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⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼
⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣾⣿
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⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⡁⠀⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣴⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣴⡿⠋⠉⠉⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠟⠛⠛⠻⢿⣿⣶⣄⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⠀⠈⠻⣿⣇⠀⠀
⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀
⠀⠀⣀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣄⠀
⢠⣾⠟⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣀⣀⣤⣤⣶⣶⠿⠋⠁⢹⣿⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢉⣿⠋⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⠀
⢸⣿⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠿⠋⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀
⢸⣿⡄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣸⣿⢶⣤⣤⣴⡶⠿⠛⠙⣿⣆⠀
⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀
⠀⠘⣿⣆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠈⠻⣧⣀⡀⠀⠀⠀⣀⣠⣴⡿⠇⠀
⠀⠀⠘⢿⣿⣦⣤⣴⡿⠻⠿⣷⣦⣤⣤⣤⣴⣾⣿⡿⠿⠿⠿⠟⠛⠉⠀⠀⠀
⠀⠀⠀⠀⠉⢉⣉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⢙⡛⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢰⠁⠀⠀⠉⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠶⠮⠭⠵⢖⠒⠿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠿⡷⣄⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣻⣄⠀⠀⠀⣀⣀⠤⠴⠒⠚⢋⣭⣟⣯⣍⠉⠓⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡝⣧⠔⠋⠁⠀⣀⠤⠔⣶⣿⡿⠿⠿⠿⠍⠉⠒⠢⢤⣀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⣧⠤⠒⠉⠀⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣴⣾⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢿⣿⣧⠙⢦⠀⠀⠀⠀⠀⠀
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠐⢄⠀⠀⠀⢻⡇⠀⠀⠀⠀⡠⢊⣭⣬⣭⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠑⣄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠑⢄⣀⢿⠇⠀⠀⠀⡜⣼⠟⠁⠀⠀⠉⢿⡄⠀⠀⠀⠀⣠⠤⠤⠤⣀⡀⠈⠙⡄⠀⠈⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⢦⡀⠀⣠⡞⠢⢄⠀⡜⣼⠁⣠⣴⣶⢦⡀⠀⢻⠀⠀⢀⣎⡴⠟⠛⠛⠶⣝⢦⠀⠘⡄⠀⠈⢧⠀⠀
⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢻⡾⠋⠀⣀⣀⠁⠁⡇⢰⢿⣄⣿⣎⢷⠀⢸⡇⠀⢸⡝⢀⣤⣄⡀⠀⠙⢷⡀⠀⢱⠀⠀⠈⡇⠀
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠈⠙⣳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣧⠀⢀⣀⣀⡉⠱⣿⣼⣆⢿⠻⣯⡞⠀⢸⡇⠀⢸⣷⣏⢙⣿⡻⡆⠀⠀⢳⠀⠀⠀⠀⠀⢸⡀
