛⢦⡝⣦⢹⣿⣾⣧⣿⣿⣿⣿⣿⡏⣞⣹⣿⣿⣯⣿⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠟⣥⠻⡴⢫⣝⡲⣙⢮⢲⡹⣿⣇⠣⣴⣥⣶⣽⣶⣯⣴⣧⣈⡔⠡⢺⣿⣿⣾⣿⣿⣿⣟⡾⣽⣳⣟⡾⣽⣿⣿⣿⣿⣾⡿⢐⡡⢒⠡⢊⠔⣡⠊⡔⢡⠃⣌⣼⣀⠢⢍⠛⢾⣵⣨⠳⣹⠌⢢⠐⡹⣿⣷⠥⣏⠮⡵⢎⡳⣥⢛⡼⢲⣙⠶⣪⠳⣍⡳⢼⠡⠳⡝⡡⠌⣿⢲⣙⢮⣜⡳⡜⣿⡿⣏⣷⣹⣿⣿⣿⣿⣿⣿⣎⠵⡳⢬⣷⣭⢲⡙⢶⣹⣶⡿⣟⢣⡞⣱⢎⠶⣍⠾⣌⡳ ⣿⠟⣼⣹⢿⠛⣙⠻⠿⣭⣮⣕⡫⢇⡗⢮⡱⡞⣜⡲⢇⡞⢿⣿⣿⣿⣿⢟⣣⢞⡱⢎⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⢾⡡⡟⡼⢳⣌⠷⣙⡎⢧⣽⣿⣿⣿⣿⣟⡿⣯⢿⣽⣻⢿⣿⣿⣿⣿⢿⣿⣿⣿⡻⣷⢯⣟⣷⡻⣾⣽⣿⣿⣿⣿⡿⠿⣷⣶⣈⠱⡌⢡⠊⠤⣼⣴⣅⣾⢿⣻⡧⢘⠢⣉⠆⡌⡙⠳⣜⡊⠤⢃⠔⣿⣿⣣⡝⢮⡱⢏⡵⣊⢧⡝⣣⡝⣺⢱⣛⣬⢳⡙⣦⠑⠤⡑⠮⣕⢣⡏⢶⡪⢵⡹⣾⡟⣴⣻⣿⣿⢿⣷⣿⣿⣿⣿⣮⢕⣫⣿⢻⣷⣿⢿⡻⢿⣖⡭⢞⡼⡱⢎⡻⢬⠳⣍⠶ ⢎⡽⠡⡜⢢⡙⠤⢛⠰⢥⢢⠹⣷⣫⡜⢧⢳⣙⠶⣙⢮⣙⢮⡙⣟⢫⠵⣪⠵⣪⢝⢮⡹⢿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣛⢯⡱⢞⡭⢲⡹⣜⢳⣍⣎⡳⢭⣚⠧⣿⣿⣻⣿⣳⢯⡿⣽⣻⢾⣽⣻⢞⣿⣿⣯⣟⣾⣿⣷⣿⣽⣾⣽⣶⣿⣿⣿⣿⣿⣿⡿⣉⣷⡾⠟⡠⢃⣜⣤⣽⣾⣿⣱⢻⣽⣳⣿⣷⣮⣔⡢⠘⡤⢑⡡⢂⠥⠓⡌⠒⢼⣿⣧⢚⣥⠻⣬⠳⣍⠶⣙⢦⡝⣲⣋⢶⣊⢧⡝⢦⡘⡴⢣⣒⡬⣓⢞⣣⡝⣖⡣⢽⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⡷⢢⣛⣿⣾⣿⣎⣽⣣⡿⣛⠼⡲⣍⢯⣱⢫⠽⣘⢧ ⡹⢆⠓⡌⠥⣌⣳⡿⠿⢶⡆⡍⡍⢛⣿⣬⢓⡮⣝⢣⡗⣎⠧⣝⡬⣓⢏⠶⣫⠵⣚⢮⡱⢫⠽⢿⠿⡿⢿⡛⢯⡱⢎⡵⢎⡵⢫⡜⢧⠳⡭⢞⡴⢪⣝⢣⣎⡗⣿⣿⣿⡷⣯⢿⣽⣳⢯⣟⡾⣽⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⡿⡐⢿⣏⠰⣉⠔⡹⣿⣿⣏⣿⣿⣧⣏⣿⣿⣿⣿⣿⣿⣿⡁⢲⠁⢆⠣⢌⠱⣈⠱⣎⣿⣿⡘⣦⢛⡴⣛⢬⡛⡼⢲⣍⡳⡜⡶⣩⠶⣹⠲⣝⠼⡳⣜⢲⡝⣎⢶⣙⠶⣙⢦⡛⢿⣿⣾⣿⣿⣿⣿⣿⣿⣟⣫⣼⣷⣿⠾⢛⠻⣿⣯⣷⣱⣍⠳⡝⡼⣒⢧⢫⡝⣚⢦ ⡹⢧⡚⡸⠰⡘⣿⣍⣻⣼⡧⡘⢌⠣⢼⣿⢜⡲⢭⣓⠞⡼⣙⢦⠳⡭⢎⡳⢥⣛⠼⣲⠹⣍⡞⣣⣛⣜⡣⣝⡣⣝⠺⡜⣭⠺⣥⢛⠮⣝⡱⣏⡼⢳⢬⡓⣾⣿⣿⣿⣿⣿⣽⣻⣞⣽⣻⢾⡽⣯⢿⣻⣽⣻⣿⣿⣿⣿⣿⡿⠟⡛⠛⠿⣿⣿⣿⣿⣣⣽⣾⡿⢂⠌⢆⡡⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⢌⡃⠎⡔⢊⠔⢢⠡⠹⣿⣷⡝⣲⠭⢶⣙⠦⣏⡵⣋⢶⡱⣝⢲⢇⢯⣱⢛⣬⠳⣝⡬⣓⢞⣬⡓⣮⢝⣣⢮⣙⢮⡜⡻⢿⣿⣿⣿⣷⣿⣿⡟⢩⢙⠣⢎⡱⢊⣹⡿⠿⣯⣿⣿⣼⡱⢭⢎⡳⡜⢧⡚ ⢣⢏⣧⢁⠣⠔⣈⠻⢋⠥⣐⠩⡎⣱⣾⠟⣬⢏⡳⢎⣏⡳⢭⣚⢭⡓⢯⣱⢫⡜⣣⢭⢳⢣⢞⡱⣎⠶⣙⠶⡹⢬⢳⣙⠶⣙⢦⢏⡽⣌⠷⡼⣜⢫⡖⣹⢿⣿⣿⣿⢿⣿⣿⣷⣻⢾⡽⣯⢿⡽⣯⢷⣳⢿⣿⣿⣿⡿⢋⠔⡡⢃⠍⡒⠤⡙⢻⡿⢏⠩⡐⢄⢣⠘⢢⡐⡡⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢨⠰⡉⠔⡡⢊⠆⡅⠣⢽⣿⣿⢆⡟⡲⣍⠷⣚⡴⢫⠶⣹⠬⣏⢮⠳⣬⢏⡖⡻⡴⡹⡜⣎⠶⣙⢦⠻⡴⣓⠮⡖⣭⢳⣿⣿⣿⡿⢟⣿⣿⢃⠎⣼⡷⣶⡨⢱⣾⣿⡱⣣⢝⡻⣾⣿⣷⣎⢳⣙⢮⡱ ⡹⢎⣼⣶⣥⣎⣰⣄⠣⡘⠤⣱⣿⠻⣥⠻⡜⢮⠵⣋⢶⣩⢳⢬⢣⡝⣣⢎⢧⡹⣜⢣⡏⢾⡸⢵⢪⡝⣣⠯⡵⣋⠗⣎⡳⢭⠞⣎⠶⡭⢞⡱⣎⠷⣸⢣⢏⣟⣿⣿⣿⣿⣿⣿⣿⣯⡿⣽⢾⡽⣯⢿⣹⣿⣿⣿⡟⡡⢊⠆⡱⢨⠘⣄⠣⣐⠡⡐⢌⢢⠑⡌⢢⠙⡄⡒⢡⢊⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⢁⠣⢌⠱⣀⣣⣘⡄⢃⠆⢿⣿⣧⠞⡵⢭⠞⣥⢯⣙⠧⢧⡛⡜⢮⡝⡦⢯⠼⣱⠳⣍⡳⢮⡹⢭⣚⣭⠳⣍⡞⡵⣪⣿⣿⡿⢫⡕⣻⣿⠑⡮⡙⢿⣾⠟⣡⢇⡒⣿⡷⣩⠮⣕⢮⡹⣿⣿⡷⣮⣶⣩ ⣹⣾⣿⢿⣻⢿⣿⡛⢷⢶⣛⢏⣶⣙⣦⢛⡝⣎⡳⢭⢖⡱⣯⣾⣿⣿⣿⣿⣿⣷⣮⡧⡝⢶⣙⣮⡷⠾⣧⣛⣴⣭⣞⡱⣭⡓⢯⢎⡳⡝⢮⠳⡭⢞⡥⢏⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣻⠷⣯⣿⣿⣿⣿⡇⢂⢣⡘⢄⠣⡘⢄⠃⢆⠓⡌⢒⠢⡑⡘⠤⢃⠬⡑⠢⢌⠒⡨⢙⢿⣿⣿⣿⣿⠿⠿⠟⡡⠎⡌⢒⠌⣲⣿⠟⡹⢿⣦⣜⠨⣿⣿⣚⡝⢮⡝⣎⠶⣭⢚⡥⢉⠹⢦⡹⢜⡣⢏⢧⣛⣬⢳⢣⣝⡣⠷⣌⡟⡴⣙⣶⣿⡿⢳⡜⡳⣜⣹⣷⣉⣒⠹⡛⢤⣛⡔⣪⣼⣟⡱⣣⣛⡜⡖⣿⣟⣳⢿⣱⢷⣫ ⣽⡷⢯⣟⣭⣿⠧⣽⡾⣛⡝⠮⣜⣻⠿⣯⣜⡣⣝⡎⣞⡹⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣹⢲⣿⣧⡌⡓⢬⠻⡅⣊⢽⣷⢲⡹⢭⡚⡵⣹⢋⡷⣙⠞⣜⡳⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡣⣽⣿⢁⠎⡔⣈⠦⡑⢌⠢⡉⢆⠱⡈⢆⠱⡐⢡⠃⡌⢆⠱⢡⠊⡔⢡⠊⡔⡠⣁⠆⡰⢈⠆⡓⢄⢣⠘⢤⣾⣼⣿⣾⣵⣿⣟⡹⣧⢺⣿⣧⢚⠷⣸⢍⣞⠲⣍⠶⡁⢎⡕⡐⢢⠘⡭⢶⣩⠶⣩⠗⣮⣙⡳⣍⢞⡱⣻⣿⢏⡼⢳⡜⣣⢳⣌⣛⢻⡛⣿⣼⣶⢿⡛⣟⡱⢮⣱⠳⡼⣸⢹⡿⣜⢧⡻⣼⡷⢯ ⣿⣽⡻⣞⣿⢇⣿⢏⠶⣱⠚⡛⣶⣿⢫⢿⣧⡓⢧⠞⣦⢹⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⣿⣿⣎⠿⣦⣣⡿⢷⣤⠿⢿⣶⡭⢳⡹⢼⣷⣋⢶⡙⢾⣡⢳⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣾⣽⣿⠏⡰⢌⡐⢂⠆⡱⢈⠆⡱⢈⠆⡱⢈⠆⡡⢃⠜⡰⢈⡑⢆⠩⠔⢣⠘⡤⠑⡄⢎⠱⢌⠒⡡⠎⠤⡉⢼⣯⢆⡽⣿⣿⣿⡿⢿⣿⠠⣿⣟⢎⡯⢵⠺⣌⠻⢌⢡⠙⡂⠞⡰⢣⢞⣱⠳⣎⡳⢭⡞⣱⢎⡵⢮⣹⣼⣿⣷⣮⡕⡳⣜⣥⠳⣎⡼⢣⡝⢦⠳⣜⡲⡝⣬⡝⢶⡩⣗⠳⣍⢾⡟⣼⢣⣗⡯⡽⣧ ⣻⢶⣻⡽⣿⢺⡟⣬⢳⣹⣶⢿⣧⣾⣏⣾⣿⣿⣾⣿⣶⣧⣻⣿⣿⣿⣿⣿⣟⣿⣻⣟⣾⡏⣽⣯⠐⡄⠻⠿⡿⢡⠘⡄⢻⡷⣍⢾⣿⡿⣿⣦⢛⡵⣊⠷⣌⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡋⠔⡨⢁⠆⣘⠐⠢⢌⢅⠚⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⢣⠘⡄⣃⠚⡄⠓⡌⠱⡈⢆⠃⢎⡘⠤⡙⠤⡑⢌⠻⣿⣿⣋⣿⡟⠻⡿⢣⠘⣿⣿⣊⠾⣱⣛⡬⣛⣄⢪⡜⡡⠚⣄⣿⢏⡼⢣⡳⣍⠷⣘⠧⡞⣜⣣⣿⡿⣽⣿⣿⣿⣿⣿⣿⣷⣾⢜⡳⣚⡭⢳⢎⡵⡹⣆⢯⢣⢟⣬⢛⡜⢮⣟⣴⢻⡾⣱⡓⣿ ⣯⣿⣳⣟⣿⡹⣟⠴⣣⢾⡿⠻⣅⣿⡿⣹⢖⣿⢿⣯⣽⣛⢏⡛⡿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣶⣿⣧⡌⡑⠆⡔⠡⢊⣐⣿⡟⣬⢻⣿⣽⣻⣷⣋⢶⣩⣾⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢇⡸⢈⠴⡁⢎⠰⣉⠱⡈⠦⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢌⠢⡑⢂⠆⡓⢌⠣⢌⡱⢈⠆⣉⠦⡘⡰⢑⢢⢑⠊⡔⣈⠛⠟⡛⢄⠣⡐⡁⢎⣿⣿⢌⣗⣣⠮⣕⣣⢎⢷⡘⠷⡷⢾⣋⣮⡱⢏⠶⣍⠞⣭⣺⣵⣿⣿⢿⣿⣿⣿⣯⣿⣟⣿⣿⣿⣿⢪⡕⢧⣚⡝⡮⣜⢧⡹⢎⡝⣮⢒⣏⠾⡱⢮⡜⣣⢟⡥⢯⡽ ⣷⣻⣷⣯⢿⣷⡻⣧⣓⢾⣇⣳⣾⣻⡜⣧⣻⣟⢺⣯⡟⣽⣿⣜⣱⣧⣿⣿⣿⣯⣭⡝⡭⣭⢭⣍⢏⠿⣦⣼⣤⡿⢿⣿⣷⣽⣰⣋⢿⣷⣟⣿⡾⠛⣉⠙⣂⠒⡡⣿⣿⣿⣝⣛⢿⣿⣿⠃⡜⠢⠔⡉⢆⠱⣈⠱⣀⠣⡘⠤⡑⡌⢒⠡⡊⢔⠡⢊⠔⡡⢊⠔⡡⢊⠔⡑⡊⠴⡑⢊⡔⢊⢄⠣⡘⢄⢢⠑⢢⡉⢆⣊⠱⡐⢢⠉⢆⠱⡈⢆⠱⡈⣼⣿⢫⠞⣦⢳⣙⣎⠶⣋⢮⡝⣣⣽⡟⣿⡹⣟⠿⣾⣬⣿⣾⣿⢿⣿⣽⣿⣿⣶⣯⣽⣻⣿⣿⣿⣿⣿⣷⣞⡥⣓⠮⣵⢚⠶⣍⣏⢞⡜⣳⢬⢳⣙⢦⡝⢦⣋⢟⡫⣜ ⢻⠿⣿⣿⣿⣾⣿⣿⡿⢋⠭⡙⢛⠛⡛⣿⣗⡬⣓⠿⣯⣳⣽⣿⣿⣻⣽⢾⣳⣿⣟⣝⣶⣵⣎⡜⢮⣙⠶⡱⢎⡵⣣⢞⡹⢻⢿⣿⣾⣽⣿⣿⡄⠹⣀⢣⣾⢟⣷⡥⠰⠄⡹⣿⠼⣿⣿⡐⢌⠱⣈⠱⣈⠒⡄⠣⢄⢣⠘⠤⡑⢌⠢⡑⢌⠢⡉⢆⠊⡔⢡⠊⡔⢡⠚⠤⡑⢣⠘⢢⠘⡄⣊⣴⣥⣊⠤⢋⠔⡨⢆⠰⠡⠜⡠⢍⠢⡑⢌⠢⡑⢰⣿⣿⢣⣛⠦⣏⢖⣎⡳⡝⡦⣽⡿⢫⡜⣿⡳⣜⣿⣿⠿⣿⣾⣿⣿⣟⣿⣾⣿⣽⡿⢿⣷⣿⣿⣿⣿⣯⡙⣏⠶⣍⠷⣪⢝⡺⡜⣜⢎⡞⡱⣎⢗⡺⡜⡼⢣⢞⡬⢳⢥ ⢧⡻⡔⣖⢦⣓⣾⠟⣠⢋⠴⣉⢮⣵⢣⣼⣿⢿⡿⣿⢿⣿⣿⣟⡛⣟⡻⣿⣷⣻⣟⣿⣿⠟⣦⢝⣣⢎⠷⣙⠮⣖⠳⣎⡝⣣⠯⡜⣭⢫⡝⣻⣿⠇⢄⢻⣿⣼⡾⢋⣔⣥⣿⢛⡜⣿⣿⣧⠘⣂⠆⡱⢀⢣⠘⣡⠊⣤⣭⣦⡑⢌⠢⡑⢌⠢⡑⢌⠒⡌⢢⡑⢌⠢⣉⠆⡑⢢⠍⢢⠑⣸⣿⣿⣿⣷⡎⢰⠊⡔⢨⠒⣉⠆⣑⣢⣑⣈⠆⡱⢈⣽⣿⢬⡓⢮⣓⢮⣙⢦⠽⣸⣱⡿⣱⢣⡝⡼⣷⣽⡿⢿⣶⣿⣿⡿⣯⣿⢯⣿⣿⡏⡼⢣⣚⣿⡹⣿⣿⡿⡜⣥⢛⣬⡳⣱⢎⣳⣹⣼⣾⣾⣷⣯⢎⡵⣹⢚⡭⢞⣜⢫⠖ ⣦⡝⡹⣎⣿⡛⢥⠚⡤⢋⡒⣼⠏⢲⣿⣯⣛⣯⢷⣿⣿⣿⣻⣿⣜⡧⢻⡜⣻⣿⣿⣿⣦⣛⡜⢮⢲⡙⢮⡝⣺⢬⡓⢧⠞⣥⡛⣼⢒⡧⣚⣿⠁⡜⢠⢂⣤⠁⠖⡠⢻⣏⡖⢯⠼⡜⣿⣿⣎⠰⡘⠤⡉⢆⠱⠠⣭⣿⣍⣿⣷⠈⡆⢱⡈⡱⢌⢂⠣⠌⡅⠒⡌⠱⡠⠎⡌⢅⠎⢢⠡⣿⣿⣿⣿⣿⣷⢈⣦⣉⠆⡱⢠⢊⠙⢋⠛⠛⠿⠗⣂⣿⣿⠲⣝⣣⢎⡳⢎⣎⠟⡴⣿⢣⢇⡳⢜⡱⢻⣿⣟⣽⣾⣿⣟⣿⣿⣻⣿⡿⢟⡳⣹⠇⣷⣲⠿⡟⢿⢿⣷⡌⣿⡿⣿⣦⣿⣿⣻⣽⣳⡟⣾⣿⢎⡼⢥⣛⡼⣍⢎⢧⡛ ⣼⢸⡱⢎⡽⣳⢈⠳⢌⣡⡾⣋⢜⡲⢌⣿⡿⣿⣻⢷⡽⣳⣟⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣮⣧⣷⣿⣦⣽⣦⣧⢛⠮⡝⡦⣝⢲⣋⠶⣍⢻⢷⣬⣶⠿⢿⣮⣴⣵⢿⢣⠞⣭⢞⡱⣛⣿⣯⡒⢡⠚⡰⢈⣬⣅⣿⣿⣿⣿⣿⡖⠨⡅⢢⠑⡌⢢⠉⡜⢨⡑⠬⡑⠴⢡⠘⡌⠜⢢⠡⣙⣿⣿⣿⣿⣿⢪⡝⡻⢿⣦⠁⠎⣼⣆⣍⡘⢄⠣⣼⣿⡿⣋⡞⡴⢫⡜⢧⢺⡙⣾⡟⣧⠎⡵⢪⣕⣿⣻⣿⢾⣿⣿⣿⣻⣾⣿⣿⣇⢏⡖⣿⠈⣼⢧⠹⣜⢣⢎⡿⣿⡿⢿⣷⣿⣟⣞⡷⣽⣾⣽⣳⣿⡮⣜⢣⡞⡴⣋⢮⣣⠝ ⣣⠗⣜⢣⡞⡵⢊⠜⠶⣿⠠⡙⢢⢘⠣⣿⣟⡧⣟⣾⣽⡳⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣜⡱⣎⣳⣌⡻⢬⢳⣚⠼⣌⣛⢦⡹⡜⣜⡎⣧⠻⡜⢮⣱⢣⢽⣿⡃⠜⡰⣱⡟⢯⡱⢭⣿⣿⣿⣿⣗⡣⠜⡠⢃⠜⡠⠓⢌⠡⡘⠤⡑⢊⠤⢃⡌⣉⠆⡱⢈⠻⣿⣿⣿⢋⠶⣩⢓⣇⢻⡏⡔⢨⢉⡙⡻⢶⣷⣿⡻⡱⢧⡙⣎⠷⣙⢮⡣⣝⣿⠼⣌⢿⣜⡱⢸⣿⡜⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣮⣼⣛⠳⣜⣬⡿⣛⠻⢿⣿⢫⡵⣫⢶⣩⢛⣿⣽⣿⣳⣯⢷⣿⠳⣜⢣⢞⣱⠹⢦⢣⣛ ⣿⣾⣮⣕⢾⡝⡌⢮⡑⣿⢠⢡⣃⠌⣳⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡵⣋⠟⣿⣿⣹⢻⣿⣧⣳⡜⡳⢎⣜⣣⢳⣙⢦⣛⡴⢫⡝⣣⢎⢧⣻⣿⣣⣼⣿⡷⡙⢶⡙⢦⡛⣿⣿⡿⠑⢢⠁⠧⢌⠢⡑⣸⣾⢳⡎⠱⡈⠜⡠⢃⠔⢢⠘⡄⢃⠆⡑⣮⡖⡭⣛⠴⡫⣜⣾⠇⡚⢷⣶⣤⣷⣿⢟⡣⡗⡝⣦⣿⢾⡿⣾⣦⡝⣼⣏⠾⡜⢮⡹⣷⢣⣿⡝⢾⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣚⣿⣟⢣⠳⣍⠻⣌⢿⣷⣜⣵⣮⡱⣏⢞⣿⣿⣟⡾⣿⣯⣷⣎⡝⢮⡜⡽⣩⠶⣋ ⣿⡾⣽⣻⣿⡰⡙⢦⠱⣹⣇⠆⡱⢺⡟⢫⣿⣿⣿⣿⠛⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⢭⠲⣍⣛⢎⡶⣩⢛⣴⣿⠿⣛⡻⣍⡛⣿⡵⣋⠶⡥⢏⡞⣜⠦⣝⣣⠽⣥⢫⢖⡹⣿⣿⣍⠰⣲⣽⡦⣹⠲⣹⣴⡟⠠⡍⢢⢉⣶⣶⣷⣴⣌⡛⢛⠡⠓⡌⢡⣑⡌⡘⢄⢣⣌⣡⣊⠔⡨⠻⣷⣭⣾⣵⣟⣥⣾⣾⡿⢿⡻⢿⡣⣞⡱⡽⣸⣿⢻⡆⢲⠹⣯⢿⣮⢿⡣⢿⡥⣓⢻⣷⡿⣙⢮⣿⠟⡛⢬⠩⡅⣿⣿⣿⣿⣿⣿⣿⡌⣏⠳⣎⢳⣾⠟⢫⠍⡩⢹⣷⣯⡞⣽⢻⠿⣿⣳⢯⣟⣿⣎⠳⣼⡱⢏⠲⢄ ⣿⣽⣟⡷⣿⣧⡙⢆⠳⣄⢻⣦⣑⣼⡟⣹⣿⣸⣿⣿⣶⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣯⢷⣻⡾⢟⡻⣛⠿⣿⣿⣛⢿⣷⣭⢣⠳⣥⣻⣾⡷⣙⠮⡕⡯⣜⢮⣹⠲⣍⡞⠶⣭⢚⡵⣙⢻⢿⣾⣿⣇⣼⣷⡿⠟⡩⢐⠣⡘⢄⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣬⣿⡟⣿⣶⣿⡟⠛⢛⠻⣷⣶⣷⣿⣿⣿⢿⣻⢻⢭⢣⡝⡶⣩⢗⡱⢮⡕⣣⣷⣿⠌⡜⡡⢎⡹⢷⣻⣧⡝⢶⡹⢮⣝⣿⡗⣭⣿⠡⢎⡕⢣⠓⡜⣸⣿⠿⣭⣿⡞⣽⣷⣎⠽⣌⣿⠣⣌⠃⣏⣰⡁⠦⣹⣿⡜⣯⡹⣝⣿⣿⣿⣯⣾⢿⣆⡙⢦⡉⢆ ⣿⣳⣯⣿⣽⣿⣿⣮⣱⣌⣆⣻⢏⠳⡜⣹⣿⣳⢿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡟⣜⢣⠳⣍⠞⣬⢻⣿⢻⣙⠻⢿⣿⣻⣿⢿⣧⣭⢳⣙⠶⣩⢖⣣⠟⡼⣜⠻⡴⣋⢶⡙⡮⢎⡽⣹⣿⠿⠿⡿⣿⢷⣾⣶⣷⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣮⣿⣿⣿⣽⣿⣿⣥⠉⣆⢡⣿⣿⣿⡿⢿⣿⡷⢬⡳⢎⣳⢚⡵⢣⡞⣭⠳⡜⣽⣯⠰⣍⠲⣉⠾⣧⠻⣕⣻⣿⣾⣿⣿⢿⣾⣽⣿⣠⢋⣼⢌⣣⢹⠰⣩⣿⡹⣼⡿⣜⣧⣿⡛⢿⣿⠛⠷⣀⣿⢞⡏⢿⣷⡈⢿⣿⣶⣹⢎⣿⠥⣫⢔⡲⢌⣹⢧⢲⣙⠦ ⣿⡽⢛⡍⢦⠹⢟⡛⣛⢿⣿⣿⣾⣧⣽⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿⣾⡿⡱⢎⣧⡿⠞⡛⠳⣯⣾⣥⢋⡟⢦⡛⣿⡴⢣⢞⣻⣷⠬⣏⠳⡞⣬⢛⢶⣩⡛⢶⣙⠮⡵⣍⢏⢶⡩⢏⣝⡳⠵⣎⡞⡴⣣⣾⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⡽⣿⣿⣷⣿⡿⣙⢮⣱⢫⢖⣫⡜⢧⡝⡲⢏⡝⣾⢇⠳⣌⢳⣌⠖⣹⡿⣜⣿⣿⢯⣿⡽⣿⣶⣭⣛⡿⣖⣞⣢⣆⣇⠻⣰⣿⢱⡹⣿⣳⣾⠧⣝⢎⣿⡇⢣⠔⡻⣷⣎⣷⡟⢌⣿⡿⣷⣯⣿⢏⡶⣡⠞⡴⢋⡌⣏⢷⡮⢵ ⢏⡱⢣⠜⣆⠛⠦⣷⣌⠖⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣵⣿⠉⡄⠣⠌⡑⣤⠹⣿⣎⡝⡲⡝⣼⣗⡫⢎⣿⡟⡳⢎⠯⡵⢎⡝⣲⢣⣝⣣⢞⡹⣜⢺⡜⢶⣩⢏⠶⣩⣓⠞⡼⣹⣿⣯⠠⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⡛⡛⠿⢿⣿⡿⠿⣿⣿⣷⣭⢎⢧⣋⡞⡴⣩⡓⡞⣽⣾⣿⡿⢿⣿⣶⣍⣻⣾⡱⣞⣽⣿⣯⢿⣳⣿⢯⣿⣿⢿⣿⣽⣾⣿⢿⣿⣧⣽⣏⠾⣵⣿⡿⣿⢳⣜⣮⣽⣷⣥⣺⣴⡟⢭⠳⣘⣾⣿⣹⡳⢿⣷⣎⣶⡙⣎⠶⡹⡜⡼⣲⢹⣧ ⡯⣕⢂⠣⡜⣸⠰⣠⠹⣯⣳⣿⣿⢿⣟⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣥⠻⣼⡟⢁⢎⣴⡿⠿⢿⣦⠱⠸⣿⡻⢷⣿⢿⣧⣝⣽⣿⢱⢫⡭⢳⣙⣮⣾⣷⣧⢚⢦⡫⢵⢎⡗⣚⠧⡞⢮⣙⠶⣩⢞⣱⡹⣿⣿⣷⣧⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠩⠔⡡⢊⠄⢆⡰⢁⣿⣿⠿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠟⡋⠔⡄⢃⡘⣿⣿⣦⢻⣷⣹⣿⣿⡾⣟⣯⣿⣻⣽⣿⣟⣾⣿⣿⣾⣿⡿⢿⡿⣾⣿⣟⢿⣹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣷⢿⣻⣾⡵⣻⣿⣿⢿⣻⣿⡿⣜⡳⡽⣱⢧⡟⣱ ⠰⡌⢮⡑⡚⢴⡓⣆⢱⣸⢿⣿⣾⢿⣽⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢯⢲⡹⠼⣿⡄⠺⣿⡜⣯⣻⡿⠞⠳⣿⡹⣭⢿⣯⣾⣟⠻⣔⣫⣶⣽⡿⣛⠿⣗⡼⣻⣯⢎⡵⣋⡞⡼⣩⠳⣍⣧⡙⢮⠱⣎⢲⡑⡻⢿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣧⡅⢃⠆⡅⢪⠐⡰⣸⡿⣿⣼⣿⣿⣻⣿⣯⣷⣻⣿⡆⠱⣈⠒⡘⠤⣸⣽⣿⢷⡳⢎⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⢟⡱⢎⣽⣷⣫⣟⣼⣳⣿⣿⣾⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣫⣿⢿⣿⣿⣿⣽⣿⣿⣯⣷⣭⣶⣷⢫⢳⡜⣣ ⡑⢎⡱⢲⣑⠢⣙⠾⢣⣼⣿⡿⣯⣿⢯⣿⣿⣿⣻⡾⣷⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⡙⢧⢻⣧⡅⡙⠿⠞⡋⠥⣈⣱⣿⠳⣥⢻⣿⣟⣿⣿⣾⣿⠟⣡⠒⣍⢲⡿⢼⣿⢻⣷⡮⣱⣙⣶⡿⣟⣟⣻⢿⡿⣷⣜⣶⣷⣷⣧⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣶⣬⣤⣷⣿⣿⣿⣿⡿⣟⢹⣿⢿⣿⣿⣷⣿⣿⣷⣤⣷⣾⣿⣿⣿⣟⣮⣽⣯⣾⣿⣿⣟⣷⣻⣾⢿⣿⣿⣛⢮⣝⡿⢋⡉⡙⢯⡙⣻⣿⣿⢿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣻⢿⣽⣟⣿⣻⢿⣿⣷⣺⠵ ⢌⡣⢍⡳⢬⢓⠭⣫⣿⣿⢯⣿⣽⢯⣿⣿⣿⣞⣷⣿⣻⣾⣟⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣧⣽⣾⡟⣯⢿⣶⣬⣦⣵⣶⠿⣏⢷⡛⣼⣻⣿⣞⣷⡿⠟⣄⢫⡔⢭⢂⣿⢇⣻⣧⢓⣾⡿⣿⣫⢷⣻⡽⢾⡽⣻⢾⣝⡿⣿⣟⣾⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠛⡄⢛⢡⣽⣿⣻⣿⣿⡿⡟⢿⣻⢿⣷⣌⣿⣯⢾⣿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⢿⣽⣟⣿⢧⡞⣣⡾⢁⠆⣴⡷⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣻⣟⡿⣾⢯⣟⣷⡾⣽⣿⣻ ⢷⣌⣇⠚⣆⢫⣼⣽⡷⣿⣻⣽⣾⣿⣿⣻⢷⣯⣟⣾⢷⣻⣾⡿⣿⣟⡷⣿⣿⣻⣾⡽⣿⣿⣿⢧⡟⣽⠾⣜⡳⣏⣿⣯⣻⡜⣧⣿⣾⣿⣳⢿⣿⣷⣹⠊⡥⢚⣤⡿⣧⣊⣼⣷⣿⡛⡴⣩⠿⣯⣷⢻⣻⢷⣯⣟⡾⣽⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣾⣶⣿⣿⣿⣿⣿⡧⣛⡜⣣⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⠜⣿⢧⡻⣼⣿⣿⣿⣿⣿⣛⢯⡛⢯⡹⢭⣍⠻⢿⣿⣾⣿⣗⡺⣹⣷⣈⣆⠿⣸⢡⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣿⣿⣽⣿⣿⡿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⢯⣿⢷⣻⣿ ⢎⡬⡙⠿⠼⡛⢏⣻⣿⢷⣻⢷⣿⡿⣞⣯⣿⡿⠿⣾⡿⢟⢻⠻⠿⣿⣿⣻⢷⣟⡷⣿⣿⣟⡿⣿⣾⣭⣻⣭⣷⣿⡿⣿⣻⢿⣿⡿⣿⣷⣿⣟⡾⣽⢿⣷⣬⣷⢋⡱⣽⡟⣭⢚⣿⡷⣷⣦⡳⢌⡻⢿⣷⣯⣿⣿⣿⠻⣽⣯⢻⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢶⣣⠿⣯⣿⣧⣧⣝⣶⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢿⣶⣭⢶⡙⣆⠛⣉⢻⣝⣮⣿⡿⣟⡿⣿⣷⢿⣹⢻⡟⣷⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣳⣟⣯⣿⢯⣿⢿⣽ ⢎⣲⣍⣋⠳⣙⢮⡰⢻⣿⣯⣿⣿⣻⣽⣻⣿⢡⡓⢦⢣⠏⣎⠳⡓⡼⣿⣿⣟⣾⡿⢟⡳⢏⣻⣿⣻⢟⣿⡻⣿⣯⣟⡷⣯⣟⣽⣿⣳⣻⣿⣻⢿⣿⣮⣗⣯⢿⣧⣿⣧⣙⣦⣿⣿⠽⡞⡽⢛⠧⣿⣿⡿⣿⣿⣿⣿⣿⣛⣯⣿⢿⣿⣿⠿⣽⣿⠛⠹⢿⣿⣿⠟⣻⣿⣟⡿⣷⣧⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠩⠙⣿⣿⣤⣂⣽⣿⣇⠨⣹⣦⣥⡾⣟⠻⣿⣽⣯⠟⡷⢻⢿⣮⣷⣽⣹⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣷⡿⣯⣿⢾⡿⣽⣟⣯ ⣿⡿⣽⡿⣷⣡⢎⡱⣃⠾⣿⣿⣟⣷⣿⠿⡡⢧⡙⢮⡱⣚⢬⢓⡹⠴⣡⠛⡿⠟⣥⢫⠜⡦⢹⣿⣭⣟⡾⣽⣳⣿⡾⣽⣳⢾⡽⣿⣳⢷⣫⢷⣻⣞⣽⡻⣿⣿⡿⢟⡙⢏⡏⣭⢒⡝⣲⢙⠮⡜⡹⣿⣿⠏⡡⢙⣯⠡⡙⣿⣿⣿⣿⠅⡌⢻⣿⣄⠣⢌⣿⡇⠸⢠⠉⠿⢿⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣅⣷⠛⡉⢌⢹⣿⣭⣟⣿⡟⣿⣋⠶⣩⣿⡿⢟⡰⢫⢜⡣⢎⡜⡥⢫⣿⣿⡽⣞⡿⣾⣽⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⢿⣿⡿⣿⢿⣿⣻⣽⢿⡿⢿⣟⣾⣟⣿⣻⣾⣻ ⣿⣽⣷⡿⢏⢥⣋⠶⣑⠎⡽⣿⣿⣿⢋⠶⣙⢦⡙⢦⡓⣬⠲⣉⢞⡱⢣⡝⣬⠹⣤⢣⢛⡬⣃⠞⡻⢾⣽⣧⣿⡿⢻⠷⣯⣟⣾⣿⠿⣯⣽⣏⡷⣞⣧⣿⠿⣯⠽⡞⠷⢞⡰⢥⡓⡜⣆⣋⠞⣓⠻⠵⡻⢿⣵⣾⠁⢆⣙⣿⣿⣿⣧⣘⠤⣩⣟⣿⣾⣿⣿⣿⣡⠆⣉⠒⠤⣉⠻⣿⡿⣽⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢷⣷⣾⠿⡷⣼⣦⢿⡛⢭⢛⡛⠿⡷⢟⡟⢻⡙⣏⢫⠝⡣⢞⡸⡱⢎⠵⣃⠞⡻⠿⠿⣿⡷⢯⣯⣿⢿⡽⣯⣟⣿⡟⣭⢓⡬⢲⡙⢦⠳⡜⣤⢋⠿⣿⣾⢟⡹⢆⣫⠛⣏⢛⡍⡻⠿ ⡬⣍⡵⢪⡝⢦⣣⢛⡜⣮⠱⣎⡛⢧⡍⣞⣡⢎⡝⢦⡹⣐⠯⣜⢪⡱⢣⠞⣔⢫⠴⣩⢖⡱⣍⢞⡱⢣⠖⡜⣤⢓⢧⡚⡴⣩⠭⡱⢎⡲⢍⣛⣛⠻⣍⠲⣍⢦⠳⣙⠺⣌⠳⢦⡹⢜⡲⣌⡛⣬⢋⡳⣱⠣⢎⠻⢿⠾⡛⣍⠧⢎⡛⠿⠿⣟⠻⢏⡻⣙⢏⡛⠿⢿⣶⣿⣶⣶⡿⢿⢿⡛⡟⣏⢟⣚⢳⡙⣞⡹⣛⡛⣏⣛⡚⡝⣓⡛⢎⡳⢛⡔⣣⠜⣦⡙⠮⣥⢋⠷⡸⢥⡚⣥⠫⣔⢫⡚⣕⢣⢣⡓⣭⢚⡥⢛⡴⢫⡜⡜⣿⣟⣾⢯⡿⣽⣳⡿⣋⠶⣡⠞⣬⢣⢝⡪⢵⣩⠲⣍⡚⣔⢣⢎⡵⢩⢆⡻⢌⡳⣜⡱⣍ ⡷⡜⣜⣣⢞⡳⢬⢏⡼⣒⠟⣬⠝⣮⠜⡶⡱⢮⣙⢮⣱⢋⡾⣌⠷⣩⣓⢏⢮⡣⢟⡴⢫⡜⡞⣬⢏⢧⣛⡜⣦⢋⡶⡹⣔⢣⣍⠳⣍⢞⡱⢎⡜⡳⣌⡳⡜⣎⡳⣍⡗⢮⡹⣲⣙⠮⣕⠮⡵⢣⣛⡴⢣⣛⡬⣛⡤⢏⡵⣊⢞⡥⣋⠷⣙⠦⣏⢧⠳⣍⢮⡹⣙⢶⣘⢦⠳⣬⠳⣭⠲⣍⢗⡎⣎⢧⢫⡝⡲⣝⠲⡽⣘⢦⡝⢮⡱⣙⢮⡱⢫⡜⣥⡛⣴⡩⠷⣌⡏⣞⡱⣣⠝⣦⢛⡬⢧⡹⣬⢣⢧⣙⢦⠳⣜⣣⢞⣱⢚⡴⢣⢻⣿⡿⢟⡻⣱⢣⣛⡼⢥⠻⣔⡫⣎⠵⡳⢬⣓⠧⣝⡜⣎⠞⣜⣣⢮⣱⢋⡶⢥⡳⢬ ⡟⡼⡱⢎⣮⢱⣋⢮⠵⣋⠾⣥⢻⣌⠟⣴⣋⠗⣎⡳⣬⠳⡼⣘⢧⠳⣬⢋⡶⣍⡳⢎⣳⠹⣜⢣⡞⣣⠞⣼⢒⢯⢲⣓⢮⠳⣜⢫⡜⣎⡳⢽⣘⢧⢳⡱⣝⡲⣕⢣⠞⣧⢳⡱⢎⡝⣎⡳⢭⡓⢧⢞⣣⢧⡓⢧⡹⢎⡵⣋⡞⡼⣱⢫⡝⡺⡜⢮⡝⣎⢧⡝⣣⢞⡼⢪⡝⢶⣙⡖⡻⣜⠺⣜⡱⣎⢗⡺⢵⣩⣛⠼⡭⢶⣩⠧⣝⡱⢮⡱⣏⡼⢲⣙⢦⠽⣙⠶⣙⠦⠳⣥⠛⢦⣋⠾⣥⠳⣥⢛⠦⣏⢞⡹⢦⣓⢮⢣⢯⡜⢧⡳⢦⡹⢮⡱⢇⣏⠶⣙⢎⠷⣥⠳⡭⢞⡭⣓⠮⡝⢦⣛⣬⢛⡜⣦⢓⡮⡹⣜⢣⣝⠲ ⡯⣕⡻⡜⣎⢳⠬⢧⡛⣭⠳⣎⠳⣌⣛⠦⡝⢮⢣⠗⣎⣳⠹⡜⢮⡝⣲⢋⡶⢥⣋⠧⣇⠟⣬⠳⣜⢣⠻⡔⢯⢎⡳⡜⢮⡝⣜⡣⡽⣸⡱⢫⡜⡮⢧⡝⣲⠱⡎⣉⠻⣔⢫⠵⣋⡞⡥⢏⠧⣝⡣⣞⡱⢎⣝⣣⠽⣩⠶⣍⢞⣱⢣⣓⢞⡱⣭⠳⣜⢎⡞⡼⡱⢞⡜⢧⡝⣚⠦⡽⡱⢎⡻⣌⠷⡸⢎⡵⢣⡳⢬⣳⡙⡶⣡⠟⣬⢓⢧⣓⠮⣜⢧⣋⢮⡝⡭⢞⡭⢲⣁⠶⣈⠶⣩⢞⡲⣛⡬⢏⡞⡜⢮⣱⢓⡎⢧⡛⢦⣫⢳⣙⠮⡵⢫⡜⢯⡜⣣⠝⡎⡐⠆⡹⠜⣃⠳⢩⠞⣭⠳⣜⠦⣏⠞⣴⢋⡶⡹⢬⠳⡼⣙ ⢷⢣⠷⣹⢎⢧⣋⠷⣙⠦⠻⢬⡛⠤⣈⠙⡞⣭⢣⠻⣜⢲⢫⡝⢶⡙⡖⢯⡜⢧⡹⢞⡬⣛⢖⡻⢬⣋⠷⣹⠺⣜⡱⢻⡜⡼⢲⣍⠳⣥⢛⡥⢏⡵⠳⣼⠱⢋⠲⣤⡃⢌⡙⣎⢳⡹⣜⢫⡝⡲⢇⢧⡛⡞⢦⢣⠟⣥⠻⡜⢮⡱⢇⡏⢮⠳⣜⠳⣭⠺⡜⡵⣋⢗⡺⢣⠞⡭⢞⡱⢽⣩⢓⢮⠳⠽⣩⢞⡣⣝⢣⠶⣙⠶⣙⢮⢣⠻⡜⣬⠳⡭⢶⡩⢖⡹⣜⢣⠳⣤⣬⠛⢤⡹⢆⢯⡱⢣⡝⡺⣜⡹⢳⠬⣏⠼⣣⢝⡳⢬⡓⢮⡹⣜⢣⡝⢶⡙⡄⢊⠔⣡⣣⢴⡁⢆⡱⢈⡟⡴⣛⢬⡓⢮⡝⣲⢋⠶⣹⢣⢟⡱⢭

⠀⠀⢀⣠⣴⣾⢿⡿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⢻⡝⣬⣓⢮⣕⢫⡽⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⠻⣏⢟⡻⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣮⣷⡞⢱⡎⢳⡜⢣⣷⣭⣿⣷⣾⣿⣿⡟⣿⡟⣿⣿⣿⣷⣶⣦⣤⣼⣿⢱⡎⢻⣬⡏⣶⢣⣮⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠋⠛⠻⢷⣽⣣⣽⣿⢿⢻⢏⣏⡳⢳⡬⣓⠧⣝⠶⣱⢎⡳⣭⣛⠿⡿⣷⣿⣎⡗⣮⢜⡞⣼⣶⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣇⠀⠀⠀⣠⣿⢿⣛⡬⢏⣮⢓⡮⣝⡣⢷⣩⣛⣬⠻⣬⠳⣝⢦⡝⣞⡱⣭⢛⡿⣿⣞⣼⡿⠋⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣄⢀⣼⡿⣝⡺⢴⣋⠷⣬⣯⣶⡷⠿⠿⠿⠿⠿⠿⠷⠿⣾⣶⣽⣘⡳⣜⡳⢎⡽⣻⣿⡁⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⡟⡵⢎⡵⣫⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣯⣜⡏⢶⢣⠿⣿⣄⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⡽⣜⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣣⠻⡼⣹⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡝⡞⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢫⢵⡓⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣜⡹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢦⡛⢧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡈⣷⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣹⢇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⡝⣾⣟⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠈⣿⣞⡱⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣟⣼⣿⠀⠀⠀⠻⠿⡿⠏⠀⠔⠁⢠⣶⣶⠀⠀⠑⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⣿⢧⢳⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣞⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣨⣿⣿⣄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢫⢮⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣧⠀⠀⢀⣴⣿⢿⣷⣄⠛⢛⣿⣿⠛⠟⣴⡾⡿⣷⣦⠀⠀⠀⠀⣠⣿⢏⣳⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⢸⣧⠈⣹⣾⠿⣟⡟⢯⡻⣟⢿⣿⣷⠛⠉⣹⡇⠀⣠⣾⣿⣭⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⠟⣿⡿⢎⡽⢲⢭⣓⠧⣝⣎⠞⣿⣷⣶⣿⣷⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⣿⣽⣩⣾⣝⡶⡽⣞⣱⣾⡻⢴⣻⣏⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠻⠛⠿⣿⡿⡟⢸⣧⡘⣿⣿⣿⣧⣿⣿⣤⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢸⣟⡵⣻⢬⢷⣻⡟⠁⠀⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⣶⣿⡿⣷⣷⣿⣾⢿⣿⣤⣄⣀⣀⣤⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⣿⣷⣿⡜⠁⠀⠈⢷⢮⣿⣽⡿⠉⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠻⠛⠂⠛

