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