⠀⢳⡀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠈⠁⠀⠀⠉⠢⠈⠛⢻⣿⠿⠛⠁⢀⣿⠇⠀⠈⣿⣿⢿⡟⣧⡷⠀⠀⢸⡄⠀⠀⠀⠀⠈⡇
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢧⡀⠀⠀⠀⠢⠤⠔⡽⠁⠚⠉⠉⠉⢗⢷⣄⡠⣀⢻⣆⣀⣠⡿⠋⠀⠀⠀⠈⢿⡷⠿⠟⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠻⡄⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠘⢦⡈⠁⠀⠀⠸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣤⡶⠟⠉⠙⠒⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡇⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠍⠠⠤⠒⠂⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⡿⠓⠲⠄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣄⣀⣠⣤⡤⠶⠛⣿⡀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠉⠙⠒⠲⠤⠤⠤⣤⣤⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⡀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡱⡀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⢹⡉⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣥⣠⣹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠤⢄⣀⣀⣀⣀⣀⣀⣠⠤⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⡀⠀⠀
⠀⣀⣀⣀⣀⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⢰⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀
⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀
⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀
⢸⣿⣿⣿⣿⡇⠀⠀⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀
⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢴⣖⠲⠶⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⣩⣴⠚⢿⣟⣿⣻⣟⡿⣶⣬⣉⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣯⣻⡿⣿⣷⣌⣿⣞⡷⣯⣟⡷⣯⣿⡿⣿⣄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣯⣿⣽⡿⣾⣟⡷⣯⣟⡷⣯⣟⣷⡿⣟⣿⣽⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⣿⣻⣟⡾⣽⣳⢿⣟⣷⢯⣟⡷⣯⡿⣽⣿⣟⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠟⠺⠷⠯⣟⣷⣯⣟⣾⣟⡿⣾⣽⡿⣽⣿⣟⠾⠟⠛⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢩⣴⣾⢿⣶⣶⣤⣑⣛⣿⠯⠿⠷⢯⣿⣛⣥⣴⣶⣶⣶⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠹⢿⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⡈⠙⠷⣦⣩⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⣠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⢶⣤⣤⣭⣟⣻⠿⣿⣿⣿⣿⢿⣟⣯⣵⣶⣿⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣽⣻⣿⠿⠿⠿⠷⠾⠶⠿⠿⠿⢿⣽⣾⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣯⣿⣷⣼⣉⣉⣩⡶⠩⠄⡈⢉⣵⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣿⡿⣽⣧⡳⣕⢲⢒⠒⢆⡠⣲⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠝⠻⢯⣿⣷⣶⣶⣶⣶⣾⣿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⠀⠀