⣿⢏⡇⣀⠂⠰⣀⠒⡐⢂⠒⡐⢂⠒⡐⢂⠒⡄⢢⠐⠤⡀⠘⢽⣻⣟⣿⣻⠿⣝⣯⢻⡝⣯⣟⢯⡛⡱⢋⠖⣩⢒⡱⢊⢖⡩⠛⠽⢫⣏⢷⣫⣟⡿⣿⣟⣿⡹⢯⡝⣯⣟⡿⣽⣻ ⣯⢟⡶⡀⠌⡐⠠⠘⢠⠃⡱⢈⠅⡊⠔⡡⢊⠔⡡⢊⠔⠰⢠⠀⢳⣟⡾⣽⣻⣝⡮⣗⢯⢷⡉⠔⡬⢱⡉⢎⠤⢃⡜⡡⠎⠴⡉⡔⡀⠙⢮⣳⡽⣟⣷⣻⢮⡽⢧⣻⠶⣯⢿⣵⣻ ⡿⣎⢷⣹⠀⡄⠡⠘⠠⢈⠰⢁⠎⡰⢁⠆⡡⢊⠔⣁⠊⡔⡁⠆⡀⠻⣽⣳⣟⣮⢗⣯⣛⠎⠀⣍⠲⢡⡘⢌⠲⣁⠦⡑⢪⠑⡴⢐⠡⢂⠈⣷⣻⢯⣿⣹⡟⣞⢯⡞⣽⢯⣟⢾⣽ ⣿⣹⣎⢷⣣⠀⠡⠈⠄⡁⠢⠌⢂⠱⡈⢆⠑⠢⠌⡄⠣⡐⢌⠰⣀⠀⠹⣷⣻⣎⢿⡲⣏⠀⡜⢠⠓⠢⠜⣈⠖⡐⢢⠡⢃⡜⢠⠃⡜⢠⠂⠑⣯⣟⣾⣳⢟⡽⣲⢻⣼⣻⣾⣻⢾ ⣷⢳⡞⣯⢳⣇⠀⢁⠂⠄⠡⠘⣀⠣⡐⠌⡌⠱⡈⠔⡡⢘⠠⢒⡀⠎⠀⠹⣷⢫⣗⣻⠂⠠⡘⠤⢩⠑⣊⠴⣈⠬⡁⢎⢡⠘⡄⢣⠈⢄⠂⠀⢼⣻⢾⣽⣫⢗⣯⢳⡞⣷⢯⣟⣯ ⣯⡳⣽⢣⣟⣾⣡⠀⠈⠄⠡⠁⡄⢂⠱⡈⠔⡡⠘⠤⡑⢌⠢⡁⢆⠩⡐⠀⢯⡟⣮⢳⠀⢁⢂⡑⠢⡉⠔⢢⠐⢢⠉⢆⠢⡑⠌⠄⠊⠄⢨⠀⢸⣯⣟⡾⡽⣞⡼⢧⣻⣽⣻⢾⡽ ⡷⣝⡾⣹⢞⣼⣻⢆⡀⠌⠠⢁⡐⠈⠤⡑⢌⠰⡉⢆⠱⡈⢆⠱⡈⢆⢡⢃⠈⢽⢳⣏⡆⠀⠠⠐⢡⠈⢒⠠⠉⠄⠊⠄⠒⡈⠐⡈⠡⠈⠄⠂⢸⡷⣯⢿⣽⢺⡝⣧⢻⡶⣯⢿⣽ ⣟⢮⡳⣝⣞⣳⣯⣟⡦⠀⡁⠂⠄⡉⠔⡈⢆⠱⡈⢆⠱⡈⠦⡑⠸⣠⠒⣌⠢⡌⡑⣎⢳⡀⠀⢁⠂⠌⡀⢂⠉⠄⠡⢈⠐⠠⠁⠐⡀⠡⠐⠀⢸⣿⣹⢿⡼⢧⡻⣞⣽⣳⢯⣟⡾ ⡿⣜⢧⣻⡸⣇⡿⣼⣻⢇⠀⠃⠄⡘⠠⢃⠜⡠⢃⠜⠤⢃⠤⢛⢣⡀⢟⡀⢧⠸⣠⠠⢄⠣⢄⡀⠀⠄⢀⠀⡘⢀⠃⠀⠘⠀⡄⢃⠀⡃⡘⠀⢼⢧⣟⡿⣸⡟⣧⢻⣤⡟⣿⡼⣻ ⣝⢮⡳⢧⡝⣾⣹⢷⡻⣞⡦⠀⠂⡐⢡⠊⡔⢡⢃⠎⡜⢡⠚⡌⢆⡉⢆⠍⣢⢑⠢⣉⢌⡃⠎⠴⡉⡔⡠⢄⠤⣀⢆⠲⣉⠖⡰⢈⠆⡁⠐⠀⡘⣿⡼⣻⡵⣻⡜⣳⢞⣽⣳⡽⢯ ⢞⢧⣛⣥⢻⡵⣛⣮⠽⣽⠶⣔⠀⢀⠣⡜⢌⠲⡌⠜⣨⠑⢪⠰⣁⠚⡌⢜⠠⢎⠱⡐⢢⡘⢌⠣⠜⣠⢑⡊⠴⣁⠎⢲⢁⢎⡱⢡⠚⠤⢃⡀⠳⢯⢷⣳⡽⣱⠞⣥⢻⣎⢷⣫⣟ ⢏⡞⢦⢣⢇⡻⣹⡜⡻⣜⡋⠀⣄⠊⡵⠘⡬⠑⣌⠚⠤⡙⡄⢣⠘⡔⡘⡌⠲⣈⠦⡑⣡⠘⡄⢣⢉⡔⠢⢌⡱⢄⠋⡆⢍⠢⡜⢡⡙⢂⠇⠤⣀⠈⠳⣧⢻⢥⡛⣬⢳⡞⣯⠶⣯ ⣾⡽⣞⡷⣞⣷⣳⣟⢷⠈⢀⡜⢠⢋⠔⣩⠰⡉⢤⡉⠖⡡⠜⢢⡑⠬⠰⢌⠱⡠⢆⠱⡀⠇⡜⢢⠡⢌⡑⢆⠒⡬⠘⣌⠂⢇⠜⠢⣌⢡⠚⡰⠠⢌⡀⠸⣷⢮⡵⣮⢷⣞⣶⡽⣶ ⣷⣻⣽⣻⡽⣞⡷⣏⠃⢠⠃⣌⠣⡘⠬⢄⠣⠜⠤⡘⢢⢑⠊⡥⢘⡰⢉⠆⠣⠔⣊⠱⢨⠑⣌⠢⠱⣈⠔⡊⠴⡁⢇⢢⠙⡌⠬⡑⢤⢂⠣⡐⢅⠢⡐⠄⠙⣯⡿⣽⣻⢾⣽⣻⣽ ⣟⡷⣽⢧⡿⣽⣛⠀⢀⠆⡩⢄⠣⢌⡱⢌⢊⡑⡊⢅⠣⡌⠱⡄⢣⡐⢣⢘⡡⢃⠆⣍⠢⡱⢠⢃⡃⢆⠎⡑⢢⢉⠒⡌⠜⡐⢣⠑⠢⢌⠢⡑⢌⢂⠱⡈⠄⠑⣟⡷⣯⣟⣾⣳⢿ ⣯⣿⣭⡿⣽⡳⢂⠜⡠⢃⠜⡠⢃⡒⢰⡈⠒⡌⠱⣈⠒⡌⠑⠈⠂⠘⣀⣦⣱⣬⣼⣤⣗⣶⣣⣦⡵⣮⣬⣥⣀⣁⠊⠐⠡⠘⠤⣉⠒⠌⣂⠱⢈⢂⠒⡈⢄⠀⠩⣟⣷⣻⢾⡽⣯ ⣛⣜⡣⢟⡳⢃⠌⢢⠑⡌⢢⠑⢢⠑⢢⠘⡡⠌⠑⢀⣠⣤⣶⣶⢿⡿⣿⣻⣿⣽⣯⣿⣽⣶⣿⡽⣟⣿⣳⣟⣿⣭⣿⣟⡶⣦⣤⡀⠉⠔⡀⠎⡐⢂⠡⠐⠂⠌⠀⢹⡞⣭⢏⣻⡹ ⣳⠮⣝⢧⡋⠔⡘⢄⠣⡘⠤⡉⢆⡉⠆⡑⢀⣠⠘⠫⢿⡻⠯⣿⣿⢿⣿⣟⣯⣿⣽⣿⣯⣿⢯⣿⣻⣽⣯⢿⣞⣯⣷⣟⠟⡓⣯⡙⠃⢀⡀⠂⢁⠢⠌⢂⠉⠄⠂⠈⣞⡵⣎⢷⡹ ⣧⢻⡜⣯⠆⢩⠐⡌⢂⡑⠢⠑⢂⠜⠀⣰⡄⠛⠃⠀⠀⠀⠀⠀⠙⣿⣟⣾⣿⣯⣿⣾⡿⣽⡿⣿⢿⣳⣿⣻⢯⣟⡇⠈⠀⠀⠀⠀⠀⠘⠈⢆⡀⠂⠌⠠⠌⢂⠁⠀⢮⡳⣎⢷⣹ ⣽⢣⡿⣜⠂⡡⠒⡈⠔⣈⠡⣉⠂⢀⡾⣯⡇⠄⠀⢠⠀⠘⡳⠀⠀⢻⣯⡿⣿⣾⣟⡷⣿⣻⣽⣿⣻⣽⣞⣯⣿⠾⠘⠀⠀⢛⠄⢠⠀⠀⢸⢯⡖⡀⠈⠡⠈⠄⡀⠁⣺⢵⣛⡮⢷ ⣾⡹⣞⡽⠀⡐⠠⠁⡌⠄⠒⡀⢀⡇⣿⣽⠀⠀⠀⠀⡤⠀⠀⠀⢀⢺⣷⢿⣻⢾⣽⣿⡻⡓⠟⢷⣟⣷⣻⢷⣻⣿⡴⠀⠀⠀⠀⡤⠀⠀⠈⣷⡹⡥⠀⠀⠡⢂⠐⠀⢼⣣⢟⡼⢯ ⣶⢫⢷⣹⡀⠀⠐⠡⠐⡈⠡⠀⣸⢷⣫⣟⡆⣆⠀⠀⠁⠀⠀⣠⡼⣟⣯⣿⣻⢯⣟⡾⣷⣄⣨⡼⣟⡾⣯⣟⡷⣾⢽⣣⡄⠀⠀⠀⠀⢀⣤⢗⡯⢳⠀⠈⡐⠠⠀⠀⢸⢧⣛⠾⣽ ⣳⢏⡷⣣⢗⠀⠈⠠⢁⠐⠡⠀⢏⡾⣱⢎⡝⣎⠳⣔⡲⢶⣞⡷⣻⡽⢯⢷⡫⣅⠈⠑⠃⠙⠃⠛⠉⠃⠀⣽⢾⡹⣞⡳⣝⢧⡲⡔⡴⢣⠜⡪⢝⡣⠂⠀⠠⠁⠀⢰⣫⢞⡭⣟⣞ ⣯⢞⡳⣝⢮⣃⡀⠀⠂⠌⡐⠀⠘⣧⠓⡎⢴⣈⠳⣌⢳⢫⢞⡵⡳⢏⡟⣮⢳⢯⡄⠐⢌⡒⠰⢌⠂⢠⡝⢯⠞⣵⣋⠷⣙⢎⡳⢍⢖⡩⢎⡕⠣⡜⠀⠀⠀⠀⣠⡟⢮⣻⡜⣷⢺ ⢳⡏⣷⣭⠛⣧⢱⠀⠀⠐⢠⠁⠀⠊⢳⡜⢡⡎⢱⠊⣧⠋⣮⡕⢫⡝⣮⣵⠋⣶⠙⡆⠀⠘⠀⠀⣴⢫⡜⣭⡞⢱⠊⢳⠉⡎⠑⡎⣬⠀⠁⡎⠁⠀⠀⠀⠀⣶⡝⣾⡏⣷⢹⡎⣿ ⡿⣜⢧⣏⠿⣭⢏⣻⡤⡀⠀⠐⠀⠈⠂⢅⠣⠘⢄⠋⡔⢩⠢⠙⠬⡑⢎⠲⡙⢆⡛⣌⠃⢦⠘⡱⠢⢍⠲⠱⡈⢇⠚⢄⠣⠌⡑⠰⡈⠌⡑⠈⠀⠀⢀⡤⢞⡵⣫⢗⡹⣎⠷⣹⢎ ⠳⣎⠳⣬⢓⢮⡹⢶⣽⣿⣷⡦⣄⣀⠀⠀⠀⠂⠠⠈⠐⠤⢈⡁⠆⡑⡈⠤⠑⢂⡐⢈⠡⢂⠱⠠⠑⣈⠰⢁⡘⠠⠌⠄⠢⠄⠁⠂⠀⠀⢀⣠⣴⡾⣿⣛⣮⢵⡳⣎⠷⢮⡝⡶⣭ ⣷⣼⣳⢶⣫⣶⢯⣻⢞⡷⣞⡿⣿⢿⣿⣷⣶⡄⢄⣀⣀⢀⡀⣀⡁⣀⢁⡈⠒⣀⠒⣈⢂⠐⢂⡑⢂⢀⡀⡁⣈⠁⣄⢠⠠⠤⠤⢰⣚⣿⣿⣻⣟⡿⡳⢏⡞⣧⢻⣜⡻⣧⡻⣵⣳ ⣟⡾⣽⢯⡷⣯⢿⣬⣋⠹⢭⢻⡝⣯⢾⣽⢾⣿⣤⡐⠨⢆⡱⢂⡑⢆⠒⣌⠱⡠⠃⢠⣿⣷⡀⠘⠰⡊⢔⡑⠢⡍⡔⢢⠌⢃⣴⡾⣿⡻⣞⡱⢎⠓⣙⣬⣛⡼⣓⢮⡝⣞⡳⢧⣛ ⣯⢿⡽⣯⢿⣹⣟⣾⣽⣳⢶⣦⣜⣆⡛⢞⣻⢾⣽⡿⣶⣤⣈⠁⠘⠤⢋⢄⠣⠁⢀⣿⡿⣿⣷⡄⠐⠱⣈⢌⡑⠒⢈⣡⡴⣿⣏⡟⠧⢋⡴⣑⢮⡙⣑⢮⡱⡩⣍⢎⡱⢬⡑⢣⡘ ⣉⠞⣩⣑⠫⡜⡌⢧⠛⣌⠳⡬⢜⡬⣙⠎⣜⠳⣎⡿⣿⣽⢿⣿⣶⣤⣀⣈⣐⡈⣼⣿⣟⣿⣿⣿⣀⣀⣁⣠⣴⣾⢿⣯⢿⣱⠎⣝⠨⠖⠐⠈⠲⢔⠋⡶⡑⢳⠤⠋⠘⠦⣜⠣⡝ ⢌⡛⢤⢣⠳⡜⣱⢊⡝⣨⠳⡱⢎⡲⢍⡚⣌⢳⣹⢿⣻⣯⣿⣿⣾⣟⣿⣟⣿⣿⣿⣯⣿⣿⣾⣻⣿⢿⣻⣿⡿⣽⣟⡾⢯⡧⠅⡠⠄⠀⠀⠀⠀⠀⠉⠀⠉⡡⡐⣄⢃⠤⣈⠒⡉ ⢢⡜⡌⢆⠳⣌⡱⣍⢲⢡⠣⠵⣉⢎⢧⡹⢜⡲⢯⣟⡿⣷⡿⣷⣿⣿⣻⡿⣿⣽⣾⣿⢿⣾⡿⣟⣿⣿⣿⣟⣿⣿⣽⣻⣭⢟⡃⣵⢩⠀⠀⠀⠀⠀⠀⠀⠀⢲⡱⡌⠎⠲⡡⠏⠜

⠀⠀⠀⢀⣤⡤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣼⣧⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠉⠙⢿⡦⠀⠀⢀⣀⣀⣀⣀⣠⣄⣤⡜⣿⡏⠁⠮⣳⡽⠃⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⣾⡿⠿⠛⠓⠓⠒⠋⠙⠛⠾⣧⠁⠀⠀⠘⣇⠀⠀⠀⠈⣿⣧⣄⡀⠀⠀ ⠀⠀⠀⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣗⠓⢻⡯⠟⡶⠋⠉⠀⠀⠀⠘⡧⡀ ⠀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣔⣗⡽⠯⢷⣖⣢⣤⡤⡗⠃ ⡸⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⡏⡅⠀ ⡇⡃⢀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣃⡇⠀ ⠸⡄⠣⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣀⣠⣤⡶⢤⡀⠀⠀⠀⠀⠀⢧⣿⣿⠀⠀⠀⠀⠀⢀⣤⠇⠀⠀ ⠀⠈⠧⡘⢕⣂⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣀⡠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡻⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠴⣿⣢⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡯⠃⣀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠊⠓⠛⠛⠋⠛⠋⠙⠋⠛⠒⠛⠛⠴⠖⠒⠋⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⣝⡫⢜⠳⣫⢵⡢⡀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⡶⠿⠻⢶⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⡟⡺⢌⡛⡷⣗⡄⠀⠀⠀ ⠸⣻⣌⡱⣋⢇⣓⠺⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢧⡸⣅⡫⡜⣱⢚⠆⠀⠀⠀ ⠀⠈⠁⠑⠉⠚⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠑⠓⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠤⣤⢤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⡿⠗⠛⣋⣩⠭⡭⣭⢛⡓⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠶⢢⢀⠀⣠⣶⡿⣷⡿⠉⠀⢀⣾⠿⠋⠉⠉⢉⢛⣻⣥⠉⠻⣗⡄⠀⠀⠀⠀⣀⢤⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⢿⡁⢸⡿⠀⠀⢀⢸⢿⠀⠀⠀⠀⢸⠿⢷⠏⠀⠀⣹⣿⡱⡀⢀⢎⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡑⣿⡇⠆⠀⠀⠌⢿⣷⣀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠇⠿⡟⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⣷⡈⠀⠀⠀⠀⠈⠛⠻⠵⣲⣖⣶⠸⠟⠛⠁⢀⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀ ⠀⠀⠀⠅⢄⠀⠀⠀⠀⠀⠀⠀⠐⡸⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⡡⠀⠀⠀⠀⠀⠀⢀⢯⡚⠻⣷⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⡇⠀⠀⠀⠀⠀⠀⡰⡽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢅⠄⡀⢀⢀⡠⢊⠆⠀⠀⠀⠉⠙⠻⠗⢺⡔⣶⢶⣖⣴⠲⡍⠷⠓⢜⠄⠀⡀⡀⢀⡬⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠒⢖⢒⠈⢿⣷⣠⣤⡌⡤⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣦⡆⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⠄⠀⠈⠁⠉⠁⠈⠈⠻⣷⣤⣀⠀⢀⣀⣴⣾⠿⠙⠛⠋⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⡁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉⠛⠚⠋⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠂⠀⢀⡀⢄⣀⢀⡀⠀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠯⠻⠓⣿⠿⣿⠛⡿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠳⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⢀⡾⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠤⣍⠉⠉⠀⣤⣀⣤⡀⢀⠀⠀⠀⠶⠷⣦⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⣷⡀⠀⠙⠀⠀⢀⣬⣿⣿⡿⣿⡁⠀⠀⠀⡀⠀⠠⢤⠀⣿⡀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀ ⠸⣆⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠂⠊⠛⠶⢦⣴⠾⣿⡚⠷⣼⣿⠟⣹⣦⣀⠀⠑⠀⠀⢀⣴⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀ ⠀⠙⠻⠶⠤⠴⠾⠛⠋⠀⠀⠀⠀⠀⠀⢀⣾⢁⣴⣟⠻⢦⡤⠼⢿⡏⠉⠻⣷⢶⣟⠛⣏⣁⡀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠛⠻⢟⣛⣛⣶⣾⢿⣄⠀⠘⠋⢿⡟⠋⠉⠛⢶⣌⠻⢦⣀⠀⠀⠀⠀⠀⢀⣴⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⣀⡀⠀⢉⣄⡀⠀⠈⠀⠀⠀⠘⣷⠀⢠⡄⠀⢹⡆⠀⠉⠛⠛⠲⠒⠚⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠾⠏⢻⣤⡟⠉⢻⣆⠀⠀⠀⠀⠀⣿⠛⠛⠁⠀⣼⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⢸⣿⠀⠀⠀⢹⡀⠀⠀⢀⣴⠿⢦⣤⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠻⠷⠶⠶⠿⠷⠾⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣟⣿⣻⣟⣿⣻⣟⢿⣽⣻⢽⢯⡟⡿⣽⢯⣟⠿⣽⣻⡽⢯⣟⣯⣟⢯⣟⡿⣽⣻⣽⢻⣯⡟⡿⣽⢯⣻⡝⣯⢽⣩⢏⢮⡱⢎⢲⡑⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣫⢿⣹⣝⡺⡔⢢⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡾⣟⣯⢿⣻⣞⣷⣻⣞⡷⢯⣻⠶⣏⢿⡺⣽⣹⡞⣽⣚⡟⣧⢷⣛⡿⡼⢶⣫⣟⡾⣽⣳⢯⣞⡿⣶⣻⣽⣳⢯⣷⣹⢧⡻⣜⣚⢦⡙⢮⡱⢬⡙⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⡜⣧⡙⢆⡡⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡿⣯⣟⣿⣽⣻⢷⣻⣞⡷⣯⣻⢏⣷⢿⣿⣾⣷⣿⢯⣽⣝⡛⠾⣧⣟⡼⢳⡝⣯⢳⡞⣽⠾⣵⣻⢾⣽⣳⡟⣾⡽⣳⢧⡟⣧⢻⡼⣩⠶⣙⢦⠳⡌⢞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡴⣩⠦⡑⠂⡌⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣟⣿⣽⣟⣾⣳⢿⣯⢷⣯⣟⣷⣯⢿⣭⡟⢯⣽⢃⢆⢺⣴⣊⠙⢦⡀⠈⠙⠧⣞⢌⡳⣹⢧⣛⠷⣯⣻⢶⣯⢟⣷⣻⡽⢯⡽⣝⣧⢻⣥⢻⡜⣎⢧⡙⣎⢆⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⢿⣻⣾⢯⣿⡱⣏⠼⣁⠒⡈⢄⠂⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣟⣷⣟⡿⣾⣽⣷⣻⣟⣾⣻⣾⣿⢿⣸⣿⢫⢼⣷⡏⣷⡾⠟⠏⠃⠀⠀⠑⢆⠀⠀⠈⠳⣔⠱⢮⡝⣯⢳⣏⡿⣞⡿⣞⣷⣻⢯⣟⢷⣭⣳⢎⡷⣚⡼⢢⡝⡜⢮⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣮⠷⣭⢻⡔⣫⠔⣊⠔⡁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣟⣷⣿⣻⣾⣟⣿⢾⣳⡿⣞⣷⣿⣿⣟⢣⣾⡏⢆⣿⢼⡇⠋⡁⠀⢸⠠⠰⡀⡀⠀⢢⠀⠀⢂⠈⠳⣜⠺⣵⡛⣞⡽⣯⢿⡽⣾⣽⣻⣞⡿⢶⣫⢟⡼⣣⡝⣧⡝⡞⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⣛⡾⣵⢫⡖⣍⠲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⡾⣟⣾⣟⡷⣿⢯⣿⣻⣽⣿⣿⣿⣿⢏⣾⣿⢘⡞⡽⢸⢣⠀⠇⠀⠀⡆⡇⣷⡈⠀⠀⢣⠀⠀⢠⠘⢿⣧⠳⣝⣎⡳⣏⡿⣽⣳⢯⡷⣯⣟⣯⢯⣟⢾⣱⣛⢶⡹⣝⢮⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⢷⣻⡜⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣯⣷⢿⣟⣿⢾⣿⣻⡿⣽⣿⣿⣿⣿⣿⡿⢎⣿⡟⢸⢡⣷⠈⣇⠣⣀⡃⠀⣧⢧⡛⠻⣦⡀⠄⢇⠀⠀⢆⠈⢿⣧⢻⣎⣷⢺⣽⣳⣟⣯⣟⣷⣻⣞⡿⣞⣯⣳⢏⡷⣝⢮⡳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣏⣯⣗⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣯⣷⢿⣻⣽⡿⣯⢿⣻⣽⣷⣿⣿⣿⣿⣿⣿⣿⡿⡞⣿⡇⡘⣾⢱⠀⣿⣤⠞⠑⢲⣿⣿⣇⠀⠈⠳⣜⣿⡀⠀⠈⡆⠈⢾⡧⢿⡜⣟⣾⣳⣟⡾⣽⣞⡷⣯⢿⡽⣞⡷⣯⡟⣾⣭⢷⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣽⣾⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢿⣽⡾⣟⣿⣳⣿⣻⡿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣳⡛⡿⡇⢹⠇⢈⣾⠻⣿⡄⢠⢾⣿⡾⡏⠈⠉⠉⠙⢿⡇⠀⢠⠸⠰⡀⢻⡞⣽⢯⣞⡷⣯⣟⣯⢿⣽⢯⣿⡽⣯⣟⣷⣻⠷⣞⣯⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣳⡿⣿⣽⢯⣷⡿⣽⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣥⢃⣧⣧⡞⠊⠁⠻⣧⠿⣘⣏⣾⠿⠽⣷⣿⠿⢿⡻⣾⣷⡇⢸⡌⡇⢱⡄⣙⢧⣿⣾⣟⣷⣻⢾⣻⣽⢿⣾⣻⣷⣻⢾⣽⣻⡽⣶⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣷⣟⣷⣯⡷⣿⣽⣟⣾⢿⣯⢿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣼⢁⣤⣶⡿⠟⠒⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⢨⣿⢹⡀⣷⣌⢻⡝⣻⢼⣳⢯⡿⣽⡾⣟⣷⣿⣳⡿⣟⣾⢷⣻⣽⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⣟⣾⣟⣾⣽⣟⣾⣯⢿⣻⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣧⠘⢿⠯⠤⠉⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠎⣿⡂⠐⣿⠀⣧⢸⡞⣆⢻⡜⣧⣻⢯⣟⡷⣿⣻⣽⣾⢿⣽⡿⣯⣿⢯⣷⢿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢷⣿⢯⣷⢿⣽⡾⣯⣷⢿⣻⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⢯⣷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣣⠀⢀⣿⢠⡏⣿⡗⣽⢸⣟⡶⣯⣟⣾⣽⣟⣯⣿⣯⣿⣟⣿⣿⣽⡿⣯⣿⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⣿⢯⣿⢯⣿⣞⣿⣳⡿⣟⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⠛⡆⠈⠻⣷⡭⡂⠀⠀⠀⠀⣤⣶⠶⠿⢿⡆⠀⢸⢀⣾⡇⠀⣸⠀⣸⣷⠸⣿⣾⣿⣯⣷⣿⢾⣽⣾⣟⣿⣷⣿⣻⣿⣿⣾⣟⣿⡿⣯⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣽⡿⣯⣿⢷⣯⣿⡽⣟⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⣸⡁⠀⣹⡄⠠⡙⢷⡌⠑⠀⠀⠀⠛⠁⠒⠂⠉⠁⠀⠐⣡⡿⠀⢀⡇⢀⡏⣼⢸⣿⣿⣿⣯⣿⣿⣞⣿⣷⡿⣿⣾⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣻⣽⡿⣽⣯⣷⣟⣿⣟⣿⡾⣟⣾⣿⣿⣯⣿⣾⣿⣿⣿⣽⢠⡟⣇⢳⡘⣿⡄⠑⠌⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⣼⣿⢸⣧⢇⣿⣼⣻⣧⢻⡿⣿⣿⣿⡿⣽⣿⣷⣿⣿⣽⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⢯⣿⣟⣷⡿⣾⣻⣾⢯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡼⣏⣷⣹⣆⢻⣽⣿⢦⠀⠂⢹⣿⣿⣿⠒⡤⣄⣀⡤⠊⣡⢿⣿⡇⢀⣧⣿⣎⣿⣸⡿⣼⣿⣧⡟⣯⢻⣱⣿⣻⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⣤⡜⠀⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡆⢤⡄⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣀⠀⠀⠀⠀⡀⢈⠻⣿⣿⣿⢿⡿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢳⣦⣤⣠⠜⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣤⣄⣀⣀⣀⣀⣤⡶⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠉⠀⢀⣈⡉⠰⠄⣈⣀⣠⡈⠻⣞⣯⢿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣉⠉⣡⡾⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠀⠀⣀⣀⠀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⢯⡷⣳⢯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣥⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋⠀⣼⠀⠀⠀⠼⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢾⠱⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠶⢦⣤⣤⣶⠞⢤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢧⡸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠣⢞⣿⠤⢹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⢲⠱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡑⠌⠾⣧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⢂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠓⡌⠱⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢝⠒⢂⣀⣠⣤⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠄⡡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡄⢃⠌⡑⢄⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢈⡐⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⡌⠌⣳⠈⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠴⣤⢳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠣⠌⢂⢍⠒⢬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑⡌⠢⢌⡘⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠿⣟⢻⡿⣿⣿⠰⣈⠑⢢⡐⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣟⡾⣽⣳⢯⣟⣿⣿⠿⠿⠷⠳⢦⣈⡛⠬⠆⡙⢌⢻⠰⢠⠉⢆⣸⣿⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⡿⣿⡽⡾⣝⠾⣜⡳⢭⡳⢫⠞⡽⣛⡿⣳⢶⣤⣀⠈⢁⠢⠑⡌⠢⢽⡎⠤⡉⢆⣾⡿⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⢟⡽ ⣿⣿⣿⣿⣟⣯⡟⣷⣹⢳⣭⢻⣬⢳⢫⢵⢫⡽⣱⢫⣜⡷⠿⠻⠿⠿⠦⢁⠃⡄⠣⡘⠷⢂⡱⣪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡰⢉⡒⠄ ⣿⣿⣟⣷⢻⡼⣽⢲⣏⠷⣎⠷⣜⣣⠟⣎⢷⡺⣵⣫⣟⡿⣶⣶⣤⣤⣤⣀⣦⣰⣵⣼⣷⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢢⠁⢆⠡ ⣿⡳⣞⡾⣹⢞⡵⣫⢞⡽⢎⡟⣬⡓⣿⡸⢧⣛⣶⣻⣼⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠆⡑⠈⠄ ⣷⢻⡵⣫⢗⡯⣞⡵⣫⢞⡽⢺⣱⢛⣶⣹⣧⣟⡶⠯⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠚⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⡈⠔⡈⠡⠀ ⡽⣣⢟⡵⣫⢞⣬⡷⠽⠚⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠌⠐⡀⠡⠀ ⡻⣵⢫⣞⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣀⠀⠀⠀⠀⢰⣠⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢂⠈⠄⠠⠐⠀ ⣟⠼⡳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⢿⡆⢠⠀⠀⢸⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡀⠈⠀⡀⠂⠀ ⢮⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠸⡿⢆⠀⠀⠘⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠈⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣄⠀⠀⣿⣮⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⢻⣿⣿⣄⣰⣿⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⣿⣿⠍⠰⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣽⠙⣿⡄⡀⡱⡄⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡍⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⢀⠄⠀⠀⠈⠀⠀⢀⠿⡇⢹⣧⡀⠌⠈⠙⢢⣡⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⢊⠴⡙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡜⠀⠃⢸⣿⣷⣧⣆⣀⣀⡈⠓⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⡍⠰⢈⠂⡙⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⣦⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⢀⡰⠯⠇⢀⣾⠻⠛⠛⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠄⡁⢂⠐⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⣀⡤⠔⠋⢀⡠⠶⠋⠀⠀⠀⠀⠀⣀⠤⠴⠋⠌⠙⠩⢛⠿⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠂⠈⠀⠂⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣭⣤⢤⣴⣶⠉⠒⠈⢉⡠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠂⠙⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⡀⠈⡀⠄⡁⠄⣁⠢⣔⡹⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⣀⠒⣤⢫⣞⣷⣯⣷⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠄⡒⢬⣻⣞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠂⠀⢀⠀⠄⠀⠀⠀⢀⠀⠀ ⠀⢂⢹⣚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣝⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡿⠃⠞⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀ ⠀⢊⢶⣹⡾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⠂⠠⠀

