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