⠀⠀⢀⣀⡤⢾⣇⠀⠈⠢⡀⠉⠉⠉⠉⠉⠛⠉⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢺⣀⣤⢖⣺⣭⣶⢾⡿⣿⣷⣤⡀⠈⠂⠄⡀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡇⢒⠁⢷⣾⢿⣽⣳⢯⡿⣽⣳⢯⡿⣿⣶⣦⣤⣠⣅⣠⣴⣶⣿⢿⣻⢿⡽⣯⣟⡿⣿⣿⣲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡾⠿⠾⠽⠾⠤⠥⠬⢿⣟⡾⣽⢯⣟⡷⣯⢿⣽⣳⢯⣟⣿⡻⠏⢿⣯⢷⣯⣟⣯⢿⡽⣷⢯⣟⡷⣯⣟⡿⣶⣦⣭⡙⣳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢟⣾⡏⠀⠀⠀⠀⠀⠀⢀⠈⣿⣻⣽⣻⢾⡽⣯⣟⡾⣽⣻⢾⠟⠁⠀⠈⠙⣿⢾⡽⣞⣿⡽⣯⣟⣾⣻⢷⣯⣟⡷⣯⡟⣱⡿⣷⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣼⠋⠀⠀⠐⠒⠒⠒⠂⠒⠊⢿⣷⢯⣟⣯⣟⡷⣯⣟⣷⠟⠁⠀⠀⠀⠀⠀⠉⣿⣻⡽⣾⡽⣷⢯⣷⣻⣟⡾⣽⣻⡝⢰⣿⣽⣳⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⣿⣇⠀⠀⢀⢀⢀⣀⣀⣐⣈⣸⡿⣯⣟⡾⣽⣻⢷⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣷⣻⡽⣟⣾⣳⢯⣟⣷⡟⢀⣿⡷⣯⣷⣻⢾⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣿⣿⡀⠀⠁⠉⢉⡁⠀⠀⠈⣿⣟⡷⣯⣟⡷⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣻⣟⡾⣽⣯⣟⣾⠁⢸⣯⣟⡷⣯⣟⡿⣞⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⢻⡇⠀⠀⠂⠒⠒⠒⠒⢺⣿⡽⣯⢷⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⣟⣷⣻⢾⠃⠀⣾⣿⣽⣻⢷⣯⣟⣯⣟⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⡟⠈⠧⠤⣤⣤⣤⣤⣤⠤⠞⣿⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣳⢯⡏⠀⡀⣿⣿⡾⣽⣻⢾⡽⣾⡽⣾⣿⣄⠀⠀⠀⠀⠀
⠀⢠⣟⣿⣀⣤⣴⡿⣿⢿⣆⠀⠀⠀⠀⣿⢘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡿⠀⢠⢰⣿⣟⣿⣯⣟⣯⣟⣷⣻⡽⣿⣿⣆⠀⠀⠀⠀
⠀⣼⣿⠹⣿⣽⣳⣟⣿⣟⣿⣷⣄⠀⣼⣿⡾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡅⠀⠎⢸⣿⣟⡾⣷⣟⡾⣽⢾⣽⣻⢷⣻⣞⣷⡀⠀⠀
⢀⣿⣿⡆⣿⣞⣷⣻⡿⣾⣟⣾⣿⢿⣿⣿⡿⣽⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡘⠀⣾⣿⡿⣽⣻⢾⣟⣯⢿⡾⣽⢯⡿⣽⣿⣧⠀⠀
⢸⣿⣿⣿⣿⣽⢾⣿⡽⠟⠊⠉⠀⠸⣷⣿⣟⡷⣯⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣻⣇⢀⡏⢻⣿⣯⣟⣯⢿⣾⢿⡽⣯⡿⣽⢷⣻⣿⡆⠀
⢸⣿⣿⣽⣻⣿⠛⠁⠀⠀⠀⠀⠀⠀⢹⣿⢯⡿⣽⣻⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣻⢾⣟⣿⣼⠀⠀⠻⣿⣽⡾⣯⢿⣯⣟⡷⣟⣯⣿⣳⢿⣿⠀
⠘⢿⣿⣷⣯⡿⣿⣶⣶⣤⣤⣤⣶⣾⣿⣿⣯⣟⡷⣯⣟⡾⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣻⣞⣯⣿⣟⣿⡇⠀⠀⠀⠙⢿⣿⣟⣯⢿⣯⣟⣯⡷⣯⣟⣯⣿⡇
⠀⠈⢻⣿⣷⣻⣽⢯⣟⣿⣻⣿⣿⣿⣿⣟⡾⣽⣻⢷⣯⣟⡷⣯⣿⣆⠀⠀⠀⠀⠀⠀⣠⣿⣟⣷⣻⣞⡷⣯⢷⣿⣻⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣻⣞⡿⣯⣿⣳⣯⢷⣯⣿
⠀⠀⠈⠛⢿⣷⣯⣿⣾⣷⣿⣿⣟⣾⣯⣿⣟⡷⣯⣟⡾⣽⣻⢷⣻⣞⣧⡀⠀⠀⣠⣾⣟⣷⣻⣞⡷⣯⢿⣽⡿⣯⣿⡏⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣽⣿⣽⣯⣷⣯⣿⢾⣽
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⣿⣿⢾⣟⣿⡾⣽⢷⣯⣟⡷⣯⣟⣷⢯⡿⣽⣤⣾⣟⣷⣻⣞⡷⣯⢿⣽⣻⣞⣿⣽⣿⡇⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠁⠀⢁⣉⣿⣿⣟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⢯⣿⣽⢯⣟⣾⣽⣻⢷⣻⣞⡿⣽⢯⣟⡾⣽⣞⡷⣯⢿⣽⣻⢾⣽⡿⣾⣽⣿⡇⠀⠀⢀⣤⣾⣿⣿⣽⣿⢀⣠⣴⣾⡿⣿⡿⣏⢻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⢿⣞⣿⢯⣟⣾⣳⢯⣿⣳⢯⣟⣯⢿⣞⣿⣳⢯⡿⣽⣯⢷⣻⢯⣿⢿⣳⣿⣿⠁⢀⣴⣿⡿⠿⠷⠛⠊⠉⢸⣿⣽⣾⣿⣳⢿⡿⡸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠯⠿⢯⣟⣾⣽⣻⣾⡽⣯⣟⣾⣯⣟⣾⣽⣯⣟⣷⣯⡿⠯⠿⠿⠛⠛⠛⠃⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠛⠚⠛⠫⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀
⠀⠀⢀⡤⠖⠒⠒⢤⡀⠀⠀⢫⢸⡡⡏⡇⠀⠀
⠀⢀⡾⣤⣄⡀⠀⢀⠷⣄⢀⡼⠀⠑⠁⡇⠀⠀
⠀⠸⣷⣾⣿⡇⠀⣿⣾⡟⣼⡧⠖⠒⠒⠓⠒⡆
⠀⠀⠫⣉⠉⠀⠀⣉⣟⣸⠸⡀⠀⣀⣀⠀⠤⡇
⠀⢀⡤⠚⠓⠒⠋⠁⡤⢍⡆⡏⠁⠀⠀⠀⠀⡇
⠠⣏⠔⡆⠀⣀⡀⠀⡇⠀⠣⣽⡉⠁⠀⠉⠉⢹
⠀⠀⠀⡇⡸⠁⠙⢄⠃⠀⠀⠈⠯⠭⠥⠤⠎⠉
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣇⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣯⣢⡈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠤⡄⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣷⡥⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣴⡖⠖⡟⣿⣿⠋⢹⡃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣻⢿⣦⣌⣷⣿⣷⣀⣧⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣹⡿⠾⠿⢿⡿⣿⣿⡿⣿⣦⣦⡄⠀⠀⠀⢂⢠⠈⠙⠛⠛⠒⠓⠒⠶⠒⠤⠦⠤⠤⢤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⡀⠀⠠⠤⠠⠤
⠸⣟⣙⠋⡙⠂⢀⣸⣿⡿⢿⣿⣏⢿⣦⠀⠀⡨⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠛⠋⠉⠉⠛⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢨⣿⣻⣟⠻⠛⢋⣹⣿⡦⠽⠻⠟⠾⠥⠌⠀⠀⠀⣧⡀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣿⣥⣤⣤⡶⠾⣿⣿⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⣹⢷⣦⠁⠓⢂⠲⢤⡄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⡝⢃⣠⣴⡿⢻⠀⠀⠀⢀⣀⠀⣀⣈⣡⣀⣿⣦⣿⣸⣹⣶⢏⣿⡼⣷⢯⣿⣆⣶⣆⣠⡠⣀⣄⠈⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢨⣹
⠀⠀⠀⠈⠛⠿⠿⠯⠷⠾⠾⢶⣶⣿⡿⠿⠟⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣽⣷⣽⣭⣳⣤⢣⠔⡣⢆⡰⢄⡒⣌⠰⢹⣀⠾⠷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⢿⣷⣯⣶⣧⣻⣬⡻⣵⣺⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠷⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⢀⣀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣶⣄⠀⠀
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠟⠿⣿⣿⣿⣷⡀
⢀⣾⣿⣿⣿⠟⠛⠉⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⣾⣿⣿⣿⠿⠋⠁⠀⠀⠙⣿⣿⣿⣇
⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠈⢛⣿⣿⡟⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠋⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡟⠁⠀⠀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⡿⢿⣿⣿⣷⡀⠀⠀
⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⢻⣿⣿⣷⠀⠀
⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀
⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀
⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀
⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠹⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣄⣀⣀⣠⣼⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣤⣤⣤⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇      cho 1 like nào!