⠀⠀⠀⠀⠀⣖⣲⣶⡿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣯⣻⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣉⠙⠫⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡴⣯⢹⡇⠀⠀⠹⣧⡀⠀⠀⠀⢀⣤⠴⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢶⡟⠉⠉⠉⠻⠞⠋⠙⢳⣆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⢀⣶⣿⣦⠀⠀⢀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠈⠉⣽⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠷⠶⠟⠃⠶⠤⣄⡉⠀⠀⠀⣰⣯⣤⣦⣤⣤⣙⣶⡿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⣦⠀⠀⠀⠀⣿⣿⣿⣷⣄⣼⣿⣿⣿⣇⣴⣿⣿⣿⡇⠀⣤⢶⡛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⢷⡴⠞⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣤⣽⣿⣟⣛⣛⡳⢿⡿⠛⠃⠀⠀⠀⠀⣾⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣟⢿⡹⢧⣛⠶⡭⣏⢿⣹⢻⠷⣦⡀⠀⠀⣀⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠙⠛⠒⢶⣦⣄⣀⣀⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⢏⡷⣙⣎⠷⣫⣜⡳⡽⣜⠮⣵⣋⢯⡝⣿⣴⡟⠙⡿⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠈⠀⠉⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⣍⡟⣴⢫⡜⢯⡵⢎⡳⡵⣎⢟⡴⣋⣾⠼⣵⣿⠋⢫⠽⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣠⣴⢦⣤⣴⡄⠀⢛⡉⠁⠀⣹⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⣴⠟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡵⣚⡼⣥⣟⡼⣓⣾⣭⠷⣷⣽⡺⣟⢿⣡⢋⡜⣿⣿⣿⠶⣞⡁⠀⠀⠀⠀⠀⣰⡶⠾⠛⠁⠉⠉⠀⢀⣄⡈⢻⠶⣮⢻⣿⣿⡿⣿⣟⠀⠀⠈⠋⠁⢨⣿⣿⡏⠉⠻⡿⠋⠉⢿⣿⣿⣿⣏⠉⢻⡇⠀⠸⣏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣟⡶⠟⣶⡿⣿⢷⣿⣏⣤⣤⡴⠟⠛⠛⠻⢷⣷⣞⢷⢺⣿⠟⠋⠁⣴⠀⠘⣿⠛⣫⣄⠀⠀⢰⣒⡆⠀⠻⣿⡟⣥⣚⣿⣿⣿⣿⡽⣞⡿⣦⣤⣀⣀⣴⡿⠿⠿⣷⡀⠀⠀⠀⠀⣼⣿⢿⣿⡿⠀⠸⣇⠀⠀⠀⠀⠀⢸⣤⣤⡤⠀⢀⣤⠶⡀⠀⣦⠀⠈⢳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣇⠏⣔⣿⡾⠋⠁⣠⣶⣤⣼⣿⣆⠀⠀⠀⠙⢿⣎⢿⣇⣀⣤⣾⠋⢠⣾⠯⣙⢿⡿⠀⢰⣄⣀⣤⠀⠀⢀⣹⡟⠉⠿⣤⡿⣿⣿⣾⣿⣿⣿⣿⣿⡦⢤⣶⣤⣬⣿⣶⣶⣶⣾⢿⣭⢿⣿⠇⠀⠀⠘⣿⠛⣷⡀⠀⠈⠻⠟⠁⠀⠈⠻⠏⠁⠀⣿⠀⠀⠀⠻⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⣴⣶⣿⣯⡟⣯⡟⠀⠀⠀⢹⣿⣽⢻⣾⡟⠀⠀⠀⠀⠈⣿⡞⣿⠉⠈⠙⣿⠋⣿⠛⣾⡞⠁⠀⢠⣤⣴⣶⡖⠛⠛⡏⠀⠀⠀⣼⠃⠀⠙⢻⣿⣿⣿⣿⣿⣿⣷⣿⣴⣾⣿⣿⣿⣿⣿⣷⣾⣿⠋⠀⠀⠀⠀⠘⣷⡟⠙⣶⣦⣤⠀⣴⣤⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠛⣦⠀ ⠀⠀⠀⠐⢿⣧⣛⣿⡜⣾⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⠄⠀⠀⠹⣶⠋⠀⠈⢻⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠾⣶⡟⠋⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠈⠉⡿⢉⣽⡶⠶⠶⣖⣛⣿⡄⣀⣀⡀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⡼⣇⡀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠻⢶⣆⣤⣶⠂⣀⣀⣀⣀⠀⠀⠀⠀⠀⠰⣯⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠁⠀⠀⠈⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣄⠀⣴⢾⣦⣿⣧⣹⣆⣾⡻⣽⣻⣿⢻⡝⣿⣆⠀⠀⢠⡏ ⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣾⣧⣿⣧⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⡾⠃⠀⢠⣤⣤⡄⣠⣼⠿⢛⠛⡋⢍⡙⡙⢛⠿⢶⣤⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢶⠶⠿⡞⡶⢶⣿⣿⣿⡏⣠⣤⣄⠀⠀⠀⠀⠀⢀⣀⡀⠀⣨⡿⠛⠋⢉⠉⠉⡉⠛⠻⡷⢽⡗⣮⣿⠻⡴⣿⠶⠶⠋⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⠟⠙⠋⠁⠀⠈⠉⠙⠳⣦⣴⣚⢫⡍⣸⠇⢀⣤⣾⡇⡈⠟⡉⢄⠢⢁⠆⢡⠂⠔⡈⠆⢌⠢⠌⠛⢿⣄⠀⠀⠀⠀⣠⣴⠟⣏⠳⡜⣪⡙⣎⠵⡙⢦⢓⡬⢛⠿⡟⢴⣿⣧⣄⠀⠀⣴⡿⣏⣿⡾⠋⢀⣤⣥⣦⣌⡐⠀⡁⠂⠄⡀⠌⠓⣮⣳⣽⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⣻⣿⣄⢹⣧⣀⠱⢀⠃⢌⡐⠌⡰⢈⠆⡘⠤⢑⠨⢄⠢⠉⡜⠠⠛⣷⡀⢀⣼⠟⡬⣙⠬⣓⡜⣡⠞⡤⣋⢝⡘⠮⣔⡋⢮⡙⣬⢋⣖⣿⠃⢸⣯⣳⣿⣯⣶⣿⠟⠉⠀⠀⠉⢻⣆⠠⠁⠄⡐⠀⠂⠌⠛⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠤⣠⠀⠙⠋⠀⢹⣶⡟⢁⠢⢁⠎⢄⠒⡌⠰⣈⠢⢑⡈⠆⡑⠢⣁⠣⠄⢃⠱⡈⣷⣾⣋⠞⡱⣌⠳⣒⢬⡱⢎⡕⠮⡬⢍⡳⢢⠝⡦⡹⢤⡋⢿⣇⠀⠸⢷⣻⡏⣿⢾⡇⠀⠀⣠⣤⣄⠀⣿⠀⠌⡀⢐⠈⡐⠠⠁⠈⠻⣦⠀⠀⠀ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢰⡶⠄⠀⠀⠉⠀⠼⡙⢎⠥⣋⠔⠀⣶⢿⡏⠔⡨⠄⢃⠌⢂⠌⡰⠁⡄⠢⢁⠔⢨⠐⡡⠄⣂⠩⠄⠃⡔⢸⣷⢪⡑⢧⡘⡣⢍⠦⡓⢎⡼⢱⡡⢏⠲⣍⠺⣔⡙⢦⡙⢦⢻⡇⠀⢰⡿⣶⣽⣿⣷⣄⠀⢿⣿⡿⣴⠟⢠⣶⠟⠛⠛⠻⣦⡁⠌⠠⢹⣆⠀⠀ ⠀⠀⣸⠇⠀⠀⢀⣤⡶⠄⠀⠈⠛⣁⣤⣴⣦⣤⣭⡙⡬⢓⡜⠢⠀⣿⢾⡁⠎⡐⠌⢢⠘⡠⠌⣄⠣⠐⣱⣮⡈⢆⣶⡅⢒⣠⡆⠩⡐⢌⠰⣿⢣⠜⣿⣧⣹⣾⣧⣙⣶⡌⠧⣜⢣⢫⡔⢫⠴⣙⠦⡹⣌⢻⣷⠀⢈⣿⣾⣿⣭⣟⢿⣿⣶⠾⠛⠁⢢⣿⢁⣀⣀⣄⠀⠘⣿⠀⡁⠄⣿⠀⠀ ⠀⠀⣿⡂⠀⢀⢸⡯⢀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠙⣷⠁⠃⠈⠀⢸⡏⢸⡇⡜⢀⠎⡐⣢⡡⠌⣿⠷⠾⠾⠋⠛⠛⠉⠛⢛⡻⣧⣕⣴⣮⣼⡿⣷⠿⣋⣼⣏⠁⠙⠛⠻⢿⡾⢿⣎⠖⣬⡇⣏⢲⠩⡵⣘⢼⡟⢠⡿⠁⡈⣻⣿⣟⣷⡎⡝⠷⣦⣅⠘⣷⠘⣿⡻⠧⠀⢀⣿⡀⠔⢠⡿⠀⠀ ⠀⢀⣸⣇⠀⣎⠶⣡⠳⡌⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⡿⠀⠘⣿⡀⠆⢂⠡⣹⡟⠛⣋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢖⡫⣅⠁⣸⣷⣯⢃⠿⣿⠟⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⡓⡬⢃⠯⢴⣉⣾⡇⣿⠁⠐⠺⠛⠈⠙⣻⣿⣮⡱⢊⡝⡻⣿⣷⣬⣁⣀⣠⣾⠿⣷⢀⣾⣇⡀⠀ ⢰⡏⠉⠁⠈⡖⡱⢆⣣⢙⠸⣧⡀⠀⠀⠀⢀⣠⡾⠃⠀⢀⣴⠟⠁⠀⠀⠘⣷⣼⠟⠳⢟⡡⢾⣿⡧⢀⡄⠀⠀⢀⣾⠆⠙⣯⠎⣵⡿⢻⡿⢟⡻⣯⣒⣁⠀⠸⣧⡀⢀⣠⡄⠸⣿⡿⠻⢷⠿⣯⡎⣕⢢⣿⢸⣇⣈⠐⡀⠛⠿⠾⣿⣿⣿⢿⣿⣾⡟⠿⡻⢿⣿⣿⣏⣯⡿⣣⣾⣿⣹⡷⠀ ⠀⠛⠶⠶⢷⣌⡑⢪⡴⢧⣤⡈⠛⠳⠖⠛⠋⠁⢀⣠⣶⣿⢷⣞⠛⠛⣷⠀⠈⠹⣦⣤⣾⣍⠯⣙⡇⠀⠙⠷⠶⠟⣁⣠⣤⣼⣾⣿⢷⡜⢿⣬⡗⣽⠋⠹⣷⣶⣬⣿⣋⣉⡀⠸⢍⢲⣩⣤⣠⣿⠳⣬⣿⠟⣏⢻⡹⠿⣶⡑⣿⣤⡽⣯⣻⣿⣻⣽⠛⢷⣧⣣⡹⢟⢿⣤⣾⡿⢿⢮⡿⠃⠀ ⠀⠀⠀⠀⠀⠈⠛⢿⣇⠀⣼⠿⢶⣄⣀⣤⣴⠾⠛⠉⠄⢿⣆⣻⣤⡴⠟⠀⠀⣴⣿⣷⡌⠙⢳⡷⢶⡶⠶⠛⠛⠛⠉⠉⠸⣧⣼⣧⣿⣿⠀⠘⠿⠿⣦⣤⣼⠇⠀⠈⠉⠛⢛⣿⢟⡻⢫⠝⡭⢣⢽⡿⣡⢛⣌⢣⡜⢣⢽⣇⠈⠁⡀⠌⣩⠀⡙⣿⣴⡄⠈⢹⣿⣾⣬⣿⠟⠛⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣄⠂⡙⠋⢁⠠⠀⢂⠁⠄⡈⣿⠉⠀⠀⢀⣠⣴⣾⣿⣟⠀⢠⡿⣅⣸⠇⠀⠀⠀⠀⠀⠀⠀⠙⣦⠉⠉⠁⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠸⢿⣼⣾⣣⢚⣱⣧⣾⣷⣡⠇⣎⠖⡜⢣⣾⠟⠻⢶⣤⡈⠻⠶⠇⠀⠄⠠⠁⣼⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠂⠡⠀⢂⠈⠠⠐⠠⠐⢸⣇⢰⣾⣿⣿⣿⣿⣿⣿⣷⡺⣤⣦⡿⠀⠀⠀⠀⠀⠀⢀⣴⠟⢻⣇⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣻⡟⢋⣿⠁⠈⠿⠛⢷⣯⠜⣿⠏⠀⠀⠀⣾⣻⣷⣶⣬⣴⣬⣴⡾⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣧⣬⣤⣥⣤⣬⣴⣼⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⢶⣤⣀⣀⣀⣀⣀⣀⣾⡃⠀⠀⢻⣆⠀⠀⠀⢘⣷⣦⣄⣤⠶⢶⡄⠀⠀⠀⠀⢀⣹⣯⠾⣿⠛⠰⣏⣹⠆⣀⣿⡚⢿⢶⣤⣀⣴⡟⢫⠭⣙⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢿⣉⣉⣿⡿⠛⠉⠁⠀⠀⠈⠉⠛⠛⢛⣿⢯⣻⣽⣇⡀⠀⣿⠷⢾⣟⢛⣿⡟⣍⠳⣻⣦⣤⣶⠁⢈⣿⠥⢫⡜⠦⣍⡝⣣⢺⡅⣏⠜⡳⢌⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢩⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣫⣿⣿⣻⢿⣿⢿⡿⣦⠙⣿⢧⡙⢦⡹⢔⣊⠶⡙⣟⠻⡥⣋⠵⣌⡓⠦⢎⡱⢺⣿⢤⠛⡜⡜⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡒⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠷⣿⡿⡿⣼⣿⣸⣏⠦⣙⢦⣵⣾⠶⠷⣯⣴⣧⣵⣑⢺⠰⡍⣝⠪⡕⡣⡝⣿⣼⣥⣳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⣦⡀⠈⠛⣿⣿⣿⣿⠷⠆⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠟⠘⣿⣧⣙⣾⠟⠁⢀⣤⣤⡀⠀⠀⠉⠙⠻⢷⣼⣂⠯⣔⢣⢝⡰⣍⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⠉⠁⠀⠀⠀⢴⣿⣿⢡⠤⣀⠈⣿⣿⣿⡶⢭⢏⡳⢾⣿⣿⠃⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣷⣾⡇⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⢷⣎⢎⡖⡱⢎⢎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⢀⣄⠀⠀⠀⠀⣠⠴⡤⠀⠈⢛⡿⢡⢫⢼⠂⣼⣿⣿⣾⡓⢮⡱⣋⡏⠁⠀⠀⠀⠈⠣⠜⠀⠀⠀⢠⣼⣇⣠⣠⢤⡤⣛⠋⣿⢿⣧⡀⠄⠀⠈⠀⢀⠀⢰⣙⡆⠀⠀⠀⣠⣈⠻⣮⠲⣍⡚⢬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⡠⢴⢻⣙⠛⠀⠀⣈⣉⣠⡴⣾⢻⡇⠛⠚⢁⣴⡿⠋⠸⣧⣙⣦⣳⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢣⠳⣜⡻⢿⡟⠶⠟⢷⣄⡀⠀⠀⠘⢷⣄⣀⣀⠀⠀⣾⣿⣿⠂⢹⡷⣌⢓⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡸⡱⡍⡖⡹⣟⠛⣿⠉⠹⣇⣀⡽⠟⣀⣠⣴⡿⣯⢶⣄⠀⢙⡿⠋⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣷⢩⠳⣌⢿⣿⣧⡀⠀⠰⣿⣛⣷⣶⠟⠻⣿⢯⡅⠀⠀⠈⠙⠉⠀⣸⡷⢌⣳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣍⢓⣭⣅⠈⠛⠛⣚⣛⣯⣽⣾⣿⡿⣿⡛⠛⠉⢠⡿⠀⠈⢷⣠⡞⠛⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⠓⠋⣸⡾⠃⠀⣁⣀⠀⣸⣿⡁⠀⣀⣴⡏⠰⢷⣤⣄⣀⣀⣤⣴⣿⣵⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠁⠹⣷⣿⣿⣿⣿⡟⠛⢻⣟⣷⠈⢻⣷⠶⠟⠁⠀⠀⠈⠙⠷⣾⣿⠿⣿⣿⡶⠶⢦⣤⣤⣤⣤⡾⣧⠀⢸⡷⠛⠉⢠⣾⣿⣿⣿⣿⣿⣾⣿⣛⠉⠀⢿⣄⢈⡿⣿⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀⠀⠈⠻⠾⠃⠀⠀⠈⠁⠀⠀⢻⡄⠀⠀⠀⠀⣠⠶⠶⣿⡽⣻⢧⢫⡽⣻⣿⠟⠛⠛⠛⠲⠿⠷⠿⠗⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠉⠉⣡⡟⠀⠀⠀⣠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣀⠛⢻⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⡼⠿⣤⣀⠀⠀⣠⣿⠤⢤⣼⣿⣣⡜⡧⢧⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⡀⣠⣼⠟⠀⠀⠀⠘⢿⣄⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣾⣧⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⣀⣄⡉⢷⣴⠋⣀⣀⠀⠀⠙⣷⡹⢧⢏⣷⠀⠀⠀⠀⠀⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣇⣹⡇⠀⠀⣰⣆⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠛⠛⠙⠳⣦⡄⠀⣿⠋⣿⠀⠀⢸⣿⣿⣿⢸⡇⢸⣿⣿⣧⠀⠀⢸⡟⠿⠾⣿⣷⣤⣀⣀⡾⡕⣎⠶⣴⣷⡆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠉⢻⡍⠉⠀⠀⠿⣅⣹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠷⠾⢃⡴⠿⣆⡀⠈⠙⠛⣁⡾⢻⣌⠛⠛⠁⠀⣠⠿⣄⠀⠀⠀⠻⣦⣈⣽⠫⣕⢎⡳⣺⠋⠀⢰⡇⢈⣿⠛⠀⠀⠀⠀⠀⠀⠀⡀⠹⣦⡀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢛⣷⡄⠀⠀⠀⣾⢡⠲⣍⣛⠓⠖⣟⠉⠀⠀⠈⢛⡖⠖⣛⢭⡒⣌⢷⡀⠀⠀⠀⠀⠸⣇⠈⠉⠩⡁⢀⠀⠐⠹⣟⣻⣤⡾⠁⢠⣶⣦⠀⠀⢻⡄⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⢋⡵⠿⣦⠀⢰⡇⢯⠳⡜⡬⠁⠀⠙⢦⣄⣀⣴⠟⠁⠀⣏⠶⣹⢰⢚⡇⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢈⡽⢣⠶⣄⠈⡇⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⢻⣎⠷⠴⠟⠀⠀⢷⡀⠁⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢈⣵⡁⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⣽⠃⠛⠛⢲⡄⠀⢀⣤⣤⡀⠀⢸⡱⣋⢞⡹⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠁⢀⡆⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⢀⢀⠀⣀⢀⣀⣀⣠⡟⠉⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠲⠶⠞⠃⠀⠸⣧⡀⠙⠗⢀⣉⣑⣪⡵⠿⣤⣄⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠀⠀⠀⢾⡏⠉⣹⣿⠋⡿⣿⣭⣿⣏⠹⣿⣦⠴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣶⣿⡏⢀⡿⣽⠉⡿⣽⠀⢫⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡗⡾⠿⢮⣤⣿⡽⠴⠾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠳⠛⠿⠁⠻⠞⠳⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣠⡶⠦⠴⠶⢶⣄⣀⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠴⣂⣀⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⢺⣿⣿⣷⣌⡒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠋⣴⣿⣷⡆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢌⢻⣿⣿⣿⣿⣿⣷⣦⣬⣙⠢⡄⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⡤⢒⣉⣥⣴⣾⣾⣿⣿⣿⡿⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣨⣥⣤⣤⣤⣶⣤⣤⣤⣬⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⠎⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣴⡄⠀⠀⣤⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠁⢀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠈⠙⠛⠷⣾⣷⣾⠿⠛⠉⠈⠙⠻⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢿⣿⣿⣿⣿⣿⡟⠁⢸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡌⢿⣿⣿⣿⠄⣇⠤⢒⡂⠩⠍⠍⠉⢁⣐⠢⢄⡀⣀⠤⢒⣂⣒⢦⡀ ⠀⠀⢳⢸⣿⣿⣿⣿⡿⠀⠀⢈⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠁⠈⣿⣿⡟⠒⠦⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⠥⠒⢁⠤⡈⡆⡇ ⠀⠀⠈⣆⢿⣿⣿⣿⣇⠀⠀⠘⢿⣿⡿⠁⠀⠀⠀⣀⣀⠀⠀⠀⠸⣿⣿⡿⠀⠀⣿⡿⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠥⢔⡵⢣⠇ ⠀⠀⠀⠈⢦⡙⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣌⠓⢊⡤⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⡜⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⡥⠒⠁⠀ ⠀⠀⠀⠀⠀⠙⣦⢈⡛⠻⣷⣤⣀⠀⠀⠀⢠⡴⠿⢿⡿⠶⣤⡀⢀⣀⠤⠒⠉⠀⢠⡜⠁⠣⣀⣹⠆⢀⣤⡀⠀⠠⡒⠉⣸⠀⠀⠀⠀⡇⣧⠀⠀⠀ ⠀⠀⣰⢉⣌⠓⠁⣇⣸⠿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⠀⠀⣿⣿⣶⣤⠒⢦⠀⢄⣇⠀⠀⠀⠀⠀⠈⣲⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀ ⠀⠀⡏⣸⣿⣷⣤⠀⠐⠀⡴⠲⣿⣿⠿⠟⠃⠀⢠⡾⢿⡄⠀⠈⢻⠛⠉⠒⠉⠀⠀⢨⣢⠀⠀⠀⠀⠠⠌⠄⣀⣀⢀⡄⠀⠀⠀⠀⠀⢧⢸⠀⠀⠀ ⠀⠀⡇⠿⢿⣿⣍⡄⠀⠀⡗⠊⠀⠻⢦⣄⣤⠶⠟⠀⠈⠷⣤⣀⠼⠀⠀⠀⠀⠄⡞⢩⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⢀⡖⡠⠐⠚⠈⡄⠀⠀ ⠀⠀⠈⠑⢦⡛⢿⣷⣶⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡽⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠡⣂⡀⡤⣊⠴⠁⠀⠀⡆⢇⣀⡀ ⠀⠀⠀⠀⠀⠉⠒⠀⠀⠄⢌⣧⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢹⠀⠀⠀⠀⠀⡰⠙⢦⠀⠀⠈⠙⢲⡆⠂⠀⠀⠀⠀⠀⠁⠤⠠⠀⠠⢄⠊⣧⠤⢢⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠞⠀⠀⠀⠀⠀⠀⠛⢳⡄⠀⠈⢳⠀⠀⣀⠀⢣⠀⣸⠀⠀⠀⠀⡏⠁⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⠯⠔⣃⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⠞⡴⠁⠀⠉⢎⡓⠥⠅⠤⠤⠅⡧⠀⣠⡇⠀⠀⠀⠀⠀⠀⠐⠊⣡⣶⣿⠗⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠍⣐⣒⣒⣒⣒⣂⠩⠭⠭⠗⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠒⢌⡛⠮⠄⠐⢂⣀⣐⠂⣒⣂⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠛⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠈⠙⠷⣦⣤⣄⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢠⡾⠂⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⢀⣴⠟⠁⠀⣀⣤⠶⠞⠛⠻⠶⣤⡀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢤⣶⢻⡟⣶⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠀⢠⡟⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣌⣛⡋⠀⠀⠀⠸⢧⡴⠛⠓⠞⠁⠀⠀⠀⠈⠛⠛⢈⣥⠟⠁⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⣾⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡽⠟⠀⠀⠀⠀⠀⢀⣤⣤⣴⣤⣄⣀⣤⣤⠶⠞⠛⠁⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣤⣤⣤⣤⡶⠾⠋⠁⠀⠀ ⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀⣀⣀⣤⣤⣴⡟⠁⠘⣧⠀⠙⠻⠋⠛⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⢋⣩⣽⠿⣯⣽⡇⠸⠋⠀⠀⣸⡟⠷⣤⡀⠀⠀⠈⠻⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠚⠛⠋⠉⠀⣰⡟⠉⢀⡀⠀⣿⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠘⠷⣤⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢈⣻⢦⣄⣀⣀⠀⢠⣴⣶⠞⠛⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠈⠛⢷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⢿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣟⣿⣷⣤⣶⣾⠿⠛⠛⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠈⠙⠛⠿⣷⣾⠿⠿⠿⠿⠿⠿⢿⣿⣿⣻⣞⣷⣻⢾⣽⣿⡁⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣳⣟⣾⣿⣿⣿⣾⣿⣷⣶⣤⡀⣀⣀⣤⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣻⣞⣿⣿⣾⣿⢿⣽⣳⣟⡿⣿⣿⡿⣟⡿⣿⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣳⣟⣾⣻⣿⣿⣻⣞⡷⣯⣟⣿⣿⣿⣯⢿⣽⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠛⢷⣯⣿⣷⣿⣿⣿⣿⣟⡿⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣯⣟⡷⣯⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠉⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣾⣷⣤⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠶⠾⢿⣿⠛⠛⠛⠛⠂ ⠉⠁⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣿⣧⣤⡤⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠘⠻⣿⡿⠶⠶⣦⠀⠀ ⠀⠀⠘⠛⠉⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣥⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣈⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⢷⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠿⠋⠁⠈⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⠈⠙⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀ ⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀ ⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀ ⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉ ⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⡀ ⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀ ⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⠀ ⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢠⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠀⠀ ⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠋⠋⠛⠷⣦⣤⣶⣶⣶⣶⡾⠃⠀⠈⢻⡾⠛⠉⠉⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⢻⡶⠛⠲⣄⣤⠼⢧⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢙⣿⡀⠀⠀⣹⢶⡄⠀⣹⡀⠀⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠛⠒⢺⡛⠛⠁⣰⠏⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢹⡇⠀⠀⠀ ⢠⡶⢼⣷⢤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠾⣿⠖⠶⠆ ⠀⠀⢈⣿⣀⡀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠠⣴⣿⣄⣀⠀ ⠀⠘⠋⠹⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠯⣦⠽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃⠀⠀⠀ ⠀⠀⣠⡴⠟⠻⣧⡶⠳⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠛⠶⠄⠀ ⠀⠀⠁⠀⢀⡾⠛⠂⣀⡈⠀⢹⣧⣤⣄⢀⣀⣠⣤⣤⣴⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⣤⠄⠛⠃⠈⢿⢹⣄⠀⠀⠀⢠⡿⠀⠈⢷⡉⣻⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⢿⣤⣴⡷⣶⡟⠀⠙⠳⠶⠲⠛⠁⠀⠀⠈⣿⡋⠀⠈⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⢸⣿⣜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⠞⠃⠙⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠶⢶⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡟⢶⣤⣀⣀⣀⣀⣀⣽⣀⣀⣷⣞⠛⢻⡅⠀⠀ ⠀⠀⠀⣿⡇⠀⠈⠉⠉⠉⠉⠉⠛⠛⠚⠛⣽⣷⣼⡇⠀⠀ ⠀⠀⢠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⢀⣀⣿⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⣿⣀⡀ ⠉⣉⣿⣦⡀⠀⠉⠀⠀⠀⣾⣷⠀⠀⠀⠉⠀⢀⣼⣿⣉⠉ ⠀⠀⠀⠀⠓⠦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠚⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠉⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣴⣶⣶⣄⠀⠀⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⢯⣟⣿⡇⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣸⣿⣿⡯⠟⠀⠀⡸⠃⠀⠀ ⠀⢀⠤⠒⠙⠋⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⢀⣤⣶⣿⣿⣻⣽⣷⠀⠀⢴⠁⠀⠀⠀ ⠄⠀⠀⢀⣤⣤⣀⠀⠀⢳⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⢀⣤⣾⣿⣟⣯⣷⢿⣽⡾⣿⡄⠀⠸⡇⠀⠀⠀ ⠀⠀⢰⣿⣿⣻⢿⣆⠀⠀⠀⠀⠉⠉⠉⠁⠑⠒⠒⠒⠠⠦⠤⠤⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠁⠀⢀⣤⣾⣿⣟⡿⣾⣽⣳⣯⣿⣞⣿⣽⣧⠀⠀⢷⠀⠀⠀ ⠀⠀⠸⣿⣧⢿⣿⣿⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣀⣠⠤⠟⠛⠛⠀⠀⠀⠀⠀⣿⣿⢿⣼⣻⢿⣧⢿⣻⣧⢿⣼⢿⣼⣿⠀⠀⢸⡀⠀⠀ ⢣⡀⠀⠉⠛⠛⠙⣿⣿⣻⣟⣿⣻⢿⡿⣿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣤⡄⠀⠈⠧⠔⠚⠉⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣼⣿⣯⣿⣽⣿⢾⣟⡿⣾⣻⣽⢿⣞⣿⡇⠀⠘⣇⠀⠀ ⠀⠙⠢⢤⡀⣀⠀⠈⢿⣷⡿⣞⡿⣯⣿⡽⣿⣞⣷⣻⣾⡽⣯⢿⣽⣻⣿⡄⠀⠀⠀⣀⣤⣴⣾⣿⡿⣿⣻⣟⣿⠟⠋⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣽⣟⣾⢿⣽⣾⣷⠀⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⠀⠀⠻⣿⢿⣽⣟⡾⣟⣷⣯⣟⣷⣯⢿⣻⣯⣷⢿⡽⣿⣤⣶⣿⡿⣟⣿⣽⢾⣻⡷⣿⣽⠃⠀⣀⡀⠀⠀⠀⣀⡀⠀⢻⣷⣟⡿⣿⣿⣿⣞⣷⠟⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⣿⣷⣻⣟⣯⣷⣟⣾⣟⣾⣟⡿⣾⣽⣻⣿⣿⣟⣯⣷⢿⣻⡷⣯⣿⢯⡿⣷⣻⣧⡘⠿⠃⠀⠀⠀⠻⠟⣠⣿⣟⣾⢿⣽⢯⣿⣯⡁⠀⠀⢾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢻⣷⡿⣽⣾⣻⣾⣽⢾⣯⢿⣷⣿⣿⣻⣾⡽⣷⣻⢿⣽⣻⣽⡾⠟⠛⠿⢷⣿⣻⣶⣆⣰⣆⣆⣰⣾⣿⣿⠾⢿⣿⣾⣻⢷⣻⣿⣆⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠹⣿⣟⣾⢷⣻⡾⣿⣽⣻⣿⣟⣾⢷⣯⣿⣽⣻⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣽⣟⡿⠟⠋⠀⠀⠀⠈⠙⢿⣿⣻⢾⣿⣧⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⢿⣯⡿⣯⢿⣳⣿⣿⣟⣾⢯⣿⣞⣷⣯⣷⠟⠁⣠⣴⣶⣦⣀⡴⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢀⣶⠟⠻⣶⣟⣿⣿⣞⣿⣇⠀⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢻⣿⣽⣟⣯⣿⡿⣞⣯⣿⣳⣯⣷⡟⠁⠀⣼⣿⣇⠀⣸⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣿⣿⡄⠻⣿⣞⣿⡄⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠉⠉⠉⢹⣿⣟⡿⣽⡾⣯⣷⠏⠀⠀⠠⣿⠋⢹⣿⠟⢿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⢿⣅⣨⣿⣄⣽⡇⠀⢻⣿⣻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢴⠀⠀⢸⣿⢾⣟⣯⡿⣷⡟⠀⠀⠀⠀⢿⣷⣾⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⢯⣄⣬⠇⠀⠀⠈⠻⣿⣿⣿⠟⠀⠀⠈⣿⣟⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⣿⣟⣾⢯⣿⣽⡇⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣼⢰⠇⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣿⣻⡾⣟⣷⣿⡇⠀⠀⡼⢰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠐⠃⠋⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⣿⣽⣟⡷⣯⣿⡀⠘⠁⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢻⣷⣻⢿⣽⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢠⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢿⣯⣟⣷⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠓⢶⡚⠙⠓⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠙⣿⣾⣿⡞⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢳⠀⠀⠀⢳⠀⢠⣴⡞⠉⠀⢠⡞⠉⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠄⠀⠀⠉⠛⠿⠷⣯⣿⣿⣷⣦⣤⣀⣀⣀⣀⣹⡀⠀⠀⠀⠀⣸⠀⠀⠀⣾⣿⡿⣿⢿⣿⣷⣾⣇⠀⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡴⠒⢲⣄⣤⣤⣶⣿⢿⡿⣿⡿⣿⢿⣿⠋⠛⠀⠀⠀⣰⡏⠀⠀⠚⠙⢿⣿⣿⣟⠛⠉⢀⣈⡉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⣇⣀⣠⠟⠛⠿⠿⠾⠿⢿⣷⡿⣯⣿⠃⠀⠀⠀⠀⣸⠃⠹⡄⠀⠀⠀⠀⢹⣿⣿⣿⣷⠋⠉⠹⡆⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠉⠁⠀⠀⠀⢀⣀⣠⣾⣿⣽⣿⣯⠀⠀⠀⠀⣠⠏⠀⠀⠳⡄⠀⠀⠀⠀⡇⠀⠀⠉⠳⠤⠞⠁⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠖⣨⠀⠀⣞⠁⠀⢻⠉⠁⠀⠈⠳⠤⠤⠞⠁⠀⢀⡀⠀⠙⠲⠤⠴⠞⠁⠀⣠⣀⠀⠀⠀⣀⠴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⠲⠖⠋⠀⢀⡦⡀⡀⠀⠀⢀⣠⠔⠋⠑⠢⣄⡀⠀⠀⣀⣠⠖⠁⠀⠉⠁⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣀⢀⣀⠤⠊⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠁⢀⠀⠀⠀⠀⠀⢯⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠰⠋⠣⡀⠀⠀⠁⠒⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠐⠂⠀⠀⡈⢏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠶⠲⣦⡖⠒⢦⣠⢤⣤⡀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠉⠂⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⣀⡤⠒⠀⠀⠀⡘⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠞⠉⠹⠟⢁⣈⣉⣠⣄⣠⣠⣀⣀⡀⠀⠈⠿⠛⢳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡄⠀⠈⠀⠀⠀⣶⠽⠒⣸⠞⣆⠀⠀⠀⠀⠀⠀⢠⣾⠁⢀⣠⣴⠶⠞⡛⠋⠉⠉⠉⠉⣉⡉⢉⡉⠙⠛⠻⠶⣦⣤⣉⠀⠈⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣽⡄⠀⠀⢀⣠⠴⣚⡯⠖⠛⢿⠀⠀⠀⠀⠘⢀⣰⣿⣾⠋⠁⠀⠀⠈⢯⠉⠀⠀⢲⠼⣿⣿⣿⡿⢀⠀⠄⠀⠀⠈⠙⠻⢶⣄⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡵⣶⡿⠷⠚⠉⠀⠀⠀⠀⢀⣠⣤⠶⠒⠛⠉⠁⠀⢿⡆⠀⠀⠀⠀⠀⠉⠙⠦⣞⣀⣈⣛⡋⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⠁⠀⠀⠀⠀⣁⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⣠⣤⡶⠾⠛⠛⢛⣙⣉⣉⣙⡛⠛⠻⠶⢶⣤⣄⡀⠀⠀⠀⢀⣴⠋⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⠀⠄⠀⠈⢻⣉⣤⠶⠒⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠲⢦⣄⣉⠛⠷⣦⣄⡾⠃⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡼⠟⠃⠀⠀⠀⢀⠀⠄⡀⢃⠠⠘⠀⠄⠘⠀⠃⠀⠀⠃⠀⠀⠀⠀⡀⠀⠘⠀⠄⡀⠄⡀⠄⠀⠀⠘⠛⠿⣄⣀⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠻⢧⣄⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠋⠀⠀⠀⠠⢐⠠⠂⢌⠐⡠⠂⢄⠡⢈⠠⠁⠌⢀⠁⢂⠐⡀⠡⢀⠡⢀⠡⠀⠌⠠⢀⠐⡀⠂⠌⠐⡀⠠⢀⠀⠉⠀⠄⢈⠐⠠⢀⠂⡀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀ ⡴⠋⠀⠀⡠⢀⠅⡊⠔⣂⠉⡄⢊⠄⡡⢂⠒⠠⢂⡑⡈⣴⢃⠂⡐⢠⢁⢂⡐⠂⡄⡉⠄⢃⡐⠂⠤⢁⠌⡐⠠⡁⠂⠌⠄⠡⠐⠀⢂⠐⡀⠂⠄⠡⠈⠄⡀⠀⠀⠀⠀⠙⢦⡀⠀ ⠀⠀⢠⢢⠑⣎⠰⣡⠚⡄⢣⠘⡄⢎⠰⡁⢎⡑⢢⢰⡞⡃⢢⠡⡘⡀⠆⡄⢢⠡⡐⠰⡈⠆⠤⠑⣂⠐⠢⢄⢃⠰⢁⠌⡰⠁⢬⡐⠄⢢⠐⢡⠊⠰⢉⡐⠠⣁⠂⠄⠀⠀⠀⠙⢦ ⠤⣉⢦⢣⡙⡤⢓⡤⢋⡔⢣⠍⢦⡉⢖⡱⢊⡴⣫⠟⡥⡘⡅⢎⡡⢍⡒⢌⢢⡑⣌⠱⡨⢜⡰⢡⢂⡍⡒⢌⢢⠱⡈⢆⠱⣈⢚⣷⢌⠢⣉⠆⡌⢡⠂⡔⠡⢄⠊⡜⡐⢄⡀⠀⠀ ⡳⣍⠞⣦⢓⡝⢦⠳⡭⣜⢣⠞⣥⢚⡵⣸⣯⡾⣫⡙⢦⡓⣜⢢⡕⣎⣜⣡⣶⢣⣬⣷⣷⡬⢒⣇⣲⡌⡱⣊⢆⢣⡑⢎⡱⢢⡉⢾⣧⢣⡜⢢⡉⢦⠩⢔⡉⠦⡑⢤⡑⠢⡔⢢⢀ ⣗⢮⣛⡴⢫⣞⢣⡟⡴⣍⢮⡝⣦⣻⢾⣽⢛⡴⢣⡝⣦⠽⠚⠻⣾⠋⣉⣀⣉⣟⣉⣀⣈⣹⣟⣉⡉⠙⣷⠞⠾⢦⣟⣬⣒⠧⣜⡹⡽⣧⢞⣡⢚⡤⣋⢦⡙⢦⡙⢦⡸⢱⡌⣇⢎ ⢯⡞⣶⣹⢳⣎⢷⢺⡵⣎⢧⡿⣾⣵⠟⣥⣏⡾⠗⠻⢇⣠⠴⠖⠛⠋⢉⡽⣭⡭⠁⠀⠀⠉⠉⠉⠉⠉⠛⠳⠶⣤⣿⠛⠛⠻⣦⢳⡹⡽⣧⡻⣜⣲⡱⢎⡼⢣⡝⡦⣝⢣⠞⡼⣌ ⡻⣼⢣⣏⠷⣎⠯⣓⡮⢽⣯⡾⣿⢶⡻⣵⡏⢀⡴⣖⣅⣀⠀⠀⢀⣴⣏⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⣹⡿⢽⣮⡝⣷⣽⢶⣍⢯⡜⣧⠽⣜⣎⢧⢏⡳⣜ ⠑⠉⠳⠌⠋⠀⣁⣤⡶⣿⡽⢿⣛⣮⡟⠉⣡⢿⡟⠡⡄⣉⠻⠶⢋⣉⣉⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠸⣟⣧⣻⣮⣻⣞⡽⢎⡿⣜⡞⣮⢏⡷⣭ ⠲⠶⠶⠶⠚⠛⠉⠀⠀⢿⣤⡇⢻⣿⡄⣰⠏⢸⡀⣧⠳⣍⡾⣭⢳⣳⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣄⠀⠀⢳⡄⠿⣷⣻⣾⢷⣭⠛⠹⣞⡵⣻⡜⣯⢞⡵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⣹⡿⠃⡿⠀⠈⢷⡨⣟⡷⣽⣞⣯⣷⣟⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⢻⠀⢹⣞⡭⡟⢹⠿⣄⠀⠙⢱⢫⢗⣯⢻ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠻⣮⣇⠀⣷⠀⢀⣴⣿⣦⡻⠷⡾⣛⣡⠞⠁⠀⠀⢀⡤⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⢸⡇⣼⡏⠾⢁⡾⠀⠈⠁⠀⠀⠈⠐⠈⠃ ⠤⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠈⠙⠷⡾⢷⡿⡿⠋⠀⠉⠓⠛⠉⠀⠀⠀⠀⠀⠘⠧⣤⣀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠉⠉⠀⣸⠃⢹⠆⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠒⠐ ⣂⡈⢢⠀⠀⠀⠀⢸⠁⠀⠀⢀⣀⣀⠀⠙⢦⣙⡦⣤⣀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣾⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠀⡆⠀⠀⠀⠐⠀⠀⣸⢿⠉⠉⠙⠒⠦⣀⣀⣀⣬⠿⠛⠲⣾⠈⠓⠦⣭⣓⢦⣀⡙⣀⣠⠶⣚⣫⡽⠳⡄⠀⠀⢀⣀⣤⠔⢋⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⡇⠀⠀⠀⠀⠀⢠⡏⠈⢳⡄⠀⠀⠀⢻⡏⢻⣦⠀⠀⠀⠘⡆⠀⠀⠀⣬⣭⣽⢻⡟⠚⠉⠉⡄⠀⢠⡟⠉⠛⣯⡅⠀⠈⠉⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠙⢦⠀⠀⠀⠀⢸⠃⠀⠀⠙⠳⢤⣤⣀⡙⣦⣌⠻⠶⣦⣴⠋⢰⡀⢎⡉⢉⣿⣽⡿⢛⠳⣒⢔⢠⣞⠁⠀⠀⠈⣙⡷⢶⣏⠉⠉⠉⠉⠉⢛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⡇⣻⠀⠀⣠⡴⠖⠲⢤⡼⠟⠉⠉⠙⠓⢒⣿⣦⣑⡈⣁⣤⢾⡏⢹⡷⣌⠳⢍⠾⠁⣿⠤⠶⠞⣛⣡⣴⢾⣥⣤⣤⠤⠶⠚⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⢠⠏⠀⠀⠀⠘⠀⢹⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡁⢨⠽⣹⡙⠆⢸⣋⢹⡇⣜⢻⠶⡶⠞⠿⣛⠉⠉⠉⠀⠙⠳⠦⠖⠲⢦⡄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⡾⠀⠀⠀⠀⢀⣤⡏⡇⠈⢿⣀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⠉⠛⠓⠶⢬⡀⡿⠉⢹⡇⣈⣿⣽⣽⣧⠶⠋⠷⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡶⠖⠋⡾⠀⠀⠀⣠⠟⠛⠒⢚⢿⣽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⣠⡿⠰⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡛⠁⠀⠀⢰⡇⠀⣴⠟⠁⠀⣄⡀⠀⠈⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠒⠛⠋⠙⢦⣼⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠻⢧⣄⠀⠀⢸⡇⠀⣿⡀⠀⢸⣉⢳⡆⠀⠀⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠀⠀⣠⠔⡹⡆⠀⠙⢦⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠃⠀⠘⣧⠀⠈⣷⣄⡀⢉⠉⠀⠀⠀⠀⠈⠛⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣰⡟⡒⡛⠁⠀⠀⠀⠀⠈⠒⠛⠁⢀⡴⠋⠀⢀⣠⣼⠗⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠲⡌⢥⢊⣵⣿⡿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣯⣢⡑⢎⠰⣁⠎⡰⢁⠎⡰⢁⠎⡰⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡓⡜⣢⢽⣾⡟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣌⡓⢤⠚⡄⢣⠘⡄⢣⠘⡄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡴⢣⣾⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⡱⢌⢣⡘⢄⠣⡘⢄⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣘⢢⠜⡠⢃⠜⡠⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⢣⠱⢌⠢⡑⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣮⢘⠆⡱⢈⠜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣦⠀⠀⠀⠉⠻⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣿⣇⢎⡱⢈⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⣀⣀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⡶⠾⠿⠋⠁⠀⠀⠀⠀⠀⢿⣿⠢⣅⠋⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠬⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠧⡑⢌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠛⠿⣿⣿⣶⣤⣶⣶⣿⣶⣶⣶⣦⣤⣄⡀⠉⠙⠓⠚⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡉⢖⡉⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡭⢏⡽⣙⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠣⡜⢢⠜⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢦⢡⠋⢖⡡⢎⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⠱⡌⢣⢎⣱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠠⢇⠚⢤⠘⢢⡉⠖⡬⢛⠿⣿⣿⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠻⣤⢣⣳⣼⣷⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡓⢬⡉⢆⡉⠆⠬⡑⠦⣉⠶⢨⢍⡛⠻⠿⠿⡿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⠿⠟⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⠲⡌⢢⠘⡌⢢⠑⡒⠤⢊⢅⠢⣉⠱⣉⢎⠱⢒⠬⠥⣋⠭⣍⢫⡝⣻⣿⣿⣿⡛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢲⢡⠣⡘⢄⠣⡘⢄⠣⢌⠢⡑⠤⢃⠔⡨⢊⡒⢌⡒⣡⠒⣌⠲⣜⣵⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣄⣀⡀⠀⠀⢿⣿⣧⡎⡱⡡⢎⠔⣡⠊⡔⡊⡔⢡⠎⡐⢎⡑⢆⡩⢒⠼⢤⣻⣼⣿⣿⣿⣿⠿⣟⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⠿⣿⣿⣿⣿⣿⣥⣓⣎⠚⡤⢓⡜⠴⣘⠆⡎⠵⢪⣜⣦⣵⣿⣾⣿⠿⠛⠉⠙⢿⣿⣝⣮⣽⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⢀⣼⣿⠿⠟⠛⠉⠉⠉⠛⠻⢿⣿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⢵⣦⣄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠟⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠲⢿⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣟⡄⠀⠀⠀ ⠀⠀⢀⣿⠏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣧⡀⠀⠀ ⠀⢠⣿⠏⠀⣾⠃⠀⠀⡠⠤⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠠⣄⠀⠀⢸⡇⠀⠹⣗⡄⠀ ⠀⣾⡟⠀⠀⢹⡆⠀⠀⠉⠑⠿⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠱⠾⠋⠁⠀⠀⣸⡇⠀⠀⢹⣞⠀ ⠘⣿⠁⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠙⠆⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⠀⠀⠈⣿⠆ ⠀⣿⡄⠀⠀⠀⠀⠈⠉⢻⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡟⠉⠀⠀⠀⠀⠀⢠⣿⠃ ⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⠉⠈⠁⠉⠈⠉⠁⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⢀⣾⠏⠀ ⠀⠀⠉⠿⣷⣤⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣤⣶⡿⠋⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣜⣾⠙⡜⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠒⠚⢻⠮⡠⣏⣷⡦⢤⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣜⢱⠄⢀⣫⣾⣯⣿⡋⣔⣢⣙⢢⣎⣀⠀⠀⢀⡔⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⢉⣀⣸⡄⠀⠀⠀⠀⢠⣀⠀⠀⠦⣼⠁⠀⠀⣳⣾⣿⣾⣿⣿⣧⠻⢀⣠⣔⣻⣏⣲⣽⣞⣓⣒⡶⠶⣿⣿⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⣇⣴⣿⣷⡀⡀⠀⠀⠸⢌⡏⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿⡿⢋⣉⡟⣉⡆⣀⡀⠀⠉⠙⢯⡢⣄⠈⠢⢸⣿⣯⣥⣮⡿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⠿⠈⠀⣹⣯⠒⡆⠀⠀⠙⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣩⣇⣸⣷⣆⠙⣆⣅⢀⣾⣿⣿⣿⣯⣤⣼⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢶⣞⡉⠈⠉⠳⢀⡴⠦⣄⡀⠀⠀⠰⣼⣿⠟⣫⠀⣰⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣏⠉⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠦⢴⠀⠀⢀⣾⣤⢢⢈⡟⠁⠀⣴⣿⣿⣿⣿⣾⣿⣧⣀⣄⠃⢹⡇⠈⣿⣿⠿⢿⡟⢻⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠠⣄⡠⡄⠀⠀⠀⠀⢸⠹⣛⣿⡏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣤⢸⣇⣀⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠈⠖⠓⠄⠀⠀⠀⠘⠦⣄⣠⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⢀⣀⢴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⠄⠀⢻⣿⣿⡟⠛⠉⢀⣄⠀⠀ ⠀⠀⠀⠀⠱⠐⢓⣀⣄⠀⢀⡼⢧⣀⠀⠀⠀⡴⠃⠀⢿⣿⢿⡿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣖⢿⣿⣿⣿⣿⣿⠃⠀⠀⠈⣏⠛⠓⠀⠒⠓⠴⠃⠀ ⠀⣶⣴⠲⣴⠞⠉⠀⠈⢧⠽⣷⡼⡻⠀⠀⣾⠁⠀⢄⠘⣿⣿⡧⣧⣧⣿⠳⠞⠛⠛⢻⡽⣿⡿⣷⡉⢹⣿⣿⡟⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢠⡄⠀ ⠛⣿⣿⡃⠈⠳⣰⣐⣚⢾⣤⢼⡵⡗⠂⠀⠻⣄⡀⠈⣠⣿⣿⠀⠈⠉⠁⠀⠀⠀⠀⠸⣿⣷⣧⢿⠷⠶⠛⢩⣇⠀⠀⠀⠀⢀⣷⡏⢩⣯⢟⢷⣜⠃ ⢰⣿⣻⣟⡉⡝⠋⣟⡀⢸⠓⢛⡇⠁⠀⠀⠀⠈⠉⠉⢹⡟⠸⣆⠀⠀⢤⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⢠⣤⡤⠟⣆⠀⠀⠠⠃⢹⣏⣻⣟⡼⠀⡞⠀ ⠀⠀⠉⠺⣯⡀⡼⠁⡿⢚⠶⡾⢥⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠘⢦⣀⠈⠁⠈⠁⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠑⠲⠤⠶⠋⠀⠀⠈⠙⢺⠯⠆ ⠀⠀⠀⠀⢈⡻⡇⠰⠃⠸⢠⠃⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢒⣶⡖⡶⠒⠊⠉⢹⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠐⠮⡼⢹⡀⠀⠀⠀⠀⢸⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠓⠠⠤⠀⠒⠛⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡈⠦⠀ ⠀⠀⠀⢀⡦⣀⡘⣇⠀⠀⠀⠀⢸⠁⠀⠀⣀⣀⣀⡤⣀⣀⣀⣠⠤⠖⣶⠷⣤⣄⣀⣀⣠⣤⠤⣿⢦⡐⡾⣅⣀⣀⡀⠀⠀⠀⠀⣠⡴⢋⡛⢦⡀⠀ ⠀⠀⠀⡼⠀⡞⣽⣻⠀⠀⠀⠀⣿⠀⠀⠀⣿⣋⡉⠠⡏⠀⠀⠀⠀⠀⠈⠓⠶⢦⡤⢤⣤⡴⡾⠿⢭⠟⢲⠒⣺⣭⣍⣽⣤⠀⠈⠻⣔⣀⣸⣿⣻⡄ ⠀⠀⠀⠙⠶⣗⣿⣿⡇⠀⠀⣰⠇⠀⠀⠀⡽⠃⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠞⠁⠐⠁⠀⢠⠞⢁⣮⠤⣄⡿⠃⢤⡀⡘⣿⣛⣨⠇⠧ ⠀⠀⠀⠀⣀⡀⠠⠞⡇⠀⠉⢻⢀⣀⡀⠀⣧⡀⢀⠀⡇⠀⠀⠀⠀⠀⠀⢿⢿⣿⡿⠀⠀⠀⠀⠀⠀⣰⠋⢠⠮⠄⢉⣙⡆⠀⠀⠦⠴⣼⣀⣠⡴⠇ ⠀⠀⠀⢰⠇⠈⠙⠒⠣⠖⠒⠋⠉⢠⠇⠀⣿⠉⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⡴⠃⡰⡥⠪⣴⠒⣿⡗⢠⠀⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⢺⣶⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣰⢋⣀⠑⣺⢣⣿⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠃⠑⢾⠉⠡⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⠧⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠁⣮⣗⢤⠞⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢧⣶⠀⠀⠬⢍⡒⣦⡤⢤⣤⢖⡯⠍⠒⠂⠀⢸⠦⡼⠚⠀⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠠⡤⢊⣷⣳⡾⣮⠻⣄⠀⠀⠀⢀⣾⢧⠀⠀⠀⠀⠀⣿⠟⠉⣷⣄⣤⠶⢦⡀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⠀⢃⣞⡵⣿⡟⣿⡇⢟⣷⡘⢦⡀⠀⠀⣿⣞⣧⡤⠔⠚⣉⣈⣷⠞⣡⣬⡻⣧⣴⣿⣆⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣻⠀⠀⠘⣌⢧⢷⠀⡇⡇⢸⣝⣝⣌⢧⠀⣼⣏⣠⣼⣧⠴⢯⡁⠀⢙⣾⡟⠋⣳⣜⣿⣿⢹⡄⠀ ⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡳⢻⡄⠀⠀⠈⠓⢻⠀⡧⢸⡄⣿⣾⠟⠋⢾⢸⣇⣶⠿⠒⠒⣾⣿⠖⣿⡷⠻⣦⡿⢿⠹⣿⣤⠇⠀ ⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢠⠞⣷⠀⠀⠀⠀⠈⣽⠁⠀⠉⠃⣈⡷⠻⠟⠚⠓⠺⣾⣾⡛⣫⣿⢫⡀⢒⣤⣿⣧⣼⠀⡾⠀⠀⠀ ⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢠⠇⠀⠘⣧⠀⠀⠀⠁⡷⠶⠖⡺⠟⠉⠠⠴⠻⢄⣀⣿⣂⠈⠳⣄⢾⣿⠿⠷⢋⣽⠿⣡⠞⠁⠀⠀⠀ ⠀⠀⠈⠑⢄⣀⣀⠀⠀⠀⢀⡠⠞⠁⠀⢁⠇⠀⠀⠀⠘⣧⠀⠀⠀⠁⣠⠔⣑⣦⡤⠞⢦⣄⣀⣀⣨⣼⡁⣀⠈⣇⣹⣦⠷⢛⣡⠞⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠑⠐⠊⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠘⣇⠀⢰⠉⠉⠉⠀⠀⠀⣰⡟⠀⠀⠀⢻⣄⡉⠓⠚⠛⣉⡤⢾⠋⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⣤⢤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠘⢇⡜⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠉⠙⠒⠛⠉⠁⠀⠐⣧⡀⠹⣦⣀⠀⠀⠀⠀

⠀⠀⢠⣶⠷⣶⣦⣄⡀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⢀⣤⣶⡾⢿⣷⡄⠀⠀ ⠀⠀⢸⣿⠀⠀⠈⢙⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠋⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⣿⡆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣸⡿⠀⠀⠀ ⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⠋⠉⠉⠙⢻⣿⣿⣿⠀⠀⠀⠀ ⠀⣀⣀⣀⣿⣿⣿⡇⠀⠀⣾⣷⢸⣿⣿⣿⣿⡇⢾⣷⠀⠀⠀⣿⣿⣿⣠⣄⣀⣀ ⠈⠀⠀⠀⠹⣿⣿⣷⣄⣀⢀⣠⣾⣿⣿⣿⣿⣿⣄⣀⣀⣀⣼⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⠦⣄⣀⠀⠀ ⠀⠀⠋⠉⠀⠀⠀⠈⠙⠛⠿⢿⢿⣿⣿⣿⣿⢿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢶⣤⣤⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣿⡇⣾⣿⣿⠇⣿⡇⠀⠀⠀⠀⠀⢠⣾⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣙⣛⣩⣾⣿⣇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠙⣿⣿⣿⣿⠁⠉⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣺⡭⠵⠚⠋⠉⠉⣹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡽⠟⠉⠁⠀⠀⠀⠀⣤⣾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⡽⠛⠁⠀⠀⢠⢤⡀⠀⣠⣞⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⡴⠋⠀⠀⠀⠰⣖⠋⠈⠉⡿⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣆⣤⣄⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣞⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢾⠞⠀⠀⠀⢀⣀⣠⠖⣶⣀⣠⣤⣼⣵⣳⣦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢯⠏⠀⠀⠀⠀⢸⣥⡿⠚⠉⠁⠀⠀⠀⠀⠈⠉⠑⠺⢭⡒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢟⠏⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⡿⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⢻⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣧⡏⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢹⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣮⡠⢿⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣸⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⠀⠀⡽⠃⠀⠹⣆⢀⣀⣀⡴⠒⣻⡉⠉⠁⠀⠉⠉⠉⠓⠒⢦⣀⡀⠀⢰⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡟⠛⠳⠇⠀⠀⠀⠈⢻⣀⡉⠀⠈⠻⠛⠀⠀⠀⠀⠀⠀⠀⣿⡗⢸⣥⣴⣿⡟⠀⠀⣀⣠⠤⢴⣒⣒⣒⣲⣦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⣤⣤⣀⠀⠈⠳⠤⠴⠂⠀⢀⣴⣿⣿⣿⣿⣷⣶⣾⡽⠖⠋⠉⠉⠉⠉⠉⠉⠓⠺⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠈⠻⠭⠿⠟⠛⢿⣿⣿⣿⣿⡟⡟⢹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡄⠀⠀⢻⡀⠀⠀⢸⠀⠘⣯⣿⡟⣽⠖⣃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣾⡄⠀⠀⠀⠀⠀⢀⡜⠁⠀⢧⠀⠀⠀⢳⡀⠀⣸⠀⠀⣿⣿⣧⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡝⣦⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣯⣇⠀⠀⠀⠀⠀⡏⣀⡴⠦⢾⣇⠀⠀⠀⢳⣄⡟⠀⠀⣿⣷⣯⡷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⠹⣷⣶⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⡀⠀⠀⠀⠀⣷⠋⠀⠀⡼⢹⣤⣤⡤⠶⣿⡤⠤⣤⣿⠁⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⠦⠴⠟⠒⠖⢿⣬⡇⠀⡼⠳⡼⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⢿⡀⠀⠀⠀⢳⡀⢀⡼⠓⠒⠻⣶⣼⠿⠉⠿⠿⠿⣿⣀⣼⡋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠾⠋⠁⠀⠰⠿⠀⢀⡶⠊⠀⠉⢻⡇⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢯⢧⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢼⣇⠀⠀⠀⠀⠀⠀⣀⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢠⡞⠀⠈⣧⣧⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⣠⣄⠀⠀⣾⠰⣶⡦⠀⠀⠤⠤⢏⣠⠞⠁⢠⣀⢀⡴⠋⠀⢠⣴⣣⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢯⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⡗⠹⣬⡟⠻⠧⣤⣈⣀⣠⡤⠶⠾⠭⠛⠀⠀⠀⠹⠿⠤⣤⣀⣸⠟⡟⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢸⡯⠥⣄⡞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠀⢸⣶⢻⣦⢀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠙⣞⢦⡀⠀⠀⠀⠀⠀⠘⢿⠛⠻⠷⣄⠀⠀⠀⠀⠀⡾⠁⠀⠙⠶⠦⣄⣀⣀⣀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⠀⠀⢸⣇⣿⣻⠭⠽⠿⢿⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢤⡀⠀⠀⠀⠀⣿⣧⣄⡟⠃⠀⠀⠀⠀⠀⠷⣤⣼⡗⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⡦⠤⠾⠃⠀⠀⠀⠀⣠⣞⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢆⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣴⡇⠀⠀⢠⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⣫⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋⠛⠒⠛⢦⡀⠀⠀⠀⢀⣼⠧⢤⡤⠞⠁⠀⠀⢀⣤⢺⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢝⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣠⠴⠞⠁⠀⠀⠀⢀⣀⠴⣞⡿⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠪⢵⣖⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣖⣮⡽⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢉⣓⠒⠯⠽⠿⣗⢒⠖⠂⠦⠤⠄⠤⠴⢖⣒⠲⠾⠿⠯⢟⢒⠛⣛⣉⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⣴⣦⣄⠴⠲⣄⣀⡀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀ ⠀⡼⠛⠿⠛⢔⡄⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⢧⠘⢐⣤⣼⣤⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠠⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀ ⠠⢿⣿⣦⣿⠀⠀⢀⠀⠀⠀⣶⣸⣿⣿⠙⠀⠀⢀⡄ ⠐⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠖⠚⠉ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⡏⠈⠋⡇⠀⠀⠀⠀⠀ ⠀⢀⣠⣼⡉⠀⢨⠿⠟⠻⣷⣜⡦⠔⠁⠀⠀⠀⠀⠀ ⠘⣿⡿⢻⢉⡐⠾⠀⠀⠀⠈⢛⣟⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⡜⠹⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⠉⠀⠀⠁⠒⠐⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢦⢤⢤⡤⠤⠶⣂⣠⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⡒⠲⣦⢴⡄⣒⣐⠂⠤⣥⢉⡓⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀⡙⠓⠶⢩⣭⢐⣺⣇⠠⠀⠉⣪⢕⡨⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⢈⡵⠋⠀⠀⠊⡆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠤⠒⠓⣦⣔⡮⣽⣿⣽⡦⠸⡀⠘⡄⠀⠀⠀⠉⠁⠐⠂⠀⠀⠒⠒⠂⠀⠀⠒⢄⠀⠀⠀ ⠀⠀⠀⠀⢰⣧⡀⣎⢾⣿⣾⡿⣿⣿⣿⢤⣤⣷⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⡑⠳⣀⣿⣿⠛⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀ ⠀⢐⠀⠀⠀⠈⢻⣬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⣼⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⡄⠂⣱⣒⣤⣀⣿⡛⠋⠂⡀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⢀⣼⠇⠈⣿⣭⢿⡝⠛⡆⠀⠀⠉⠉⠁⠀⠀⠀⡔⢢⡄⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠤⢤⠤⡐⠀⠀⠀⠀ ⣾⠇⢀⠀⡸⣿⣿⡧⠶⠧⡀⠀⠂⠀⠈⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⠌⠉⠀⠈⠑⠠⠄⣀⠀⣷⢗⣄⠀⠀ ⠈⠉⢻⣰⡄⠻⡷⡄⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣶⣲⣒⣶⡾⣥⡹⢸⠀⠾⣷⡀ ⠀⠀⢠⡎⠀⠀⠈⢪⣢⡰⠈⠑⠤⣠⣀⣀⣀⣀⣀⣀⣠⠠⡠⢴⣿⣭⣾⣿⠟⠒⠒⠂⣹⢙⣮⣄⠀⣸⠃ ⠀⠀⠈⠀⠀⠀⠀⠠⡽⠁⠀⠀⠀⡇⠀⡉⠉⠣⡀⠀⢄⠀⣹⣷⡻⠟⠁⠙⠲⣄⣀⣰⡃⠀⣩⡏⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡇⠀⠈⠐⠄⣼⠀⠈⠄⢼⡟⢣⢀⡠⣇⠀⢐⠗⠛⠓⠲⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⢸⣀⣀⣀⣬⡾⠊⠀⠀⢀⠘⠷⠾⠿⡊⠑⢛⠛⢦⣄⡠⢧⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠑⠀⠔⠁⡤⠤⠷⢴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⠀⠀⣀⠞⡄⠀⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠉⠁⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⡀⢠⣤⣰⣶⠒⠀⠐⠚⠁⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠹⣧⡄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠈⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣄⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⣿⣦⡀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⠻⣿⣦⠀⠀⢨⣷⣦⣤⣤⣄⣀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠈⢿⣿⡍⠀⠉⠉⠉⠙⠛⠻⠿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⣠⠖⠺⣶⣄⠀⠀⣠⡞⠉⠉⠲⡄⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⢠⡟⠈⢩⣤⣝⣹⠘⠷⠤⢶⡆⠀⣘⠀⠀⠀⣠⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠘⣇⠈⢿⣄⠀⠀⠀⠀⢀⡿⠃⢠⡟⠀⣠⣾⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠱⣄⠈⠢⡀⢀⡴⠋⢀⡴⠋⢀⡾⠛⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠈⠳⣄⠈⢯⣀⡴⠋⠀⣰⠀⠀⣤⣄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⣼⣿⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠢⠼⠀⠀⠀⡼⠁⠀⢸⣿⣿⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⠃⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⡌⠣⠁⠀⠘⠛⠛⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⣠⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⡀⠀⠀⠀⣰⣴⠟⠀⢰⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣀⣀⣀⣀⠘⣿⣇⣀⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠈⣿⣧⠀⠀⢀⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⠿⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠟⠛⠿⠿⣿⣿⡿⠿⣿⣿⣾⣿⣿⡆⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⢀⣠⣿⣿⣿⣿⣿⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⠀⣤⣴⣿⣿⣿⣷⣿⣿⣟⡿⡋⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢸⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣶⣶⣿⣿⣿⣿⣿⣿⣟⡿⠗⠋⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣿⣿⣿⣿⣿⣿⣇⡇⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣭⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠻⣿⣿⣿⣷⣿⣿⣿⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⠋⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠛⡛⣻⣿⣳⠃⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⡏⠀⢸⣿⠿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠩⠭⠟⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣇⣀⣾⣿⠀⠹⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣦⣀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⡟⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢹⣿⡀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⠃⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣠⠖⠋⠉⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠓⠢⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡾⠁⠀⠀⠀⣺⠇⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣆⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⣳⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢷⣄⣀⡠⠶⠋⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⡀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠴⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⣿⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣙⣒⣶⣶⣶⡿⠟⡋⣽⣿⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⢠⣄⡤⣴⣚⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣷⠀⣿⣋⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣤⣄⣀⣀⢹⡋⠛⠛⠛⠋⡖⣩⢎⡵⣩⠞⡥⢿⡇⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀ ⣮⣷⡾⣿⢷⣫⣟⣾⣽⠿⠿⢿⠛⣩⢡⢿⣞⢛⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢿⣿⣿⣿⣷⣿⣷⣮⣖⣧⢫⢕⣻⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠄ ⣿⣛⠟⠉⠋⠱⣯⣾⣿⡄⠀⠈⣷⣩⠛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⢮⣷⠀⠀⠀⠀⢹⠄⠀⠀⢀⢂ ⠀⢀⠌⢂⠒⣘⣉⣡⣤⣤⣶⣦⣨⣿⣾⣾⣿⣿⡿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢲⡂⣝⢫⢆⡹⡐⢀⠀⢸⡍⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡻⢿⣿⣿⣿⣿⣿⣿⣫⢿⡀⠀⠀⠀⠸⡆⠀⡀⢠⠂ ⣬⡳⣾⣿⢿⣟⣿⡿⣯⣿⣿⢿⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡝⡰⢃⢞⡰⣉⠆⡐⠈⣷⢻⠀⠀⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣿⣿⣿⣿⣿⣷⣻⡆⠠⠀⠀⠐⣧⠐⡌⢆⠡ ⡿⣽⣮⠹⣯⣿⡿⣽⣷⣻⣽⣿⢯⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣟⡣⢜⣵⣯⣶⣶⣧⣶⡤⢀⢻⡜⡇⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣶⣽⡿⣿⣿⣿⠿⣧⣤⡄⢄⢺⣿⡧⢘⠄⡡ ⣿⣳⡟⣿⣬⠻⣿⣟⢶⣿⣻⣾⢏⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⡿⣏⢳⡱⢎⡼⢩⡛⠿⢿⣧⣟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣴⡍⠱⣚⣿⡟⢠⠎⠄ ⠷⣯⢟⡧⣟⣿⣜⢯⢾⣍⣽⣇⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⡗⢮⣣⡝⣮⣔⠣⡝⣝⠲⣌⢻⣆⠀⠂⠀⢀⣠⡴⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣞⣯⢻⣿⣯⣷⠀⢄⢻⡜⢠⠊⡐ ⣟⠾⣯⢟⣽⣻⡾⣏⣾⡿⣫⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢳⡼⡹⢧⣳⣞⡹⢿⣷⡩⢞⡽⣌⢧⣻⣦⡱⣶⠋⠁⠀⠀⠀⠀⡀⢀⢠⡿⣿⣿⣿⣿⣞⣯⣿⣿⣿⡶⢊⠜⣇⠢⡑⠀ ⣮⣟⡾⣯⣿⣳⢿⣼⢟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣹⢳⡞⣵⣋⡜⣫⢟⡣⢿⣿⣣⢿⣼⣷⢿⡻⢷⣮⣤⣀⡀⠂⠤⢁⠄⣃⠣⣞⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡀⠘⠦⡁⢀⣁ ⣷⣾⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡧⣯⢳⡽⣿⡴⢻⣶⣯⣞⣧⣿⣿⢿⣙⣎⠶⣹⢣⡻⣜⡟⣿⣶⣄⠊⡜⡰⢋⡶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣮⣗⣻⣹⣌ ⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣯⣳⡽⣹⢿⣧⡦⣍⠭⣹⣻⣯⠷⣭⢎⡳⢥⢳⡱⣍⠾⣱⡞⣿⣧⣶⣷⣿⣾⢷⣿⣭⣿⣿⣿⣿⢻⣿⣿⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⡽⣞⣯⡟⣼⢳⣎⡳⢥⢻⣯⣟⡼⣎⡳⣭⢲⡱⢎⡳⢥⡛⢷⣿⣯⢗⡳⢎⡳⣬⢣⢛⣿⢿⣿⣽⣿⣿⣗⢯⣿⣿⣿⣿ ⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣻⢾⡽⣭⢷⡺⣝⢮⣹⣿⣞⡷⣽⡳⢧⡳⣝⢮⣱⢣⡝⣮⣿⣛⢮⣝⡣⣝⢦⣋⠶⣈⠯⢿⣧⣿⣿⣿⣳⣿⣿⣿⣿ ⣵⣾⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⢘⢿⣿⡽⣯⣟⣿⢮⡷⣯⣞⣦⣿⣿⣿⣷⣟⣯⢿⣼⢳⣎⣳⣾⣟⣧⣛⡞⣶⢹⡜⣦⢋⠶⣩⠖⣩⣿⢿⣿⣿⣿⠸⣿⣿⣿ ⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⠰⡈⠬⡹⢿⣿⣽⣾⣿⣽⣿⣿⣿⡿⣿⣟⣿⣿⢿⡿⢿⠿⣟⣻⣿⣿⣿⣧⠿⣜⡧⡞⣥⢫⡳⣱⣎⣵⣿⣿⣿⣧⣿⠆⣿⣿⣿ ⠀⢹⣿⡷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠠⢁⠢⡑⢌⠲⣉⢏⡻⡝⢯⠯⡝⢧⠻⡔⣿⣿⢽⡲⣝⣎⠳⡽⣧⣝⠮⡹⣿⣿⣽⢳⡝⣎⢧⡳⣽⣿⣿⣿⣿⣿⣿⣾⣇⢻⣿⣿ ⠀⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠎⡰⠙⡌⠷⡝⣮⡳⣟⢯⠿⣝⢯⡿⡝⣿⣿⣾⢷⡿⣿⣿⣷⣿⣿⣷⣷⣝⣿⣿⣿⣿⣟⣯⢷⣿⣿⣿⣿⣿⣿⣿⣟⣿⣼⣿⡿ ⡜⠰⡌⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠁⠃⢡⠛⢆⠳⡝⠎⡎⢳⡉⢇⡷⢹⡿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣻⣿⣿⣼⢿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠰⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠘⠀⠇⠘⢃⠹⡈⠞⡎⠻⢿⣿⢿⣿⣻⣟⣿⣻⣿⣟⣿⣻⢿⣟⡹⢿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⡀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢁⠈⡀⣁⠢⢀⠅⢊⠰⣉⠞⣻⣿⣷⣟⣯⣷⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿ ⣿⡜⡤⠁⠙⠻⢿⣿⣿⣿⡀⠀⠀⠀⠻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠠⠐⡀⠄⡰⢈⠰⠈⡔⢢⠙⡴⢫⣟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⡤⣁⠤⢣⢉⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠁⠐⢀⠐⠀⡀⠀⡀⠀⠠⠀⠀⢂⠡⠐⡁⠐⣀⣂⢁⠒⠤⣉⢒⡱⣚⢼⡹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⠛⠛ ⣿⣿⣿⣄⢏⠦⣉⠌⣿⣿⣿⡆⢀⠈⠀⠀⠀⠀⡀⠄⠠⠀⠁⢂⠀⣐⣤⣤⣀⡀⠂⠠⠀⠀⠄⠠⠀⠅⠂⠌⡐⢤⣿⣿⣿⣿⣾⠐⠄⡢⠔⡭⢎⡳⣝⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣡⣤⣤⣶ ⣿⣿⣿⣿⣌⠶⡡⢞⡨⣿⣿⣿⣆⢈⠀⠄⠠⠀⠄⢂⠐⡠⢁⠢⠘⣿⣿⣝⡿⣿⣦⠀⡑⣈⠰⢀⡡⢘⡐⢈⠐⣾⣿⣿⣿⣿⣿⡏⠄⡱⢈⠖⣩⠞⣬⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣎⢵⣪⣷⣿⣿⣿⣟⣳⣊⠌⠠⢁⠆⠢⢈⠔⡡⢆⠡⠙⠿⣾⣷⡿⢿⣡⣐⣀⠱⠈⡔⢡⠘⠤⢈⠹⣿⣿⣿⣿⡿⠡⣆⠱⣊⠜⣤⢋⡖⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⢊⡱⣈⢆⡱⣈⢒⡡⢂⠤⢀⣶⣿⣿⣿⣿⣿⣶⣶⣤⣉⡰⡡⢈⡉⡛⢛⢩⠰⡱⢌⡳⢨⣙⢦⢫⡜⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠱⡰⢌⠲⢌⠲⣄⠃⢦⢁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣆⠱⣘⢣⢣⡛⡴⢣⢣⢣⡜⣮⢳⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⢾⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢠⣿⠃⠳⢌⡓⢎⡱⢢⡙⢂⢣⠒⡤⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣧⣝⡼⣡⢏⠲⣹⣎⢷⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⣷⡟ ⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⠀⠐⠀⠘⡌⠴⠡⣌⠃⣎⠱⣌⠣⡝⢎⡲⢤⣩⢩⢍⣋⠟⡿⢿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⠟⠀ ⣿⣾⣻⣿⣽⣻⣿⡿⢯⣟⡿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠠⠁⢆⠳⢄⡳⣌⢣⡝⢪⡱⢆⣣⢎⡚⡜⢪⠳⣍⠶⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⣿⣽⡿⣟⣾⣿⣿⡿⣿⣿⠀⠀⢀⠀⡄⢀⣧⠘⣿⣆⠀⠀⠀⠀⠀⢁⠠⠌⠐⠠⡈⣁⠊⡕⣩⠹⣌⠯⣝⢻⣏⢿⡞⡿⢶⡻⣽⣶⣿⣿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤ ⣿⣻⡿⣿⣻⣿⣿⡿⣿⣿⣿⣮⣇⣞⣴⣳⣿⣆⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠄⠃⡐⠢⡙⢢⠛⡬⠳⣌⠳⣭⠹⣎⣵⣿⣿⠿⣩⢏⡳⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡿⣽⣽⣿⣿⣳⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠹⣆⠘⠻⣿⣶⣶⣶⣶⣶⡆⢨⢀⡈⠀⠁⠌⡡⢌⠡⣉⠖⡩⢌⠳⣄⣻⣾⣿⠟⣡⢚⡱⢊⡵⢩⠶⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⣟⣾⡿⢿⣿⣽⣿⣿⣿⣿⠿⠿⠿⠏⠴⣄⡌⠳⢦⣤⣉⣉⣉⡉⠉⢀⡴⢿⣿⣷⣮⣄⣡⣀⣒⣀⣆⣥⣾⣾⣿⠿⢋⣡⡼⠃⡄⢃⠎⡐⢃⠞⡌⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⢊⠔⣩⡿⠉⠀⠀⣼⠃⢲⣌⡙⠻⠿⠿⡿⢿⠿⠿⠟⠛⣉⣡⣶⡿⢿⣿⣵⡈⠄⡘⠠⠁⠈⠀⠀⠳⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⣾⠁⠀⠰⣰⠇⠀⠀⢻⣝⠻⡶⢶⣤⣤⣴⣤⠾⡿⢻⡍⢧⣛⢧⣛⢿⣾⡐⡀⠀⠀⠀⠀⠈⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡜⣿⣠⣤⣴⣯⡀⠀⠀⣼⢯⠱⣋⠖⢢⠒⡴⢈⠧⡑⢇⠞⡥⣋⢞⡭⣞⣽⣿⣴⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢧⣹⢳⣏⠶⣭⢻⣦⣾⣟⣢⢳⡾⠾⠛⠋⠉⠁⠚⠳⠎⣜⠰⣍⢮⢳⡞⣼⣿⣿⣷⣴⣤⣀⣀⣀⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠰⣂⠳⢌⠦⠱⡌⠦⠱⡌⠦⠱⡌⢦⠱⣌⠲⡱⡘⠆⠃⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⢦⡑⢎⡔⠣⡜⢢⠱⡌ ⢓⡌⠳⡌⢎⡱⢌⢣⠓⣌⢣⠓⡜⢢⠓⡌⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢢⡙⢦⡘⡱⢌⢣⠓⡜ ⢬⡘⣱⠸⣌⠲⣉⠆⡏⡔⢣⡙⡌⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⡘⢦⠱⡑⡎⢥⢋⡜ ⢢⢱⢂⠗⣌⠳⣌⢚⠴⣉⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⡩⢆⡳⡑⢎⡱⢊⡴ ⢎⠦⣋⡜⢆⡳⢌⡚⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡴⣲⢦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢲⣉⠶⣉⠶⣡⠝⡬⣑⢣⢒ ⡸⢸⢁⡾⡈⡶⢉⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣱⢏⡾⣱⡎⣷⠹⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢷⣈⢱⠾⣀⠿⣰⢉⢶⢉ ⡱⣩⠎⡴⡹⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⢞⣜⣣⢯⣕⡻⣜⡳⠉⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣎⠳⣎⡱⢣⢇⣏⠺⣌ ⠑⠂⠝⠲⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡱⣏⠾⣜⢮⢳⢎⡷⢣⠇⢸⡱⣖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢬⡱⣋⠮⣜⠳⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣹⢎⠛⠂⠋⢟⢮⡝⡯⣝⢶⣹⠚⠀⠀⠀⢠⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠘⡥⢳⡍⡞⣥⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣝⠀⡲⣝⢧⣚⢮⡳⣝⡚⠶⣁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠘⢧⡚⡵⡂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠮⠳⢹⢎⡇⠍⠞⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢣⣛⡴⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⣣⠞⣭⢋⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠙⠚⠿⢏⣿⣿⡀⢼⡹⣬⢛⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣤⣶⣶⣶⣤⣠⣾⣿⣿⡇⢸⡱⢮⡹⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⡗⣭⠳⣍⡳⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡇⣜⡳⣭⢓⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣎⢷⣉⡾⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢼⡹⢦⡳⣜⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⣀⣀⣉⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢫⢗⣫⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡯⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣡⠞⣝⢮⡱⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣬⣁⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣜⣜⢫⡞⣥⣛⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⢡⣶⣲⢦⡶⣴⢢⣦⣀⣈⣀ ⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠟⣉⣠⣞⡷⣭⣟⠾⣭⢷⣣⢟⡼⣳ ⢿⣚⣷⣻⢾⡵⣯⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣿⠟⣫⣵⣌⢟⣳⡟⣾⣳⣞⡿⣎⡷⣝⣮⢳⢧ ⣯⣻⡼⣏⣯⢿⣽⣻⣞⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣛⡿⢿⣿⣿⣿⢟⣻⣭⣭⣟⣋⠁⠀⠀⠀⠉⠀⠁⠀⠀⡷⣎⢷⡹⡞⡵⣎⠿⣸ ⢿⣵⣻⢿⡽⣟⣾⣳⣯⣟⣯⡿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⢟⣵⣾⣿⣿⣿⣿⣿⣧⡍⠟⣱⣿⣿⣿⣿⣿⣿⣷⣆⢿⣿⣿⣿⣇⢦⣼⠱⢯⣏⢷⣫⠷⣭⡛⡵ ⣟⢾⡽⢯⡿⣽⢳⢯⡷⢯⡏⠙⠳⢯⢟⡀⠀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢘⣠⣝⡳⢎⡷⣩⢗⣣⢛⡵ ⢿⡾⣹⡏⣷⡏⣿⢏⡾⣏⠀⠀⠀⠀⠈⠸⢹⣇⢷⡾⡹⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⢇⣎⡹⢇⢷⢱⡾⣈⠷⡾ ⣻⢼⡳⣝⣧⢻⣎⠿⣜⡇⠀⠀⠀⠀⠀⠀⣠⠜⠃⠁⠁⠀⣠⣤⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡾⢭⢎⣳⡙⣎⠳⡜⣥⢛⡴ ⡽⣎⢷⡹⣎⢷⣚⢯⣳⠀⠀⠀⠀⠀⠀⢟⣴⡿⢦⡌⣰⠃⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡱⢎⡗⢯⢎⡲⡝⣎⡳⣙⢦⣋⠖ ⣻⠼⣧⢻⡜⣯⢞⡵⡃⣀⡄⣤⡄⠀⠀⠈⠍⢳⠟⡰⢍⡇⣿⣷⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣺⠱⣬⢜⡻⠿⠿⠿⠿⣟⡋⢁⠮⡝⣝⢮⣋⠮⡵⣙⠦⡝⡜⢦⡙⡞ ⢯⣛⣮⢯⣝⣮⢻⡼⣏⢷⡳⢆⠳⡀⠀⠀⠀⠉⠘⠛⠈⠀⣿⣿⣿⣷⣬⣛⡿⠿⠿⠿⠿⠿⢟⣛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⣢⡍⣾⢰⣫⢳⡱⣍⢞⡱⣙⢮⡱⡹ ⡯⢝⣮⢗⡯⣞⡽⣺⠽⣮⣝⢯⡡⠁⣄⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡵⢺⠴⣋⠶⣣⠳⡜⢮⡱⢭⢲⡱⡹

