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