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀
⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀
⢸⣿⣿⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀

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Khám Phá –> Biểu Tượng Cảm Xúc FB

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠄⠂⠈⠁⠉⠘⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠡⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠀⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⢀⠀⠀⠄⠀⡤⠮⠦⠄⠨⠀⠄⠨⠀⠄⠁⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠠⠤⢤⣀⣠⠤⠤⠤⠄⠄⠂⠊⠀⠀⠠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡎⠏⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⢹⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡪⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣂⠄⢄⠀⡀⠤⠠⠄⠂⠠⠀⠄⠄⠈⠅⠆⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡥⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡁⠁⠀⠀⠈⠀⠀⠂⠀⠐⠀⠂⠐⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠅⠄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠅⢁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠔⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢐⠀⠀⡅⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠈⡐⠀⠄⠄⢀⢀⠀⠀⠀⠀⠀⢀⢠⣒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⡀⠀⡃⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠂⠀⠄⢀⠀⡈⠠⠀⠁⠀⠀⠀⡑⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢣⠀⢹⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠡⠄⣣⣄⡀⣀⣨⠿⠭⠄⠓⠁⠈⠀⠁⠁⠁⠁⠀⠒⠕⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⢂⠠⠠⠄⢀⢀⠀⣀⡀⡂⠅⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⡿⣿⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣯⣷⡿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⣯⣿⣤⣄⣀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣯⣿⢷⡿⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⢯⣿⢿⣻⣿⣿⣶⣤⣀⣾⣿⣿⢿⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⣽⣿⢿⣿⣟⣿⣾⢿⣿⣿⡿⣟⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀.            ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣗⡻⣿⣿⢯⣿⢿⣾⡿⣟⣾⣿⢿⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣤⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⣿⣿⣏⢷⣹⣿⣿⣿⣻⣯⣿⣿⣻⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣿⣞⣧⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡝⣾⠽⡿⣿⣷⣿⣿⢿⣾⣿⣿⣿⣿⣝⣻⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣯⣯⣹⣻⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣭⡳⣽⢳⢏⣿⠿⣿⣿⣿⣿⣿⡿⣎⡵⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡄⢀⣠⣶⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣯⡝⣿⠙⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡟⢻⣮⡞⣽⢲⣽⠛⣿⣿⣿⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣽⣥⣻⢧⣛⣶⣳⣽⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡿⣿⣿⣻⣽⣿⣾⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⢿