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⠀⠄⠠⣀⢤⣀⣄⢠⠔⢠⡀⢄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠀⠐⠀⠠⠀⠀⠄⠄⠠⠀⠐⠀⠀⠀⠀⠀⢄⠐⢐⠄⠀⠀ ⠈⠄⢡⠏⢊⠍⠡⡁⠅⠄⠈⠠⠣⢄⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢟⠰⣆⣄⢄⡀⢀⠢⠱⠜⠀⠀⠀⠠⠐⠀⡀⠀⢣⠈⣀⠃⠀⠀⠀⣀⣼⠠⠀⠐⠕⠄ ⠐⠸⡁⠐⣡⡉⢀⢧⠨⠡⠅⠄⡈⢆⠀⠀⠀⠀⠀⠀⠐⣽⢣⣳⡄⠀⠀⠀⠀⠀⣠⢇⠀⣄⡤⠢⣵⠈⠁⠑⢙⢄⠀⠰⣄⡆⠀⠀⠣⠈⠄⣀⠂⠄⢽⣯⣀⠴⡁⣤⢩⣝⢣⠜⠀ ⠠⠁⣏⢊⡀⢀⣨⣸⢦⠈⠨⠡⢁⣠⠃⠀⠀⠀⠀⢀⡀⠈⠙⠉⠁⠀⠀⠀⠀⡖⡅⢄⠉⠙⢍⣀⠊⠨⠠⢀⠁⡔⢤⢁⠑⠈⡠⢄⢀⠀⠒⢁⠈⠤⠒⣚⡁⠂⠉⢚⠷⠀⡇⠀⠀ ⠀⠀⢸⠲⡚⢿⣇⢬⠧⢅⠂⣈⣈⡛⠀⡠⠒⣶⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠰⣯⡨⢾⠶⣊⣥⠃⢐⢀⠈⠨⠰⣘⠀⣭⡚⠠⠐⠠⢀⡂⢁⠂⠌⠰⡣⡃⠝⣖⡀⡆⡙⠁⠀⠀⠀ ⠀⠀⠀⠀⠛⠑⠁⢢⠂⡔⠕⠜⠀⢇⡕⡕⠌⠸⡐⢀⠇⠀⠀⠀⠀⠀⢠⠂⠀⠈⠘⢗⠶⢃⢜⠈⠨⠐⢐⢀⠈⡁⡆⠮⢾⢓⠪⠐⣠⣟⠀⡠⠉⠀⠈⠚⡊⢶⢅⡞⠯⣍⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡧⡡⣄⣡⠀⢇⣇⠚⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠈⢆⠐⠔⢀⡨⣈⠸⠈⠁⠈⢃⠢⠱⠥⢻⣟⣻⠇⠀⠁⠀⠀⠀⠈⠁⠀⠀⠈⠑⡀⠀⠀ ⠀⠀⠀⡀⡂⠀⠀⠀⠀⠀⠊⡀⢰⡯⣹⡯⣭⡒⣞⡯⠕⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⡤⢤⣄⢈⡤⣅⠀⠀⠀⠀⠀⢸⡁⠰⡁⣆⢝⡑⠀⠀⠀⠀⠀⣠⣤⠈⠐⢈⠁⠠⠐⠠⢀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⢀⠀⢛⢻⡣⡄⡤⢘⣣⡃⢀⠀⠄⠀⠀⣀⣤⠿⣇⣸⡟⠛⣇⣸⠟⢿⣀⣿⣤⣀⠀⠀⠀⠸⡘⢠⡛⢀⢻⡣⡀⠀⠀⠀⠀⠃⢀⣇⠀⠄⡘⢀⠃⠄⡀ ⠀⠀⠀⠀⠀⠀⠃⢂⠌⡰⠒⠈⠂⢕⢬⢪⠼⠧⠟⠃⠠⢰⠰⢀⡞⢡⡀⠂⡾⡍⡝⠊⡤⢜⠒⠍⡈⡆⠠⠈⠻⣆⠀⠀⠀⠈⡾⡄⢇⡢⢵⠀⠀⠀⠪⣈⢢⠷⠁⢂⠐⠠⢈⠐⡀ ⠀⠀⠀⠀⠀⡀⣐⠎⠌⠀⠀⠀⢀⠀⡂⠄⠂⠱⢀⠌⡐⣠⠴⠚⠁⣄⡬⠖⠛⠛⠒⢤⠓⢋⡤⠛⠒⠛⢦⡀⠡⢸⣧⣀⠀⢄⠰⢎⢹⠑⠐⠁⠀⠀⢁⠨⠃⡐⣈⣄⡈⣐⣀⠂⡐ ⠀⠀⢠⣤⡀⡡⡐⢄⠡⡀⠱⠀⠐⣀⠃⡈⠄⡁⠂⢄⡟⠁⡀⠄⠈⡞⠁⠀⠀⢀⣀⠀⢳⠏⣀⡀⠀⠀⠀⢹⡆⠀⠀⢈⢳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣆⠶⠃⣤⢭⠣⡽⠀⠄ ⠀⣴⡻⡧⢃⡀⠘⢍⣂⠐⡐⠐⢂⠀⠐⠀⠂⠄⡁⢺⡇⠐⠀⠂⡁⣧⠀⠀⠀⠺⠿⠃⣼⡐⠿⠟⠀⠀⠀⢸⣇⠁⠄⠀⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⣐⠸⣇⣳⠉⠉⢟⣁⡄⠌⠠ ⠀⠈⠃⠰⠟⠒⠈⢢⣹⢬⠀⡁⢂⠐⡈⠐⡀⠂⢄⡾⠃⠀⠆⡀⢠⡾⢦⣀⣀⣀⣤⠾⠋⠳⣄⣀⣀⣀⣤⢿⡀⠐⢀⠑⠠⣯⠀⠀⠀⠀⠀⠀⠀⠀⡨⢶⣍⠆⣝⡲⣜⡎⠀⠌⡀ ⠀⠀⠑⢤⠘⡠⢤⣿⢅⠏⣳⠀⠀⠂⠄⡡⠀⠡⣽⠀⠪⡠⠀⠂⣾⠁⡠⢌⠉⠉⠀⠀⢀⠀⠈⠉⠉⠉⡀⠈⣧⠀⠀⠐⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠻⢝⣮⣴⡤⢧⣋⢂⠁⠂⠀ ⠀⠀⡂⡈⠹⣈⢧⢌⡞⢘⠀⠀⠀⠈⠀⠐⠀⠢⢽⡈⠄⠈⠪⡠⢹⡸⡐⢠⡓⠀⠠⠈⠀⢀⠂⠠⠀⡏⠐⣃⡟⠐⢀⠀⠀⠁⣼⠐⡄⡂⠀⠀⢀⠀⠀⠀⠈⠚⠵⠁⠀⠀⠀⠀⠀ ⠀⠄⠀⢂⠂⡀⣄⡁⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠆⠉⠀⠀⠪⡛⢮⣁⣈⠻⢦⣄⡁⣀⣤⠶⢛⣁⣥⠿⠁⠊⠠⠑⢂⣴⠏⠀⠌⠡⢡⠈⠄⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠄⡁⢂⠐⠊⡑⡀⠀⠀⠀⠀⢀⡶⠒⢆⣤⠀⠀⢻⠀⠅⠀⠀⠀⢈⡶⣿⠛⠛⢻⣿⣛⣿⡛⠛⠛⣿⡲⣄⠈⠢⠀⠒⢸⡇⡀⡏⠁⠀⠀⢱⠀⠖⢈⠫⠉⠃⢀⠦⠀⠀⠀⠀⠀ ⠐⠠⠐⠠⢈⠀⠃⠃⠀⠀⡠⢄⠈⠑⡜⠊⡸⠀⠀⠘⢧⡀⠁⠄⢀⠸⣸⠃⠄⡁⠚⠛⡙⠛⡁⢂⠡⠈⣷⡹⡐⠄⠈⠂⣸⠇⠐⣰⣀⠀⢠⢁⠣⠅⠄⠈⣨⣵⠀⠈⢉⡆⠀⠀⠀ ⠠⠁⠌⡐⢀⠂⢱⡬⠤⢲⡤⡏⠀⠀⠁⠉⠀⠀⠀⠀⠈⠙⢲⣆⢐⡤⠿⠷⠚⠒⠓⠒⠒⠓⠒⠒⠒⠿⠿⢇⡀⣭⣤⡞⠋⠠⠁⠭⢁⢁⠜⠅⠉⢨⠲⣾⣧⠾⡪⠱⢈⡒⠀⠀⠀ ⢀⠁⢂⠐⡠⠨⢚⡀⣶⣯⡍⢱⠀⠀⢀⠄⠄⠀⠀⢀⡠⠐⠊⣡⣤⠄⢖⣶⡆⢹⣾⠀⢵⠋⢕⢰⣿⡦⢰⣦⠄⣌⢙⠓⢬⡀⡁⢂⠁⡈⠈⡔⢤⢗⠠⠑⠨⢤⢧⠨⠚⠉⠀⠀⠀ ⠀⠌⡀⠚⢿⢷⡁⠄⠀⠁⠒⠎⢀⡄⠃⠀⠀⠀⢀⡨⠆⠀⠀⠹⣾⣄⠘⡮⡅⡾⠽⠄⠫⠶⠞⠨⠏⢀⠿⠛⢉⡆⠈⠀⠰⢅⡐⡀⠂⠄⠡⢸⢸⣘⠡⣀⣡⢌⡺⢇⠊⠀⠀⠀⠀ ⠈⡐⠠⠉⠡⠑⡞⡪⢩⢬⠓⡟⡛⠮⠀⠀⠀⠘⡅⠀⠸⡀⠀⠈⢃⣉⣤⣤⣤⠖⠒⠒⠒⠒⠒⠓⢠⣤⣤⣀⡙⠀⠀⢀⠆⠀⢈⠇⠡⢈⡐⠈⣱⡇⣽⣭⢭⣻⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠚⠶⠯⢎⠚⡎⠁⠀⠀⠀⠀⠀⠐⠳⡀⠀⠓⢶⡏⠈⢳⡽⣿⠏⠀⡀⠀⠀⠀⠀⠀⠀⠻⡟⣳⠏⢹⡶⠈⠀⠀⡌⠐⢒⠀⠀⠀⠷⠷⣏⡢⠖⣬⡾⡧⠀⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⡄⠀⠀⠀⠀⠀⠀⡖⠑⣥⡔⠊⠁⠀⠀⠀⢻⠚⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠁⢢⡜⠀⢠⠀⠀⠀⠀⠀⠈⠈⡔⠒⢢⠈⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⢀⠀⡄⠀⠀⠀⠈⢂⠌⠠⠠⠀⠀⠀⠀⠀⠈⡰⠃⠂⠀⠎⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠈⡨⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⢩⡠⢘⠀⠀⣠⠈⡁⢈⠠⠄⠈⠨⠀⡀⠀⢀⠠⡃⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⠵⠐⠄⡈⠀⠀⠀⠀⠀⠀⠀⢀⢴⣏⡆⠀⠀⠀ ⠀⠀⠀⢹⣾⡴⣲⡲⡀⠀⠄⠂⠄⠋⢁⠀⠈⠂⡠⠑⠀⠢⠈⡶⡒⠒⡤⡤⣤⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⢶⣽⢿⠥⢄⠀⠀⠀⠂⣄⠤⠀⠀⠁⠀⠀⢠⠡⢂⢡⢸⠀⠀⠀ ⠀⠀⠐⣇⠗⡻⠕⠔⣳⡄⠠⠁⡎⠀⢐⡠⠂⠀⡄⢡⣈⣴⢛⡕⠨⢿⣏⠑⠎⠀⠀⠀⠀⢪⣺⢯⠀⠀⠀⠠⡔⠁⢨⢃⠆⠀⣇⠀⠀⠀⠀⠀⠀⠊⡠⠰⢺⠁⡡⢉⢀⣶⣦⡄⠐ ⠀⠀⠀⢺⡭⠦⢔⣬⣵⡤⠁⢂⠘⡀⠀⠀⢀⠐⡁⡬⠧⡞⣪⡣⣀⠬⣢⠑⠀⡀⠈⢒⠀⠈⠙⠛⢀⠀⡲⠓⢸⠄⡄⠊⠀⣨⢼⡂⠀⠀⠀⠀⠀⠀⠀⠀⢢⡷⠂⠮⡼⢷⠾⠃⠀ ⠀⠀⠀⠎⠫⣍⡏⣏⡉⡄⠆⢂⠐⡀⠂⠌⡀⠂⠌⠯⡩⣞⢥⣉⡞⡗⠋⠀⠀⠁⠀⢀⠂⠀⠀⠀⠀⡍⠂⠀⠀⡧⢬⠷⣾⣇⣫⡇⠀⠀⠀⠀⠀⠀⠀⢪⠳⢃⠆⡏⡇⢁⠐⢐⠀ ⠀⠀⠠⠃⠀⠐⠛⠁⠡⠆⠈⠄⠂⠄⡁⠂⠄⠡⠈⠄⡉⠫⡽⠯⠒⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⢄⠀⠈⠠⠉⢡⡴⠶⠚⢄⠃⠇⠀⠀⠀⠠⠂⠊⣜⢉⢖⠮⡴⠁⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠐⠠⡀⠡⠈⠄⡁⠂⠄⠁⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⢂⡅⡇⠀⠀⠀⠀⠀⠠⢁⠂⡉⠌⠒⠃⠌⡐⠠⢀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⠀⠀⢼⣿⢿⡿⣿⣿⡆⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢜⠿⣿⣽⣷⠟⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣉⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠠⠃⠀⠀⠀⠀⠀⠀⡀⡀⢠⡀⠀⡆⠀⡇⠀⢰⠀⢨⠆⢀⣠⣴⡶⣦⡀⠈⢛⣡⠁⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⡎⠀⣇⠀⣇⠀⣇⠀⣧⠀⣟⠀⣿⠞⠋⠉⠀⠀⠈⢿⡄⠀⠉⠀⢀⣾⠛⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⣀⣀⡀⠀⠀⢿⠀⢻⡀⢿⡀⢿⡀⢻⡀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⢀⣾⠟⠋⠙⠛⠛⠺⢷⡈⠳⠈⠗⠈⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡟⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢲⣶⠟⢋⠍⡙⢻⣤⣤⣤⣤⣄⡀⠀⢸ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⠎⢰⣈⣐⠉⣷⠀⠀⠀⠉⣿⡀⠀ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠎⠰⣿⣋⣽⡷⣿⣄⠀⠀⠀⣾⠁⠀ ⠀⠀⢻⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣧⣼⡿⢁⠒⡠⠘⣷⢤⣤⣟⡀⠀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣬⠂⣁⣳⣿⡆⠤⡉⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⣿⠈⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⠾⠋⡔⣠⡿⠀ ⠀⠁⣿⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠐⠒⢿⡗⠒⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣷⣌⣂⣵⣾⠟⠁⠀ ⣀⣠⣽⡶⠶⠂⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⢠⡚⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⡤⠆⠀⠀⠀⠀⠀⠀⠀⣎⠙⣦⠀⠀⠀⠀⠀⢰⣿⡗⠀⠀⠀⠀⣉⣉⣁⡿⠀⠀⠀ ⠁⠀⠈⢿⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⣩⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⣹⠏⠛⠂⠀ ⠀⠀⠴⠚⠻⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⣳⢯⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⢻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⢶⡿⠛⠿⢦⣀⠀⠀⠀⠀⠀⠈⣙⣳⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⡾⠋⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⠀⠢⣀⠉⡉⣙⣿⢻⡟⢻⣉⣿⣽⡋⣰⠏⢻⡄⠀⠀⣠⠿⢦⡀⠀⣠⡴⠞⣿⢡⡿⢀⢿⡉⠙⠓⣶⠶⢶⣦⠶⣶⣶⠶⠾⠛⡫⠁⠙⠧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠉⠘⣿⠀⠀⠋⠁⠀⠙⠃⠀⠈⠷⣴⠞⠋⠀⠀⠙⣿⠋⠀⠀⠘⣿⠃⡌⢌⡙⢛⡋⢅⠒⣿⣀⠒⠤⣹⣷⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣿⣄⣀⡀⢰⡟⢌⡐⢢⠘⠤⢘⠠⢊⠼⣧⣼⠶⠋⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⠋⠁⠈⠉⢛⣿⠑⠢⢌⢂⠩⡐⢡⠊⠔⣂⠉⢿⡆⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣤⣤⣦⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⢰⢻⣧⡌⠑⢢⡌⢢⠑⠂⠉⠒⢠⠉⡄⢻⣶⢳⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣽⢻⡟⣿⢻⣏⣿⡹⣏⢿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣟⣷⣥⣂⡘⠄⢢⠉⠜⣠⢃⣘⣴⣾⣻⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡞⣽⢿⣿⣳⢞⡶⣻⣝⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⣭⢿⣛⣿⣻⣟⣻⠯⠟⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠾⠿⢿⠻⠾⠿⠷⠾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠓⠒⠚⠋⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠛⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢆⠙⣡⠏⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⢰⣒⠆⠀⠀⠓⠊⠙⠚⠁⠀⠸⠭⠇⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠾⠛⠋⠉⠁⠀⠀⠈⠉⠉⠛⠳⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠿⢉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡉⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⢿⣄⠀⠀⠀ ⠀⠀⣠⡟⠁⠀⣿⠁⠀⠘⣟⠛⠛⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⢋⡟⠇⠀⠀⣿⡄⠀⠻⣦⡀⠀ ⠀⣸⠏⠀⠀⠀⢿⡄⠂⠀⣿⠀⠀⢹⠃⠀⣿⣠⡴⠦⣤⣻⠆⢠⡇⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀ ⢀⣿⠀⠀⠀⠀⠈⢿⣤⡀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠇⠀⣠⡾⠃⠀⠀⠀⠀⢹⡇ ⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣷⣆⣹⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣸⣇⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠹⣦⡀⠀⠀⠀⢀⣠⡾⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡟⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⠀⠀⠀⠀ ⠀⠀⢰⠒⠒⠲⠤⠤⠖⢒⣾⣿⣿⣯⠀⠈⣇⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣿⣦⠀⠀ ⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⠏⠀⠀ ⠀⢀⣟⣀⡀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠈⠝⢻⠂⠀⠀ ⠀⠠⢿⠒⢂⠈⠁⠀⠀⠖⠄⠀⠈⠁⠠⣉⣹⠉⠀⠀ ⠀⠀⠸⡎⠁⠀⠀⠐⠒⡄⠀⡔⠲⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠙⣆⠀⠀⠒⠤⠇⠘⠤⠔⠄⠀⢾⡴⣆⠀⠀MADE BY VICTORIA ⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠚⠛⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⡶⠶⠶⠶⣦⡀⠀⣀⣴⠶⠶⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀ ⠀⣾⠃⠀⠀⠀⠀⢀⣤⠶⠛⠛⠉⠀⠀⠀⠉⠛⠛⠶⣤⡀⠀⠀⠀⠀⠸⣧⠀ ⢰⡏⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⢿ ⢸⡇⠀⠀⠀⠠⣿⠀⣀⣤⠶⠛⠛⠛⠙⠛⠛⠛⠶⣤⣼⠀⠀⠀⠀⠀⣠⡇⠀ ⠸⣷⠀⠀⠀⠀⢻⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠀⠀⣿⠗ ⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁ ⠀⠀⠙⣷⣴⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣦⡾⠋⠀⠀ ⠀⠀⠀⣸⠃⠀⠀⣾⣿⠇⠀⠀⣄⠀⠀⠀⣠⠀⠀⢸⣿⡷⠀⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⢿⡀⠀⠀⠈⠉⠀⠀⠀⠉⣿⠛⣻⠉⠀⠀⠈⠉⠁⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀ ⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⡶⠶⠶⠶⢶⣤⣂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⢿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣽⡿⢴⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⣮⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠃⢀⠀⣠⣤⣄⣠⣤⡀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣶⣦⡀⡀⠘⣏⡄⠀⠀⠀ ⠀⠀⢠⣾⠏⢠⡟⢸⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⣿⢺⣿⣿⣿⣿⡇⢹⡄⠙⣿⢄⠀⠀ ⠀⣰⡿⠃⠀⣼⠀⠀⠙⢾⣿⣟⡿⠋⣀⠀⠀⠀⢀⠘⠿⣝⣛⡿⠋⠀⠀⣷⠀⠘⢿⣂⠀ ⣰⡿⠁⠀⠀⠹⣆⠀⠀⠀⠙⠋⠀⠘⠷⠖⠛⠲⠾⠃⠀⠈⠛⠁⠀⠀⣰⠏⠀⠀⠈⢿⢇ ⣿⡇⠀⠀⠀⠀⠙⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠋⠀⠀⠀⠀⢸⣿ ⠘⣿⣄⠀⠀⠀⢀⣠⣾⠏⠛⠛⠻⠟⠻⠿⠿⠿⠛⠿⠟⠛⠛⠙⢿⣦⡀⢀⣀⣰⣧⡉⠀ ⠀⠈⠛⠛⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⠲⢾⡿⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⢶⣶⠆⣰⣿⣁⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠁⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣀⣀⣀⡀⠸⠿⠷⠾⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠿⠛⠉⠉⠉⠁⠈⠉⠉⠉⠛⠻⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⣽⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢁⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠘⡆⠀⠀ ⠀⠀⣰⡿⠁⠀⣼⡇⠀⠀⢶⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣀⣠⡴⠀⠀⠸⣷⠀⠈⣿⠀⠀⠀ ⠀⣼⠏⠀⠀⠀⢿⡆⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢰⡿⠀⠀⠀⠱⣦⡀ ⢰⡏⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⢹⣞ ⢸⣇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⢻⣆⡀⠀⠀⠀⠀⣠⡾⠏⠀⠈⠉⠉⠉⠛⠙⠛⠛⠋⠛⠙⠋⠉⠉⠉⠁⠀⠙⢷⣄⡀⠀⠀⠀⢀⣠⡿⠀ ⠀⠀⠈⠛⠛⠞⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⠛⠛⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠛⠒⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠛⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣛⠶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣊⣧⠀⠀⠀ ⠀⠀⠀⣰⠏⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢹⣆⠀⠀ ⠀⢀⣴⠋⠀⡟⠀⠘⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠇⠀⠀⢻⠀⠘⢧⡀⠀ ⢀⡾⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣞⡤⠶⢤⣺⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⢷⡀ ⢸⡇⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⣯ ⠘⣧⠀⠀⠀⠀⢀⣼⠏⠛⠓⠒⠲⠶⠶⠶⠶⠶⠖⠒⠛⠻⣝⠁⠀⠀⠀⠀⠀⣼⠃ ⠀⠘⠻⠤⡤⠼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠧⢤⠤⠿⠃⠀

⣿⠀⣦⣠⡀⢀⡀⠈⠙⠛⠛⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣷⠦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⣶⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣷⣶⣶⣶⣶⣬⡻⠻⣄⠀ ⢿⣷⡙⠛⠛⠛⠃⠀⠀⠀⢰⢿⡿⡿⣷⢦⡄⠀⠀⠀⠀⢠⡿⠉⢿⡿⣷⣞⡟⡶⣤⣀⣤⣾⠿⢛⣹⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠈⠿⢿⣦⣽⡄ ⠘⠻⣿⣶⣄⡀⠀⠀⠀⠀⠘⠫⣷⣓⣮⣷⡿⠀⠀⢀⣴⠟⠀⢀⣿⣷⠌⠛⢿⣦⣵⣿⡿⠃⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢣⣄⠀⠀⠻⢿⡇ ⠀⠀⠀⠋⠛⢻⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⠶⣛⣁⣠⣴⡿⠛⠃⠀⣠⣴⡿⠋⠉⠀⠠⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣷⡄⠀⠹⣿⣷⠀⠀⠈⠃ ⣠⣴⣶⣶⣶⣾⡏⣽⣿⡏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣍⠀⢀⣴⣾⠟⠉⠀⠀⢀⣤⣾⣿⠗⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡢⠀⣿⣿⣆⠀⠀⠀ ⡟⠁⠀⢀⠉⢿⣿⣿⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡿⠋⠀⠀⣀⣴⣾⠿⠿⠛⣿⠿⢿⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣥⣴⣟⣸⣿⠃⠀⡀ ⠀⠀⢸⣿⢻⡄⢹⣿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠃⣀⣴⡾⠟⠉⠀⠀⠀⠀⠹⡇⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⣟⣙⠋⢙⣷⣿⣿⢿⣧⣅⡇ ⠀⠀⢺⣿⣮⣧⣿⣿⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⠓⠘⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢹⣿⢷⡀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣹⣷⣶⣾⣿⠿⠉⠀⠙⢿⡇ ⣦⣀⡄⠐⠋⠉⢁⣿⣯⣁⠙⣦⣀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣼⣿⣛⣀⣀⣀⣀⣀⣤⣬⣽⣶⣶⣶⣿⡿⣿⣟⢩⠁⣠⣴⠤⠄⡀⠸⡇ ⠙⠻⠿⣶⣶⠿⠟⠋⠙⣿⣶⣦⢩⣿⣶⣶⣶⠿⠿⣟⣯⠈⠸⢿⣿⣆⠀⠀⢠⠀⠀⠐⢋⠉⣀⣠⣴⣾⣿⣿⣿⢿⣿⠟⠋⠉⢻⣿⣦⣄⣴⡟⢀⡙⢾⣿⣷⣜⡷⠋⠙⠉⠢⠀⠀ ⠀⢀⣄⣀⣄⠁⠀⠀⠀⠈⢻⣷⣟⠦⣦⣿⡿⠀⠀⠙⠟⠩⡼⣆⡉⣛⡿⣿⣷⡶⠶⠾⠿⠟⠛⠋⣵⣿⢋⣀⠉⣾⡟⠀⠀⠀⢀⣀⠌⠙⣿⣆⣾⡇⠀⠉⣻⣿⣶⣦⣠⠀⠀⠀⠀ ⠰⢾⣿⣿⠀⠀⠀⢐⣠⣴⣶⠿⠿⠿⠛⠛⠛⠿⠿⠶⣶⣤⣝⣾⠭⢽⠛⠛⣒⣚⣛⣀⣀⣀⣀⢸⣿⠋⣾⣿⠇⢿⡇⠀⠀⠀⠀⠛⠻⠿⠛⠛⠙⠁⠀⣴⣿⢫⡟⢹⣷⠀⠀⠀⠀ ⠀⠘⠋⠉⠥⣄⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣴⠿⠛⠉⠉⠉⠉⠉⠛⠛⠻⢿⣯⣿⣷⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡍⢼⠃⣸⣿⠀⠀⠀⠀ ⡄⠀⠀⠀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⢉⡀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠻⣿⣿⣿⣤⣀⣀⠀⠀⣀⣤⣤⣶⠾⣿⡻⢿⣾⣿⠿⢛⠀⠀⠀⠀ ⡂⠀⠀⠠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣾⣷⣿⣧⣤⣤⣆⣄⣀⣂⣀⡀⠀⠀⠀⠉⣿⠻⠙⢿⣿⣁⣤⣿⣿⠏⠀⠀⣦⣧⡀⠀⠀⡠⡈⠄⠀⠀⠀ ⡇⠀⠀⢘⣿⣇⠀⠀⠀⠀⢀⡀⠀⣠⣿⡀⢀⣀⣀⡀⠀⠀⠀⢿⣧⠐⠛⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣷⣥⣄⣀⠀⣿⢁⠀⠀⠉⠛⢟⡋⠁⠀⠀⠀⠘⠿⣗⣚⣮⠐⠏⠁⠀⠀⠀ ⠁⠀⠀⠀⠻⣿⣦⣤⣀⣀⣘⣿⡿⠿⢽⠿⣿⣿⠛⢛⡿⣿⣦⡄⢿⣷⣄⡄⠀⠀⠀⠀⠀⠈⠀⠂⠐⠈⠉⠙⢋⣾⡟⢇⣀⣤⣴⣶⣾⣦⣤⣤⣴⡶⠶⠶⠶⢾⣧⣤⣤⣀⡀⠀⡇ ⠀⠀⢾⣦⣶⡏⠉⠙⠛⢻⡟⣿⣃⣤⣰⣿⠋⠀⠀⠀⠈⠰⢻⣷⣸⣟⢛⢷⣦⣤⣀⣀⣂⣀⣀⣀⣀⣀⣠⣄⢿⣿⠾⠟⠛⠉⠀⠀⠀⠾⠛⠉⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⢻⣿⡇ ⠀⠐⠿⣿⡿⢶⣄⣀⣀⡼⣹⠏⠋⠉⢻⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⡀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠟⠻⣿⠒⠀⢀⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃ ⡀⠀⠀⠙⠀⢸⢨⡭⠽⠞⠋⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⡟⠋⢻⣷⣝⡳⢦⣄⣀⠀⠀⠀⢀⣀⣀⣀⣄⠀⠀⢀⣤⣿⡿⣹⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡃⠀⠀⠀⠴⣫⡾⠁⠀⢀⣤⣶⠿⠛⠛⠉⠉⠉⠀⠉⠉⠙⠿⡷⣀⣀⣜⢿⣷⣬⣐⠈⠉⠒⠒⣾⣿⠛⠹⣿⣷⡻⣩⣿⠟⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠘⠋⢉⣀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⠈⠹⠻⣿⣯⡙⢛⠻⠷⢶⣾⡟⢻⣷⣜⠋⢻⣿⣿⣿⣖⣾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⡀ ⠀⢀⣠⣶⡿⢟⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠘⠻⣷⣧⠀⠀⢈⣿⣷⣎⠿⣿⣿⠿⠛⠛⠻⣿⣿⡽⠇⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇ ⣴⠿⠋⠁⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⢀⣀⣀⡙⣿⡎⢠⣾⣟⠹⢿⣿⡿⢗⣛⡀⢀⣐⡛⢿⣿⢄⣀⣀⡀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⢩⣿⣾⡇ ⠁⠀⠀⢠⣴⣾⣠⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⢱⡾⠿⠏⡻⣿⢿⣿⠂⢘⠿⣷⣶⣾⡟⡯⢁⣛⡯⢧⣐⣿⣿⢟⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢻⡇ ⠀⠀⠀⣻⣿⠿⣿⣿⣿⣇⠀⠀⠀⣀⡀⣠⣤⣞⣿⠆⠀⠀⠀⠀⠸⠮⠵⠼⠞⢫⣾⡟⠃⠀⠀⠀⠀⢸⣿⣮⡍⠷⢻⣋⣱⣿⡟⣿⣯⠈⠉⠛⠿⠻⠿⠷⣶⣶⣶⣦⣞⣛⣉⣸⡇ ⠀⠀⣸⣿⡿⣆⠉⣛⣛⣁⡀⠀⠀⠙⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣟⢈⣀⠀⠀⠀⠀⠀⠈⠛⣿⠷⢶⣿⡟⣿⣷⣯⣻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⠉⢹⣿⢻⡇ ⢀⣴⣿⣿⣧⡟⣻⠹⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⢻⡯⣝⠲⠿⣿⣖⠀⡀⣾⣾⣇⡂⠀⠈⠻⣿⣌⣁⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⣀⣴⡿⠟⠛⠻⣿⡇ ⣻⣿⠏⢛⣿⣿⣷⣾⣬⠛⠁⢀⣀⣀⣀⠀⣀⣀⣠⣤⣶⡾⠿⠛⢯⣍⢀⣸⣿⠿⣎⠀⣼⣞⣯⠞⠃⣾⣿⣿⠥⣤⣤⣸⣿⡙⠻⠿⠆⠀⠀⠀⠀⠀⠀⢀⣾⡿⠙⠁⢀⣀⣀⣹⡇ ⠟⠁⢴⣾⣿⣻⣿⣷⣶⣭⣴⣶⡶⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠘⣿⣾⠟⠃⠀⠿⣿⣿⣿⡿⠁⠀⠀⠇⠋⠉⠝⢯⣿⣿⣥⣀⣠⠶⣄⡀⠀⠀⠀⠀⢼⣿⠿⠀⣾⣿⠛⣿⣿⡇ ⠀⠈⢸⣿⣿⣿⣏⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣟⠀⠀⠀⠀⢸⡿⡻⠿⠁⠀⠀⠀⠀⠀⢀⠈⣎⠙⠻⠿⠶⢶⣶⣮⣤⣒⣐⡐⠈⣿⣤⠂⣿⣀⡾⠻⣿⡇ ⠀⠀⠈⣿⣷⣽⣿⡿⠻⢿⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣀⣠⣴⣤⣴⣷⣾⣶⣶⣤⣤⣄⡀⢀⠀⠸⣿⡇⠀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠻⢷⣿⣷⣥⣴⢾⡇ ⠁⠀⠀⣸⣿⠙⢛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⡾⠿⢷⣶⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣀⣀⣠⡞⠿⣶⣧⣿⣷⣶⣤⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⣉⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣀⠌⡃ ⠛⠛⠛⠻⢷⣶⣦⡀⠀⢩⡛⠿⢶⣤⣤⣶⠿⠟⠀⠀⢢⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠉⣆⣀⠀⠀⠈⠋⠛⠿⠿⣶⣶⣶⡶⠾⠿⠛⠛⠛⠛⢿⡇ ⠀⠀⠀⠀⠀⠈⠙⠻⡿⣶⣶⠾⠿⠛⠋⠁⠀⠀⠀⣤⡟⠀⣠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⢰⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠚⠿⣿⠇⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⠀⠀⣻⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢠⢟⣿⠽⢿⣷⡇⣿⣿⣍⠒⠤⠠⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠏⢸⡇ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣠⣤⣶⣿⣉⣴⣿⣿⣨⢶⣿⣿⣷⢶⠀⠀⠀⠀⢻⣿⣷⣦⣿⣿⠀⠀⠀⠀⠘⠮⠿⣯⣵⡾⣿⣿⠋⠛⠿⣾⣦⣅⣂⣀⠀⠀⠀⠉⠀⣀⣀⣴⣾⡇ ⣄⢀⠀⠀⠀⠀⠀⠐⠀⢹⣿⠿⢿⣻⡿⠟⠋⠂⢿⣿⣯⣖⣒⠪⠟⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⣀⣀⣤⣴⣶⣛⣭⣵⡾⠟⠱⠀⠀⠀⠀⠙⠿⣟⢿⡿⠿⠿⠿⠿⠛⠛⠉⢸⡇ ⠛⠿⢷⣶⣶⣶⣶⣶⣾⡿⠋⠀⠉⠸⣷⣦⠀⠀⠈⠻⢿⣦⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣦⣶⣾⡿⣿⣿⣿⣿⡻⠋⠉⠁⠁⠀⠀⣤⣆⣤⣶⡆⠀⢸⣾⣇⡀⠀⠀⠀⠀⠀⠀⠘⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠻⣿⣿⠟⠛⣛⠃⠀⠀⠀⠀⠈⠉⠉⣉⣉⣉⢩⣿⠏⠉⠉⠿⣿⣦⣠⣾⠛⢷⣿⣿⣆⠀⠀⠀⠀⠀⣸⣿⠿⣿⣇⡀⠀⠙⣛⠋⠁⠠⡄⠠⠀⠀⠀⠀ ⠃⠀⠀⣀⣴⡇⠀⠀⢀⡄⠀⠿⠛⢄⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠻⣟⣿⣇⠀⠀⠀⣠⣄⠉⢿⣷⣸⣿⡏⢻⣿⣷⣶⣆⠀⠾⠿⢿⣾⡿⠛⠿⠠⣬⣴⡆⠀⠀⠀⠉⠁⠀⢀⡇ ⡁⠀⠀⣿⣿⡟⠋⡐⣯⠭⣔⠒⡩⠔⠂⠓⡀⠀⠀⠀⣼⣿⡿⣀⣤⣬⣽⣿⠁⠀⠀⠀⠛⠛⢿⠟⠛⠋⠑⢺⣿⡋⣾⢿⣿⠃⠀⠀⠈⢿⠀⠀⠀⠑⣽⣿⣿⠛⠀⠀⠀⠀⣀⣼⡇ ⠅⠀⠀⠀⣨⣵⡆⠸⠀⠀⠈⠀⠀⠀⠀⠀⠁⡭⠻⣴⣿⣿⢧⣿⣏⠀⢻⣟⢀⣾⣿⢿⣦⡄⠀⠀⠀⠀⠀⣈⡁⢸⡇⣸⣿⡃⠀⠀⠀⠈⠀⠀⠀⠀⢀⣘⣯⣤⣴⣶⠶⠿⠛⠋⠁ ⠀⣀⣀⣸⣿⣋⣨⣭⣶⣶⣶⢶⣶⣶⣤⣤⣄⣃⡼⠛⠻⣿⣥⡙⠻⠷⢿⣿⢸⡿⣶⠀⢻⣷⣀⣀⣠⣤⣶⡿⠿⠷⠿⣟⣑⡲⣪⠝⢂⣜⣢⣤⣴⣾⣿⣿⣭⣁⡀⠀⠀⠀⠀⠀⠀ ⠟⠛⢻⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣤⡙⢿⣿⣭⣥⣾⣿⣧⣀⣹⣦⣼⡿⠛⠉⠉⠁⢀⣤⢤⡤⠾⡛⣖⣦⣷⡾⠟⠋⠉⠉⠁⠀⠉⠉⠉⠛⠻⣷⣶⣶⣶⣶⡆ ⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⣿⣶⣾⣯⣭⣥⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠟⠋⠙⢳⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠉⠀⠀⠉⠃ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡧⠌⠙⢿⣷⣷⡀⠀⠀⠀⠀⠀⣠⣖⡦⣀⠀⠀⢀⣶⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠈⠙⣿⣶⣄⡀⠄⠀⣛⡋⠀⢈⣠⣤⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣆⠀⣾⣷⡀⠀⠀⠀⠀⠈⠙⠻⠿⠶⠷⠾⠿⠟⠛⣩⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆ ⠤⠼⣿⣟⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⡆⢹⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠁⠀⠀⠀⠀⠀⣿⣷⣦⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇ ⠀⣯⡁⣹⡇⠀⠀⠀⢻⣧⣤⣤⣤⣤⣾⡟⠀⠀⠘⠛⣟⣿⣁⣹⣌⠻⣿⣎⣟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⣤⣤⡄⢀⣤⡀⠀⠁⠘⣫⠭⣶⣦⢤⣄⠀⠀⠀⠀⢀⡿⢸⡇ ⣦⣭⣡⠁⠀⠀⠀⢀⣠⣭⣭⡀⠈⠻⢿⠄⠀⠀⠀⢾⡋⠃⡉⢭⣿⣧⣿⡿⣷⣄⡊⠙⠒⠀⠄⠀⠀⢀⠀⢘⣻⣷⡍⠛⠛⠛⠙⠃⠀⠀⠀⢧⣉⢯⢭⡡⣿⡇⠀⠀⣠⡾⠁⢸⡇ ⣭⣽⣿⣟⢿⣿⣶⡿⠋⠉⣹⣧⣤⣄⣀⣀⣀⣀⠀⣈⢛⣾⣿⣿⣿⣿⡟⠇⠈⠽⠿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠝⢿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠉⠁⠉⠉⢉⣠⣴⣞⣋⣦⣶⣿⡇ ⠀⠀⠉⣿⡿⠿⠋⠀⠀⣼⡿⠉⠙⠉⠙⢻⣿⣿⣿⠿⠿⠿⣿⣿⣿⠷⠶⠿⠿⠿⠶⠶⢾⣿⣿⣛⢿⠿⠿⠿⠿⠿⠿⠛⢋⣙⢻⣿⠿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠹⢿⣾⡇ ⠀⢠⣾⠿⠁⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠈⡿⣷⣻⣷⡰⣴⡿⠋⠳⠴⠀⠀⠐⠀⠀⠀⠀⠀⠉⢿⣷⣄⡀⡀⠀⢠⣤⣶⡾⠿⣾⣿⣸⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇ ⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢻⣇⣿⡇⣿⢙⠀⢰⣿⣼⣿⣧⣤⣴⣶⣇⣤⣴⡆⠈⢿⣗⠢⢽⣿⠿⠃⠀⣀⠘⢿⣿⣷⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃ ⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢼⣿⡏⢴⣿⣼⠀⠸⣿⠹⡿⠿⣿⣿⣿⡏⣿⡟⠁⠀⣸⡧⢠⣾⣿⡃⠀⣾⣿⢻⡀⢸⣧⡈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠛⢻⣿⡄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠣⣸⣿⣆⠈⣻⣿⣦⣼⣿⣷⣥⣤⠐⢁⠐⠀⠩⡅⢀⣴⡿⠉⠀⢹⣿⣆⠀⠛⢿⣿⣷⡿⣿⣷⢌⠳⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⡇ ⠀⢸⣏⣠⣿⣿⡿⠷⠶⣶⣤⣶⣶⣶⣛⣡⣾⡿⠛⠀⠀⠉⢉⣻⣟⣩⣿⣿⠷⠶⣶⣶⣦⣴⣾⡟⠁⠀⠀⠀⠈⣿⣯⣛⢂⠐⠃⠀⣢⣼⡿⣿⣼⣈⡻⢶⣶⣦⣶⡾⠟⠻⠁⢸⡇ ⠀⠈⠛⠿⠛⠫⠀⢀⡀⡀⠀⠀⠿⣿⣭⣴⣟⣠⣤⣄⣴⣾⠟⢿⡿⠋⠻⠟⠀⠀⠀⠀⠀⠉⠻⣿⣷⣍⣭⣤⣤⣀⣽⠛⢿⡿⠿⠿⠟⠉⠀⠘⠿⣿⣝⠈⡉⠙⣿⡄⠀⠀⠀⠘⠇ ⡂⠀⠀⠠⠶⠶⢦⣼⣿⣿⠊⠀⢀⣠⣿⠿⠛⣩⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣭⠉⢿⣿⣧⡂⡁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠶⡾⡟⠁⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠂⠉⠁⢨⡿⡟⢋⣴⡿⠟⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⠿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⣚⡁⡀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⢘⣣⣿⡿⠏⠀⠀⠀⣨⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢰⣿⣦⠀⠀⠈⠛⠻⢷⣧⣄⡀⣶⣦⣵⣾⢆⠆⠀⠏⡟⠁⠀⠀⠀⠀ ⡄⢀⠀⠀⢀⣠⣴⣿⠋⡁⠀⠀⣀⣤⣾⣿⡏⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠈⠻⣿⡇⠀⠀⠀⠀⠀⢉⣙⣿⣿⣿⣻⣿⣶⣶⣤⣤⣻⣤⣀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠛⠛⠻⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⢀⣴⣾⣿⣿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣼⣿⣿⣆⠀⠀⢀⣾⣿⡿⠋⠉⠻⣿⣧⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⠟⠛⠻⣿⣿⣦⡀⣾⣿⠏⠀⠀⠀⠰⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⢙⣿⣿⣿⣿⣦⣤⣤⡄⠀⣿⣿⡁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣷⡀⠀⣠⣴⣾⣿⡏⠀⢹⣿⣿⠛⠛⠀⠙⣿⣷⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⢙⣿⣿⠀⠛⠛⠙⣿⣷⣶⣾⣿⣇⠀⠀⠀⠀⣹⣿⡇⠹⣿⣿⣷⣤⣄⣀⣀⣀⣤⣴⣿⣿⡿⠛⠁⠀⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⢸⣿⣏⠀⠀⠀⢀⣼⣿⡟⠙⠻⢿⣿⣶⣶⣿⣿⠟⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀ ⠀⠀⣼⣿⣿⣦⣤⣴⣿⣿⠟⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀ ⠀⣸⣿⣿⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄ ⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⢻⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⣾⣿⡇ ⠘⣿⣿⡆⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⢠⣿⣿⡇ ⠀⢻⣿⣷⡀⠀⠀⣿⣿⠁⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⡀⠀⠀⢻⣿⠀⠀⢀⣾⣿⡿⠀ ⠀⠈⢻⣿⣿⣄⠀⣿⣿⡀⠀⣾⣿⣟⣉⠉⠻⠿⠀⠀⠀⠀⠀⢰⡿⠿⢿⣷⠀⠀⠀⠀⠀⠸⠿⠋⠉⠙⣿⣿⠀⠀⣾⣿⠀⣠⣾⣿⡿⠁⠀ ⠀⠀⠀⠙⢿⣿⣷⣿⣿⣷⡀⠉⠉⠀⢉⣶⠆⠀⠀⠀⠀⠀⢀⣈⡻⠿⠟⣋⣀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠉⠉⢀⣼⣿⣿⣾⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣦⣄⡐⠛⠉⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⠿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠃⣠⣴⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀ ⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀ ⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢿⡇ ⢸⣷⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⣿⡄⠀⠀⠀⠀⠀⢻⣇⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣦⣀⠀⣸⡿⠀⠀⠀⠀⠀⢠⣿⠀ ⠀⠸⣷⡀⠀⠀⠀⠀⠀⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠟⠀⠀⠀⠀⠀⢀⣾⠏⠀ ⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⣀⡀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⣄⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⡿⠁⠀⢰⡟⠉⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⢹⣆⠀⠀⢻⣏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡇⠀⣄⠘⠷⣤⣴⠟⠀⠀⠀⣠⣴⢦⣄⠀⠀⠈⠻⣦⣴⡾⠃⣀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⢰⡄⠳⠤⠄⠀⠀⠀⠀⢰⡏⠀⠀⠙⣧⠀⠀⠀⠀⠀⠒⠓⢋⡵⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡘⠛⠁⠀⠀⠀⠀⠀⠘⢧⣬⣠⣴⠏⠀⠀⠀⠀⠀⠈⠉⢉⣠⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣴⣿⣠⡶⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⡈⢻⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⠿⠟⠛⣻⣿⣎⣻⣷⠶⠟⠻⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣈⣻⡿⢹⣿⣏⡉⠛⠛⠛⠿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡋⠀⠀⠀⠘⠋⢩⡿⣿⡿⢷⣄⡀⠀⠀⠀⣉⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⢉⣿⣿⣿⣏⠙⠓⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢀⣴⣿⠁⠸⣷⠀⠙⠻⣦⣄⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⣠⡾⠋⣿⠃⠹⣷⣦⣀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡿⢹⣿⠀⠀⠹⣧⠀⠀⠈⠻⢿⠿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⢀⣾⠟⠁⢠⣿⠀⠀⢹⡏⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀ ⠀⠀⠀⣠⣴⣿⠟⠁⠀⠻⣷⡿⠃⠀⠀⢸⡟⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣴⣶⡿⠆⠘⢷⣆⠀⠀⠀⠀⠈⠻⢿⣷⣦ ⢀⣤⣾⡿⠟⠁⠀⠀⠀⠀⠈⢀⣼⠀⠀⣿⣃⣀⣀⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣤⡀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠉⠛ ⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣴⡶⠶⢾⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡄⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⢰⣿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⠏⠀⠀⠀⣴⣿⠿⠿⢿⣶⣄⡀⣀⣠⣤⣾⡿⠟⠉⠻⣿⣷⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠻⣿⣶⣄⣀⣴⠛⣩⣴⣶⡶⣶⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣁⣀⣀⣀⣼⣿⠁⠀⠀⠀⠙⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠈⠛⠿⣿⣶⣄⡀ ⠀⠀⠀⠀⣠⣾⣿⠿⢋⣀⠀⠀⠀⠉⢛⡟⠁⣾⡿⠋⠀⠀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⢿⣧⣄⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿ ⠀⣀⣴⣿⡿⠟⠁⢠⣿⠛⠻⢷⣶⣤⣾⠀⣸⣿⡁⠀⠀⠀⠀⢠⣿⢿⡏⠀⠀⠀⠀⠀⣠⡾⢋⣙⣷⣦⣀⠀⠀⠀⠀⠙⢻⣿⣷⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠟⠋⠀⠀⢀⣾⠇⠀⠀⠀⠀⣹⠃⢰⡿⣿⣷⣤⣀⣀⣠⣿⠟⢸⣅⣀⣤⣤⣶⢿⡏⠀⢸⣿⠃⠉⣿⠛⠻⣿⠟⠛⠛⠁⢻⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢰⡏⢀⡾⠀⠀⠈⠙⠛⠻⢿⠏⠀⣾⡉⠉⢹⡏⠀⢸⡇⠀⢸⣿⡇⠀⢸⠀⠀⣿⡄⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢀⡿⠀⣼⠃⠀⠀⠀⠀⠀⢀⡿⠀⣼⠛⠛⠿⢾⣷⣄⠘⣇⠀⢠⣴⣦⠀⢸⡇⠀⢸⣇⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⣼⠃⣰⡷⢤⣄⡀⠀⠀⠀⣾⠁⣰⠏⠀⠀⠀⠀⣼⣿⣤⣿⣤⣤⣽⣯⣤⣴⡷⠶⠿⠋⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣯⣀⡀⠀⠀⣸⠏⢀⡿⠀⠀⠈⠉⠛⠲⣼⠃⢀⡟⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠈⠙⠳⠶⣯⣀⣾⠁⠀⠀⠀⠀⠀⢠⡏⠀⣾⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣤⣀⢀⡾⠀⣼⠃⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⢸⣿⣶⣶⡶⠿⠋⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⢶⣦⣤⣀⠀⣄⠀⠀⠀⠀⠀⠉⠙⠓⠶⣧⣄⡀⠀⠀⢰⣿⠀⠀⠀⢀⣴⣶⣔⡀⠀⣠⣴⡿⠿⣶⣶⣾⠟⠃⠀⠀⠀⠀⢀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⠛⠷⢶⣤⣤⣀⠀⢀⣀⠀⠀⠀⠈⠉⠛⠲⣿⠛⠻⠿⠿⡛⠋⠉⣛⠛⠛⠛⠉⡀⠀⠀⢀⠀⠀⠀⣠⣾⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠉⠙⠻⢦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠉⠉⠉⠙⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣆⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⣰⡟⢷⣄⠀⠀⠀ ⠀⠀⠀⣀⣤⠿⠳⢶⣟⣋⣥⣤⣤⣄⣀⣼⠋⠀⠀⠹⣧⠀⠀ ⠀⣠⡾⠋⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠉⢻⢷⣷⡀⠘⣧⠀ ⢠⡟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢹⠂⢹⡆ ⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢀⣼⠃ ⠀⣽⠃⠀⢠⢲⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⡆⠀⠈⢿⠀ ⠀⣏⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⢸⡇ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀ ⠀⠀⠘⠿⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠼⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⠿⠛⠉⠉⠉⠀⠈⠉⠉⠉⠛⠿⢯⣖⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠙⠻⢿⢶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠑⠿⡿⣆⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠃⢀⠀⠀⠀⢀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⡀⠐⢽⡧⠀⠀⠀ ⠀⠀⢀⣴⡿⠃⢠⡿⠁⠀⢸⡿⠸⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠇⢟⡆⠀⠀⢿⡄⠀⢻⡧⡀⠀⠀ ⠀⢠⣾⡿⠁⠀⣼⡇⠀⠀⢻⣧⣠⣟⠇⠀⠀⣦⣀⠀⢀⣀⣴⠀⠀⠸⣷⡄⣾⡇⠀⠀⣿⣷⠀⠈⢻⣗⡄⠀ ⢠⣿⠏⠀⠀⠀⢿⡆⠀⠀⠈⠻⠟⠋⠀⠀⠀⠈⢿⠋⠙⡿⠁⠀⠀⠀⠙⠳⠟⠀⠀⠀⡼⡇⠀⠀⠀⠨⣷⣄ ⣾⡟⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣹⠃⠀⠀⠀⠀⢸ ⣿⣇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⢹⣿ ⠘⣿⣆⡀⠀⠀⠀⠀⣠⣾⡿⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⢻⣷⣄⡀⠀⠀⠀⢀⣠⠿⠀ ⠀⠈⠙⠿⠿⣶⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀

⠀⠀⢀⣴⠾⠛⠷⢶⣄⠀⠀⠀⠀⠀⣠⡶⠾⠛⠳⣦⡀⠀⠀ ⠀⢠⡿⠁⠀⠀⠀⠀⠙⣷⡀⠀⢀⣾⠋⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⣀⣾⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢙⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⠀⠀⠻⣆⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠀⠙⣷⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣋⠀⠀⠀ ⠀⣠⡴⠟⠋⣁⣤⠶⠚⠛⠛⠙⠛⠛⠛⠾⢿⡁⠈⠻⣆⠀⠀ ⣰⠟⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠠⠈⣿ ⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻ ⡿⣷⠀⠀⢠⣄⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⣇ ⣻⠇⠀⠀⢀⡽⢿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣄⠀⠀⠀⡇ ⢻⡀⠀⠀⠈⠀⠀⠁⢠⣗⣠⣤⣄⣲⡄⠈⠀⠀⠈⠀⠀⣾⠇ ⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾ ⠀⠈⠙⠳⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡾⠟⠁⠀⠀

⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⠉⠙⢲⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠈⠀⠀⠀⠀⠈⠘⠋⠉⠉⠉⠛⢓⣾⢋⠽⣷⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢀⡄⠀⠀⠀⠀⠀⠀⠐⣶⡲⣾⠏⡜⣤⣿⣏⠁⠀⠀⠒⠒⡂ ⠀⠀⠀⠈⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣙⡔⣳⡿⣭⡷⢤⣤⣀⣸⠋ ⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣽⡿⠿⠛⢿⣿⢙⠣⡆⣽⣿⠀ ⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣎⣵⣾⣿⣧⠀ ⠉⢿⡖⠤⠀⠀⣰⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣷⡚⠛⠀ ⠒⠘⢾⣲⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠋⠁⣻⣷⣄⠀ ⠀⠄⠚⠫⣂⠀⠀⠀⠀⠀⢠⣶⣶⠄⠀⠀⠐⢿⠿⠁⠀⢀⠖⡖⣯⣿⣟⡀ ⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢙⡲⣿⡇⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⢀⡽⢻⣖⠲⠤⣤⣤⣤⣤⣤⣶⠾⠓⠊⢫⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢻⣿⠧⣾⣯⠙⠉⠁⠀⠀⠀⠈⠳⣄⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⡼⣗⡞⠀⠀⠀⣦⠀⠀⠀⠀⠙⢦⠀⠀⢠⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⢧⠞⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠈⣧⠚⠁⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⡇⢀⠞⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠔⡿⠀⡠⡻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⡞⠀⠀⠀⠀⡰⠋⠓⠦⣄⡀⠀⣀⡴⠧⠤⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠶⠚⠓⠒⠒⠉⠉⡉⠉⢁⠀⣀⡀⠀⠀⠀

⠀⣖⣯⣽⣤⡄⠀⠀⠀⠀⠂⠄⠀⣀⣠⠞⠁⠵⣄⠀⠀⠀⠀⠀⠸⢼⢯⣽⢷⠴⡿⠆⣀⣰⣯⡷⢾⡖⣆⠀⠀⠀⠀⠀⠀⣤⢤⡚⠁⠀ ⡯⠛⠓⢾⣣⠗⣆⣀⠀⠀⢀⡤⣯⣭⣷⠀⠀⠀⠸⣯⠄⠀⠀⠀⡀⠈⠓⠛⠉⠀⠀⢁⣺⠋⠉⠉⠻⠵⠋⠲⢤⡀⠀⢰⣋⡟⡿⠟⠀⠀ ⠀⠒⠀⠀⠀⠀⠀⢈⡇⠀⠈⣗⣷⡞⠁⠄⣀⠈⢁⡞⠁⢐⡾⢷⢷⢶⣲⢤⠀⠀⠀⠀⢹⡀⠉⣀⠀⠀⠀⠀⡤⠃⠀⠘⠧⡿⠁⣀⠀⠆ ⠣⣀⠛⠀⢰⠄⣀⡎⠀⠀⠀⢈⣯⡄⠲⠀⠉⣠⠞⠀⠀⡎⠀⠤⠈⢿⣹⣾⡀⠀⠀⠀⠀⠑⢄⡉⠀⠺⢀⣤⡃⠀⠀⠀⠰⣻⣄⣀⣀⠔ ⢀⠈⠓⠢⠴⣞⠟⠓⠀⠀⠀⠈⠘⠹⠓⠚⠋⠀⠀⠀⠀⡇⠰⠆⠀⠘⠛⢺⠁⠀⠀⢀⣸⣄⡤⠈⠙⠛⠯⠃⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀ ⠉⢳⣤⣄⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⢧⠀⠤⠀⠀⠀⢪⠀⢀⡴⠉⢠⠙⣝⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣆ ⠁⢸⢻⣋⡷⠀⠀⠀⢀⠀⠀⠀⠀⠀⣻⡿⠾⠲⣄⠀⠀⢨⢷⡦⡤⠴⠲⠚⠀⡞⠀⡦⠀⠀⣼⣽⣥⠇⠀⣄⣄⣤⣤⣤⠀⠀⢠⠎⠋⣄ ⠀⢿⣛⡿⢀⠰⣹⣶⣫⣯⣹⡀⢠⠾⠁⠀⠚⠀⣀⠳⡄⠀⠀⠈⠁⠀⠀⠀⠀⣇⢠⡄⠀⠈⠻⡽⠊⠠⡼⠞⠹⢿⡳⣾⢤⢝⠉⠀⠀⠀ ⠀⢠⠏⠀⠀⡟⠁⡤⠉⢷⢿⣽⠛⠤⡀⠀⠠⠀⠉⡀⠸⡄⠀⠀⠀⠀⠀⠀⠛⠽⣶⣀⣀⠀⡘⠁⠀⠀⡏⠐⠂⠀⠹⠽⠾⡈⠙⢆⡤⢦ ⠤⠜⠀⠀⠀⢷⠀⣠⠀⠀⠉⠉⣇⠀⢙⡎⣽⢦⣀⣉⢸⡧⠄⢀⣀⢀⣀⣠⣇⣞⡁⠀⠉⠓⠃⠀⠀⠀⢳⠀⠷⠀⠀⠀⠀⠣⡀⠈⢇⡿ ⠀⢀⢀⠀⡀⠈⢧⠈⢠⡄⡀⢀⣈⠇⠈⠙⢯⢺⣻⠟⠻⠋⠀⠀⡇⠈⠀⢀⡈⠻⡄⠀⠀⠀⣰⣠⣰⠀⠀⠳⡀⠐⢂⢀⡴⠖⠁⠀⠀⠣ ⡤⠚⠟⠺⢧⠀⠈⠓⣤⣦⣦⠊⠁⠀⠀⠁⠈⠉⠈⠀⠀⠀⠀⢀⣇⣀⠀⠀⣀⠀⡇⢠⠖⠚⠉⢋⡙⠳⡀⠀⠈⡗⠟⠯⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠁⠈⢧⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣀⠀⣯⡶⢾⠀⠀⠉⠀⡇⠙⢆⠀⠀⠀⢠⡀⢳⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⡤ ⣀⡀⠀⠘⠃⠈⡆⠀⢱⣰⣱⣀⣈⠀⠀⠀⣏⠉⠋⠉⠛⣳⡃⢧⣽⢾⡆⣈⢁⡸⠀⠀⣸⣖⡆⠀⢈⡁⢸⠀⢀⡼⠚⡞⡶⣶⣄⠀⠂⡇ ⣸⡓⣄⠐⠂⣠⠃⡰⠋⣈⠉⢿⢾⠗⣦⠀⡞⠀⠀⠀⠋⠀⡇⠀⠈⠉⠹⠿⠛⠆⠀⠀⠻⠿⣽⣦⢨⣡⣼⡠⡏⠀⠶⠀⢻⣻⣨⠏⡠⣧ ⠇⢿⡻⠲⣞⠏⢲⠇⣤⠀⠁⢸⡾⣻⠁⣎⡽⣽⠀⠀⠛⠀⡇⠀⠀⠀⣦⣦⢧⢤⡀⠀⠀⠓⠻⠟⠉⠯⠃⢸⠀⠿⠀⡀⠾⢯⡼⢀⡗⣏ ⠀⠀⠀⠀⠀⠀⢸⠀⢈⠐⠀⠈⢩⠏⠸⣏⡷⣾⣄⠒⠀⡼⠁⠀⢀⣴⠋⠁⠶⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⠄⠀⠀⢼⠂⠈⠓⠯ ⠀⠀⠀⠀⠀⠀⢈⢷⣍⠁⢀⡀⢸⠀⠀⠀⠉⠩⡿⡾⠯⠀⠀⠀⢯⡀⠀⠀⠀⠘⠃⠈⢧⠀⠀⠀⠀⠀⠀⠐⢳⢷⠤⠴⣆⡼⠂⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠁⠈⠙⠉⠉⠉⠉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣦⢖⣦⡀⠚⢀⡾⡄⠀⠀⣠⡤⡄⡀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⣴⣻⡭⣷⢤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠋⠈⠧⣀⢀⠀⠀⠀⠀⠻⢼⢧⡿⣿⠿⠝⢀⣄⣸⣹⡗⣾⣿⡄⠀⠀⠀⠀⠀⠀⡴⠴⡋ ⠠⣽⠟⠛⠳⣿⡼⠲⣀⡀⠀⠀⣤⠴⣯⣝⡆⠀⠀⢀⢘⡯⠀⠀⠀⢀⠀⠘⠒⠋⠁⠀⠀⣝⣾⠃⡀⠍⠛⡛⠙⠒⠤⡄⠀⢸⣩⣟⡷⠃ ⠉⡇⠘⠃⠀⠀⠀⠀⠀⣹⠃⠀⢹⣺⣶⠋⠀⢀⡀⠉⢠⠏⠁⢸⡾⢾⢲⣲⡶⢤⠀⠀⠀⠀⢫⡀⠁⣄⠀⠀⠀⠀⡼⠁⠀⠘⢮⡿⠀⡄ ⠀⠙⢦⡘⠃⠀⡄⢀⣸⠃⠀⠀⠀⣹⣯⠐⠓⠈⢁⡴⠋⠀⢠⡏⠐⠖⠈⢯⣿⢮⠀⠀⠀⠀⠀⠙⢦⡉⠀⢛⣀⣼⡁⠀⠀⠀⠒⡿⣤⣀ ⢀⢀⣄⠙⠒⠦⢶⡿⠙⠂⠀⠀⠀⠀⠋⠟⠒⠊⠁⠀⠀⠀⢸⡅⠶⠀⠀⠘⠓⡏⠀⠀⠀⣀⣆⣆⡆⠈⠉⠙⠏⠃⠁⠀⠀⠀⠀⠀⠁⠀ ⠉⠉⢟⣦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣇⠠⠤⠀⠀⠀⢣⠀⢠⠞⠁⢠⠈⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄ ⠀⠁⢨⣛⣏⣱⠀⠀⠀⠀⣀⣀⠀⠀⠀⢈⠷⠳⠓⠢⣄⠀⠀⠸⢳⢴⠤⠞⠒⠚⢀⠏⠰⠆⠀⣀⢯⣽⡴⠃⡀⣄⣀⠤⡤⢄⠀⠀⣠⠋ ⠀⠀⠻⣿⡽⢀⣐⣮⡗⣮⡽⣏⣇⢀⡴⠏⠀⠐⠃⢀⡈⢳⡀⠀⠀⠈⠀⠀⠀⠀⢸⡀⢠⡂⠀⠉⢚⡗⠃⢦⡽⠟⠹⢿⣓⡼⣤⣞⠉⠀ ⠀⠀⢰⠋⠀⠀⡜⠀⡤⠈⠛⡟⣫⡏⠓⢄⠀⠀⠀⠈⢁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠩⢻⣦⣀⡀⠀⡏⠀⠀⢸⠀⠐⠃⠀⠻⠷⢻⠈⠙⣄ ⠙⠲⠞⠀⠀⠀⢱⡀⢠⡄⠀⠈⠁⢹⡀⠘⢻⢹⡷⣤⣈⣄⣽⠒⠀⢀⠤⢄⡤⢼⣰⣨⠀⠀⠉⠙⠁⠀⠀⠀⢧⠀⠇⠀⠀⠀⠀⠳⡄⠸ ⠀⠀⢠⢀⣀⡀⠀⢳⡀⠀⠄⠀⢀⣀⠽⠀⠈⢹⣙⣿⡿⠉⠃⠀⠀⢸⡀⠀⠀⢨⠁⢳⡀⠀⠀⢀⣦⣤⡰⠀⠈⢣⡀⣘⢀⢀⠶⠚⠁⠀ ⠤⠔⠋⢋⡛⢦⡀⠀⠛⢺⢶⢷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⡀⠀⢀⡄⢸⣇⡔⠛⠋⠘⣤⠉⢦⠀⠀⠨⠟⠟⠇⠀⠀⠀⠀ ⡄⠀⠀⠈⢁⡀⢣⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣂⢀⢸⣴⠾⡇⠀⣈⠁⢸⠃⢹⡄⠀⠀⠀⣤⠈⡇⠀⠀⡀⣀⡀⠀⠀⠀⠀ ⣣⠤⡄⠀⠈⠁⢸⠆⠠⣸⢼⢼⣤⣤⡀⠀⠀⢪⠀⠉⠁⢈⠻⣏⠺⢴⣻⣿⣀⣁⣤⠏⠀⢀⣗⣶⡄⠀⣈⠀⢸⠀⣠⠗⠛⢷⣖⣲⣄⠀ ⢧⢿⣹⣄⢉⣁⣼⠀⡟⠁⠤⠀⢿⢷⣋⡆⢀⣎⣀⠀⠀⢉⠀⢸⠀⠀⠀⠀⠛⢋⠛⠀⠀⠘⢻⢻⣽⣦⣅⣴⣇⢰⠁⠐⠒⠈⣏⣻⡼⢁ ⠘⠾⠿⠟⠹⠿⠊⢹⠀⣶⠀⠀⣾⣿⣿⠆⣿⡶⢿⠀⠀⠙⠀⡞⠀⠀⠀⢸⣼⠾⠦⣄⡀⠀⠘⠚⠛⠋⠹⠉⠀⡎⠘⠇⠀⠘⠯⢽⠟⡨ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⠀⠀⠀⢸⠁⠸⢧⣿⣟⢄⠉⣀⡼⠁⠀⢀⠴⠃⠀⠶⠀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠦⠀⠀⠀⡏⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠼⣷⣄⣀⣠⣀⣸⠀⠀⠀⠈⠉⠟⠝⠟⠀⠀⠀⠫⣄⠀⠀⠀⠀⠋⠀⢱⠀⠀⠀⠀⠀⠀⠐⠫⢗⡦⠤⠶⠤⠇⠀⠀ ⡀⠀⠀⠀⣠⣄⠀⠀⠀⠃⠀⠀⠉⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⠈⢷⢪⣧⣄⡘⡁⣾⠤⠀⠀⣀⡤⢦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⢸⣫⡷⢾⡗⣆⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠳⣄⡀⠀⠀⠀⠀⠘⢾⠳⣿⡽⠚⠎⠁⢤⡼⣵⣟⣻⣏⣇⠀⠀⠀⠀⠀⢀⣰⠲ ⢀⡺⠗⣉⠉⠻⠿⠋⠳⠤⣀⠀⠀⡖⣺⢶⡾⠂⠀⠀⣄⠽⣖⡀⣀⢀⢠⠀⠈⢉⠉⠀⠀⠀⠨⣿⠉⣄⠀⠙⠛⠁⠑⠲⣤⠀⠘⣯⣟⡻ ⠀⢻⡀⠉⣀⠀⠀⠀⠀⢠⠟⠀⠀⢯⣿⡞⢀⠀⣠⡄⢀⡼⠁⠀⡼⠞⠛⣟⣯⡗⣦⠀⠀⠀⠀⠻⡀⠀⣤⠀⠀⠀⠀⡴⠃⠀⠀⠳⡿⠃ ⠀⠀⠱⢄⡉⠀⠒⢀⣤⡇⠀⠀⠀⠠⢿⣦⡈⠁⣀⡴⠋⠀⠀⢸⠀⠘⠃⠈⡧⣿⣳⠀⠀⠀⠀⠀⠙⠦⣄⣀⢉⣀⣾⡁⠀⠀⠀⠐⠻⢦ ⢀⣆⣄⡆⠉⠑⠚⠯⠋⠉⠀⠀⠀⠀⠈⠘⠉⠉⠁⠀⠀⠀⠀⢸⠐⠛⠀⠀⠉⠉⡇⠀⠀⢀⡤⠧⢧⡇⠀⠉⠙⠏⠁⠀⠀⠀⠀⠀⠀⠁ ⠁⣀⠘⣿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢰⠀⠀⠀⠀⠸⣆⠐⠂⠀⠀⠈⣧⠀⡴⠋⠀⠦⠀⣿⣯⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⢀⣯⣽⡴⠋⠀⡄⢀⣠⣀⣀⠀⠀⢀⡼⠛⢋⠉⠳⣄⠀⠀⠏⠟⡗⠚⠉⠉⠁⢸⠁⠸⠃⠀⢰⢷⡾⡞⠁⡀⣄⣠⢶⡴⣦⠀⠀⣠ ⠀⠀⠘⢾⡷⠋⢤⡽⠿⠻⢿⣳⣼⢄⣴⠋⠀⠀⠈⠀⢤⠈⢳⡀⠀⠀⠀⠀⠀⠀⢀⣸⡄⠶⠀⠀⠈⣻⠟⠱⢳⡟⠙⠘⢿⣹⣾⣦⢎⡀ ⠀⠀⠀⡏⠀⠀⢸⠁⠐⠂⠀⢹⠿⢾⡈⢳⣆⣠⣄⡀⠀⡤⠀⡇⠀⠀⠀⠀⠀⠀⢀⠘⣻⡧⠤⣄⣠⠇⠀⠀⢸⡀⠘⠁⠀⢹⡵⢳⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⠿⠿⠟⠛⠛⠛⠿⠿⠿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣶⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠉⢾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠆⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢂⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠁⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠹⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠁⢠⣿⡇⠀⠀⣤⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣤⡄⠀⠈⣿⣧⠀⠹⣿⣦⠀⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠘⢿⣷⡀⠀⠀ ⠀⣸⣿⠃⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⡿⢿⣶⣮⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠈⢻⣿⡀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠘⣿⣇⠀ ⠀⢿⡇⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣼⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⡟⠂ ⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠻⢿⣶⣦⣤⣤⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣶⣤⣤⣴⣶⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⣰⡾⠟⠛⠙⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠋⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡷⣾⢶⣦⡄⢀⣼⣷⣶⠶⡶⠾⠶⠶⠶⢶⣶⣼⣿⣀⠀⠀⣤⣶⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣼⢡⢏⣽⣿⠟⠋⠁⠀⠀⠀⢀⠀⠂⠠⠀⠀⠈⠉⠻⢿⣾⣿⢹⡰⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⣯⣾⠏⠀⢀⠠⠐⠀⠁⡀⠂⢀⠐⠀⠠⠁⠐⠀⢀⠀⠙⢿⣧⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠃⠀⠂⢀⠀⠀⠐⠀⠀⠄⠀⠠⠈⠀⠠⠐⠀⠠⠀⢀⠀⢻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠁⠀⠠⠀⠀⠐⠀⠁⠠⠈⠀⠄⠐⠀⠀⡀⠂⠐⠀⠀⠀⢿⡇⠀⠀⠀⡞⠁⠈⠉⠒⢄⣠⠤⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠇⠀⠀⠂⠀⢀⠁⠂⠀⠂⢀⠂⠐⠀⡈⠀⠀⢀⠂⠐⠈⠀⢸⣿⠀⠀⡇⠀⡞⠉⠓⣆⣽⡥⠤⢤⡀⠙⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠂⠁⢠⣾⣶⣤⠀⠁⠄⠀⠀⠂⠠⢀⣴⣷⣦⡀⠠⠀⠀⢸⣿⠀⠀⡇⠀⡇⠀⠀⠛⠉⠀⠀⠀⡼⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⢄⡀⠀⢘⣿⠿⠟⢀⠀⢠⣥⡄⠀⠀⠐⠿⣿⠟⠃⠀⠀⠀⣼⡟⠀⠀⠹⡄⠘⢆⠀⠀⠀⠀⠀⡴⠁⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣮⡣⠀⠈⣟⡖⠀⠈⢀⣸⣿⣇⠀⠐⠀⠀⣟⡒⠀⠀⠀⣲⣿⠃⠀⠀⠀⠈⠦⠀⠳⣄⡤⠔⠃⠀⠀⠀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⣀⡀⠀⠛⡋⣉⣙⠟⢀⠀⢀⠀⣀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠈⠣⠀⡇⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⣻⡛⠛⢿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣿⡇⢰⣿⣿⣿⣿⣷⠁⡀⠉⠰⣿⡀⠈⠙⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⣿⠠⠀⢿⣿⣿⣿⡿⠀⠀⡄⠀⢻⣷⡀⠀⠈⣿⣧⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢾⣏⠀⣰⣿⠈⠀⠀⠀⠈⠀⠀⠀⠀⢿⠀⣠⣿⣷⣦⣶⣿⣿⣯⠉⡩⢙⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣜⠀⢼⡧⠡⠌⣿⣿⠛⢡⠊⡔⢡⠊⡔⢨⠛⡿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⡀⣀⣤⣤⣤⣤⣤⣄⣾⣿⣏⠁⠀⢻⣧⠑⢢⠐⡄⢊⢄⠣⡘⢄⠣⡘⢄⠣⡐⢄⠂⢆⠩⢛⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠟⠉⠉⠈⠉⠉⠉⠻⣿⣧⣤⣴⠾⢿⣯⡢⢁⠚⡰⢈⠆⡱⢈⠦⡑⠌⢆⠱⡈⠜⣈⠆⡡⢾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣧⣦⣥⣮⣄⣃⣒⣬⣜⠠⠓⡘⢢⠁⠎⣴⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣍⣏⣥⣷⣷⣾⡶⠿⠟⠋⠁⠀⠀⠀⠀ ⠄⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡇⢀⣠⡀⣀⡀⠀⠀⠀⣸⣿⣿⠉⠀⠀⠀⠉⠓⢦⡀⠀⣠⡴⠒⠛⠋⠛⠓⠦⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠊⠀⠘⣿⣇⡼⠟⠛⠛⠓⢦⣴⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠈⢳⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠙⡏⢸⠚⢻⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠚⠙⢲⣤⡶⠒⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢷⣾⣻⣀⣶⣤⢦⣀⡀⠀⣧⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⣇⠀⢾⣿⣿⣷⠄⠀⣳⠀⠀ ⠀⠀⠀⠀⠀⢷⠀⢀⣄⠀⣀⠀⣶⠀⢿⣤⡴⢿⣿⢀⠀⢀⠾⠟⣹⡿⠹⣏⢿⡉⠉⠙⢳⣦⡀⠀⠀⣸⠋⠓⠒⠋⠹⠦⣤⡴⢯⠀⠀ ⠀⠀⠀⠀⠀⣟⣀⠈⣋⠘⠛⠁⠀⣴⠛⢻⡿⠛⠛⢾⣿⡿⠾⣿⠷⣤⣠⡼⠷⣽⣶⣆⡘⢋⣻⣦⠾⠓⠒⠶⢤⡀⠀⣀⡆⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⣏⣩⠿⠟⠛⠓⣶⢻⠇⠀⡟⠀⠀⢰⠀⢿⡀⠐⣾⠄⠈⠉⠉⣹⢷⣮⣿⣟⣿⠋⠠⠀⠀⠀⠀⠀⠻⣿⢳⡶⠚⠁⠀⠀ ⠀⠀⠀⠀⣠⠞⠧⠤⠴⠶⠚⠉⢹⣆⡞⢷⣤⣤⠟⠀⠈⢙⡾⠁⠀⠀⠀⠀⠘⠻⢿⣤⣿⣽⣧⡀⠐⠦⠄⠀⠾⠀⣿⠉⠉⠛⠒⠲⣄ ⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⣼⣋⣿⣻⣧⣽⣂⣤⣤⣴⣾⡗⠂⣤⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⢟⠓⣲⡶⢦⣤⣶⣿⢦⡀⠀⠀⢀⡼ ⢰⡏⠀⠀⢠⡆⠿⠀⣼⣿⣵⠉⢹⣤⢏⣾⡋⠁⢀⠠⣿⣍⣯⣥⠉⠁⠀⠿⠖⠀⣿⠇⢭⣿⣿⣾⣄⣿⣷⣀⠀⣿⠁⠀⠉⠙⠛⠉⠀ ⠈⢧⣀⣤⢿⡄⠀⠀⠀⠀⠀⠀⡼⢷⣾⡹⠇⠘⢻⣃⣉⣴⣿⣿⡷⣶⣤⣤⣀⣀⣀⣼⣿⢿⣥⠀⠉⠀⣤⡟⣷⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣺⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⣟⣶⣻⣿⣻⣋⣿⣶⠧⣿⢿⡛⠙⣿⢯⡽⢙⣿⡾⢿⣀⣿⣁⣹⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡙⣦⠀⠀⠀⠀⠀⠀⡴⢲⣀⣿⠙⣇⠀⠀⣩⢹⣏⡟⣇⣈⣧⣰⣏⣀⡇⠘⠛⠻⣼⣿⣛⣻⣯⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠲⠶⠶⠖⠒⠚⠓⠚⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠸⡼⡀⡇⢸⠀⢧⠀⡃⠀⡇⡸⢰⢣⠿⠇⣀⢜⠟⠀⠙⠛⠳⠶⢾⡭⣽⢛⡷⠩⡽⠀⠀⠀⠀⠀⢀⠒⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡅⠀⢀⣀⠤⠴⢒⣪⠽⠿⢷⣜⡌⣆⢸⠀⡇⢰⣡⣣⣧⡿⠾⣿⡚⠁⠀⠀⣰⢪⠽⣶⣇⡉⠉⠛⠒⠒⠊⠓⠐⠒⠒⠒⡋⠉⢡⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠛⠉⠁⠀⠠⣟⠉⠀⠀⣠⠤⠛⣻⣾⢬⢦⢧⢿⢟⡛⠮⣄⠀⠈⢙⣷⡴⢖⣿⣴⣶⣨⣟⡏⠉⠉⠒⠋⠒⠒⠊⠑⠒⠊⠉⠉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡤⠧⣀⣘⠷⠷⠾⠼⠾⠶⠿⢃⣀⡴⢧⣶⠭⠤⠤⡼⠙⢮⣏⣹⣟⣿⣷⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⣰⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣦⣿⡓⠓⠂⠀⠀⠒⠒⠚⠉⠙⠓⠦⠤⠤⠴⡇⠀⠀⠀⠉⠛⠶⢽⣿⣋⣻⡿⣶⣄⣀⣠⠴⣊⡁⠀⠈⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣲⠤⣄⡀⣀⣀⠀⠀⠀⠀⠀⣀⣠⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣻⣿⣏⣿⡷⠀⢉⣆⣀⣸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠛⠊⠽⠻⠍⢽⣽⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠩⣎⡷⠿⠯⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⣤⡴⠖⠛⠋⠉⠙⢿⣿⣤⣌⠲⠤⣄⣀⠀⣀⣤⣴⠾⠯⣤⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠉⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⢷⡔⢬⣭⡉⣙⡋⡉⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠤⢤⢤⡠⠤⡤⢤⡤⠴⠚⠉⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠫⠿⠿⠿⠻⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠋⠀⢠⢇⡮⠁⠀⠑⠲⢽⡢⣄⠀⠀⠀⠀⢀⡞⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣀⣀⠀⢀⡀⠀⠀⠤⠤⠤⢄⣀⠀⠀⠀⠀ ⡇⠀⠀⠸⡎⢇⠀⠀⠀⠀⠀⠙⠸⠷⡄⠀⣰⣾⠁⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⢻⣄⠀⠀⢳⡈⠳⣄⠀⠀⠀⠀⠀⠰⡜⢾⠛⣇⠐⠒⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠄⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠙⢶⣴⣦⣵⣄⠀⠀⠀⠀⠀⠀⠰⠇⠘⢦⣹⣎⠚⠉⠁⠀⠀⠈⠓⠒⠦⠤⠀⠀⠀⠀⠈⢛⡟⠤⢤⡀⣰⣿⣿⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠙⠳⠶⠶⠶⠶⠚⠒⠒⢤⣌⠛⠳⣦⣄⣀⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠦⠤⣄⣵⣷⣽⡃⠀⠀⠉⠳⢦⣦⣤⣠⣀⢀⣀⣀⡀⣀⣠⡴⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠚⠛⠲⣴⠋⠀⠉⣷⣿⣷⣶⣏⣉⢹⣀⣠⣤⣤⣶⣾⡿⠟⠛⠉⠻⡍⠙⠒⠒⠒⠤⢭⣉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢺⡉⠀⠀⠀⠀⠀⠀⠘⠳⣦⠴⣇⠉⠛⠿⣟⠛⢻⠆⠈⠉⣉⡉⠻⣇⠀⣠⡇⠀⣹⠀⠀⠀⠀⠀⠀⢀⣩⣦⠀⠀⠀⣀⣠⠤⠤⠤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠮⢍⣒⡒⠤⠤⠤⢄⣀⣿⣀⣏⣟⣲⣦⣌⣱⠃⠀⠀⣰⡟⠀⢀⣘⣯⣁⣀⣴⣃⠤⠤⠔⢒⣒⡩⠵⢂⡇⣠⠔⠋⢁⣀⣤⣤⣤⣀⠙⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠢⣄⡀⠈⠉⠉⠛⠒⠒⠒⠦⠤⠤⠬⠭⠭⠿⢦⣴⠞⠫⣭⠭⣤⡤⠶⠶⢶⣒⠒⠚⠋⠉⠉⢀⣠⢴⡚⡞⢀⣤⠖⠋⠁⠀⠀⠀⠙⡆⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⢯⣼⣉⡒⡦⢤⢤⣤⣄⣀⣀⣀⣀⣀⢀⢀⡀⣈⠓⣦⣀⡟⣓⠀⣢⣿⣟⣮⣝⢶⣖⢒⣍⣩⠽⢒⢏⡷⠋⠀⠀⠀⠀⢀⣀⣤⡚⣁⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠉⠑⠛⠚⠧⠿⠼⠤⢧⠿⠼⣏⣿⣸⣍⣯⣹⣹⣷⡍⡻⠿⣤⣈⣻⡷⣽⣙⡍⠁⠀⠀⡼⠋⠀⠀⠀⠀⠀⠸⢯⣈⠛⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⠦⣔⢦⢍⠻⢴⣬⣃⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠭⠽⠶⠿⠛⠋⠀⠀⢠⡯⠒⠒⠲⡄⢰⡒⢺⣍⣀⡤⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢡⣿⡇⢀⡗⣀⡽⠂⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⢿⡉⠉⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠹⣤⡛⠛⠛⠋⢁⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢴⡿⠛⠉⠣⣀⠀⠀⠀⠙⠢⣀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⣠⠔⠉⠉⠓⣚⠝⠙⠻⢗⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⢳⠋⠑⠦⣀⠀⠈⠑⠦⣄⡀⠀⠈⣑⡦⠤⠖⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠛⠢⠤⣶⡋⠀⠀⣠⠴⠊⠁⢀⣠⠖⠋⢻⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣜⢦⣀⣀⠀⠉⠓⠢⠤⢄⣈⠝⠋⠁⠀⠀⠀⢀⣠⠞⢹⠿⠿⢟⡖⠒⢲⠒⠒⢲⠚⠛⣿⠛⠻⡳⢤⡀⠀⠀⠀⠉⠛⢯⡤⠴⠒⠋⠉⢀⣀⠤⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢷⣤⣉⡉⠙⠒⠒⠒⢫⡀⠀⠀⠀⠀⠀⣿⡦⣴⠃⠀⢀⡜⠀⠀⢸⠀⠀⠸⡄⠀⠘⣄⣀⡽⠀⡇⠀⠀⠀⠀⠀⢀⡗⠒⠉⠉⣉⡩⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢽⣻⠶⢲⣭⢭⣙⣢⣤⣀⠀⠀⠉⠻⢾⣍⣑⡛⠒⠂⠤⠘⠀⠀⠀⠓⠉⣉⣩⣤⠖⠊⠁⠀⠀⣀⣀⣴⣮⡴⠶⢋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢃⢺⠐⠐⠐⠠⠀⠄⠄⠠⠐⠀⠖⠒⠂⠐⠐⠒⠒⠁⠃⠡⠠⠀⠄⠌⠊⠚⠉⠓⠐⠂⠄⠄⠔⠐⠒⠐⠂⠒⠒⠂⠒⠂⠦⠤⠤⣤⣪⠀ ⢳⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⠅ ⣯⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢍⣆ ⣦⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠃⠈⡂⠀⣳⡅ ⢐⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⠉⠀⠀⠀⠀⠀⠀⢘⠀⣓⡧ ⣮⠇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡚⣕ ⣬⡃⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡊⣽ ⣹⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⢈⣆⠔⠀⠒⠒⠊⠃⠒⠒⠤⣊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⣿⡂ ⣿⡂⡅⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡰⠂⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠓⠀⠀⠀⢄⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⢞⠦ ⣞⠄⡃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠽⣧ ⣻⡆⡇⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠇⠀⠀⠀⠀⣰⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⢐⢸⡟ ⣿⡇⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⡘⠀⠀⠀⠀⠀⣯⡾⡟⠄⠀⠀⠀⠀⠀⠀⣰⡿⣖⡀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢈⢨⣿ ⣹⡇⡆⠀⠀⠀⠀⡴⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⣿⣝⣿⡇⠀⠀⠀⠀⠀⠀⣛⣇⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢘⢾⡗ ⣻⡇⡇⠀⢀⣀⡜⠁⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⢳⣼⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠨⠚⡯ ⣿⡃⡃⡸⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⣤⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢨⠅⡢ ⣼⠖⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠠⡀⡤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢐⣁⠦ ⣷⠂⡃⠳⣄⡀⠀⠀⣀⣀⣀⣠⠎⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⢙⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢐⣇⠅ ⣻⠃⡇⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣰⠂⢂⠀⠄⠠⠙⡢⢞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⠃⠀⠀⠀⠀⠨⠿⡄ ⣗⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⡄⠁⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⢴⣓ ⣿⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢼⡵ ⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣚ ⣏⣧⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢣⣠⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⣫⣏ ⠼⡍⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⡷⢇⡀⠀⠀⠀⣀⡸⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠗ ⡿⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⠉⠋⠉⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣯ ⢧⡗⠧⠄⠤⢀⢀⠀⡀⢀⠀⡀⡀⠀⢀⠀⡀⢀⠀⢀⠀⡀⠀⡀⠀⡀⠀⡀⠀⠄⠀⠀⠄⠄⠀⠀⠠⠀⠠⠀⠀⡀⠀⠀⡀⠀⠀⠈⡎⠿

⠀⠀⠀⠀⠀⠀⢀⣠⣄⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡎⠔⢹⡵⠧⡇⠙⢧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢓⡇⠈⠀⠀⠀⠀⠀⠂⣏⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠟⡣⡳⠐⠀⠀⠀⠀⠀⠀⢙⡇⢇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠗⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡺⣁⡥⠅⠀⠀⠀⠀⠀⠀⠀⢁⠌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⠏⠀⠀⠀⠱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡪⠆⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢉⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠃⠀⠀⠀⠀⠀⢣⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡔⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡇⠀⠀⠀⠀⠀⠀⢓⡕⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣏⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⢄⡀⠀⠀⠀⠀⠀⠹⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⢇⠈⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡓⠶⠶⡦⣀⣀⠀⠀⡅⠀⠀⠀⢖⠠⠀⠀⠀⠀⠈⣖⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⣦⡀⠀⣳⣠⣾⣿⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠲⣢⠃⠀⠀⠀⠈⣷⣗⣀⢀⣠⡮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠻⣷⡋⠉⣏⠟⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣔⠟⠣⡭⠫⡄⡈⣓⡄⠀⠀⡀⣔⣒⣥⣝⡊⠂⠙⠙⠩⠱⣐⡐⣄⡀⠀⠀⠀⠀⠈⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠄⣛⠆⠘⠂⠉⣰⡇⠋⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣨⣂⡀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⡡⠷⠀⠀⣠⢞⠃⠀⠄⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠉⡽⡀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢟⡥⠀⠀⡊⠄⠀⠀⠀⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⡟⠻⡇⠀⠀⠈⢳⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡏⠁⢸⡏⠀⠀⠁⠀⠈⠻⠟⠁⠀⢠⠒⡆⠀⠀⠇⠈⡇⠀⠀⠀⠘⢯⡦⠀⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣑⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣬⣭⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⢦⠾⠹⠭⠍⡉⡛⢻⣷⣲⣓⡶⠶⠖⣀⢀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡒⠃⠀⠀⠀⠀⠁⠈⣿⣕⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡐⡈⠀⠀⠐⠢⠀⠀⠀⠉⡧⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠡⣀⡀⠀⠀⡆⠂⠀⠀⠀⠁⠂⣺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢂⢀⡁⠀⠀⠓⡁⡂⠀⠀⠀⠀⠀⢝⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⡁⠨⠀⠀⠀⠈⠲⡔⡀⠀⠀⠀⠀⠈⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠄⠀⠸⠀⠀⠀⠀⠀⠠⡎⠄⠀⠀⠀⠀⠉⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠪⣟⢟⢩⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣙⣄⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⢮⠛⢿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣸⡟⣿⣿⣿⣃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢸⡋⠯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣻⡿⣾⣼⡿⡎⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⣷⡀⠀⠀⢺⣧⣀⡐⣛⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣄⢆⡷⠏⢷⠉⠋⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡖⠈⢳⡀⠀⢱⡇⡁⠮⢤⠈⢝⣿⡂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢟⡡⠋⢡⠸⠫⠙⡌⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣇⠄⢼⠛⠎⣺⣷⠈⢄⠐⠁⢀⡕⡵⡶⠠⠾⠁⢡⠙⢽⠒⣢⣀⢀⢔⣿⠎⠉⠀⠅⠀⠁⡄⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠹⠛⠛⢚⠦⣩⣼⢢⢆⢖⣦⠑⠱⣀⣈⠀⠈⡯⠉⣻⢿⠁⠔⠉⠄⠌⠀⡌⡔⢅⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⣀⣿⢀⠀⠀⣰⠯⠇⠒⢮⠸⠀⠰⣟⠸⢖⣿⠀⣁⡬⡔⡨⠁⡊⣀⡀⡁⡰⣂⣄⣏⣃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠁⠀⢰⠮⡏⢂⢁⠖⠮⠋⡢⡍⠖⢟⠄⠛⠉⠐⢳⣔⠂⡈⠁⣟⠍⡢⠀⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠴⣉⠀⣳⡄⠀⠀⠝⠋⠁⠀⣀⣖⠀⠀⠀⠐⡔⡄⠈⠥⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢷⡵⠀⠉⣿⡷⠀⠀⠀⢚⣿⡏⠉⠀⠀⠀⠀⠉⢉⢦⣭⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⣯⣧⡀⠹⠃⠻⣦⠟⠀⠉⠁⠀⠀⠀⠀⡠⢆⢾⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡴⠞⢊⡡⠋⠍⣥⠶⢖⢖⢠⠃⠵⡍⡉⢇⠟⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠒⠙⣿⣀⢁⠁⠐⠅⠀⡁⠈⠴⠈⠐⠁⠢⡢⠡⠠⣀⡸⡀⣳⢦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠝⡄⠀⣀⡫⠉⠉⢡⡀⠍⢀⢌⠀⣐⠀⡡⠔⣄⢆⠃⣾⠉⠉⠂⢒⣾⠉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⢘⣇⠴⠞⠃⠳⢇⡀⢀⣬⠏⠻⣖⣿⣀⡀⠀⠈⢳⣄⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉⠙⢻⡄⠀⠀⠀⠀⡽⠯⡁⠀⢸⠃⠀⠙⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡄⢄⠴⠂⠀⠀⠀⢻⠀⠁⢸⠄⠀⠓⠶⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢠⠖⠲⣄⡀⠀⠀⠀⠀⡴⠒⠢⣀⣠⠤⠖⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠙⠒⠒⠒⢺⠃⢠⢤⡿⠤⣀⢀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠸⣄⣨⢿⡀⢀⡿⡄⢉⠆⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⡈⣠⠞⢦⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀ ⢀⡀⡧⠤⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠉⢩⠏⠈⠀⠀⠀ ⠀⠀⣳⡠⠄⠀⠀⠀⠀⠀⠀⢆⡰⠀⠀⠀⠀⠀⠀⢀⡀⡜⢯⠉⠐⢤⠀ ⠀⠈⠀⣱⢴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠴⡾⣄⠸⣋⣷⠀⡇ ⠀⠀⠀⠀⠀⣠⢽⡛⠙⣟⠛⢟⣻⡿⡻⠛⡯⡽⠒⣤⡿⣮⣇⠘⢋⠔⠁ ⠀⠀⠀⠀⡎⠀⠀⢘⠄⢸⠉⠉⠉⠉⠉⠉⢱⢰⠓⢩⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠙⡖⠂⢊⠀⣸⠤⠤⠤⠤⠤⠤⢼⠸⠒⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣅⠇⠃⢁⣿⠉⡉⠉⢩⠒⡞⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⠯⠯⠭⠴⠧⠀⠀⣉⠤⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠦⠄⣀⣀⣀⡠⠤⠮⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⢿⣷⣤⡀⣠⣾⡿⠟⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣄⣿⣇⠀⠀⣾⣿⣿⣷⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣆⠀⠀⠀⠈⠿⠿⢿⣿⡿⣿⣆⡀⠘⠻⠿⠋⢀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⠻⢷⣦⣤⣤⣴⣾⠿⠋⠀⠈⠙⠿⠷⠶⠶⠿⠟⠋⠉⢿⣷⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠈⣁⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠐⣾⣿⡇⠀⣠⣾⣿⡿⢿⣿⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠈⢀⣿⡟⠁⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⣼⢿⣿⣧⣾⣿⡿⠋⠀⢸⣿⡀⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣴⣿⠇⠀⣠⡾⢃⣾⣿⣿⠟⠁⠀⠀⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⠻⣿⣦⣤⣀⣀⠀⠙⠻⠿⢷⣶⣿⣿⣛⣡⣤⣿⣵⣾⣿⣿⠟⠁⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⠉⠙⢿⣿⣀⡀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣧⣀⣠⣾⣿⣿⣿⣷⡄⠀⢸⣿⣷⣾⣿⣶⡀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠈⠉⢀⣿⣿⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠻⠿⠿⠿⠋⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠁⠀⠀⠻⢿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡄⠤⠄⣴⣖⡀⠀⢠⣂⠤⢠⡲⣂⡀⠀⠰⢦⠍⡥⡶⡀⠀⠠⠂⠤⢠⣲⢢⡀ ⠀⠏⡐⢂⠍⣙⡧⠀⢰⢨⡑⢌⢩⢻⠅⠀⡧⠄⠦⢙⠻⣟⠀⢰⢱⣦⢁⣭⣻⠅ ⠀⠛⠂⠥⠮⠒⠀⠀⠘⠣⠸⠤⠆⠋⠀⠀⠝⠽⢐⡇⠣⠃⠀⠈⠓⠡⠧⠌⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⠒⠒⣮⣯⡄⠀⠰⠔⠒⢲⣽⣥⡄⠀⡔⠐⠒⣮⣮⣦⠀⠀⠇⠒⠲⣥⣵⡄ ⠀⣧⠼⠄⠦⢌⡗⠀⢸⢡⡉⠤⢂⣹⠂⠀⣧⠍⠓⡠⢬⡟⠀⢸⡡⢎⠱⢠⢻⠃ ⠀⠈⠑⠚⠒⠉⠀⠀⠈⠉⠓⠒⠋⠁⠀⠀⠈⠈⠓⠒⠉⠀⠀⠀⠙⠑⠚⠃⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡔⠠⡄⣼⢿⡄⠀⠰⠔⠒⢲⣽⣥⡀⠀⣞⡳⢞⡷⣿⡧⠀⢠⣔⣤⣾⣖⣤⡄ ⠠⢇⢡⢠⣉⠹⡇⠀⢸⢿⣾⢳⣶⣿⠂⠀⡷⡉⠌⡰⠙⡅⠀⠸⣟⣾⣳⢿⠟⠀ ⠀⠛⠂⠮⠔⠛⠁⠀⠈⠉⠒⠓⠂⠁⠀⠀⠣⠋⠁⠉⠓⠊⠀⠀⠈⠙⠛⠁⠀⠀ ⠀⠀⠀⢠⣠⣄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀ ⠀⣴⣶⣾⣟⣧⡀⠀⠐⢍⢲⠼⣊⠕⠀⠀⡀⠀⠀⠻⢵⡶⠀⠀⡀⡀⠉⢙⢟⠀ ⠀⢿⣿⣿⣿⣿⡇⠀⠸⢬⠗⣰⢃⠮⠃⠀⣣⠒⠀⠀⠂⠏⠀⠀⠓⣡⣤⡈⠙⠀ ⠀⠈⠛⠛⠛⠋⠀⠀⠀⠘⠓⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠃⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⡈⢳⡀⠀⠀⠀⠀⠀⠳⡟⣬⢣⢃⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢿⡄⠀⠀⠀⠀⠀⢻⠤⡓⢎⡌⢅⠣⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⣄⣤⣤⣤⣴⣾⣿⣿⣿⠛⠒⠒⠛⠒⠦⢤⣀⠀⠈⣷⢉⡖⡈⠎⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠓⠓⠋⠉⠉⠁⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠱⢄⣻⣬⠐⠄⡈⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⡆⠐⡀⠂⠀ ⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡤⢴⡒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠖⠚⠋⠉⠉⠉⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀ ⣤⣤⣀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⡆ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⣤⣆⠀⠀⠹⠿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡛⠟⠀⠀⠀⣠⣿⣿⠏⠉⠉⠙⠛⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠾⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣀⣬⡷⠟⠁⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣌⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣀⣀⠤⠤⠄⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠧⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢳⣦⣤⣿⣿⣿⣿⣦⠀⠀⠀⣤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⠖⠊⠁⠀⠀⠀⢀⠔⠊⠉⠉⠲⣤⡔⢋⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⣠⠤⠖⣦⣯⠴⢖⢋⠫⢍⡩⠍⣋⠙⠲⢦⢿⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⣰⠋⣀⡴⠚⡩⠐⡌⠆⡌⢒⠢⠰⡁⠦⡉⢆⠡⢃⠹⢦⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠓⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⢰⣧⠞⢅⠢⡉⢅⠣⡘⢄⠣⡘⢌⠱⡈⢆⠱⣈⠒⣡⠊⡔⠻⣄⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⡴⠋⢉⣿⠥⡘⢄⠣⡘⢄⠣⡘⢢⠑⡌⢢⠑⡌⢢⠑⡄⠣⢄⠓⣌⠢⠹⡄⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣆⠀⠀⠀⠈⢢⡀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⣟⠋⡤⠑⡌⢢⠑⡌⢢⠑⢢⠑⡌⢢⠑⡌⢢⠑⡌⠱⣈⠒⡄⢃⡹⢿⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢣⡀⣀⠀⠀⠱⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣠⠏⡄⢣⠰⡉⠔⡡⢊⠔⡡⢊⠅⣊⠔⡡⢊⠔⡡⢊⠔⠣⢄⠣⡘⠤⡑⣺⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢙⣪⠥⠤⠚⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⣟⣖⢡⢂⠱⡈⡜⢠⠃⡜⢠⠃⡜⢠⠊⡔⢡⠊⡔⢡⢊⠱⡈⢆⠱⡘⢤⣻⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠡⠌⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣶⠏⠀⠂⠁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⢰⠉⡀⠀⠀⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡉⠒⠀⡈⠠⡡⠋⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠷⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⣡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣗⣧⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⡀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⣣⣛⡦⡙⠦⣙⠰⣇⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠫⡿⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡱⠎⡖⢲⡑⢎⡡⢗⠬⡓⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠈⠉⠉⠉⣡⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⣑⢎⡜⡵⡘⢵⠚⣶⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣞⢷⣫⢻⢿⡿⣵⣿⣿⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢟⣷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠙⣦⠹⡄ ⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡇⢈⠳⡌ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠁⡘ ⠙⠻⢿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⠃⠀⠀⠐ ⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⢀⣄⡀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢙⣟⠁⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢘⣿⠁⠀ ⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⢀⣠⣾⢻⣏⠹⢦⣀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣇⣠⠶⢻⣟⡻⢦ ⡔⢮⡱⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣾⣿⣵⣿⣽⣯⣶⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⣼⣿⢱⣋ ⡜⣣⢝⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢦⡙⣼⣿⢢⢇ ⡼⡱⢎⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢦⡱⢻⣿⡜⣎ ⡳⣝⡺⢼⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣄⡀⠀⢠⣄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣘⢦⡹⣹⣷⢺⡜ ⠷⣭⡝⡧⢯⣽⢩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⢁⣀⡈⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⢶⡩⢖⡱⢣⣿⢣⡟ ⡿⣱⢏⡷⣜⣮⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠻⢿⣿⣿⣿⣿⡟⡦⡝⢦⡠⣝⡾⣣⣟ ⣽⣣⢿⣹⢾⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣵⢫⡷⣹⢼⣳⡽⣞ ⠷⠶⠯⠟⠯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠳⠻⠽⠞⠯⠿⠽ ⠀⠀⢀⠀⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣶⣄⣀⣀⣀⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⣄⣠⣴⠇⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠂⠍⠰⠃⢿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢀⣀⠉⠉⠙⠉⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⡤⠖⠉⠉⠀⠀⠀⣹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⠐⠀⠄⠀⠀⢿⣿⣿⣿⣿⣿⣷⠀⠀⠉⠈⠙⠂⠀⠀⠀⠀⢀⡤⠖⠒⠒⠓⠒⡿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠠⠐⠠⠀⢀⠀⠈⢻⣿⣿⣿⣿⣿⣧⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠄⠠⠀⠠⠐⠀⠀⠀ ⠠⠐⠀⠄⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣶⣤⣅⣊⣔⣨⠐⡄⢢⠐⠄⢢⢐⣠⣂⣜⣤⣶⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⡀⠂⡀⠂⠁⠄⠠⠀⠀⠀⠀⠀⠈⢩⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⡔⢂⡀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀ ⠁⡀⠁⠠⠀⠡⠈⠀⠀⠁⠀⠀⠁⢸⣦⠟⠁⠀⠀⠻⣿⣿⣿⣿⠟⠋⠉⠛⠿⣿⣿⣿⠀⠀⠻⡟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⡸⢿⡋⠀⠀⠀⠀⠀⠀⠈⢹⡯⣤⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠳⡄⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠦⡙⠴⢓⡸⢄⠢⠤⢄⡄⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠁⠐⠀⠂⠐⠤⠀

⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠝⠉⠉⠛⠷⣦⣤⣶⣶⣶⣶⡾⠃⠀⠈⢻⡾⠛⠉⠉⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⢻⡶⠛⠲⣄⣤⠼⢧⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢙⣿⡀⠀⠀⣹⢶⡄⠀⣹⡀⠀⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⢺⡛⠛⠁⣰⠏⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢹⡇⠀⠀⠀ ⢠⡶⢼⣷⢤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠾⣿⠖⠶⠆ ⠀⠀⢈⣿⣀⡀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠠⣴⣿⣄⣀⠀ ⠀⠘⠋⠹⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠯⣦⠽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃⠀⠀⠀ ⠀⠀⣠⡴⠟⠻⣧⡶⠳⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠛⠶⠄⠀ ⠀⠀⠁⠀⢀⡾⠛⠂⣀⡈⠀⢹⣧⣤⣄⣀⣀⣠⣤⣤⣴⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⣤⠄⠛⠃⠈⢿⢹⣄⠀⠀⠀⢠⡿⠀⠈⢷⡉⣻⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⢿⣤⣴⡷⣶⡟⠀⠙⠳⠶⠶⠛⠁⠀⠀⠈⣿⡋⠀⠈⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⢸⣿⣜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⠞⠃⠙⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠶⢶⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⡆⠀⣼⢿⣿⠷⣦⣄⣀⣴⣶⣶⣬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣧⣾⣿⡂⡍⠙⣸⣿⣟⡙⠄⠦⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣶⣿⠿⣋⡙⢻⣿⠾⠟⢿⢿⣿⣿⣷⠀⠀⢹⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠏⠁⠀⠈⠉⠉⠛⠲⠦⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⣤⣼⡏⠉⠛⠲⢤⣄⣀⡴⠾⠛⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣼⡄⠀⠀⠀⠀⠈⣿⣇⢿⣿⡿⣷⣄⡐⣲⣿⡟⠻⢶⣭⣷⡿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢷⣄⠀⠀⣼⠋⠙⠷⣶⡶⠟⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣈⠳⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠉⢹⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡇⠀⠀⠀⠀⡐⣠⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣸⣄⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣼⡟⠁⢫⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣀⠘⣏⠉⠉⣯⠉⠉⠀⠀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠁⠀⠀⠈⢟⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠷⠞⠛⠉⠉⠉⠹⠿⠶⢿⣗⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣿⣆⣀⣀⣀⣈⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣻⡦⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⠟⠶⢶⣴⣿⠟⠋⠉⠛⠛⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣿⠿⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⠀⠀⠀⠀⠀⣀⣤⡶⢿⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣧⣴⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠛⠛⠟⠛⠉⠁⠠⠀⠀⠀⢀⣩⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠋⢁⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠀⠈⠙⣷⣈⡉⢙⠛⣿⠋⠉⠉⠉⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⠀⢐⣾⠏⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢿⣀⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠹⠷⠶⢤⣤⣤⣴⣟⡻⠶⠶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣤⣤⠶⠞⠋⠉⣿⣷⣦⠀⠙⢢⡀⠀⢀⣠⣄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢶⣤⣴⡶⠞⢛⡟⠛⠳⢶⣤⣤⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠲⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣀⢀⣩⣴⣂⠀⠀⠀⠙⣶⣶⣶⣠⣴⣔⠄⠀⠉⠉⢳⡆⠀⠀⠀ ⠀⠀⠰⡐⠈⠉⢻⣾⠋⠉⢻⣶⣶⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡆⠀⠀ ⠀⠀⢸⡇⠀⢰⣾⣿⣀⣀⣸⣿⣦⣬⣾⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠃⠀⠀ ⠀⠀⢘⣻⣦⣐⣰⣾⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢱⡆⠀⠀ ⠀⠀⢹⡇⠘⠛⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠀ ⢀⣰⣾⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣷⣄⡀ ⠘⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠙⠛ ⠀⣠⡼⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢓⠺⢯⡄⠀ ⠀⠈⠁⢠⡽⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡴⠎⠁⠈⠁⠀ ⠀⠀⠀⠈⠁⠈⠉⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠴⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⠦⠼⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠛⠶⠋⢹⡆⠻⠦⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠉⣳⡄⣠⡶⣤⣀⠀⠀⠀⠀⠀⠘⠧⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢿⡛⠀⠀⣹⡷⠶⠶⠶⠶⢤⣄⡈⠉⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡶⠛⠁⣸⠃⠀⠀⢀⣀⣀⣿⡄⠀⠀⠀⠸⣷⣴⣿⠿⠃⠀⠀⠀⠀⠀⠈⢹⣟⠛⢙⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠒⠲⠃⠀⢀⣴⣿⣿⣿⣿⣧⡀⠀⠀⣸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣤⡀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⢀⣠⢴⣾⠟⠛⢿⣿⣿⠇⠈⠁⠀⣴⡏⠀⠈⠛⢀⣄⣀⣀⠀⠀⢠⣿⣷⠘⢉⡟⠋⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⣠⠟⠉⠛⠲⠶⠶⠛⠁⡼⠁⣀⠀⠘⠉⠁⠀⢴⠟⠀⠘⣷⡀⠀⠀⠀⢿⣭⡟⠀⠀⠈⠟⠋⠀⠀⣷⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⢿⡄⠀⠀⠀⠀⠀⠀⢰⠃⠸⣿⠀⠀⢰⣿⣳⠀⣀⣀⣠⣿⣿⠋⠛⣾⣬⣏⣀⣀⣀⢀⣤⣄⣀⣠⣽⣇⠀⠀⠀⠈⠙⠳⢦⣄⠀ ⠀⠻⢦⣄⣀⣀⣠⠴⢿⣄⠀⠀⣀⣀⣈⣻⣥⣾⡁⣹⡟⠋⠙⠷⠿⠋⠉⠉⠛⠛⠿⣿⡁⢙⣿⡉⠀⢿⡄⠀⠀⠀⠀⠀⠀⠙⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣟⠉⣿⣭⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⣻⠀⠀⠻⣦⡀⠀⠀⠀⠀⣰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⣦⠀⠀⠈⠙⠛⠒⠒⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⣀⣀⣤⡤⠤⠶⠶⠶⠲⠶⠶⠤⠤⠤⠤⠤⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣷⡀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠛⣻⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣄⡀⠀⠀⠉⠉⠁⠀⣠⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⣫⣴⣿⣿⣿⡿⠿⠛⠛⠛⠛⣿⡿⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣤⣤⣴⣾⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⣸⣿⠇⠀⠈⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠋⢀⣀⣀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⣿⣿⣿⣿⠀⠀⣀⣿⡿⠃⠀⠀⣠⣤⣴⣶⣶⣿⣿⣿⣧⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣠⣼⣿⣿⠟⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⢿⣿⣿⠟⠀⠀⠿⠟⣠⣴⣾⣿⠛⠛⠉⠉⠉⠉⢻⣿⣿⡿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⢠⣤⣤⣀⣼⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⢀⣀⡀⣾⣿⣷⣦⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⠟⠁⣴⡟⢶⣤⣀⣀⣀⣀⣀⣼⣿⣻⣷⣞⠛⢻⡌⠻⣿⣿⣿⣿⣷⡀⠀ ⠀⣼⣿⣿⣿⣿⠋⠀⠀⣿⡇⠀⠈⠉⠉⠉⠉⠉⢻⣿⣿⣿⣽⣷⣼⡇⠀⠙⣿⣿⣿⣿⣷⠀ ⢸⣿⣿⣿⣿⠇⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⣇ ⣿⣿⣿⣿⣿⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠀⠀⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⢀⣀⣿⠀⠀⠠⣶⣦⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⣿⣀⡀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠉⣉⣿⣦⡀⠀⠈⠀⠀⠀⣾⣷⠀⠀⠀⠉⠀⢀⣼⣧⣍⠉⠀⣼⣿⣿⣿⣿ ⢸⣿⣿⣿⣿⡆⠀⠉⣠⡿⠷⢦⣄⣀⣀⠀⠀⠀⢀⣀⣀⣠⡴⠾⠷⣤⡀⠀⢠⣿⣿⣿⣿⡏ ⠀⢻⣿⣿⣿⣿⣄⠀⠀⠀⠀⣠⣼⣭⣿⣟⠛⠛⣻⣿⣭⣧⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠀ ⠀⠀⢿⣿⣿⣿⣿⣦⡀⠀⠀⣿⢀⣿⡇⢸⡇⠀⣿⢀⣿⡆⣹⡇⠀⢀⣴⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣄⠙⠛⠁⠙⠋⠀⠀⠙⠛⠉⠛⠋⣠⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⡳⢦⣀⢀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠛⠳⢦⣤⠴⠶⠶⢶⡟⣡⠳⡌⡭⢻⡟⠉⠁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡘⡔⣳⡏⣽⠟⣓⠶⣤⣠⠤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⡴⣡⣻⣇⡙⢆⡣⣽⢦⡓⢦⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠮⢧⡾⠿⢞⡱⢊⣽⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡬⠖⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠤⠔⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠢⠤⡄⠀⢀⣀⣧⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠠⠶⠖⠺⡷⠒⠂⠀⣴⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠈⡏⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣷⡤⠄⠀⠙⠿⠿⠟⠉⠀⢀⠀⣠⠤⣀⠀⠀⠉⠻⠿⠟⠃⠀⠀⠉⢻⠿⠶⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢳⣄⣀⠀⠀⠀⠀⠀⢀⠌⠀⠓⠤⠚⠀⠣⠀⠀⠀⠀⠀⠀⠀⣲⣿⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⠞⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣍⡓⠶⣶⠦⠤⠤⠤⠤⠤⢤⡤⢖⠲⣩⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⢫⠱⣬⢫⠱⢆⡭⠲⣤⣤⠔⣢⠣⣜⢪⠱⣏⡍⣓⠤⣀⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠋⠁⠪⢎⡵⢃⠮⡱⢎⡔⣋⡧⣜⠚⣤⠳⡌⢖⣩⠚⣧⢎⡲⠛⠈⡅⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⣠⠟⡬⢩⠖⣱⠪⡔⢣⡗⡏⣜⢢⢓⢬⢃⡖⣍⡒⡷⣁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⢿⡘⡴⢋⡜⢆⡣⢝⢢⡗⡏⡴⢃⡎⢖⡩⢒⡴⡿⠁⠀⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠷⢾⣬⣵⣮⣥⣷⣽⣰⣯⣼⣼⠬⢷⡞⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢣⢒⢆⡲⢩⢼⡇⡖⡰⢆⢎⡼⡽⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⣬⣶⣵⣧⣾⣷⣼⣵⡮⠶⠞⠥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⢯⣿⣧⢾⣿⣿⣿⣷⣶⣿⣿⣿⡿⣥⣟⣾⣿⣿⣿⣿⣿⣟⢿⣿⣯⣙⢿⣽⣏⣡⣯⣵⣇⣄⢢⣴⣣⣤⣷⣽⣿⣿⣿⣿⣦⣴⣿⣶⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⣶⣿⣿⣿ ⣿⣯⢿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠉⠀⠀⠀⠈⠉⠛⣿⡛⣭⣿⣿⡟⠀⠀⠀⠈⠑⢌⠩⣟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⢿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠓⠀⡤⠤⠀⠀⠀⠀⠀⠀⣖⣴⠮⣥⣤⣿⣿⣿⡇⢀⠀⢀⠀⠀⠈⢳⣤⣈⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣀⢀⣠⡤⠤⢤⣤⢤⣤⢤⢴⣶⣿⣿⣿⣿⣿⣿⣿⣻⢿⣤⣷⣶⣷⣦⣶⣾⣾⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⡿⢿⣻⣿⠾⣿⡽⣫⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⠿⡟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⣾⣿⣿⣿⣿⣷⣿⣷⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⣿⣿⣿⣿⣋⢯⣻⣿⡟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿ ⣟⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣿⣿⠟⠛⠉⠙⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⣭⣙⡿⣷⣽⣿⣿⡯⣦⡵⢞⣭⢷⣶⣾⣷⠻⢿⣿⣿⣿⣯⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣮⡴⣿⣿⣿⣿ ⠀⠉⠛⠿⠿⠿⠟⠛⠛⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⠟⢁⣻⣿⠋⢶⣛⣛⣿⣿⠟⢁⣴⣿⢯⣿⣿⣟⣩⣿⣿⣿⣿⣿⠛⣛⠻⣟⣥⣤⣭⣟⣪⣻⣯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡏⠀⢬⣿⢃⣴⣿⣯⡿⠛⣁⣴⣿⣿⡿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣾⣶⠿⠛⣺⣭⠟⣨⢞⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠒⣿⣿⣧⡀⣼⣿⣲⣾⣋⣽⣁⣿⣿⣿⣿⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣧⠀⠀⠉⠓⠿⠚⠋⠉⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⡭⠯⡭⢭⣭⣽⣿⣈⡿⢯⣿⣿⣿⣿⣶⣷⣿⣶⣿⣾⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠘⣟⢻⠛⠛⢳⣞⠛⣛⣿⣿⣭⣿⢿⡟⠻⣿⣿⣿⣿⣾⣿⣿⡿⠷⠛⠻⣧⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠖⢉⠁⢀⡀⠀⡾⣽⣷⠾⠶⣿⣿⣿⣿⣿⠋⠀⠀⠈⠙⠿⣿⣿⣻⣻⢟⣍⣀⣀⠀⠀⢹⣿⣿⣿⣿⢿⠛⠻⡏⢹⣾⣿⠀⠀⠀⠀⠈⠉⠉⠂⢠⣤⣄ ⣰⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⡿⠀⠘⠋⠉⠉⢀⣠⣞⣻⣗⣒⡉⡿⢄⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣅⣘⡛⢿⠂⢸⣿⣿⣿⣿⣾⣦⣠⠿⢶⣼⢢⡄⠀⠀⠀⠈⢉⣉⣡⠞⠋⠙ ⠀⠉⠁⠀⠀⠐⣾⣽⣵⠆⠀⠀⠀⠀⠀⠘⠒⠒⠒⣻⣿⠋⠉⠉⢉⣹⣿⠒⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⢿⣿⣷⢿⣿⡿⣝⣃⣶⣿⣯⣿⣿⣿⣿⣿⣄⠀⠀⠔⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣭⣾⣿⣿⣿⡍⢀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢃⠀⢻⣷⡟⠋⣿⠃⠘⡇⠈⣿⢀⢸⠋⠹⡆⢠⣀⣀⣀⣀⣀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⠽⣟⣽⣿⣻⢿⣽⣿⣧⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣶⣿⣤⣾⣿⣦⣿⣤⣼⣶⣼⣧⣾⣿⣯⡉⠋⢻⣿ ⣶⣦⣤⣤⣤⣤⣀⣀⣠⣤⣴⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣳⣿⣯⣿⡾⣻⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣽⣿⣿⣿⣿⣿⣿⠿⣿⠿⢿⠛⢹⣿⡿⣞⣽⡕⡀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠙⣇⣀⣾⣇⠑⠂⣿⠂⠰⡆⠀⠀⠀⠀⠀⢀⣀⣁⢠⣶⡄⠀⠀⠀⠀⠀⠀⡿⣸⣿⡿⠛⣿⠉⢜⡇⠀⡏⢙⣾⣌⣹⡿⣽⣳⡞⣷⣸⡄⠀ ⣿⣿⣿⡿⢧⣛⣯⢋⣿⡝⣿⠟⣿⢿⣿⣷⡀⠀⠀⢀⣿⡿⠉⡏⠉⠄⢻⠀⢀⣿⡄⠀⠀⠀⠉⠉⣀⡤⠼⠛⠁⠀⠀⢶⠞⠁⠀⢀⣿⢿⣇⠒⣿⠀⠨⡇⠀⡇⠈⢻⡳⠜⠿⢷⣯⣽⣯⣿⣄⢀ ⣿⣿⠿⣽⠳⡜⢦⢻⡿⣜⣿⣻⡹⢾⡽⣿⣿⣗⣞⣿⡿⢧⠀⣟⠀⠀⢾⠀⠂⣿⣾⡀⠀⠀⠔⠋⠁⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⣾⢛⣾⡟⢒⣾⠴⢰⣇⣄⡿⣿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹ ⣷⣿⣯⡝⢣⢍⢣⢻⣏⣷⣻⣧⢻⣝⣾⠷⣿⡿⢮⣽⣟⣏⣛⣿⣪⣀⣻⡁⠁⣻⣟⣿⣶⣦⣄⣀⣀⣀⣀⣀⣀⣶⣾⡷⠙⠿⠿⢿⡌⢚⡏⠜⣿⢨⣾⣏⣃⣿⣭⣿⠛⢯⡀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⣮⣭⣭⣭⣭⣉⣹⣶⣫⣭⣿⣶⣿⣷⣿⠀⠀⠈⡇⢠⠀⣿⡁⠈⣽⢶⣳⣿⣾⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⢿⣦⠀⠀⢱⣾⣗⣶⡟⠛⠟⠏⠓⠀⢋⣹⡷⣤⣙⠒⢤⣄⣀⡀⠀⠀ ⠄⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⢷⣿⣿⠀⠀⠀⡇⠠⠈⣿⢀⠀⢸⢯⢤⣽⡿⣦⣿⣿⣿⣷⡹⣞⣇⢀⡤⠒⠊⢻⣿⣿⡄⠀⠀⠋⠀⠀⠘⢆⠀⠀⠀⠀⠀⠚⠻⢦⣭⣙⡛⠞⡾⢽⢥⣤ ⣭⣥⣿⣿⣿⣽⣷⣿⣻⣿⣿⣳⣟⣾⣻⣽⣿⣟⡓⠛⠛⠛⠛⠋⠉⠉⠉⠭⠿⣿⣴⠿⠛⢿⣞⣧⢿⣼⣻⣅⠀⠀⢀⣾⣟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⠯⢶⣼ ⠋⢉⠻⣿⣻⣞⣷⣟⣿⣿⣷⣿⣾⣷⣿⣿⠈⡛⠧⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⡀⣸⣿⣽⣛⡾⣽⣻⣷⣶⣾⣿⣿⣿⢀⣀⣌⣻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠊⡥⣲⡿⠿⢻⣿⣻⣿⣿⣿⣛⣩⣭⣭⣿⣧⡙⠜⢦⡈⠝⢦⣤⣀⠀⠐⠂⠐⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢯⣧⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠛⡘⠂⣁⠤⣨⣿⣍⡝⣆⣀⣀⣀⠀⠀⠀⠉⠙⠛⠛⠿⠻⠛⢿⠟⠛⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠉⠛⠿⠿⠿⠿⠿⠿⠛⠿⠛⠛⠛⠉⠉⠂⠁⠈⣀⣤⡞⣿⣏⣶⣀⣉⣀⡈⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⡶⢿⠿⣬⣳⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡳⣖⠶⣶⡒⢶⡖⡶⢲⠶⢶⡛⢿⡽⠽⣽⣭⣽⡳⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠵⣮⣚⣤⣛⣦⣹⣜⣧⣛⣬⠟⡶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣧⣈⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣀⣼⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠉⢻⣿⣿⣿⣶⣦⣄⣀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣴⣶⣿⣿⣿⡟⢉⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⣿⣟⣿⣿⣿⣶⣤⣅⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂⣨⣤⣶⣿⣿⣿⢿⣿⣿⣿⣿⠇⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣐⣀⣀⣀⣀⣀⣀⣀⣂⠀⠀⠠⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⢻⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢥⣃⠁⢀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣶⡕⣎⣧⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡀⡈⣸⡨⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠐⠈⠀⠐⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⡜⡰⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠂⠀⠀⠂⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢲⠐⠐⢰⣿⣿⣿⣿⣷⡟⢻⡾⣿⣻⡿⣿⣿⣿⣷⣿⣿⣿⢿⣻⣯⢷⡟⠻⣾⣿⣿⣿⣿⡆⠃⠂⡖⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⣭⣄⣀⣾⣿⣿⠟⠁⢸⠀⢰⡇⠀⠉⠛⠷⣿⣽⣻⣯⣿⠾⠛⠉⠀⢸⡅⠀⡗⠈⠻⣿⣿⣷⣈⣠⣬⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣿⣿⣿⣿⡟⡁⠀⠀⣸⠀⢘⡇⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⢸⡆⠀⣏⠀⠀⠈⢻⣿⣿⣿⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⢀⣼⣦⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣴⣧⡀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿⡿⠀⠀⠀⣼⠋⡼⣿⣽⡽⠛⢷⡄⠀⠀⠀⣀⠐⠀⠀⢠⡾⠛⢯⣯⣿⢧⠉⣧⠀⠀⠀⢿⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⣿⠇⠀⠀⠀⢻⠂⢰⡎⢛⡧⣀⣼⡿⠀⠀⣰⣿⣆⠀⠀⢿⣧⣀⢼⡟⢱⡆⠀⡏⠀⠀⠀⢸⣿⡏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡇⠀⠀⠀⠈⢧⣌⣻⣾⣴⣿⠟⠁⠀⠠⣿⣿⣿⠀⠀⠈⠻⣿⣦⣷⣟⣡⡼⠁⠀⠀⠀⢰⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢿⣶⣤⡀⠀⠀⢸⡏⠁⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣿⠈⢹⡇⠀⠀⢀⣤⣶⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠻⣿⣿⣿⣿⣿⣷⣶⣿⣿⣆⠀⢠⠀⠀⣤⠀⠀⡄⠀⣰⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢙⣿⣿⣿⣿⣟⣿⣿⣿⣷⣾⣶⣤⣿⣤⣶⣷⣾⣿⣿⣿⣟⣿⣿⣿⣿⣋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢷⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣽⣯⣿⣻⣟⣿⣿⣿⣿⣟⣿⣿⣿⣼⣾⣧⣷⣾⣾⣿⣿⣿⣿⣷⣦⡾⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠤⠠⠀⠄⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⡿⠟⠛⠻⢿⣿⣾⣯⣿⣿⣿⠟⢁⠀⠀⠠⠀⠤⠄⠌⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢈⠄⣹⣿⡿⠟⠋⠡⠀⠀⠀⠀⠀⠌⠙⠻⢿⣿⣏⠠⡁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣬⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣥⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀ ⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⣼⣿⡻⡿⣿⣦⡾⣷⡀⡀⢀⡀⡤⣠⠶⠞⠶⣦⡀⠀⣴⣶⣤⣶⣾⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⢸⣷⡀⠀⠀⣼⣿⣽⣫⡿⣺⣿⢜⡝⣿⣟⡿⡿⣿⣿⢀⠊⡐⠄⠽⣾⢗⢵⣿⣻⢮⣯⢿⣷⠀⠀⠀⠀ ⠀⢠⡟⠈⣹⠇⢰⣿⡳⣷⢽⣫⡿⣽⢿⣿⣻⣯⣻⣻⡾⠛⠠⡁⠲⠮⣴⠾⠛⠛⠛⠿⣟⣮⢿⣽⡆⠀⠀⠀ ⠀⠀⠙⣦⡿⢀⣿⡯⣿⣝⣯⢷⣻⡽⣳⢷⣯⣾⣷⣽⣿⡌⠂⠌⠾⠖⡟⠀⠟⠃⢰⣤⢸⡿⠷⠷⠶⢦⣀⠀ ⠀⠀⠀⠈⠁⣼⣟⣟⣾⡺⣗⣿⣵⠿⠛⠋⠉⠀⠀⠈⠻⣤⣇⣪⣬⠆⣿⢀⡀⠀⣀⣡⡿⣤⣐⠐⢄⠉⣿⠀ ⠀⠀⠀⠀⢠⣿⡻⣾⢵⡿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⠾⣾⡾⢫⠡⠐⣤⡩⠃⢴⡵⠟⠀ ⠀⠀⢠⣶⣾⣿⣽⡳⣿⣽⠃⠀⠀⢺⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠨⢈⣣⣈⣾⠀⠀⠀ ⠀⠀⢸⢗⢵⣪⣿⣟⣷⢿⣄⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠙⣮⣴⣿⢿⣿⡇⠀⠀ ⠀⠀⢘⠛⢷⣭⣻⣾⣻⡗⡿⣦⡄⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠉⢳⠀⠀⠀⣿⡿⣽⡳⣿⣧⠁⠀ ⠀⠰⣿⢷⣌⢳⣵⢝⢿⡹⣺⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠛⠂⣾⣿⣝⣟⢾⡧⠀⠀ ⠀⠀⠹⣷⣫⢟⢗⣝⣎⢞⣯⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠛⣲⡿⣷⢽⣞⣿⠇⠀⠀ ⠀⠀⠀⠈⠛⠛⠛⠋⠙⢷⡮⢿⣟⠶⣦⣤⣄⣴⠶⠶⢦⣄⣤⣤⣤⣄⣀⣀⣠⣼⣿⡿⣻⡳⣿⡾⠋⠀⠀⠀ ⠀⢀⣤⡴⠴⣤⣤⡶⢛⢛⠛⣷⡝⣿⣿⣟⣿⡯⠀⠀⠀⠀⢿⣟⡿⣻⢿⣿⣿⣿⣽⡿⠟⠛⠉⠀⣸⣆⠀⠀ ⣴⢋⠔⡠⢑⠐⡄⢊⠔⠨⣷⡈⡛⢮⣝⣿⠁⠀⠀⠀⠀⠀⢸⣿⡽⣻⣳⢟⡾⣷⡄⠀⠀⠀⠀⣼⠃⢙⡷⠀ ⡇⢂⢇⣦⠑⣟⠷⢶⣵⡠⢹⢃⠌⡊⣿⣿⣷⣄⣀⣀⣤⣤⣾⣿⣽⣫⣯⢿⣝⣯⣿⣦⣄⠀⠀⠘⢷⡟⠁⠀ ⣇⠅⠢⡻⣎⠙⡳⠶⠾⡋⡐⢕⢌⣄⡝⢛⣳⣽⡝⡿⣿⣫⣿⠟⠋⠉⠙⠛⠿⣾⣻⣿⣻⣷⣦⣤⣬⣅⠀⠀ ⢻⡌⠢⡑⠝⢌⠄⣟⠻⣦⡾⠷⢟⡉⢷⡼⠏⢹⡿⣞⣋⡿⠃⠀⢀⠠⠀⡀⠀⠈⠻⣯⢿⣷⡿⣽⡻⣿⡧⠀ ⠈⢷⡡⡈⢆⠹⡐⡹⣦⣴⣦⣰⡏⣹⣴⠶⣦⡾⢑⢍⣻⡅⠀⠂⠄⢀⠂⠠⠁⢂⠀⢻⣿⢾⣽⢷⣿⡋⠁⠀ ⠀⠀⠙⢶⣠⠑⢎⡣⣠⣥⣨⢉⡢⣐⣴⣎⡔⢤⣣⡷⠛⢧⣌⠀⠂⠄⠐⠐⠄⢄⠁⣂⡙⢿⣯⣷⠿⠃⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠉⠋⠛⠉⠁⠈⠙⠋⠁⠀⠀⠀⠙⠛⠶⠟⠛⠛⠶⠦⠕⠮⠙⠲⠽⠷⠶⠶⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠁⠈⠛⡆⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⣠⡇⠀⠀⠀⠀⠀⢈⡿⣤⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⣿⠋⠀⠀⠀⠀⠀⠀⡞⢻⠛⠀⠀⠀⠀⠀⠀⣠⣴⡖⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⢀⣴⠟⠋⠉⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⡟⠋⠉⠉⠙⢷⣦⣿⣿⣹⣦⣴⡖⠒⠒⢲⣿⣾⠖⠒⠒⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢽⡇⠈⠀⠀⠀⠀⢸⣧⣼⠒⠒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⡀⠀⢀⣿⣤⣤⡀⠀⢀⣤⣤⣤⡌⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⠀⠀⣿⡉⣿⡿⠁⠀⠈⠻⣶⠋⠁⠀⠀⠙⣶⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣇⢀⠀⠀⠙⠓⣿⠀⠀⠀⠀⠀⣿⡷⣶⠀⠀⠀⢸⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠚⠉⠉⠉⠹⢯⣄⣒⣰⣾⠿⢦⡀⠀⠀⣰⡿⠷⠏⠀⠀⢀⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⡟⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠛⠒⠚⠿⣅⠀⠀⢀⣀⣾⠏⠀⠀⠀⠠⣷⣄⣀⡠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⠬⠼⣏⠀⠀⠀⠀⠀⣼⡿⠛⠃⠀⠀⠀⠀⠉⠹⢦⣀⠀⠀ ⠀⠀⢸⡟⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⡏⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠿⣆⠀ ⠀⠀⢸⡃⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⡆⠀⠀⡇⢰⠏⠀⠀⠀⠀⠉⡇⠀⠀⠀⠹⡆ ⠀⠀⢸⣇⠀⠀⢸⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡟⠉⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⡇ ⠀⠀⠈⣿⡇⠀⢸⠉⠉⠀⠀⠀⣤⡦⠴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠛⠁⠀⠀⠀⠀⠐⠒⠚⡇⢀⡞⠀⠀⠀⠂⠀⠀⠀⠲⣄⠀⠀⠀⢠⡇ ⠀⠀⢀⣾⢷⡀⢸⣆⣀⣀⠀⠀⠙⠋⠓⠛⠂⠀⠀⠀⠀⢰⠛⢻⠛⣳⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⢀⣾⠃ ⢠⣴⠟⠁⠀⠻⣤⣻⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⣠⡾⠛⠋⠀⢀⠘⠻⢦⡀⠀⠀⠀⠀⢀⣿⣋⣀⣀⠚⢛⣛⡛⢛⢒⡨⠞⠁⠀⢀⣿⡃⠀ ⣿⠟⠀⠀⣿⠀⠀⠻⢿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡄⠙⣷⡄⠘⢷⠀⠀⣀⡴⠟⠤⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⣤⣿⡟⠀⠀ ⡟⠀⠀⠀⠻⣄⠀⠀⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣸⡁⠀⠀⣄⠙⡛⠋⠀⣠⣾⢶⣟⠉⠤⠤⣤⣤⣄⣀⡀⠀⠀⠈⠙⠛⢦⡀⠘⡿⡇⠈⠀⠀ ⣿⣤⠀⠀⢀⡞⠃⠀⠀⠀⠀⠀⠀⠙⡷⠤⣤⣀⣀⣀⣼⡛⠋⠀⠀⠀⠀⣤⠀⠀⠈⠛⠇⣠⡞⠛⠁⠀⠀⢹⡟⠳⠤⣤⡈⠉⠉⠚⠣⠄⠀⠀⠀⣿⠀⡇⡇⠀⠀⠀ ⠙⣿⡀⠀⠀⢷⣄⣀⠀⠀⣠⡤⠞⠛⣤⠋⣠⠞⠋⠉⠙⢷⡄⠀⠀⠀⠀⠈⣦⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⣿⠦⣤⣀⡀⠈⠉⠐⠂⢤⣀⡈⠙⠀⠀⣇⡇⠀⠀⠀ ⠀⠈⠻⣦⡀⠀⠉⠉⠙⠉⠁⢀⣠⠛⠀⡴⠃⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⢿⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⠈⠁⠐⠠⠄⠀⠀⣻⠀⠀⢀⣾⣏⡀⠀⠀ ⠀⠀⠀⠈⠛⣄⡀⠀⠀⣠⠾⠟⠁⣠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠒⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠛⠦⠿⣟⠛⠳⠤⢔⡉⠁⢀⣴⡿⠛⠻⡄⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⢠⣞⠁⠀⣠⠞⢁⡴⠛⣦⠀⠀⠀⠀⠀⠀⠀⠸⣻⣀⣀⣁⣀⣙⣿⣤⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⢀⣼⠏⠉⠲⠤⡈⠉⢿⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⡀⠘⠫⠠⠞⢁⡴⠋⠀⣠⠞⠑⣦⡀⠀⠀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠈⠳⣄⠀⠀⠈⣤⠈⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣠⣸⣿⣀⠀⠀⢰⠋⠀⣠⠖⢁⣠⠶⠋⠉⣱⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣻⡝⢦⡀⠈⠳⣄⡞⠁⠀⠐⠛⢷⢤⡀⠀⠀ ⠀⠀⢘⣇⣹⣿⣿⣷⢆⡀⢈⡁⠛⣁⠴⠉⣀⡠⠞⠉⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠞⠉⠀⠀⠈⣿⠆⠙⠷⣀⠀⠀⢀⠶⣀⡀⠀⠘⡇⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⡴⠒⠲⣼⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠉⠉⠛⢛⣿⣶⣷⣤⣀⣟⢛⣾⠛⠛⢾⠿⠷⢶⣾⠟⠁⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⠈⣿⣁⣬⣶⡾⢿⣤⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠖⠲⣤⠞⠓⠿⣦⠲⣿⡋⠀⠀⣷⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠾⣿⣄⣀⣿⣄⣀⣨⢶⢠⣸⠷⢾⡛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣼⡛⢹⣏⠀⡟⠁⠈⣹⣧⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠈⣾⡞⠙⢿⡙⠶⠶⠋⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠉⠧⣤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠀⠀⠘⠛⣿⡏⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠐⢶⣿⠷⢶⣤⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⢀⣤⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣄⡀⠀⠀ ⠀⠀⠀⢀⣤⣴⠿⠛⠉⠀⠀⠀⢀⣨⣽⣿⡶⠆⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠸⣧⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠈⠉⠉⠀⠀ ⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠙⢿⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣼⠿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡿⠟⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣷⣄⣀⣀⣀⣤⡶⠟⠃⠀⠀⠀⣾⠋⠁⠀⠈⠙⠻⢶⣶⣤⣤⣤⣴⡶⠶⠶⢶⣶⣶⣶⠶⠾⢿⣿⠻⣯⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠉⠻⢿⣦⣄⣀⣤⣴⡾⠋⠁⠀⠀⠀⣀⣤⡾⠟⠁⢸⣿⠉⠀⠀⠀⠀⠉⢿⡆⠀⠀⠀⢹⣇⢹⡆⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣶⣤⣤⣴⣶⣾⣿⣯⣄⣀⠀⣼⣿⣄⡀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⣿⣌⣷⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⡿⠉⠙⠓⠿⣿⡿⠷⣯⣟⡷⢶⣤⣴⣿⣣⣶⣦⡄⣠⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⢀⣿⠀⠀⠀⠉⠙⠛⣷⡿⠿⣏⣏⠈⣻⣹⣁⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢀⣀⣿⠇⠀⠘⠮⣽⡿⠹⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣶⠟⠋⠁⠀⠀⠠⢾⡽⠃⠀⠘⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣶⣤⣤⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡁⠉⠀⠉⠛⢷⣾⣤⣴⣶⣴⠿⠿⠛⠻⠾⣦⣤⣦⣤⡿⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢈⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠿⠋⠉⠻⣷⣤⣀⣀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠚⠛⠛⠛⠋⠉⠛⠛⠛⠛⠲⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠶⢤⣤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣷⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠲⠶⣤⣀⣠⣤⣤⣤⡿⠛⠿⡴⠾⠛⢻⡆⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠐⡿⣿⠿⣶⣤⣤⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠈⢯⣡⣿⣿⣀⣸⣿⣦⢓⡟⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⣄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠉⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾⠁⠀⠀⠀⠀

⠀ ⠀⠀⠀⠀⣾⣿⣿⣷⣄ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣶⣶⣶⣄ ⠀⠀⠀⣀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⢇⠠⣏⡖⠒⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⢀⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⢸⣿⣿⡿⢋⠁⠀⠀⠀⠀⠉⡙⢿⣿⣿⡇ ⠀⠀⠘⣿⣿⠀⣿⠇⠀⢀⠀⠀⠘⣿⠀⣿⡿⠁ ⠀⠀⠀⠈⠙⠷⠤⣀⣀⣐⣂⣀⣠⠤⠾⠋⠁ ⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢋⣾⣿⣿⡇⠀⠀ ⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣏⣠⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠉⠉⢿⣯⡛⠻⠿⣿⣶⣶⣶⡄⠀⠀⢀⣀⣀⣤⣼⣿⣿⣿⣭⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠸⣿⣿⣦⣤⣴⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢉⣉⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢖⣟⢈⣩⣾⣿⠟⠛⠿⢿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⣿⣿⡿⠛⢉⣭⠽⠤⠿⢿⡿⠛⠁⠀⢀⣴⡆⠙⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣾⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣹⡏⠀ ⠀⠀⠀⣀⠤⠠⡀⠀⠀⢿⣿⣿⣿⠇⠀⢻⣿⣿⡄⠀⢠⢤⡄⠀⠈⠉⠐⣤⡟⠁⠀ ⢠⢎⡉⠁⠀⠀⡗⠀⠀⠈⢿⣿⣿⣇⠀⠈⠿⠋⠀⠀⢰⣿⣆⣀⡀⣠⡼⠋⠀⠀⠀ ⠀⠓⠤⣀⣀⡜⠁⠀⡠⢄⠀⠙⢻⣿⣷⢿⡿⠒⠒⠉⢹⣿⣯⠀⠹⣧⡤⢤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⡇⠀⡇⠹⣿⣃⣾⡶⣺⣻⣼⣿⣿⣀⣰⣷⣝⠉⣴⣿⡄ ⠀⠀⠀⠀⠀⠀⠣⠤⠤⠴⠇⠀⠈⠒⠻⣍⣙⣛⢺⣾⣯⡿⣿⣿⣿⣿⣿⣯⣹⣿⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠙⠛⡟⠛⣉⠄⢠⠈⠉⠉⢸⠿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢠⣧⡈⠀⢀⡄⠀⣀⡠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠁⠀⠈⠻⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣴⢟⣶⡿⢿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠙⣿⡏⠀⠀⠘⣯⡉⠉⠹⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣯⠟⠀⢰⣿⠀⠀ ⠀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣤⣿⡃⠀⠀ ⠀⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀ ⠀⠀⠀⠀⣤⠴⣿⣿⣿⣿⣿⣿⣌⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣨⣿⣿⣿⣿⣿⡿⠤⡤⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⢻⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠞⠛⠙⢿⣿⣷⠀⠀⠀⠀⠀⠈⠉⠛⠟⠛⠉⠁⠀⠀⠀⠀⠀⣾⣿⠿⠋⠛⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⢻⣿⠛⠛⢛⡿⠛⢛⠛⢿⡛⠋⠙⢿⡟⠻⢷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⢰⡿⠁⠀⠾⠿⡿⢶⣿⣶⡿⠿⠶⠀⠈⢷⡀⠀⠙⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⣿⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⣧⣴⣿⣿⣿⢿⣧⠀⠀ ⠀⠀⠀⢀⣿⣿⣟⠿⣿⣿⣿⣿⣉⣉⣟⣉⣉⣹⣋⣉⣹⣏⣉⣉⣏⣉⣹⣿⣿⣿⣿⢟⣿⣿⣧⠀ ⠀⠀⠀⣸⣿⣿⣿⣿⣶⣿⣹⡿⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⢿⡟⣦⣶⣿⣿⣿⣿⡆ ⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⡀⠀⠙⢻⣿⠟⠉⠀⢀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⢿⡇ ⠀⠀⠀⠉⠀⡿⠁⠀⢻⡿⢿⣧⣤⣴⣿⣷⣦⣤⣴⣿⣤⣤⣴⣾⣷⣤⣤⣼⡿⣿⡏⢻⡏⣿⠘⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⡃⠀⠁⠋⠀⠀

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠁⠀⠈⠙⠛⠿⣷⣦⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣶⠿⠿⠟⠿⠶⠶⣤⣤⣀⠀⣠⡾⠛⠉⠁⠁⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⡀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠳⢦ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠻⡿⠛⣟⡿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣟⢡⠤⠀⠀⠀⠻⣿⣦⡈⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣷⡄⠀⠀⠀⠀⣼⣿⠟⡏⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⢻⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣦⡀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⣿⣿⣿⣧⣴⣶⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠿⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇⠉⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⢿⣿⣿⣄⠀⢀⣠⣤⣤⣀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⣿⣿⣿⡆⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠿⠛⠁⠀⠀⢀⣀⠈⢹⣿⣿⣷⣄⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠸⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⢷⣄⠉⢻⣿⣿⣧⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⣿⣿⡇⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⠀⠀⠀⢀⣸⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠙⡿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⣾⣿⣿⡇⠀⠀⠀⠉⠛⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣿⣿⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⠟⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠘⣿⣿⣿⣷⣶⣦⣤⣤⣤⣴⣶⣿⡿⠟⠉⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⣀⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠏⠀⠀⠙⢿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⠟⠿⣷⣦⣄⣀⣀⣤⣴⣾⠿⠋⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⣤⣿⣿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠉⠉⣿⠟⣫⣭⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣄⣀⠀⣿⣿⡇⠀⠙⢿⣿⣶⣄⣀⠀⢀⣀⣠⣴⣾⣿⠟⠁⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠛⠿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠛⠻⢿⣿⣷⣾⣿⣷⠀⠀⠀⠉⠻⣿⣿⡿⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠻⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⣀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣀⣀⡀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣥⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣷⣶⣤⣄⣀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣦⣠⣾⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣦⣤⣠⣤⣴⣶⣿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣤⣤⣤⣀⣀⣤⣀⣤⣤⣤⣾⣿⠃⠃⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⠀⠀⠀⠈⢿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠉⠉⠛⠛⡿⠿⠿⢿⣿⣿⣿⣿⡿⣿⣿⠏⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⡈⠉⠉⠉⠙⠛⠛⡛⠛⢻⡟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠶⣦⣤⡶⠋⠉⠉⠉⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠟⠀⠀⠀⠀⣶⣦⣄⣀⣠⣶⣿⣷⠀⠀⠀⠀⠿⠿⣿⡿⠋⠀⠀⠀⠀⠰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⣀⣤⣤⣤⣮⣍⠀⠀⠀⠀⠀⠀⠛⣿⣿⠟⣛⣿⡟⠙⠀⠀⠀⠀⠀⠀⣴⡾⠟⠛⠛⠻⢷⣶⣿⣿⣿⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢿⣦⣾⠿⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠉⠁⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣇⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠀⠀⢀⣼⣿⡿⠉⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠉⠁⢀⣤⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣆⡀⣀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣠⣴⣿⣿⣿⣶⣀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠻⣿⣦⣄⣠⣾⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠻⢿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⡿⠿⠛⠉⠈⠉⢻⣿⠄⢸⣿⣿⠘⢀⣼⣿⣿⣿⣿⣦⡀⣠⣤⣶⣦⣄⠀⠉⠻⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠃⠀⠀⠸⣿⣿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⣼⣿⡇⠀⢸⣿⣿⡏⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣀⣸⣶⡄⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⡀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣄⣼⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡟⣿⣿⡟⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⣶⣄⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠁⠀⢹⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣴⠾⠳⢦⣤⣤⣤⣶⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⣿⣿⣌⣙⣻⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⠿⠛⠉⢀⣡⣴⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⢀⣴⣿⠟⠉⠉⠉⠻⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⣴⣶⣭⣉⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⣠⣾⠟⠛⣣⣶⡾⠿⣶⣦⡉⠛⢿⣦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣾⣿⡿⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢀⣾⠟⠁⠀⠀⠀⠙⣿⡆⠀⢹⣿⢰⣦⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣿⡿⠻⣿⣷⣿⣿⣿⣦⠀⠐⣜⣿⡄⠸⣿⣶⣶⣶⣶⣶⣶⣿⡷⢠⣿⡏⠀⢀⣴⣿⣿⣷⣿⡿⠛⢿⣿⣿⡿⣿⣿⠛⠛⠛⠳⠶⢶⣦⣄ ⠀⠀⠀⢀⣠⣾⣿⠿⠿⠿⠿⣿⣷⣤⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⢹⣿⣷⣶⣿⣿⡇⠀⢸⣿⡇⠀⠀⣻⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⡷⣿⡟⠀⣠⣾⣿⡅⠀⢘⣿⣷⣶⣾⣿⣇⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⡿⠋⠁⠀⠉⠻⣿⣶⣿⡟⠀⠀⠀⠈⣿⣧⡀⠀⠀⢀⡀⠀⠉⢙⣷⣿⣷⡿⠟⠉⢻⣿⣴⣿⠟⠉⠀⠈⠙⣿⣦⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡿⠃⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣿⡇⠀⠀⠀⠀⠈⠻⢿⣶⣶⣿⣿⣷⣶⣿⡿⠛⠁⠀⠀⠀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠃⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠙⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠂⠐⠀⠀⠻⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠻⢿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣀⡀⠀⣀⣠⣼⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣤⣀⡀⠀⠀⣀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠟⠛⠉⠻⣷⣿⢿⣦⣄⠀⠀⣠⣿⢫⣿⣿⣷⠀⠀⠀⠀⢀⣤⣿⢿⣿⡿⠋⠛⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠻⣷⣿⣿⣦⣀⣿⡏⢸⣿⣿⣿⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣶⣤⣤⣤⣤⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⡿⠿⠉⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣤⣼⣿⢻⣿⣠⣤⣾⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣟⣿⣿⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠉⢻⣿⣿⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⣻⣷⣾⠿⢿⣶⣮⡛⠻⣿⣆⠀⠀⣠⣾⠟⠉⠁⠀⣠⣿⡿⠛⠉⠙⢻⣿⣾⡿⠛⠉⠉⠛⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠿⣿⣿⣿⢿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⣿⠁⣸⣿⠋⠀⠀⠀⠈⠻⣷⡄⠈⣿⣷⣾⡟⠁⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠈⣿⣷⣀⡀⡀⡀⠀⠀⠀⢰⣿⡟⣽⣿⠋⠀⠀⠀⠀⠹⣿⡇⠛⣿ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⢸⣿⣴⣿⣿⣶⣶⣶⣶⣶⣾⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⢻⣿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠉⠉⠉⠙⢻⣿⣧⠀⢀⣭⡀⠀⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣇⡂⠀⢀⣀⣤⡝⢛⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠘⢿⣿⣦⣈⣉⣁⣀⣉⣻⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⠿⠿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠈⢿⣧⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢀⣴⣇⣀⣀⣀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⢿⣿⠿⠟⠁⠀ ⠓⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⡿⠿⣷⣤⣀⣀⣠⣴⣿⢿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠿⠿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣤⣴⣄⠀⠀⣀⣴⣿⣿⡿⠋⣿⡇⠐⣋⡿⣿⡟⠛⠋⢡⢾⣿⡌⠻⣯⣿⣷⣄⡀⠀⢀⣤⣤⣴⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠀⠀⡀⢀⣼⣿⠁⠀⠀⠀⠀⠀⣤⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⡋⠀⠀⣿⡇⠛⢃⣼⣿⣬⣤⡞⣀⡀⣿⡇⠀⠈⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀

⠉⣿⢸⣿⢸⣿⢸⣧⠸⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⠸⠏⣸⣿⣼⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠁⢀⣾⣿⣿⣿⠟⠛⠋⢩⡟⠁⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡑⠟⣰⣿⡿⠋⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣭⠽⣷⣦⠤⠤⠶⠶⠶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⡴⠞⠋⠡⠄⠀⠁⠤⠒⠈⠁⠀⠀⠈⠑⠒⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣀⣀⣀⣀⣠⠴⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠸⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢲⡀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡞⠐⣻⠛⠁⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢰⣿⣿⡆⢀⠏⣧⠀⠀⠘⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣉⠒⠂⠀⢀⣀⣲⡾⠟⠉⠦⣹⢯⣁⠢⢄⡀⠀⠈⠉⠙⠛⠁⠀⠀⠀⠘⠿⢿⡵⣯⢀⣻⣤⠄⠀⠀⡛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⠉⠉⠹⣯⠀⠀⠀⠀⠀⢠⡿⣉⠛⠒⠾⠭⣦⣦⣤⣀⣠⣀⡒⠒⠒⠉⠳⣴⠞⠉⠀⠀⢀⡠⠞⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⠙⢳⣄⠉⠉⠉⠉⠉⠛⢻⡇⡤⠒⠒⠊⠉⠀⠀⠀⢠⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⣀⣤⣤⣴⠚⠻⣄⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⠀⠉⠉⠁⠀⠀⠀⠈⠙⠛⠛⠻⣯⣩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⢿⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⠀⠀⠀⠀⠀⠀⠘⣿⡄⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⡄⠀⠀⠀⠀⠀⠀⠘⢿⣄⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠑⢄⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⢣⠀⠀⠀⠀⢠⣇⠀⣄⣙⢷⡄⠀⢈⣁⠀⣀⣭⣍⠳⣄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⡤⣦⡉⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⡄⠀⠀⠀⠀⢿⣆⠜⠘⣧⠀⠀⡇⠀⠉⠻⣄⠙⠧⠈⠑⠢⠤⣀⠀⣀⣾⡟⠀⠀⡸⠀⠘⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⠀⠀⠀⣷⡌⢻⣦⠀⢿⡆⠀⣇⠀⠀⠀⢨⡆⢠⠶⠤⢀⣀⡴⢾⠛⢱⡇⠀⠀⡇⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠀⠀⠚⠿⡖⠁⠀⢸⣷⡀⠈⠑⠒⠄⠜⠀⢸⠀⠀⠀⢀⢞⣿⠀⣼⠷⠀⠀⡇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢨⢷⡄⠀⠀⠀⠀⠀⠀⣆⠙⢷⡀⠀⠀⠀⠀⠀⠀⠉⠀⢊⢱⠿⢣⣰⡿⠀⠀⠀⢀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡜⠠⡻⣆⠀⠀⠀⠀⠀⣿⠀⠀⢰⠈⠑⢢⡀⠀⢀⣀⣾⠛⠁⡰⣷⣿⠁⠀⠀⠀⠸⡄⠀⠀⠀⢸⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⣀⣈⣚⣁⣀⡀⠀⠀⣿⢀⠀⢸⠀⠀⠀⡁⢀⡏⠀⠀⣇⡼⣽⠟⣿⣆⡀⠀⠀⠀⠱⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⠈⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⣀⣤⡤⢶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡞⡟⡴⡙⣬⠓⣆⠧⣩⢛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⣬⠱⡲⢍⣆⢛⡤⢛⡴⢩⡚⠴⡹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⡹⢤⢓⡭⢲⡘⢎⡴⢋⡴⢣⢍⡳⣙⢬⡹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡜⣎⠼⡰⢣⡙⢎⡴⢋⡴⢋⢦⢓⡜⣢⠕⡫⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣆⢳⣉⠧⣹⠸⡔⢫⡔⣋⢦⢋⡴⢃⡞⢥⣋⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣦⡙⢦⣃⠧⣹⠡⢞⡘⢦⢋⡴⢋⡜⡲⢜⣊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⣦⡱⢫⡔⣋⢎⡹⢌⡳⢌⡳⢸⡱⣃⠞⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢯⡿⣽⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⡜⣥⡎⣵⠉⣶⢩⡖⢣⡕⡎⢹⣴⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣷⣿⣯⣿⡟⣯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⢻⣿⡝⣯⡟⣿⢳⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⡧⣞⣡⠛⣤⠫⣔⠫⡴⣉⢧⣜⡮⢇⠀⠀⠤⠀⠀⠀⠀⠀⢠⣾⣟⡷⣯⢷⣻⢾⣽⣿⡽⣿⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⡽⣳⢯⣻⢶⣻⡽⣽⣫⣟⡾⣽⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⣝⢢⠝⣢⡿⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣽⣻⡽⣯⢟⣿⣾⣳⣟⣿⠀⠀⠀⣀⣴⡾⡿⣽⠶⣯⡽⣏⣟⣧⣟⣧⣟⣳⡽⣞⣽⣳⣽⣻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣵⣻⣞⣷⡿⣭⢻⣦⣠⣾⡿⢯⣷⣟⣳⣟⣳⢯⣟⠾⣵⣞⣳⣞⡷⣻⡽⢮⡷⣞⣳⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡼⣷⡿⣿⣯⣝⡳⢞⣿⢧⡿⣭⢷⢯⣟⣳⡽⣧⣟⢾⣳⢟⣯⢷⢯⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣸⣟⣶⠟⠻⢷⣬⢻⡿⣯⢟⡾⣝⣻⢾⣭⢷⣻⡵⣞⣯⡽⡾⣽⣞⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡷⣿⡾⣇⠀⠀⣸⣏⣟⡻⣷⣯⣟⣽⣫⣷⣻⣞⣷⡽⠿⠼⠟⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠽⠶⣻⣯⡟⣿⡿⣞⡼⣳⣭⡟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⠃⠈⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⢸⣿⣿⠿⠀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠻⣷⣤⣶⡿⠁⠀⠀⠀⠀⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈.⣶⣴⣾⣿⣿⣷⣶⣿⣿⣷⣦⡤⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣳⣿⣿⣿⣿⣿⣾⡽⣿⣽⣿⣿⣿⣟⣯⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸.⣿⣷⣻⣞⡿⣿⣿⣿⣻⢿⣿⣿⣻⣿⣿⡾⣽⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣷⣯⣷⣯⣿⣟⣿⣳⢯⣿⣾⣳⣟⡿⣽⣻⠽⣯⢟⡿⣶⢶⡦⣤⢤⣄⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⢾⣳⢿⣿⣿⣿⣳⣯⢟⣳⣽⣻⣭⠿⣽⣹⢿⡿⣰⢋⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⣟⡿⣿⡼⣟⣧⣿⣟⡿⣇⣧⡟⣼⠿⣧⣿⡿⢣⣃⡜⢿⣿⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣯⣟⣷⣿⣽⣳⢿⣿⣿⣽⡶⢿⢟⡛⣏⠳⣸⡑⢦⣙⣾⣯⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣿⣿⣿⣽⡿⠞⠻⣧⣙⢎⡖⢭⢲⡙⢦⡹⣆⡟⠻⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⣰⢿⡻⣾⣶⣷⣾⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣧⢳⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡜⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⣀⣬⣰⣀⣤⣠⣄⣠⣄⣠⣄⣄⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠏⠀⢘⠛⠘⡏⣙⡙⣯⣛⠏⠉⣛⣏⠒⢙⣋⢟⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡾⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⢀⣀⢤⡀⠀⠀⠀⠀⠙⢆⡀⠀ ⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⣠⡼⠟⠛⠛⠓⠙⠚⢡⣀⣀⠀⠀⠀⠀⠉⠃ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢫⣍⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡆⠀⠁⠤⣀⠀ ⠀⠀⠀⠀⠀⢀⡶⠛⣶⡼⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⣀⣿⠀⠀⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⣠⡿⠙⣽⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠈⠛⠃⠀⢾⠇⠀⠰⠾⠁⠀⠈⠻⢿⣿⡀ ⠀⠀⠀⡊⠀⢸⣿⣿⣿⣿⣿⡳⡤⢀⡀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢀⡔⠉ ⠀⠀⠀⡂⠀⢠⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣶⣶⣶⣟⠙⠳⣦⡀⠀⠀⠊⠀⠀ ⠀⠀⢸⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠟⢱⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠛⠛⠻⠿⣽⣿⣿⣿⡛⠛⠉⠀⠀⠠⠉⡉⠉⠉⠉ ⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠃⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀ ⢠⡟⠉⠀⠀⠀⢰⡶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠈⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠒⠒⠒⠒⠛⠛⠀⠈⠉⠉⠉⠙⠓⠒⠲⠶⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀hiiiiiiiii

⣿⣿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⡃⠠⣿⣿⣿⣿⣿⣿⣿⣿⠁⣶⣶⣦⣌⣠⣥⣐⡀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢻⣿⣿ ⣿⣿⠆⠀⡦⠌⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠉⢁⣤⣿⣿⣿⣿⣿⣿⣿⡇⢸⡿⢿⣿⠿⣿⣌⢓⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⣾⠬⢛⣿ ⣿⣿⣤⣤⡀⢰⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠹⢦⣽⣦⠼⠛⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣌⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢐⣿⣶⠀⡀⠀⢉⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠛⠛⢋⣁⠐⠀⠐⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠉⠀⣼⣿⣿⣦⣁⠰⠈⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⡗⢲⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⣈⠉⣩⣿⣿⣷⠀⠀⣦⣙⠻⣿⡿⠆⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡀⠻⣟⠛⣛⡉⣿⠟⢀⣶⣾⣿⣿⣿⣿⡿⠇⠈⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠈⠙⠂⠙⣿⣿⣿⣷⣦⣜⠻⠷⣴⣷⠆⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⣛⣛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡄⠒⠆⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⡛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⢿⠻⠿⠻ ⡄⠀⠀⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣷⠠⠀⡀⠨⠙⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣤⣄⠂⠁⡄⠁ ⣷⣶⣶⣄⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠸⠻⣿⣿⣷⣆⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠠⣄⠘⠿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣿⣿⣿⡦⢄ ⣿⠿⣿⣉⡐⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠶⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠰⣤⡟⠛⢿⠛⠀⠀⠘⢿⣿⣿⣿⣿⣿⣟⡁⠀⠉⣠⣴⣿⣿⣿⣿⣿⡀⠀⢿⡙⣿⠟⠿⣇⣸ ⠿⠶⠾⠋⣁⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⣛⠾⠿⠿⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣛⠛⠳⣚⣛⣡ ⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠉⠻⠟⢻⣿⣿⣿⠛⣛⠋⠀⠆⠠⠄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠙⣿⣿⣿⣿⣿⣿⡏⠙⠟⠛⢿ ⣁⠀⠷⠀⠾⣿⣽⣷⠐⢿⣿⣿⣶⣶⣤⢤⡄⠀⢽⣿⣿⣿⣿⣟⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⣁⣀⠙⠿⣿⣿⣿⡿⠿⠃⢐⠀⠤⠐⠀⠿⠿⣿⣿⣄⡀⠲⠆⠐⣿ ⣿⣦⣰⣶⣾⣿⣿⣿⠆⠸⡟⠻⡟⠛⣳⣴⠆⢀⣹⣿⣿⣿⣏⠉⠠⠦⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢈⠃⢰⣾⣿⣿⠃⢰⣶⣶⣦⣴⣶⡶⢶⡀⠀⢻⣿⣿⣷⣠⣾⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠙⠷⠿⠛⣋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣀⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⡄⢻⣿⠿⣿⠛⢛⣶⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣤⣿⡶⠞⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠋⡉⠙⠠⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡟⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣾⣀⢃⠐⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⢩⣭⣭⡄⠎⢀⡈⠀⢩⣿⣿⡿⠟⠂⣰⡀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⡿⠶⠄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃⢤⠀⢠⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣾⣿⠃ ⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⢿⣿⡏⠀⠀ ⢸⣿⣿⣽⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣦⣿⣿⣿⣻⣽⡾⣿⣿⠁⠀⠀ ⠀⠙⠛⣿⣿⣿⣿⣷⣴⣆⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⢿⣻⡷⣯⣷⢯⣟⣿⣷⠀⠀⠀ ⠀⠀⠀⢿⣿⣾⣽⣻⣟⡿⣿⣿⣷⣿⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣟⡿⣾⣻⢯⣟⣷⣯⢿⣯⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⣟⣾⢷⣻⣟⣷⢯⡿⣽⣻⣿⣿⣷⣿⡄⣀⣠⣤⣤⣴⣶⣶⣶⣶⣿⣶⣦⣽⣿⣟⣾⣟⡷⣿⣻⣽⡾⣽⣟⣾⣿⡏⠀⠀⠀ ⠀⠀⠀⠘⣿⣿⣯⣟⡿⣞⣯⣿⣻⣽⢷⣻⡾⣽⣿⣿⣿⡿⣿⣻⣟⣯⡿⣯⣟⣿⣻⣟⡿⣿⣿⣿⣿⣿⣷⣻⢷⣟⡿⣞⣯⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣷⣻⣽⢿⣽⣞⣯⣟⡿⣽⣻⣽⣿⣿⢷⡿⣽⡷⣯⡷⠟⠛⠚⠓⠿⢾⣟⣷⣻⣞⡿⣿⣿⣿⣿⣾⣻⢿⣽⣿⠂⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⡽⣾⣻⢷⣯⣟⣾⣟⡿⣽⣳⡿⣯⣟⣿⣳⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣯⡷⣟⣿⣳⣯⢿⣿⣷⣿⣻⣾⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⣽⢯⣿⢾⣽⣳⣯⢿⣻⣽⣻⢷⣻⣷⣻⡇⢀⣶⡆⠀⠀⠀⣿⡧⢰⣿⣻⣽⢷⣻⣽⣯⣟⣿⣿⣟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣯⣿⣽⣷⣻⢿⣽⣳⣿⣻⣽⢾⣻⣽⣦⣉⣁⢀⣀⡀⢨⣴⣿⣯⣿⣾⣟⣯⣷⣟⣾⢯⣿⣯⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣾⡽⣯⣟⣷⢯⣟⣾⣿⠿⠷⠿⣿⣿⣶⣿⣷⣿⡿⠛⠉⠀⠀⠉⠛⣷⣿⣾⣻⣽⣿⡥⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣾⣽⣻⣽⣻⢾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠋⠁⠀⠀⠀⠀⠀⣠⣞⡅⠙⣿⣽⡾⣿⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⡷⣿⣽⣳⣿⣿⠃⠨⣳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡆⠀⠘⣿⣟⣿⠯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⣷⢯⣿⢾⡇⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣽⣻⣽⣿⡇⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⢰⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣯⢷⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⣀⡔⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣽⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⡄⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⣷⣿⣿⣿⣽⣯⣿⡿⣿⢿⡿⣿⣿⣿⣿⢿⣿⣻⣟⣿⠛⠛⢿⣿⢿⣏⣀⣽⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠟⣿⠏⠀⠀⠀⠹⣿⣯⣿⣽⡷⠟⠉⠙⠻⠷⣿⣿⣟⣦⠀⢈⣷⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⠀⢰⣄⡽⠿⡟⠉⠀⠀⠀⠀⠀⠀⢰⡏⠈⣿⡆⠾⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣾⣾⣷⣾⣯⠉⠀⠀⣸⠟⢦⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢹⣇⣠⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⣽⣿⣂⠙⠷⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢿⣿⣟⣿⣾⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢻⣿⡿⠆⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠛⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢸⣾⣯⡀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣤⣴⠿⠃⠙⠻⠶⣶⣶⡶⢶⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣴⣆⣀⣀⣶⡶⣒⠢⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠈⠬⣥⣭⠭⠭⠤⠄⢠⣉⣉⡚⠙⠬⢭⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣢⣈⠛⠭⠿⣧⣒⣲⣖⡤⠥⠾⢯⠶⡢⣈⠛⠽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⣀⡀⠀⢀⣠⠤⢤⡀⠉⠘⠫⠶⠲⢦⣤⠜⣓⣲⣀⣉⣀⡸⣖⡡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠁⠀⠀⠀⠀⣨⠟⠁⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣏⣄⢀⡤⣖⣲⣿⣖⢶⡆⠀⡆⣀⠹⡍⠉⠉⠉⠉⠑⠒⠒⠤⠄⣀⣀⣀⡀⠤⠤⠤⠀⠀⠤⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⠠⣠⣿⣟⣟⢧⣿⣿⡟⡿⠋⠈⠠⣛⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡷⡆⢸⢱⢻⣿⣿⣿⣿⣻⣽⠿⢿⣓⣾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡤⠊⠔⣀⣷⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠘⠿⣦⣘⣥⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⠀⠀⠀⠀⢾⣷⣦⣄⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢀⠒⢁⡠⣅⣐⣂⣠⣼⣯⠌⠁⠋⢀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀ ⠀⢀⣼⣃⠈⠩⣷⡜⡻⣿⡿⠶⢆⠐⠂⠀⠉⠛⠛⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⣀⢀⣀⢀⡇⠀⠀⠀⠀⠀ ⢀⣽⠿⠉⠀⠀⢹⣿⣧⣿⣇⣠⣴⠀⠀⠀⡄⠀⠀⠰⠀⠀⠀⠈⠷⠬⠽⠃⠀⠀⠀⠀⠀⠙⠿⠛⠀⠀⠤⣀⠀⠀⠈⠁⢀⠧⣄⠀⠀⠀⠀ ⠸⢿⣃⣤⡔⠲⠜⣿⡿⠿⠿⠉⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠐⠀⠀⢀⠀⠩⢷⣢⢤⣸⢾⠓⠿⣦⡀⠀ ⠀⠀⠀⠻⣇⢧⠖⠙⢯⣦⡄⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣻⣿⡍⠙⢩⣷⢶⣤⡃⢸⠀⠘⢾⣿⡄ ⠀⠀⠀⠰⢨⠉⠀⠀⡈⠻⣿⢄⢀⠖⠉⠓⢄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤⣶⣿⣯⢾⣿⣿⡿⠒⠲⠚⠊⢹⡎⡿⣧⡀⠀⠀⣺⠃ ⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⢻⠟⠀⠀⠀⠀⢸⠙⠛⠛⠛⠿⣯⠉⠉⠉⠉⠑⠒⣺⣷⣟⡷⠿⠙⠿⣄⡀⠀⠀⢠⡟⠀⠘⢿⡟⠒⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⢸⠀⠀⠢⠄⡀⠈⢦⠀⠈⢃⠀⢸⣻⣟⡛⡁⠀⢠⠀⠈⢻⢢⣲⡿⣦⡀⢀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠑⢁⢾⠇⠀⠂⠀⢸⣿⠁⢘⣠⣤⡜⣆⣀⠀⡹⠁⠈⠉⠉⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠀⠀⢰⡇⠀⠀⣀⣀⢥⣾⠞⠀⠀⠀⡀⠈⠻⢖⣺⡶⡛⠉⠓⠛⡻⢷⣄⣀⢀⡼⣸⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠱⡀⢀⡤⠊⠀⠀⠈⠯⣹⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠠⠀⠀⢀⢀⠟⠉⠀⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⢀⡴⠋⢣⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⠋⠉⠁⠀⠀⢸⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⢀⠀⣠⣴⠦⣀⣀⣠⠤⠋⠀⠀⠀⠀⠀⠀⢀⡾⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠘⠲⠬⠿⠷⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠐⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣾⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⢛⠛⡛⢛⠻⠟⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⡟⢋⠠⠐⡈⠄⢂⡐⢀⠂⠌⠠⠀⠄⡉⠙⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⠧⠅⠂⠄⠡⠐⡈⠄⡐⠂⢌⠠⢡⠈⡐⠠⢉⠐⠠⢈⠛⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⡇⠨⠄⠡⠈⠔⠡⠐⠠⠄⠃⠄⠊⢄⠘⠠⢁⠂⡌⠐⠠⢈⠰⠨⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠠⠁⠌⡀⠃⠌⠠⢁⠂⠌⡈⢌⠈⠄⠨⠐⡈⠐⠠⡁⠅⠂⠄⡁⠂⠄⠛⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡅⠌⡐⠠⠁⠌⡁⠆⠌⠄⣁⠢⠌⡈⠁⠆⠄⡉⠄⠡⠈⠅⠒⢠⠁⠌⡐⠈⠌⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣧⠐⡄⠡⢈⠐⡠⠌⠄⡡⢀⠢⠠⠡⠉⠤⠁⠌⠌⠡⠁⠌⡁⠆⡘⢠⢀⠡⢈⡐⠈⠻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡆⠰⢁⠂⡐⠠⡈⢂⡐⠄⠢⠡⠘⡐⢠⠉⠄⡡⠌⠌⡐⢀⢂⠡⢂⠰⢀⠂⠄⡁⠆⠌⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣄⠂⡐⠠⢁⠂⠄⡐⣈⠐⣁⠒⡐⢠⠘⢠⠐⣈⠐⡀⠆⣀⠒⣀⠒⢠⠘⢠⠐⡈⠄⠡⠘⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣦⠐⡁⢂⠌⡐⠠⢀⠒⡀⠒⡐⢠⠈⠄⡒⢀⠒⡀⠒⣀⠒⠠⡈⠄⡘⢀⠒⠠⠈⠄⠡⢈⠙⢿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣧⠀⠀⠀⠀⠀⠀⣴⢾⣏⠉⠙⢳⣄⠠⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠠⢁⠂⠄⠡⢢⠁⠂⠌⠠⢈⠑⣀⣶⣿⣿⣿⡿⠏⡁⠄⠃⠌⡈⠌⡈⢐⠀⠒⡨⠐⠂⠄⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⢀⠀⠀⢸⡏⠖⣘⡗⠆⠀⣿⠆⠀⠀⠀⢠⣾⣿⡟⣇⢹⣿⣿⣷⣦⣌⣄⣁⠢⠠⣁⣌⣴⣶⣿⣿⣿⣿⠿⠋⠄⢂⠐⡈⠐⠂⠌⡐⠐⠂⠌⢂⡑⠨⠀⠅⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⠀⠀⢘⣿⣂⠫⡭⠅⣠⡿⡹⠀⠀⠀⠀⠙⠻⣿⣷⣦⢉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠋⠄⢂⠡⠈⠄⠂⠌⡐⢉⠐⠠⢁⡘⠠⠂⠄⢃⠡⠘⡘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠈⢛⢻⢶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⢈⠔⠠⢀⢉⠉⠋⢋⠉⣁⠂⡐⠄⠡⢈⠐⡀⢂⠡⠈⠌⡐⢀⠢⠈⠔⠡⢀⠡⠌⡐⠂⠄⠡⠐⡈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣧⡐⢈⡐⢀⠂⠌⡐⠂⠌⡀⠒⢠⠈⡁⢂⠐⠠⠂⠄⢃⠐⠄⢂⠡⠉⠤⢁⠂⡐⠄⢂⡉⠌⠄⠡⠐⠠⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⣀⣴⣿⠟⡀⠃⠄⡐⢈⠐⠂⡄⡁⠆⡀⠃⢄⠒⡀⠂⠌⢠⠁⠌⡠⠈⠔⠂⡌⠰⠈⢄⠂⡐⠈⡄⠂⡌⠌⢂⠑⢂⠡⢀⠹⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⣿⣿⣶⣤⣤⣴⣶⣾⣿⠿⢋⠁⠡⠙⠻⠿⣿⣿⣿⣿⡿⠟⡁⠆⡐⢁⠂⡐⠠⢁⠂⡐⡀⠆⡈⠔⡀⢂⡐⠡⢘⠠⢈⡐⠄⠃⡌⠂⡄⣁⠊⢄⠒⢠⠁⡄⢃⠐⡈⠂⡜⠀⠆⡀⢂⠘⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣧⡓⡀⠩⢹⠛⢟⠛⠛⡍⠠⢁⠂⡘⠄⠃⠌⡐⢀⠂⠡⢀⠒⠠⠐⠠⠐⡀⢂⠄⡁⢂⠰⢀⠒⠠⠐⡐⠐⠂⢄⠑⠠⠒⠠⡐⡈⠂⡄⠡⡐⠠⠘⢠⠈⠄⠒⣀⠂⠒⠠⠁⠄⢃⢂⠐⠠⣈⠘⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢃⣻⠁⠤⠁⠌⡈⠄⡈⠡⢀⠁⢂⡄⢁⠈⡐⡐⠈⠄⢨⠐⡀⢂⠡⢈⢂⠡⡈⠄⢢⠐⠄⠢⠄⠌⠄⢡⢀⠉⢌⠠⢈⠂⠡⠒⠠⢀⠃⠄⠡⠄⡑⢈⠤⠈⠌⠰⠀⡌⢂⠡⠌⠒⠠⢂⠌⡁⢀⠂⡜⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣐⠠⠈⠄⡁⢂⠐⡐⠠⢁⠂⠌⢠⡐⣠⣥⣵⣤⣧⣾⣴⣶⣶⣶⣦⣥⣦⣥⣄⣧⣀⣌⢠⠁⢌⠐⡈⢂⠐⠨⢀⠒⠠⢈⠡⢈⠁⠆⠡⠈⠅⠂⠔⠠⢂⠉⠌⠠⢃⠐⠄⠂⠌⡐⢁⠢⠐⣨⠀⠒⡀⢻⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⠀⡁⢂⠐⡈⠐⠠⣁⣬⣴⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣶⣶⣥⣦⣈⡁⠂⠌⡐⠀⠆⠂⠌⡠⢁⠡⢈⠡⠌⠰⠈⠌⡈⠔⡈⠌⡈⠅⠂⠌⠠⠌⠡⠐⠌⡐⢠⠈⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠄⡧⠐⡀⠂⠌⠤⣧⣷⣿⡿⠟⠋⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣶⣥⣁⡸⠈⡐⢀⠂⡐⢂⠐⣈⠡⠘⢠⠐⡐⠠⠁⡔⢈⠡⢈⠡⢘⠠⢉⠐⠄⠂⠌⢿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⡑⠠⡁⠍⣼⣾⣿⡟⡏⢀⠀⢀⣲⣼⣷⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣤⣆⠰⠄⢂⠐⡀⢂⢁⠂⡐⡀⢃⠡⠐⢂⠂⡂⡐⣁⠂⠄⠊⠄⠡⠈⢼⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠐⠡⢐⣾⣿⡿⠕⠁⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣮⣄⠢⡐⢀⠂⡐⠐⡀⠆⢂⡑⢂⠂⠔⡐⠠⠘⠠⠉⠄⠡⢈⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⢈⠡⣼⣿⡟⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⣿⣿⣦⡑⣠⠀⠡⠐⡈⠄⡐⠂⠌⡐⠠⠃⡌⠠⠁⠌⠠⢁⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠂⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠛⢿⣿⣶⣘⢠⠡⢀⠡⠄⡑⢂⠡⠡⠌⠠⠁⠌⠠⢱⠀⣾⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⢻⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣄⠀⣀⠛⣿⣿⣄⣢⠀⠐⠠⠐⢂⠁⢂⠌⠠⠑⡈⢁⠂⢴⣿⣿⡇⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠐⠀⠈⢻⣿⣧⡀⡡⠌⡐⠡⠈⠄⡈⠄⡑⠠⠚⢁⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣯⡍⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣧⠐⠠⢀⠡⠌⡐⠠⠁⡄⠑⡈⣶⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣝⣑⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣷⡈⣅⠂⡐⠠⠄⣁⠢⠄⠡⣲⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢻⣿⡇⡅⠂⠄⠡⠂⡄⠂⢌⣾⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⢠⠈⠻⢿⣦⣤⣂⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣦⠁⠌⡀⠃⢄⣩⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⣠⣨⣿⣿⡹⣿⣛⡗⣶⡖⡶⢮⣕⠫⠿⣷⣦⡀⢄⠀⠀⠀⠀⠉⢉⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠁⠚⡀⢂⢰⣵⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⡿⣷⣾⡟⡃⠖⡃⣿⠿⠿⣿⣮⡓⢧⡸⢩⠓⢧⡛⣿⣦⣤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⠃⢌⣰⣱⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣟⢶⣿⡁⡇⡏⡮⢻⣋⣴⣿⠟⣝⠢⣕⢫⡙⢦⡙⣬⢻⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣾⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠏⠅⠀⢂⠀⢡⠻⢿⣿⣉⠞⣌⠳⡜⣢⠝⡦⣙⢤⢣⠽⣿⡅⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣾⣾⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⢿⡆⠆⡈⠸⣽⠬⠮⣸⣿⡜⣚⠬⣓⢥⠓⡮⣑⠮⡌⢇⡺⢸⣿⡄⠀⠀⠀⠀⠄⣻⣿⣿⡉⡍⠉⡙⢉⠛⡛⠿⠿⣿⣿⣿⡟⠛⠛⠻⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣬⣶⣿⠁⣷⣸⣿⠿⡿⢿⢟⡱⡍⠶⣉⠶⣙⠲⣉⠶⣉⢎⡜⣣⢻⣷⣶⣶⣿⣿⣿⣿⣿⣿⣅⠁⢂⠐⠄⣈⠐⡀⠆⡈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣏⣻⣆⣾⡿⣟⢮⡑⢏⠦⣳⡹⢬⡑⡎⠶⣙⡬⢳⡘⢮⡜⣡⣿⣿⡟⢩⠀⠀⠀⠉⠙⢿⣿⣎⢠⡈⠆⠠⠒⣀⣢⣵⣿⣿⣿⡗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣷⢝⣻⢏⡳⢎⢦⠹⣌⢳⢻⡿⢣⢇⡽⡑⠿⣿⠳⣙⠲⣌⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣷⣶⣾⣿⣿⣿⣿⣿⡿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⢢⣓⢭⣖⡻⠬⣍⠎⣝⠣⡎⢖⡩⢇⡭⣓⢬⠓⣆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠛⠛⠋⠉⠁⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣯⡼⢧⡟⣿⢳⠬⣙⣼⣧⡝⣌⠳⡜⣲⣿⡬⣓⡦⣻⣿⣧⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⢀⣠⣄⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠯⠉⡝⠿⣷⣮⣱⡍⢎⠵⡼⡽⢏⢎⠳⡜⢣⡹⣴⣱⣾⠿⠿⢿⣿⣶⣤⣤⣤⣴⣾⡇⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣤⣾⣿⣿⠿⠿⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠈⠀⠀⠀⠉⠛⣿⣿⣾⣷⣾⣷⣮⣷⡿⠿⠟⠛⠋⠀⠀⠀⠀⠈⠉⠙⠛⠛⢿⣿⣿⣶⣶⣶⣶⣶⣿⣿⡿⠋⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⠙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣼⣓⣄⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠿⢿⡿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⣐⣀⣀⣨⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣤⣶⣶⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠿⠿⠟⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣶⣶⣾⣿⣿⡿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣶⣤⣄⣤⣤⣤⣆⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠍⠉⠉⢉⣭⣥⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⣘⣤⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⡋⠛⠻⢿⣿⣦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⣿⡿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠛⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠇⣿⣿⣿⣿⠃⠀⢀⣤⣤⡈⣿⣿⣿⣿⣿⡏⣴⣶⡄⠀⠀⢹⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⡶⠶⠶⢿⣿⣿⣿⡄⠀⠈⠻⠿⢃⣿⣿⣿⣿⣿⣧⡙⠛⠃⠀⢀⣼⣿⣿⡿⠛⠉⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣶⣤⣤⣶⣿⣿⣏⠁⢹⣿⣿⣿⣶⣤⣶⣿⣿⣿⡿⠁⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣀⣤⠾⠻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡛⠷⣤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠰⠀⠀⠀⠐⠈⠀⠀⣴⣶⣶⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣿⣿⣎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣾⡿⠿⠿⠛⠛⠛⠛⠻⠿⣶⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⡉⠙⠛⠛⢷⣶⣶⣶⣶⠶⠿⠛⠛⠛⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⠛⠋⠉⠀⢀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡾⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⣰⣿⠇⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣿⣿⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⢿⡿⠋⠀⠀⢠⣄⣤⣤⣶⠄⠀⠀⠻⢷⠀⠀⠀⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⣶⣶⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡤⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⠙⠃⢀⣴⡿⠋⠙⠛⠿⠿⠿⠷⠾⠾⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣀⣀⣤⣤⣴⡾⠟⢻⣿⢻⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣼⣯⣤⣤⣤⣤⣶⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠿⠟⠛⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠁⠀⠀⢸⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣠⣼⡿⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⢨⣿⠟⠉⠁⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⣰⣿⣿⣧⠀⠀⠀⢀⣼⣿⣿⣿⡄⠀⠀⣿⣧⠀⣀⣀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡜⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣤⣠⣿⣿⣿⣿⣿⣷⡀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣹⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⡟⢠⠐⣬⣷⣿⠏⡀⠃⢄⡐⠈⠄⣿⣧⣿⣿⣿⣷⣤⡀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡄⠀⠀⢛⣯⣿⣿⣿⣁⠉⠉⠁⠀⣼⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣽⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠛⠁⠉⠀⠀⠀⠀⠀⣴⣿⣏⣀⣒⣼⣿⡟⢀⠐⡁⠂⠤⡘⣶⣿⠟⣹⣿⣏⣿⡍⠁⠀⠀⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠀⠘⣿⣿⠟⠿⣿⣿⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⢿⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⡿⢿⣿⣯⣄⡢⢤⣁⣶⣽⣿⠋⡔⢛⣻⣿⣿⣿⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠁⢀⣤⣤⣄⣀⠀⠀⠀⠀⢐⣿⣿⣿⣄⠀⣾⣿⣿⣿⠿⡇⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠏⢻⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠿⢹⣿⣶⡿⠟⢻⣿⣷⣿⣿⣿⢿⣿⣷⣾⣿⣿⢿⣿⣿⡿⠿⠉⢀⡒⢈⠐⢼⣿⡀⠈⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠉⠉⠻⣿⣄⣠⣴⣿⠟⣩⣿⣿⠟⠛⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀ ⠀⠀⠀⣼⣿⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠀⢰⣿⡟⠉⣿⣿⣿⣿⣀⣈⣿⣿⡠⠄⢂⠄⡀⢂⠄⠨⠄⡈⠼⢿⣷⡜⠉⠈⠉⠻⠿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣇⠀⠀⣀⣴⣿⣿⣟⣩⣴⣾⠿⠏⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣦⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧ ⠀⠀⠀⣿⣿⡀⠎⠀⢀⣿⠀⠀⠀⠀⣴⣧⡀⣰⣦⣶⣶⣶⣾⣿⣿⣆⡀⠀⠀⣱⡄⠀⠀⠻⠋⠀⠀⣸⣿⣷⣶⣿⣿⣟⠛⣿⣿⣿⣿⣷⡾⡔⠢⠐⢄⣊⠅⡊⢔⡃⠞⡹⣿⣤⠀⢀⣴⡾⠿⣿⣿⣿⣿⣿⡀⠉⠁⣼⣿⣧⣿⠟⠉⠈⢻⣷⣾⡿⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠈⠟⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠾⡷⠀⠀⢸⣿⡛⠿⢿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣸⣿⣿⣿⡇ ⠀⠀⠀⠛⣿⣷⡄⢠⣿⣿⣧⠀⣀⠠⣿⣿⣿⡿⠋⠀⠈⠉⢛⣻⣿⠿⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠿⠿⢿⣿⣶⣬⣦⣁⡂⢌⡱⣰⣿⣿⣾⠛⠛⢿⣿⣿⣿⣌⣹⣿⣿⣶⣿⣿⣿⣟⣿⣆⣀⣀⣾⣿⣿⡧⣿⣾⢷⣦⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣩⣽⡿⠛⠛⠉⠁⠀⠀⠉⠉⠳⠿⣿⣿⣿⣾⣾⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⢹⣿⡇⡿⣿⣿⣿⣧⣭⣀⣽⣿⣿⣤⣄⡀⠀⠠⣿⣿⣷⠀⠀⠈⠛⢿⣧⣤⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠉⠉⠀⠀⠀⠀⠀⠈⠉⣽⡛⣻⣿⣤⡣⣙⣻⣿⣷⡀⠀⢀⣿⣿⣿⣿⣿⣻⡼⣳⢯⣯⣟⣿⣿⣿⣿⡟⠉⠈⣿⣧⣿⡇⠀⠙⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⢀⣼⣿⡧⠀⢸⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣷⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⡟⢿⣷⣳⣿⣿⣿⡿⠚⠛⠛⠹⣿⣿⣿⣷⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠈⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡏⠀⠀ ⠀⠀⢀⣾⡿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⣿⣿⡇⣀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠁⠀⠀⢀⣠⣤⡀⠀⠀⢽⣿⡟⠛⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠟⠋⠉⠙⠻⣷⣄⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⠀⠀⠀ ⢠⣾⣿⢿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣦⣤⣾⣏⣽⡇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⠀⠀⠰⢈⣳⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣶⡿⠋⠉⠉⠙⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀ ⣿⣿⣅⠊⠀⠀⠀⢠⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣶⠿⠋⠉⠛⣿⣤⣼⡿⠷⣦⣤⣶⣿⣿⡟⠁⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⢃⣿⣿⣄⣀⣀⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⠋⣀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀ ⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣏⡀⢤⣽⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠁⣿⣧⠀⠀⠀⠀⠘⢿⣿⢿⣿⣿⣧⠾⠿⣷⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠁⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣴⣦⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠈⢩⣽⣿⡟⣷⣶⢾⣿⣿⠻⣷⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⠋⠉⢻⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣷⣄⡀⠀⠀⢈⣠⣼⣿⢿⣿⠀⠀⠸⠇⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠈⠀⢀⣤⣀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⢰⣶⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀⠀⠀⣾⣿⢿⣿⣇⠀⢸⣿⠀⠻⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠛⢿⣿⡟⠀⠀⠘⠻⠿⠿⣿⠿⡿⠛⠛⢾⣿⣿⣦⣤⣀⡰⣦⣼⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠿⣿⣿⢿⣷⣶⣾⣿⣿⠆⢀⣤⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠸⢹⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⣿⡇⠀⠉⢻⣿⣿⠟⠀⠀⠀⠈⠉⠹⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⠛⠛⣿⣷⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⡟⠉⠛⠿⣿⣿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣦⡀⠀⠀⠀⠀⠈⠀⠀⠸⠿⠛⠋⠉⠀⢻⣿⣟⢋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣆⠀⠀⠘⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠈⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠳⢀⠀⣹⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⡛⢿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⣀⣀⣨⣿⣿⣿⣿⠁⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠛⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣾⣿⣿⣿⣿⣿⢿⣶⣀⡀⠀⠀⠀⠀⢸⣿⣇⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣷⣦⣀⣄⣀⣀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀ 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⠀⠠⠘⡆⡖⠀⠀⠀⠀⠀⠹⡄⠢⠀⠉⣩⡿⠟⢃⢀⠘⣿⣿⣿⣿⣿⣿⢢⠀⠀⠸⡟⣿⣿⣷⡴⣄⠀⠈⠁⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⠏⠀⠀⠤⣰⠀⠀⠀⠉⠀⠀⠾⢱⢫⠒⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡡⢜⠨⡄⠀⠀⠀⣀⠀⠹⣄⣱⡾⡙⠴⠉⠈⠆⠠⢸⣿⣿⣿⣿⣿⣦⢀⣀⣀⣿⣮⡻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣳⣭⢻⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠁⡘⠹⡄⠀⠀⠀⠀⠀⣠⣤⣡⣋⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠈⠁⠈⠀⠀⠀⠈⠻⠆⣰⡯⣱⠹⣌⢅⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⣼⣿⡏⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠹⣿⣿⡿⠀⠀⢹⠰⣇⠀⠀⠀⠀⠘⠫⠉⠉⠉⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡖⠀⣿⢱⢣⡛⡬⢎⡂⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠀⠿⠛⠀⠀⡀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⢹⡿⠃⠀⠀⢻⡘⢯⠀⠀⠀⠀⠀⢄⠁⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⢧⣋⠮⡵⣋⠶⡑⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⣽⣧⢻⣿⣯⢿⢷⡀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣯⡻⢿⣇⠀⠀⠀⠀⠁⠀⢀⣹⡌⡟⠀⠀⠀⠀⠀⠘⡆⢥⢃⠠⣤⠐⠀⠀⠀⠀⠀⠀⡈⠄⠂⢁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⡇⢎⠵⣣⣍⣆⡑⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠈⢷⡹⣿⣿⣿⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢿⣿⣦⣻⣆⠀⠀⠀⢀⡠⠋⢾⢸⡄⠀⠀⠀⠀⠀⠀⢻⢰⣩⠒⣼⠁⠀⠀⠀⠀⠀⠀⠄⡀⠂⠠⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡶⠋⠁⠀⠈⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢨⣇⣿⡟⠯⣿⡌⠁⢀⣀⣤⣴⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⠀⠈⠀⠀⠀⢸⢢⡇⠀⠀⠀⠀⠀⠀⢹⢢⢧⡹⢄⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠁⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡆⡝⣄⡄⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡄⠀⠹⣾⡽⣾⡟⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣟⣯⢿⣷⡀⠀⠀⠀⢸⢒⠀⠀⠀⠀⢀⣠⣼⣾⣿⣶⣿⣶⣥⡀⠀⠀⠀⠀⠀⢂⠁⡐⠈⡀⠄⢁⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⢿⣷⡟⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣠⠖⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣄⠀⠈⠻⢅⣶⣿⣿⣿⣿⡿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣞⣿⣆⠀⠀⠘⣮⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⣐⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⢽⡆⠀⠀⠀⠀⢀⡼⠥⣠⠴⡚⠱⠊⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠃⠀⠀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣶⣄⣠⣤⣤⣤⣿⣿⣿⣿⣷⣿⣦⣴⣶⣿⣶⣿⣿⣿⣿⣿⡿⣟⡿⣻⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣀⣠⣴⢿⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⡽⣯⢷⣛⡾⣵⣻⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠙⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡻⠀⡴⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣟⣷⢻⣞⣽⣳⢯⣯⣽⡳⣟⡾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠙⣄⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⡽⣞⣯⣞⣧⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⢢⠀⠀⠀⢸⣿⣿⡿⠿⠿⠛⠛⠛⢿⣿⣿⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣽⣻⢽⡶⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣻⢧⣟⣧⣟⣿⣿⣿⡽⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣀⣀⡀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠓⠉⠂⡔⣻⣗⠾⣯⣿⢻⢶⣤⡀⠀⠀⠀⣿⡿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣳⡟⣾⢞⡽⣾⣿⣿⣿⣿⣿⣿⢿⡽⣞⣳⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢠⠙⣼⡿⣿⡹⣿⠻⢷⠯⡜⡙⢦⡀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣟⡾⣝⣯⡟⣷⣿⣿⣿⣿⣿⡿⣯⡽⢯⣽⣛⣾⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢵⣿⡙⣷⣹⠃⠉⠂⠁⠂⠁⠂⠙⠀⢹⣯⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣾⣽⣟⣮⢿⣷⣿⣿⣿⣿⣿⣿⣷⣻⣻⣼⣛⡶⣯⣿⣿⣿⣿⣿⣿⣿⣳⢯⡾⣽⣻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣸⡾⣿⢃⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣯⣿⣷⣿⣿⣿⡿⣿⣿⣿⢯⣷⣛⡷⢯⣟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣷⢻⢿⣿⠁⠀⠀⠀⠀⠀⣀⣤⠖⠁⠘⣯⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣻⠶⣏⣿⢻⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⢛⣿⣼⠋⠀⠀⠀⠈⠉⠉⡉⠀⠰⡀⠀⣿⢿⡆⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣗⡯⣿⢽⣺⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠈⠿⠿⠂⠀⠀⠾⠂⠀⠀⣷⠀⡤⣹⡄⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣟⡾⣽⣳⠷⣾⢽⣳⣯⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⣶⣣⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣠⣤⣄⣀⣀⣀⠀⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣽⣳⢯⣿⣽⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠉⣉⠉⠉⠉⠈⣿⡟⣿⡶⣿⣽⣿⣿⣧⣤⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠯⠿⠯⠿⠽⠿⠽⠯⠿⣽⢯⣿⣟⣿⣻⣟⣿⣶⠶⣶⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⣻⠀⠀⠀⠀⣿⡻⠟⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙⠙⠛⠻⠾⠽⣯⣿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⡿⠿⠛⠉⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⡿⠋⠉⠻⢿⣿⣿⣿⣥⡀⠀⠀⠀⠻⣿⡉⠢⠑⡬⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣦⣄⣀⡙⢷⡀⠐⠀⢋⠐⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠌⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣶⣶⣤⣄⡀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠈⢻⣟⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢻⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠁⠀⠈⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⠻⠿⣽⣻⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⠀⠈⠻⠿⢷⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⢉⣠⣤⣤⣤⣤⣀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⠷⠾⠙⠿⢿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣄⣀⠀⡀⠀⠀⠠⢈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣟⣷⣦⣀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠀⢠⣿⣿⠟⠛⠛⠿⣿⣧⡈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠁⠔⠒⣁⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⢀⠣⡑⢬⠒⡥⣑⢊⡏⠀⢰⢃⠵⣺⣽⣿⣿⣿⡇⠈⢂⢹⣿⣿⣿⣶⣫⠑⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣛⣿⣿⣿⣶⣦⣶⣶⣶⠂⠀⠀⠀⠀⢹⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣁⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠂⠀⠀ ⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠙⢢⡙⡐⢂⡟⠀⢀⡿⠚⣉⡤⣼⣿⣿⣿⡃⠀⠀⠃⠹⣿⣿⣿⣿⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣡⠀⣸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢆⡱⠞⠁⢀⣩⠴⠚⡍⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠆⣍⡋⠁⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠘⣀⡤⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⡄⠈⠀⠹⠃⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀ ⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡾⠃⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⣿⣤⣤⣄⣠⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣄⡀⠀⢀⣀⣠⣶⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠹⢧ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⣾⠁⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣈⣉⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠉⠛⠛⠛⠋⢩⠷⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠢⠀⢳⠁⠂⠈⣳⢆⠀⠀⠀⠀⠀⠀⠀⠐⠠⠈⠀⠀⠀⠁⠀⠀ ⠀⠠⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⢖⠶⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠙⣿⣋⣹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⠟⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢦⠈⠄⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠄⠒⣀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠏⠠⣴⢺⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠂⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠰⣉⢦⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠉⠈⠻⠛⠉⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⢄⠠⡀⢆⠡⢊⠱⣂⠌⢳⡀⠀⠀⠀⡚⠀⠀⠠⠈⠀⡐⠠⢁⠧⣿⣿⣿⡯⢀⠀⠀⠀⠀⠀⠀⠒⣨⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⡀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢿⣫⠿⣽⣫⢿⣹⢯⡻⣝⢯⡻⣝⣯⡻⣝⣯⠻⠽⣏⠿⣝⠯⠿⠯⣿⡹⣏⢿⣹⢏⡿⣽⢻⡽⣫⢿⣹⣏⣿⣹⣏⡿⣽⣫⠿⣝⡯⣟⣽⣫⣟⣽⣫⢟⡽⣫⠟⠽ ⠀⠀⠀⠀⠀⠀⣰⢟⡟⢓⣿⠾⢭⣯⣷⣯⣷⠟⠁⠙⠉⠙⠎⡷⢤⡺⣝⠮⠀⠀⠀⢱⡛⡼⣣⠟⠮⡗⣭⢳⡹⣣⢏⠏⠀⠀⠱⣎⠷⣱⣫⣝⣮⣷⣟⠉⠁⠈⠙⠳⡏⠾⠱⣆⠴ ⠀⠀⠀⠀⢀⣰⣿⣧⡇⢻⣵⣿⣬⡿⣯⠿⡵⣈⡀⠀⠀⠀⢠⠙⠢⢅⢂⠛⠴⣐⢂⢎⠱⢓⡀⠀⠀⠘⣴⣣⣧⣀⠪⢁⢤⠤⠞⣌⣻⢛⣷⣿⡿⠁⠀⠀⠀⠀⠠⠀⠀⠠⡐⣍⠚ ⠈⠀⡠⠊⠉⠉⠉⠙⣾⣾⣾⡞⢿⠋⠐⢲⣖⠒⠂⠠⢒⡌⢀⠀⢩⡄⢪⣌⣒⢧⣬⡶⠓⢮⡄⠠⠖⢻⠁⠀⠀⠉⠙⠛⠶⢭⣜⡧⢠⣻⡿⡼⡇⠀⠀⢄⠦⠠⡚⠄⠀⠁⠈⢂⠉ ⠀⡎⠀⠀⠀⠠⠊⠊⠁⡽⣹⣷⡸⠘⠷⠶⠄⠠⠄⠠⠀⠠⡄⠲⠄⠘⠶⠶⠧⠦⢦⢠⠈⠘⠓⠀⡄⠘⢷⣤⡁⠂⠀⡀⠀⢲⡄⠙⢷⡜⢧⢼⣧⠀⠀⠀⠖⠄⠓⡀⡰⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⢠⠎⠀⡟⠉⠙⠋⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣾⣾⣤⠶⣧⣤⣀⡀⠀⣈⡛⢷⣦⣌⡀⠀⠹⣆⢻⣿⢀⠀⠈⣷⣄⠀⠀⠐⠤⠊⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠐⠃⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⣤⣀⣀⠀⢸⠙⣇⢛⣶⡗⢸⡧⢿⣟⢻⣬⠹⠄⠨⠿⢿⣿⡶⣿⣘⣿⣈⡀⠁⠀⣻⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢦⠘⣦⣋⡯⢏⡳⣾⡄⣻⣏⡨⣿⠹⣟⢻⣿⣽⣿⣫⣆⠀⡆⢸⣿⣠⠷⣼⠿⡀⠱⠢⡤⣟⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠤⠤⢶⢈⡹⢟⣨⣥⡺⣶⣹⣿⣿⠿⠃⠈⠁⠻⠀⠙⠓⠓⠏⠈⠻⠓⠛⠋⣽⣿⡷⠼⡞⠁⣾⠿⣄⠛⠛⢻⡟⠙⠆⠈⢷⡄⠀⢀⠠⡔⣠⠄ ⠀⠀⠀⠀⠄⠀⠀⢀⠰⠀⠀⠀⡏⣸⣿⡼⣇⣽⢶⣿⣿⡰⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠟⠀⠀⠷⣄⠉⠓⢌⠙⢦⣸⠀⠀⠀⠀⠀⢙⡆⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⣠⠛⢠⣿⣷⣏⠁⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⢑⣆⡟⠓⠢⣄⠀⠀⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢰⠃⢠⡟⠃⠉⠛⠀⠀⠀⠀⠀⠀⠀⣴⠒⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⢰⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠃⡰⢃⡴⢋⣾⠀⠀⠀⠀⠀⠀⠀⠀⢊⡞⠁⠀⠀⠈⠑⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠹⣯⡳⣄⠀⠀⠈⠳⠤⣤⡴⣟⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠂⠀⠀⢰⣀⣠⣫⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⢠⡴⠋⠀⢄⠀⠘⢷⡜⣆⠀⠀⢀⣀⣙⣄⠈⠻⢧⡐⠀⠀⠂⠐⠀⢽⡂ ⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠒⠲⢾⣷⣄⠈⠻⣼⡉⠁⠀⠀⠀⠈⠉⠑⣄⢹⡐⠂⢒⠈⠠⣟⠂ ⠀⠀⠠⠄⠂⠔⠁⠀⠀⢼⣿⠟⠀⠀⣀⠀⢀⠀⠄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⢶⣦⣄⡀⢨⠿⢷⡀⣧⣇⡀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡷⡄⠐⠀⡖⠀ ⠀⠀⢇⠀⠰⠇⠀⢀⣡⡾⠉⠀⠀⠀⠐⠌⠄⠊⠄⠂⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⠋⠛⢾⢿⣷⣦⣨⢿⠟⠉⣽⠦⡄⠀⠀⢀⠀⠾⢴⡂⢷⣀⠉⠉⠀⠀ ⠀⠀⠈⠢⡀⢀⡴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠮⠭⢿⡇⠀⣠⣾⠋⣠⣿⠟⠭⠯⣍⠉⡓⠿⣸⣧⠀⠀⠀⠐ ⢀⣠⣤⣶⡟⢻⠀⡀⡿⠀⠂⠈⠐⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⡟⢁⣴⡿⠓⠶⣦⣄⣀⠀⠈⠽⣼⣿⡇⠀⠐⠀ ⣏⢿⣿⣫⢖⢜⠂⠈⡟⠀⠀⠀⠠⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡟⢿⣶⡀⠉⠻⣿⣷⣤⣀⡿⣿⡇⠀⠀⠀ ⠉⠛⠛⠛⠃⢸⠀⠈⡟⠀⠀⣀⠴⠛⠒⠞⠲⢶⡧⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⢿⣿⣦⡀⠈⢻⣙⣿⡇⢾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⠀⠀⠀⢀⣷⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣿⣟⣿⢄⣴⡛⢨⡇⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠂⢳⡀⠀⠀⠀⠀⣀⣀⣤⣴⠤⢷⠤⢤⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⢮⣹⠿⢻⣿⠁⢰⣾⠿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⢹⠤⠤⠴⠋⠉⠉⠃⠀⠀⠈⢣⠀⠀⣠⠤⠼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⢦⡄⠀⠀⠀⠠⠤⢤⣼⣧⣀⣞⣧⣶⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⢢⠠⠐⠚⠒⠀⠀⠀⢀⣀⣷⡾⠓⠀⠀⠀⠀⠀⠀⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣠⣿⠈⣼⢹⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠰⠞⠋⠉⠀⢀⣨⣦⡀⠀⠀⢀⡠⠺⠚⣠⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⠟⠁⠀⠀⠀⠐⢶⣿⣷⣶⢉⣉⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢈⣀⣈⣷⠚⣭⣿⣖⣛⣉⡧⠟⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⢀⠔⢿⡟⡯⣿⣿⡿⠋⠀⠀⠀⠤⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣟⣉⣥⠾⠚⠋⠉⠉⢉⠏⠀⠀⠐⠦⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣽⢻⣧⣄⢻⣷⣽⣿⡇⠀⠀⠀⣠⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠁⠢⡄⠀⠀⠀⡎⠀⠀⠀⠀⢠⣞⢈⣒⠶⠚⠋⠓⠳⣴⡻⣄⣲⠞⣫⠥⠙⣆⠉⠈⠻⢿⡄⢻⠚⡆⠀⢘⠯⡏⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣄⠀⠈⠀⠀⠀⠈⢧⠀⢀⠁⠀⠀⠀⣰⡏⠀⠁⠀⠀⠀⠀⠀⠀⣹⡷⠹⣧⣶⣤⣤⣶⣿⠀⠀⠀⠈⣗⣼⡃⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣸⡅⠀⠀⠀⣀⡀⠈⣆⣀⣀⣠⣿⣄⡿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡚⣯⣭⣿⣖⣻⡶⠶⠖⠫⠕⢻⡁⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣠⡶⣄⣀⡀⠀⠀⠀⠀⠱⣇⠀⠀⠀⠻⣿⠞⢹⡾⠀⠉⠻⡍⢳⡀⠀⠀⠀⠀⣀⣠⣾⣿⢹⣮⢳⣿⣆⠙⢷⡶⢶⣶⣶⣶⣶⣶⣿⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⡤⣅⠀⠀⠀⠀⡸⠘⢦⡀⠀⢰⠇⠀⠓⠉⠉⠀⢀⣷⣴⡿⣶⣶⡖⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣗⣆⡙⣦⣄⠀⠀⠀⢠⣿⣶⡿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⢻⠿⣛⠀⠀⠀⠀⣷⠀⠀⠉⠒⢦⡦⡶⢶⡶⣶⣿⣻⣿⡿⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣾⣿⢿⣷⢁⡼⠃⣠⣴⠋⢘⣷⣷⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⡬⡷⠚⠉⠓⠒⠤⠼⡀⠀⣠⣔⣋⡷⠚⠉⠀⠀⢉⠏⠀⡝⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⢟⡿⠿⢐⠾⢹⡘⢙⣾⠟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠠⣤⣄⢀⠀⡟⠣⠤⠤⠤⣀⠀⠀⢣⣀⡟⠀⠀⠧⢀⠼⠧⣄⢿⠀⢸⣧⢿⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⡤⢿⠃⠀⡜⠀⠀⣿⢣⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⢿⡀⠱⣽⠀⠀⠀⠀⠀⠫⣍⠓⢼⣇⠀⠂⠀⢿⠀⠀⠈⠉⠓⣿⣧⣟⣩⣷⣀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠁⠀⠈⢠⣀⡁⢲⠀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⣿⣭⡇⠀⣴⣶⡆⠀⠈⠙⠲⠾⣷⣤⣤⣾⣆⠁⠀⣴⠞⠙⠙⠋⢝⣺⣽⣷⣤⣀⣀⣠⠴⠋⢁⠜⠀⠀⠀⠀⠀⢨⣾⣷⠟⠿⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣸⣿⣿⡄⠐⢸⣿⠷⢆⠀⠀⠀⠀⣠⣬⣏⡉⠉⠉⢙⡏⣰⣶⣦⣤⣤⣈⢓⣿⡿⠟⣿⣷⣄⣀⠤⠤⡤⠤⣄⣀⣤⣫⠟⡿⠽⣦⡛⠢⡄⠀⠀⢠⠀⠀ ⠀⠂⠁⠀⠀⢠⡞⡭⠂⢀⡏⣤⠷⠶⠮⠭⠄⣈⣉⣣⡀⣠⠾⣇⠀⢀⣹⠆⠀⢸⡇⣤⣤⣤⣬⣭⣉⣻⣿⣟⡀⠸⣿⣾⣅⣈⡉⠁⠙⠐⠯⣇⠈⣤⠌⠀⢸⡍⢢⣄⡲⡇⢸⡇⠀ ⠀⠀⠀⠀⢠⡟⡼⠁⠀⢸⠟⠁⠀⠀⠀⣤⣄⠈⠙⢿⣍⢁⠼⢯⡿⡉⠀⠀⣠⡾⠿⣍⣉⣹⣛⣛⣿⣿⣿⣿⣿⣿⣿⣟⣉⣙⠛⠛⠷⢶⣤⠏⠀⠀⠀⠀⠈⠙⣿⣿⣿⠃⣾⡁⠀ ⠀⠀⠀⠀⢸⡜⣇⣀⡴⡟⠀⠀⠀⠀⢀⠀⠙⢗⢦⡈⢻⣿⣿⣿⣽⣻⡷⠿⠛⣀⡴⠋⣠⠿⢋⣠⣴⡿⠛⣿⣿⣏⡉⠻⣝⢻⣿⣷⣦⣄⡼⠷⣦⢤⣀⣤⣰⣼⣿⡿⣃⣼⡿⡀⠀ ⠀⠀⠀⢀⢠⣿⣦⣤⣆⠱⡀⠀⠀⠀⠑⠛⠦⢀⣠⣵⣿⡿⣿⠯⢿⣭⡀⠀⠀⡭⠖⣋⣥⢾⠿⠋⠁⠀⡀⡙⢯⡹⢿⣷⣬⡛⠺⣌⣿⠟⠓⠤⢬⣍⣉⣙⣛⠿⢋⣴⣿⠟⠦⠁⢀ ⠀⠀⠀⠘⠃⢆⡫⣭⢻⢦⡙⣦⠰⠶⠶⢲⢿⣟⡽⠓⣩⡿⢿⠿⣶⣦⣄⣀⣀⣴⣿⠟⣋⡌⠐⣄⢊⡒⠰⢌⢧⢛⣮⣫⢝⠿⣷⣦⣍⣉⣛⠒⠚⠓⠲⠋⠁⢰⣿⢫⢁⡊⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⣤⣚⣥⠻⣷⣌⣛⣒⣛⣉⣭⢴⣶⡿⣟⢇⣎⢣⣃⢿⠉⢹⡿⢫⢕⡪⡔⣇⣀⣇⡆⢧⡙⡬⣶⠟⠛⠳⣏⡗⠚⣽⣙⠯⠻⢻⠿⣿⣦⣀⣠⣾⡟⢦⡑⢦⡄⡀⢤ ⢀⡠⣔⡲⢦⡝⣶⡱⣎⢷⣣⢟⡻⣿⣄⣉⣠⣼⢻⡜⣞⢮⣜⡳⠊⠻⣿⢯⣙⢯⡈⠉⣟⢶⡱⣞⡼⣣⢟⣴⢻⡀⠀⢀⣿⡹⣞⡧⣏⡳⣞⣽⢺⣥⢻⣽⢻⣝⡺⣇⢯⣳⣚⢤⡸ ⣯⢟⣵⣻⢳⣻⢖⡿⡼⣧⣛⡾⣳⢽⣺⡽⣳⢏⣷⣛⣮⢟⣼⣳⢦⣴⣛⣮⢟⡾⣽⣫⢟⣧⣟⢮⣗⣻⢮⣟⢿⣻⣟⢿⡻⣟⣻⢟⣻⣽⢻⡟⣿⡻⣯⢟⡿⣹⠿⣽⣫⣗⡯⢷⣻

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⢿⣷⣤⡀⣠⣾⡿⠟⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣄⣿⣇⠀⠀⣾⣿⣿⣷⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣆⠀⠀⠀⠈⠿⠿⢿⣿⡿⣿⣆⡀⠘⠻⠿⠋⢀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⠻⢷⣦⣤⣤⣴⣾⠿⠋⠀⠈⠙⠿⠷⠶⠶⠿⠟⠋⠉⢿⣷⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠈⣁⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠐⣾⣿⡇⠀⣠⣾⣿⡿⢿⣿⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠈⢀⣿⡟⠁⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⣼⢿⣿⣧⣾⣿⡿⠋⠀⢸⣿⡀⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣴⣿⠇⠀⣠⡾⢃⣾⣿⣿⠟⠁⠀⠀⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⠻⣿⣦⣤⣀⣀⠀⠙⠻⠿⢷⣶⣿⣿⣛⣡⣤⣿⣵⣾⣿⣿⠟⠁⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⠉⠙⢿⣿⣀⡀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣧⣀⣠⣾⣿⣿⣿⣷⡄⠀⢸⣿⣷⣾⣿⣶⡀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇ lovely♥ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠈⠉⢀⣿⣿⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠻⠿⠿⠿⠋⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠁⠀⠀⠻⢿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠉⠉⠻⣮⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣾⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⣀⡀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⣸⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠙⠛⠛⠛⠳⢷⣾⡟⠉⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⣤⡿⠟⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣶⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⣼⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠹⠆⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠀⣿⠀⠀⠀⣴⠛⢳⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀ ⠀⣸⡿⠁⠀⣟⠀⠀⠀⠃⠀⠀⠀⠀⢰⣇⣤⠖⠲⠶⠛⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀ ⣰⣿⠃⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⡶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣧⠀⠀⠀⠀⠀⠀⠀⣽⡿⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣧⣀⣀⣀⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣟⣯⢷⣿⣳⢯⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⣻⢾⠇⣷⡿⣯⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠳⢿⣦⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠀⣿⡽⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠻⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡽⣽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⢻⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣧⢇⣀⣀⣤⣤⣤⣤⣤⣀⡄⢀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣿⣶⠿⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⣶⣶⣶⣿⠟⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⣠⣶⡿⠛⠉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⠄⠀⠀⠀⠀⠀⠀⣼⣷ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠁ ⠀⣰⣿⠋⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣠⣴⣿⠟⠁⠀ ⢰⣿⠃⠀⠀⢰⡏⠀⠀⠠⡏⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣹⡄⠀⠀⢹⣿⠋⠁⠀⠀⠀ ⣿⡏⠀⠀⠀⢿⡁⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⢘⣿⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠘⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠛⠁⠀⠀⠀⠀⠀ ⠙⣿⣆⠀⠀⠀⠀⠀⢀⣿⡟⠛⠿⠿⠷⠷⠾⠶⠷⠾⠾⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣶⣤⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⢿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⠀⢀⣠⣤⣾⣿⣿⠿⠿⠻⣿⣿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⡿⠀⠀⠀⠀⠉⠉⠙⠿⣿⣿⣆⣀⣀⣠⣤⣤⣤⣤⣤⣶⣿⣿⣿⢻⡟⣿⣿⣿⣶⣾⣿⡿⠟⠋⠉⠁⠀⠀⠀⠈⣿⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⡟⠛⠛⠛⢛⣿⣿⣿⡱⣏⢷⢺⡭⣏⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢽⣿⣿⡆⠀⠀ ⠀⠀⠀⢨⣿⣯⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡦⠒⠶⠀⣼⣿⠿⣭⢳⡝⣮⣳⡽⣛⡞⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢂⣿⣿⡇⠀⠀ ⠀⠀⠀⢸⣿⡷⢨⠇⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠀⠀⠀⢘⣿⣯⢻⣜⣳⣿⣿⡿⣿⣷⣿⣿⢿⣿⣿⣦⣀⠀⠀⣀⣀⣀⣀⣜⣠⣿⣿⣇⠀⠀ ⠀⠀⠀⢸⣿⣷⠈⡄⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⡝⣮⣝⣻⣿⣯⣳⣿⡿⢯⡝⣮⠽⣹⢿⣿⣆⣰⣿⣿⢿⣿⢿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⡇⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢲⢧⣳⣛⣿⣿⣿⣏⢷⡹⣎⡟⣵⣯⣿⣿⣿⣷⣎⠷⣎⢯⣛⣿⣿⡇⠀⠀ ⠀⠀⠀⣼⣿⡿⠋⣱⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣾⣵⣮⢿⣽⣿⣿⣮⣳⣝⣾⣿⣿⣿⢿⣹⣿⣿⡹⣎⠷⣭⣿⣿⡇⠀⠀ ⠀⠀⢸⣿⡿⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⠀⠀⠀⠀⠈⠛⠻⠿⠾⠿⠛⠉⠈⠻⠿⠿⠿⢿⣿⣿⣷⣿⣿⢷⡹⣎⡟⣶⣿⣿⣇⠀⠀ ⠀⠀⢸⣿⠁⠼⠏⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⡶⣹⢎⡷⣹⣞⣿⡿⣿⣿⠀⠀ ⠀⢀⣿⣿⠀⠂⡀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣥⣿⣼⣷⡿⠏⢥⣻⣿⠀⠀ ⠀⢈⣿⣿⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠏⠋⠁⠀⠀⣼⣿⣿⠀⠀ ⠀⢈⣾⣿⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠈⣿⣿⡀⠀ ⣀⣺⣿⣿⣤⣤⣤⣤⣿⡆⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⣿⣦⣤⣤⣤⣴⣿⣿⣿⣦ ⠙⠿⣿⣿⡃⠀⠀⠙⠁⠀⠀⠀⠀⢸⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏ ⠀⢠⣿⣿⣷⣷⣿⣿⡦⠀⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠠⣿⣿⣶⣼⣿⣿⣿⣿⠅ ⠀⣴⣾⣿⣿⡟⠀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠹⠿⣿⣿⠟⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⡀⠀⢸⣿⣿⣿⣿⡿⠀ ⠀⠈⠛⠉⣿⣿⣶⡿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⣷⣄⠀⠀⠀⠀⠻⠄⠀⣠⣴⡿⠿⠿⣷⣤⣄⠀⠀⠀⠀⠈⠉⠛⠿⣷⣿⣿⣿⣿⠛⠁⠀ ⠀⠀⠀⠀⠌⠻⠟⢿⣦⡀⠀⠀⠀⠀⠀⣰⣿⠋⠁⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠈⠉⠿⣧⡀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣀⣀⣶⡿⠁⠀⠀⠀⠀⠀⢀⣽⣿⣇⣄⣀⣠⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣄⣤⣶⣿⡿⠛⠁⠈⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡃⠀⠀⠀⠀⠀⣶⣾⣿⣿⣭⣬⣭⣭⣭⣭⣿⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⡅⠀⠀⠀⠀⢀⣿⣿⢁⠉⠉⠉⠉⠉⠉⠹⣭⣿⣿⠆⠀⠀⠀⠀⠀⣻⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡱⠠⠤⠠⣤⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣤⠀⡄⢠⢲⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢠⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣾⣿⠏⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠾⣿⡃⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⣏⣿⣇⣲⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⣀⡘⠋⠁⠀⠀⠀⠀⠀⢼⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣿⡿⡉⠄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠃⠀⠀⠀⠰⡡⣿⡗⢡⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⣀⣄⣀⣀⣴⣷⣿⣿⣶⣆⣀⣀⣀⣀⣀⣀⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣄⣀⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣴⣶⠿⠛⠋⠁⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠈⠙⠻⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⣀⠀⠀⠀ ⢠⣿⠏⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣰⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠉⠁⠀⠀⣀⠀⠸⣶⠖⠀⠀⠀⠀⠘⠿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆ ⣿⡆⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡾⠿⣦⣤⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠹⣿⣦⣀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣴⣿⠃ ⠀⠈⠙⠛⠛⣛⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡟⠛⠛⠋⠀⠀ ⠀⢀⣴⣾⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀ ⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⣿⡄⠀ ⠀⢻⣷⣤⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣤⣀⣠⣿⠇⠀ ⠀⠀⠈⠉⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⣰⣿⠿⠿⠶⢶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⡶⠾⠿⠿⣿⣄⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠷⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀

⣿⣻⣟⣿⣻⣟⣿⣻⢟⣿⣻⣟⣿⣻⣟⣿⢻⣟⡿⣽⣻⣟⡿⠛⠉⡀⡤⢴⡰⣒⢖⡲⣚⠴⡳⣜⢲⡒⢦⠤⣤⣀⠄⠉⢉⠛⠿⢿⣻⡿⣿⢿⡀⠈⢧⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⡥⠀⢹⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿ ⣷⣻⣞⣷⣻⣞⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⣻⢾⡽⣷⣻⠞⠁⣠⠖⡽⣘⢧⠳⣍⢮⡱⣍⢞⡱⢎⢧⡙⣎⠳⢦⡙⣎⡛⢦⢤⣂⡀⠉⡙⠿⣻⣧⠐⠨⡳⡜⣥⢛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⠶⠈⢘⣿⣟⣯⣿⣻⣽⣟⣯⣿⣻⣽⣟⣯⣿⣻⣽ ⣿⣳⣟⣾⣳⢯⣟⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣟⣿⣳⠏⠀⡴⢣⡛⡴⣋⢎⡳⡜⢦⠳⡜⢮⡱⣋⠶⡹⣌⡛⢦⡛⡴⢭⡓⣎⠶⣩⠳⣤⡀⠄⠙⢣⠀⠱⣙⢦⣋⠶⣩⢞⡱⢎⡵⢣⡝⢮⡱⢎⡵⢣⡝⢮⡱⢎⡵⢣⡝⢮⡑⢎⡐⠀⣿⣾⢯⣷⢿⣽⠠⢸⣷⢿⣽⡾⣯⣷⢿⣽ ⣷⣻⣞⣧⠟⠛⠾⢳⣟⣾⣳⣟⣾⣳⢯⣿⣳⣯⣿⡍⠠⢸⡱⢣⡝⡲⣍⢮⡱⣙⢎⡳⣙⢦⠳⣍⢞⡱⢎⡝⣲⠹⣜⢣⡝⣬⠳⣥⢛⡴⣩⢓⡦⣀⠌⠀⠌⠶⣩⢞⡱⢎⡵⢫⡜⣣⠞⣥⢛⡼⣘⢧⡚⣥⢛⡼⣘⢧⡚⢥⠚⡬⠐⠈⣿⣽⠏⠛⢋⠗⡠⢹⣾⢿⣳⠿⣯⣟⣯⣿ ⣯⢷⡛⠀⣀⢦⣄⠠⠘⣷⣻⣞⡷⣯⣟⣷⢿⣳⣯⠇⠀⡧⣝⢣⢞⡱⢎⠶⡹⡜⢮⡱⣍⢎⡳⡜⢮⡱⢫⡜⣥⢛⡬⢳⡜⢦⡛⡴⣋⠶⣡⢏⠶⣩⠖⣥⠂⡀⠳⢎⡵⢫⡜⣣⠞⣥⢛⡴⣋⠶⣩⢖⡹⢆⡏⠶⣉⠦⣙⢢⡙⠴⠁⡘⣿⣽⣶⣿⣤⠆⢡⣂⠌⡙⢃⣐⣾⢿⣽⣾ ⣯⣟⡁⠄⢏⠶⣌⠃⠠⠈⢁⠉⠉⠁⡉⠘⠛⠋⠿⠇⢀⠳⣎⠳⣎⠵⣋⢞⡱⣙⢦⠳⣬⢣⢳⡙⡦⣝⢣⠞⡴⢫⡜⣣⠞⣥⢛⡴⣍⢞⡱⢎⡳⢥⡛⡴⣋⢦⡀⠌⠚⡵⢪⡕⣫⠖⣭⠲⡍⠞⡱⠎⠑⠣⠘⠱⢈⠒⠡⠢⠙⠌⡐⠸⢿⣽⣾⣳⣿⣈⣴⡿⡿⠐⣂⠌⡙⠿⢓⠻ ⣷⣫⢷⣤⣀⣂⡀⠌⠠⢁⠂⠌⠠⠁⠄⡁⠂⠌⠠⠐⠠⠘⣬⠳⣬⠳⣍⢮⡱⣍⢎⡳⢬⢣⢧⡙⢶⡩⢎⡽⣘⢧⡚⣥⢛⡴⣋⠶⣩⢎⡵⢫⡜⣣⢝⡲⡍⢦⡉⢦⠐⠈⠳⠘⠁⡉⢀⡐⣀⣂⠤⡤⢥⠦⡥⢦⠤⢦⠥⣆⢥⡰⣀⣂⠄⡀⠉⡙⠾⣟⣯⡿⣷⣳⣾⠿⡐⠌⡂⢾ ⡷⢯⣻⢞⡽⡽⣇⠈⡐⠠⠈⠄⣁⠊⡐⠠⠁⡌⠄⡁⢂⠁⡀⠻⣔⢫⡜⢦⠳⣬⢣⡝⣎⠳⣎⡝⢦⡝⣎⠶⣩⢖⡹⢆⡏⢶⡩⢞⡱⢎⣜⢣⢞⡱⢎⡱⡘⠆⠉⠄⡁⣌⠴⣘⠶⣩⢧⡹⡜⣬⢳⡙⣎⢳⡙⢮⡙⣎⠳⡜⢦⢳⡱⢎⡽⣱⠲⣤⣀⠀⡉⠻⢿⣽⡾⣷⣴⣷⣌⣼ ⣟⣯⡽⣏⡿⣝⡧⠀⠄⠡⠘⠠⢀⠂⠄⡁⠆⡐⢀⠒⡀⠂⠄⡁⠘⢧⡚⣥⢛⡴⢣⠞⣬⠳⡜⣜⢣⠞⣬⢳⡱⢎⡵⢫⡜⣣⠝⣮⢱⢫⡜⡣⢎⠑⠊⡀⣐⣠⢓⠮⡕⣎⠳⣍⢞⡱⢎⡵⣙⢦⢣⡝⣬⢣⡝⣲⠹⣌⠻⣜⢣⢧⡙⣎⠶⣡⡛⡴⣩⢓⠦⣄⠂⠙⢿⣯⣷⢿⣽⣻ ⡿⣼⣳⢯⡽⡾⣽⠀⠌⠠⠑⠠⠁⠌⡐⢀⢂⠐⠄⠂⠄⡑⠠⡀⠡⠀⠙⠦⣫⢜⣣⢛⡴⢫⡜⣎⢧⡛⡴⢣⡝⢮⡜⣣⠚⠁⡈⢀⠉⠢⠑⢁⠠⣈⡴⢪⡕⢮⡙⢮⡱⢎⡽⣘⢮⡱⣋⠶⣩⢎⡳⡜⢦⠳⡜⣥⢛⡬⣓⢎⡳⢎⡵⣊⠷⣡⢛⡴⢣⢏⡞⣬⠳⣄⠂⠙⢾⣟⣯⣿ ⣿⣱⣟⡾⣽⢽⣳⠄⡈⠄⡑⠈⠤⢁⠐⠂⠄⡨⢀⠉⡐⠠⠁⠄⡡⢈⠐⠠⢀⠙⠦⢫⡜⣣⠞⡜⢦⡹⣜⢣⢞⡱⢎⠁⢠⢒⠩⡌⢆⡁⠌⢰⣋⠶⣩⠳⣜⢣⡝⣲⡙⣎⠶⣩⢖⡱⣍⢞⡱⢎⡵⣙⢎⣳⣽⣦⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⣮⣜⢦⡛⣬⠳⣄⠂⠹⣿⢾ ⣷⣻⢾⡽⣏⡾⣽⠆⢀⠂⠄⡁⠢⢀⠊⡐⢈⠐⠠⠈⠄⠡⡈⢐⠀⡂⠌⡐⢀⠂⠄⠂⢉⠐⠛⠜⢣⠳⠬⣓⢮⠱⡃⠈⠴⡉⢂⠁⣊⠰⢀⠂⡝⢮⡱⢫⡜⣣⠞⣥⢛⡬⢳⡱⢎⡵⣊⣮⣵⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⢈⣿⣿⣷⣯⣖⡹⣌⢧⡀⠘⣿ ⡿⣽⢯⣿⣹⡽⣞⣇⠠⠐⠈⠄⡁⢂⡐⠄⡈⠤⢁⠡⠈⠔⠠⢁⠂⡐⠐⡀⠆⡈⠄⡁⠂⠌⠠⠈⢄⡐⣠⢀⠈⠡⢀⠁⢂⠐⡠⠒⡠⢘⠠⢀⢸⢣⡝⣣⠞⣥⢛⡴⢫⡜⣣⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⣈⣴⣿⣿⣿⣿⣿⣿⣷⡜⣦⢳⠀⡘ ⣿⣹⢻⡶⣻⣼⢳⣏⠀⠄⡁⠂⠐⠠⠐⣀⠂⠔⡀⢂⠡⢈⡐⠀⠆⡈⡐⠀⠆⡐⠐⡈⠐⡈⠄⣩⠒⢬⡐⢎⠀⠡⠌⡘⠠⠐⡀⠑⡀⠃⡀⢢⢏⠶⣙⢦⡛⡴⢫⣜⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣬⣶⣿⣿⣿⣿⣿⡿⢟⡛⡛⢿⣶⡍⢧⠀ ⡷⣭⢷⡻⣵⣫⢟⣮⢇⠀⡐⠈⠠⠁⢂⠀⠌⠐⡀⢂⠐⠠⢀⠁⢂⠐⠠⠁⠂⠄⢁⠠⠁⠠⠀⢥⠚⡰⢈⠠⢈⡐⠈⠄⣁⢢⡑⠦⣤⠱⣜⢣⢎⡳⣍⠶⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠄⠛⠋⠛⠙⠋⠛⠙⢋⢖⣷⣾⣿⢆⢺⣿⡸⠀ ⢿⡜⣧⢟⣧⢟⣯⢞⣯⢆⠀⠌⠐⡀⠂⢈⠀⠂⠄⠠⠈⠄⠂⢈⠠⠀⠡⢀⠁⠂⠄⠂⠌⠠⠁⠂⡝⠰⡁⢢⠡⠄⠃⡐⡌⢦⣙⠳⣌⠗⣎⢧⣋⠶⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣥⣬⣴⣤⣥⣦⣴⣤⣥⣮⣘⠫⣍⣱⣮⣿⣿⣇⠃ ⣟⡼⣫⣞⢮⡟⣮⠿⣼⢯⡷⣬⣀⠄⠁⢂⠈⡐⠈⡀⠂⠄⡁⠂⠠⢁⠂⠄⡈⠔⡈⢐⠈⠄⡁⢂⠈⢡⠐⡁⠆⣉⠐⢠⡙⢦⣍⠳⣎⠽⣘⢦⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠺⣵⢳⡝⣮⣽⣳⢿⡽⣯⣟⢷⣫⢟⡷⣶⣲⣤⡥⠄⡁⢂⣠⡅⢉⠻⣦⡔⢀⠂⡐⠂⠌⡐⢀⠂⠌⡀⠌⢀⠃⠠⢐⢢⡙⠶⣌⠗⣎⠳⣍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠒⢋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠌⢻⡼⣳⢯⣟⣯⣟⡷⣯⣻⢼⣛⡾⣵⠳⠉⢀⣰⡴⣯⢷⡀⢂⢐⣯⣞⡆⠐⠠⢁⠂⡐⢈⠐⣴⣴⣬⣀⡂⠁⣎⠶⣩⡓⢮⡹⣌⢻⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⢈⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀ ⠐⡀⠂⠹⢧⡻⣜⣳⢯⡟⣧⢯⣛⡮⠗⠁⢠⡼⣞⣧⢟⣞⡧⣟⣞⡻⡶⡽⣆⠡⠈⠄⢂⠁⢂⣼⣿⣿⣿⣿⡇⠀⣏⠞⣥⢛⢦⡓⣎⣿⣿⠿⠛⠋⠉⢁⠀⠠⢀⡐⠈⡐⣸⣿⣿⣿⣿⣿⣿⡿⠟⠉⢀⠄⡊⠔⣁⢊⠘⠠⠁⢉⠈⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡧⠀ ⠐⠠⢁⠂⠩⣗⢯⡞⣧⠿⣭⢷⠋⠁⠄⢼⡏⢁⠡⠀⠌⡾⣝⡾⣭⢷⡻⣕⠫⠿⢀⠘⠠⠈⣴⣿⣿⣿⣿⣿⡇⠀⣏⠞⡴⣋⠶⡹⣼⣿⡀⢠⣐⣨⣴⣶⣾⣿⠟⠀⣐⣴⣿⣿⣿⣿⣿⣿⡟⠁⢠⠊⠔⣨⢐⡡⢂⠂⠌⣴⣿⣿⣿⣿⣿⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣟⣾⠁⡀ ⠐⠠⢈⠐⡀⠹⣎⢷⡹⢶⡹⠎⠐⠠⠐⡈⢷⣬⣀⣢⢴⡳⣏⡷⡽⢮⢗⣻⠦⠀⠌⡐⢀⠂⣿⣿⣿⣿⣿⣿⡇⠠⣙⠶⣡⠻⣔⡣⣿⣿⣷⣾⣿⣿⣿⣿⡿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⡈⠐⠠⠉⢈⠃⠎⠠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⠹⣿⣿⣿⣿⣿⢿⣽⠏⠀⣡ ⢈⠐⠠⠂⠄⡁⢹⣎⡟⡧⠁⡐⠈⠄⠡⠐⠠⠙⠽⢣⡿⡹⠝⠚⠽⣳⠆⡈⠐⡈⠐⡀⠆⣼⣿⣿⣿⣿⣿⣿⡇⢀⠹⣎⠵⣋⠶⡱⣿⣿⣿⣿⡿⠿⢿⠟⠀⢄⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠠⣤⣷⣿⣷⣦⡌⠠⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⢯⣿⠏⠀⣰⣿ ⠠⠈⢄⠁⡂⠐⡈⢾⠉⢀⠐⠠⢁⠊⠄⡑⢂⠁⠂⠄⡐⠠⢈⠐⠄⣀⠂⠄⢡⠀⢃⠐⣠⣿⣿⣿⣿⣿⣿⣿⠁⡀⠂⡝⢮⡱⢫⡕⣿⣿⡟⣡⣼⣷⣌⠦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣆⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⣯⡿⠁⢠⣼⡿⣽ ⠠⢁⠂⡐⢈⠐⠠⢈⠐⠠⠈⠔⠠⢈⠐⡀⠂⠌⡁⠂⠄⡁⠂⠌⡐⢠⣈⣴⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⡁⠈⢧⡙⢧⡚⡼⣿⡇⠼⣿⡿⢟⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠉⡀⠤⣿⣯⢿⣻ ⠐⡀⢂⠁⠂⠌⡐⠠⠈⠄⠃⠌⡐⠠⠁⠤⠑⡀⢂⣉⣰⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣷⡈⠀⢏⢧⡙⣖⢻⣿⣧⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠰⢤⡐⠈⠙⢿⣿ ⠐⡀⢂⠡⠌⡐⢀⠂⠡⠈⠔⠂⠄⠡⣈⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣄⠈⠒⡹⢌⠧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⢦⡘⡱⣈⠀⡙ ⠐⡀⠢⠐⠠⠐⠠⢈⠐⠡⢈⠐⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠊⣠⣿⣿⣿⣿⣿⣿⣿⣷⣀⠄⠉⢎⡱⡘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⠠⠀⠧⡱⢌⡳⡄ ⠐⠠⠁⠌⠠⢁⠂⡐⢈⡐⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡀⠄⠙⠢⢍⠳⢿⡾⣽⣯⢿⣽⣻⣽⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣄⠠⠑⣏⠶⣙ ⠀⠂⡁⠄⠡⢀⠂⡐⠠⠐⡀⣿⣿⣿⠿⠿⠛⠛⠉⠉⡀⠄⢀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣷⡦⢁⠠⠉⠐⡈⠙⠚⠿⠯⠿⠽⠻⠞⠃⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢀⢸⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣻⣧⡀⠌⢳⡍ ⠀⡁⠠⠐⡀⢂⠐⠠⢁⠒⢰⣿⣋⢀⣄⣢⡔⠈⠠⠁⠄⡈⠄⠠⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢐⣾⣿⣿⣿⠿⠋⢁⢀⣂⠴⣈⠖⡤⢡⠆⡤⣀⢄⡐⣠⢠⡁⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢻⡿⣷⡄⠘⠻⣿⣿⣿⣿⣿⣿⣽⡿⣽⣻⣷⠀⠂⢹ ⠀⠄⡁⠐⠠⠀⠌⡐⠠⢈⢸⣿⣿⣿⣿⣧⣠⣬⠀⡁⠂⠄⡈⠄⠡⠐⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⣰⣾⣿⠟⠋⠀⢄⡰⢦⢫⡜⣳⣬⡾⣴⣧⡞⡰⢡⠎⡴⢡⠆⡥⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⠐⢨⣿⢯⣿⣦⣥⣿⢿⣿⣿⣿⣿⣿⣽⣟⣷⢿⡇⠈⡀ ⢶⡲⣖⣻⠀⢁⠂⠤⢁⠂⠸⣿⣿⣿⣿⣿⣿⣿⣷⣤⠁⠂⠄⡈⠐⡈⠐⣸⣿⣿⣿⣿⣇⣀⠉⠉⠉⣀⣀⣤⣶⣿⣿⠟⠁⢠⡌⡞⣥⢛⡬⢳⡜⣭⢣⣓⡶⣴⣢⣑⢣⠚⡔⢣⠚⡴⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⠀⢢⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣇⠠⢀ ⡷⣹⢎⡷⡌⠀⠌⡐⠠⢈⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⣀⡡⣀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠌⡳⣜⡱⢎⡳⣜⣧⡾⡞⢿⡹⡹⢥⣋⠗⣮⠱⣌⢣⡙⠄⡐⠸⣯⣿⣿⣿⣿⣿⣿⣿⣻⡾⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰ ⡽⣣⢟⣼⢣⠈⠐⠠⢁⠂⠌⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠑⢮⡱⣋⠖⣏⢧⠳⠙⢂⠁⠡⠁⡈⠙⢦⢛⡬⢣⠍⢀⣔⢀⣿⣿⣿⣿⣿⣿⣿⣟⣷⢿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠑ ⣽⢣⡟⣼⢫⡆⠁⢂⡐⢈⠐⠠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠫⢭⡉⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠑⠭⠚⡈⠄⣐⣬⣶⣾⣿⣿⣿⣦⠀⠙⡜⠁⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢢ ⡞⣧⢻⡵⣫⢞⡄⠂⡐⠠⢈⠄⠡⠙⣿⣿⣿⣿⣿⣿⠟⡡⢎⡙⢦⡙⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⠷⠆⢀⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠐⢀⣶⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⣼ ⡽⣎⡷⣹⡷⣯⢞⣄⠠⠁⠂⠌⠠⠁⠌⢻⣿⣿⣿⡏⡜⡱⢊⡜⢢⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⣻⠿⠍⢁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⣿⣿⠨⣽⡣⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿ ⣿⣽⣻⣽⣻⢧⡻⣜⣣⡄⠡⠈⠄⠡⠈⠄⡘⠻⣿⣿⣶⣥⣯⣼⡿⠿⠛⠛⠋⠉⠉⢁⠠⢀⠠⠀⠄⠉⢈⠉⠙⠛⠺⠋⢁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢀⣸⣿⡟⣡⣿⢡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣻ ⣞⡳⢟⡾⣽⢣⡟⣼⣓⡞⣦⣁⠐⠠⢁⠠⢀⠐⠀⠙⠻⠛⠉⢁⠠⠐⡈⠐⡈⠄⡁⢂⠐⡀⢂⠡⢈⠐⠠⢈⠐⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡾⠁⣰⣿⡿⠱⣼⡏⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣯⣟ ⢮⠽⣹⠼⣥⢻⣜⡳⣼⢹⡲⢭⣛⠶⣤⣀⡂⠈⠄⠡⠐⠠⢁⠂⠄⠡⠠⢁⠰⠐⡈⠄⢂⠰⢀⠂⠂⠌⢁⠠⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡟⠋⢀⣴⡿⢏⣒⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣺⡽⣾⣹ ⣏⠆⠀⠄⡀⠄⠀⡁⠁⢃⠛⠵⣋⠾⡥⠃⠁⠌⠠⠁⠌⡐⠠⠈⠄⢃⠐⠂⠄⠡⠐⡈⠄⠂⠤⠈⡁⢈⠠⢀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠞⠋⢁⢠⣴⣾⢿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡳⣟⡵⣯

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⣙⢮⢳⢭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠄⡠⠀⡀⠄⡀⢀⠂⡐⢠⣀⣤⣤⣾⣿⣿⣿⣿⣧⠚⣤⡓⢦⡓⡌⢆⠠⠀⠀⠀ ⢯⡞⡽⣎⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣤⣄⣡⣀⣴⣴⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠶⡤⡙⢆⡱⠸⡄⢢⢑⢂⠀ ⣷⣹⢳⡽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣴⣻⣾⣼⣧⡜⣄⠣⠌⠀ ⡷⣭⣳⢳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣉⠀ ⠛⠵⢫⠷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⠀ ⣶⣦⣳⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠬⠀ ⣿⡽⣷⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠀ ⣿⣿⣹⣻⣾⢷⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣧⠿⣿⣿⣟⡿⣼⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠟⠃⠘⠛⠻⢿⣿⣿⣿⠿⠛⠛⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⢰⣻⢾⡿⣏⣿⣳⣯⣟⣿⣻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣶⣀⠀⢀⣠⣴⡾⠿⡟⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀ ⠀⠜⢫⡽⣯⢿⣽⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣯⠀⠀⠀⣨⣿⣿⣿⣿⣻⢥⢯⣹⡱⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀ ⠀⠀⠱⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⣝⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡷⣧⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣻⡄ ⠀⣴⣶⣛⣾⣿⣿⣿⣿⣿⢿⣫⢳⡱⢎⣓⢮⣶⣿⠋⠀⠀⠀⠈⠛⢷⣙⠿⣿⣿⣿⣻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⣷⣤⡈⠛⠛⢣⠹⣵⡇ ⠀⠈⠛⣾⣿⣿⣿⣿⢿⣱⣋⣖⢣⣝⣹⣾⣿⡿⣿⣦⣴⡄⡀⠀⢂⣘⣿⣶⣬⣻⣿⣿⣿⣿⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠈⠻⣷⡄⠀⠂⠩⣽⡇ ⠀⠀⠀⢼⣿⣿⣿⣟⣮⢷⡽⣎⣷⣾⠟⠉⠀⠀⠀⠀⠈⠛⠻⠷⠿⠛⠉⠙⠛⢿⣾⣿⣿⣿⣿⣆⡀⣤⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠈⢿⡄⠀⡁⣿⣇ ⠀⠀⠀⢾⣿⣿⣿⣿⣯⣿⣿⣿⡟⠁⠀⠀⢠⣶⣶⣄⠀⣠⣦⡀⠀⠀⠀⠀⣀⠀⢻⣿⣿⠿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢻⣿⡀⠀⠘⣧⡐⡡⢿⡟ ⠀⠀⠀⠐⣯⣿⣿⣿⣿⣿⡟⣿⣷⠂⠀⠀⢺⣿⣿⣿⣾⣿⣿⣷⠀⠀⠀⣿⣿⣿⣾⣿⣿⣷⣿⣿⣶⣾⣿⣿⣿⣿⣿⣾⣶⣶⣤⣄⣀⡀⢀⣀⣤⣴⣦⣽⣿⡇⠀⠀⣿⢰⡝⣸⣧ ⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡏⠠⣶⠀⢻⣿⣿⣿⣿⣿⡿⢻⣿⠿⠛⠽⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⣎⣿⣧⣿⣯ ⢀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠀⠀⠈⠀⠀⠻⣿⣿⣿⡿⢃⣾⡟⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣿⡟⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣧⣿⠏⠀⠀⠀⢹⣿⣿⣿⡉⢼⣿⣾⣿⣿⣿⣿⢿⡃ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠈⢻⣿⣿⣦⣤⣶⡾⠆⠾⣿⣶⣶⣦⣴⣦⡤⣤⣼⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⢸⣿⡟⠛⠛⠻⠯⢿⠆ ⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠿⢷⣤⣶⣿⠿⠟⠿⢿⣿⣧⣿⡿⠛⠿⠿⠿⣿⣿⣿⣤⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⢿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄⠀⠀⠀⠀⠈⢿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠑⠀⠀⠀⠀⠀⠀ ⠰⡈⠄⡀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⡀⢰⡂ ⢡⡜⢰⢱⢠⠉⢻⣧⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⡄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣽⢻⠁ ⠆⣆⢣⢎⡲⢈⣴⣿⣶⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣝⣞⣻⢿⣾⠇ ⣿⣿⣿⣿⣿⠿⣿⠿⡿⠿⠿⠿⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⡇ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇ ⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣹⢿⡹⢿⡁ ⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣷⣤⣀⣀⣀⣀⣠⣀⣀⣼⡿⠿⡿⢿⣿⣷⣶⣤⣤⣤⣤⣄⡀⣤⠾⠟⠤⠀⠀⠀⠀⠀⠀⠀⠀⠎⢐⠃⠣⠘⠡⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠁⠈⠈⠉⠉⠉⠁⠈⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⢞⣡⣀⢤⡠⢄⠀⠄⠆⠒⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢣⡇⡔⣱⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡶⣯⢻⢻⣿⣯⣲⣶⣮⡷⡷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠂⡼⣩⢡⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢸⢠⣧⣿⡼⠀⠀⠀⠀⡠⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠉⠛⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⣨⣾⣿⣿⣿⣄⣤⣤⡘⠁⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⠎⠙⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⠛⢻⣿⣿⡿⣿⣿⢂⡀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⡫⣿⡿⠿⠿⠿⠟⠛⣿⣤⠀⠀⠀⢼⡢⣀⡵⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠉⢿⣿⠖⠴⣐⣾⣿⣿⣿⣷⠀⢀⠙⢆⠀ ⣿⡿⣿⣿⣿⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠹⣷⣄⣄⠤⢸⣯⠉⠐⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠂⢈⣡⣫⣄⣸⣿⣿⣿⣿⣿⣿⣾⣶⡌⡄ ⢸⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡣⣀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⠳⣦⣽⠿⠖⠛⠛⠛⠛⠿⢿⢿⣿⣿⣿⣿⡿⠇ ⠀⠹⣽⡿⣻⡉⣋⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⢀⣩⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⡟⠁⡀ ⠀⠀⠙⢏⣿⣿⣩⠤⠀⠉⡀⠀⠀⠰⠿⠃⢀⣀⡈⠁⢐⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣷⠀⣴⡆⠀⠀⠀⠀⠀⠀⣶⡶⠀⣋⠷⢠⠃ ⠀⠀⠀⠀⠈⢙⣿⣷⣲⣤⡽⢛⣿⣶⢲⣞⡛⢙⣶⣾⢿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢄⠈⠁⠀⠀⠛⠋⠀⠀⠀⠀⣒⢈⠕⠁⠀ ⠀⠀⠀⢀⡾⣿⡿⣿⣿⣿⣿⣿⣟⢏⢿⣿⣿⡛⣷⣽⡛⢷⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⣻⠯⣹⠒⠂⠀⠀⠀⠀⠙⣗⠺⠁⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣿⣟⣿⠉⢸⣯⢿⣷⣄⣸⡿⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣠⠦⢼⣹⠃⢀⠀⠀⠀⢀⠤⢀⢘⠤⡓⠤⠖⠁ ⠀⠀⠀⠀⠀⠉⣿⡻⣾⣿⣾⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢵⡺⢹⡳⡀⢀⡞⣠⠊⠈⢀⣱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣻⠿⢨⣿⣿⣿⡟⠈⠙⠃⠀⢈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠸⡅⠁⠘⣿⣶⠃⠀⠀⠀⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣗⣧⡼⠞⠀⠀⠙⠛⠲⠾⠗⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠃⠀⠀⠉⠓⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣐⣦⣥⣼⣶⢶⡶⣦⣬⣴⣀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠒⣵⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢰⣭⣅⣦⣵⡾⠟⡫⠍⢦⠱⡐⢆⠲⣁⠎⣩⠙⡛⢷⣦⣕⡀⡀⠀⢠⣪⠭⠭⠵⠚⠀⠀⢻⡡⡀⠀⠀ ⠀⠀⠀⠀⠠⣀⣿⣧⣿⠛⡥⠘⣆⠱⣉⠦⢡⠓⡬⢑⠢⣍⠰⠩⢜⠢⢌⡹⢻⣮⣢⠘⢜⣆⠀⠀⠀⠀⠀⠀⠉⠒⣅⠂ ⠀⠀⠀⢰⢹⣏⣽⡦⢡⢋⠴⣉⠤⢓⡰⢌⠣⢜⡰⢉⠲⢄⡋⡕⢊⡱⢊⠴⡁⠞⣷⣵⣼⣹⠀⠀⠀⠀⠀⢀⡴⡚⠕⠁ ⠀⠀⠀⠀⠱⣽⡟⣐⠣⣌⠲⢌⡒⠥⢒⠬⡑⠦⢌⠣⣑⠪⠔⣌⠣⡔⡩⢢⠍⡜⠤⢿⡟⣇⣤⣤⣶⣄⠀⡾⠘⠀⠀⠀ ⠀⠀⠀⠀⣖⣿⠰⢡⠒⡤⢓⠢⡜⢌⡃⠖⣉⠦⣉⠖⡡⢎⡑⢢⡑⠦⢱⠡⡚⢌⡜⢌⣿⣹⢈⢧⠣⠫⢓⡣⠃⠀⠀⠀ ⠀⠀⠀⢰⢸⡧⣉⠦⡙⢤⢃⠣⠜⢢⢡⢋⡔⠢⣅⠚⡰⢡⢊⠥⡘⡜⢢⠱⢡⠎⡰⢊⢼⣇⡿⡜⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢸⡇⢲⠰⣉⠆⢎⡡⢋⢆⠣⡒⠬⣑⢢⡙⡰⢃⣜⣦⠱⡘⢢⡍⠲⢌⡱⢊⢼⡏⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢺⡏⢆⠓⡤⢋⠆⡥⢋⠤⣣⣅⠓⣤⣿⢷⣵⣼⠞⠷⣧⣼⡿⢿⣅⣎⣴⢃⣾⡻⡏⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣸⡗⣌⠣⢒⡉⢖⡰⣉⢆⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⣶⡍⢛⠛⣿⣿⢿⣕⣢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢻⡷⢨⠜⡡⢚⣤⢚⡟⠋⣱⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣸⣾⠟⢉⡽⢧⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢌⣾⢃⢇⢪⠱⣟⠉⠋⠁⠀⠈⠛⠁⠀⠀⠀⢠⣀⣀⡰⠆⠀⣀⣤⠞⠉⢻⡀⣻⠲⡼⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠔⣥⡟⢣⢊⡔⣊⡑⡛⠷⠶⠶⡶⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⡾⠋⠁⠀⠀⠀⠀⠻⣷⢞⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢾⡗⣨⢑⠢⢜⢠⢒⣩⣜⣥⡷⠟⠋⠁⠀⠀⠀⠀⠙⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⡼⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢬⣻⣷⢊⡱⢊⢦⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⣤⡾⢫⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⢸⣇⢎⡴⡿⠉⢷⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡋⣿⢻⠋⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠝⣿⡿⢯⡔⠘⢷⣀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢟⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⢻⣾⣽⣷⡞⡹⢛⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠚⠋⠿⣶⣭⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢣⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⡀⠀⢀⡴⢏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠈⣸⠷⢾⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⣧⣀⣀⣠⡴⡾⣏⠀⠀⠀⣠⣴⠃⠀⠀⢧⡃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠓⠂⠈⠈⠊⢓⣒⠚⠝⠋⠙⣒⠦⠖⢞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