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣽⣯⡷⣝⢾⣷⢫⡳⣎⣿⡻⣝⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢹⣷⣛⢮⠿⣝⢧⣛⢾⢷⡹⣎⢿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣸⣿⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣜⣫⢞⡝⣮⢝⡮⡳⣝⡹⣾⣄⣾⣿⣿⣿⣷⣶⣶⣶⣴⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣾⢬⢻⣟⡼⣧⢳⣿⣜⡳⣽⣿⣿⡿⣿⣽⣿⣿⣻⣼⣿⣿⢿⣾⡿⣿⡿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢶⡘⢦⣭⣿⣿⣻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣿⡿⣿⣿⣿⣶⣤⣀⢀⣀⣠⣶⣶⣾⣿⣿⣷⡶⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢻⣟⣼⣿⡜⣿⣣⣿⣜⡳⣽⣿⡿⣟⣿⣽⡿⣿⣳⣽⣿⣯⣿⣯⣿⡿⣿⡵⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢦⡙⣾⣿⣿⠙⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡀⠀⠀⠀⠀
⠀⠀⠀⣴⢿⣲⢻⡝⣟⢧⡿⣎⠷⡿⣿⣿⢿⣯⡿⣿⡷⣿⣼⣿⣯⣷⣿⣷⡿⣷⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⡿⢟⡭⢲⣝⠋⠿⢣⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣷⠀⠀⠀⠀
⠀⠀⠀⢻⣽⣻⣧⢻⡜⣧⡝⣮⣽⢻⣿⣿⡿⣯⣿⣿⣿⢧⣿⣿⣽⣷⣿⣾⢿⡷⣯⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡘⢧⡒⣖⢻⡜⣲⢛⡏⡗⣧⢶⣻⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣽⣿⡆⠀⠀⠀
⠀⠀⠀⠀⣿⢷⣺⣝⣻⢶⣛⢧⢯⣿⣿⣿⣟⣿⣿⣿⢾⢯⣿⣯⣿⣾⢿⣾⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⢸⣿⣿⡿⣿⣾⣵⣪⢱⢫⢝⡺⣱⡙⢦⣧⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡷⣿⣯⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠻⣮⣻⡝⢯⡞⣝⢮⣿⣷⣿⣿⣻⣿⣟⣯⡟⣿⣿⡿⣷⣿⢿⣻⣾⡽⣾⣿⡇⠙⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣷⣶⣿⣿⣿⢿⣿⣶⣷⡶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⣽⣧⢷⣿⣾⣭⣿⣽⣻⢷⣿⣿⣽⣷⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⢿⣧⣿⣬⣷⣿⣿⣿⣽⣿⣿⣻⣷⣻⣿⣿⣟⣿⣾⡿⣿⣿⡽⣿⣿⠃⠀⠈⢻⣿⣿⣿⣿⣷⡄⠀⠀⣰⡖⠶⣶⡄⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠸⣿⣟⣾⢿⣿⣦⡙⠛⣽⣿⣿⣿⠏⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⢯⣶⣿⢋⡥⢚⣼⣿⣿⣿⣿⣿⡏⡻⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣟⣿⣿⣯⣿⡿⣿⣿⢳⣿⣿⣯⣿⣯⣷⣿⣿⣷⣻⣿⡏⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡄⠀⡏⡜⢧⣽⡇⠀⠀⢀⣿⣿⣿⣿⢿⣿⣻⣿⡇⡤⣹⣿⣭⣿⣿⣷⡜⠻⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣽⣿⢯⣿⣿⣿⡇⢎⡔⢣⣿⣿⣿⣿⣿⣿⡇⡱⢌⣿⡿⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢯⣿⣿⣿⣽⣳⣽⣿⣼⣳⢯⣻⡽⢯⡿⡽⣞⣽⣿⡧⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⠃⠀⣯⡙⡖⡼⡇⠀⣠⣿⣿⣿⣿⣻⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣸⡴⠾⠽⣟⡿⠿⢿⠰⡙⣅⠳⢌⢼⣿⣽⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⡽⣶⢿⡽⣼⣿⣽⣫⢷⡻⣏⣷⡿⣻⣾⣵⠇⠀⠀⠀⣴⣿⣿⣿⣿⡿⣁⣤⣼⣧⣽⣘⠵⣳⣼⣿⣿⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣾⣿⢿⣿⣫⣿⣿⣿⡿⣵⣿⡆⢣⠘⣧⡙⣂⣷⣟⡉⠿⣯⣾⣿⣿⣿⣿⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠋⣿⣻⣵⣻⣟⡿⣟⡶⣯⣟⣽⣛⣾⣷⣇⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⢏⡟⡵⢣⠖⣎⠶⣩⢿⡾⣿⢾⣿⣿⣿⣿⢿⣻⣿⣽⣾⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣟⣧⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⡟⠁⠈⢻⣽⣿⣿⣿⣧⠘⡋⡑⠢⠑⣿⠰⣿⠸⠿⠟⡰⠉⣿⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢧⡯⢷⡾⣝⣳⢯⡷⣞⣧⣟⠾⣽⣻⢯⡇⢀⣶⣿⣿⣿⣿⡟⠁⠘⣧⠳⣭⣞⣬⣓⣱⢎⡿⠼⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣞⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣽⣦⣕⣨⣡⠿⡃⢇⢿⡀⢇⠣⡐⣱⣿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡽⣟⡳⢿⣭⢿⣾⣽⣞⣾⣻⣳⣽⢾⣿⢿⡿⣿⣿⣿⠋⠀⠀⠀⣯⢛⡴⣊⠶⡹⣜⢻⣏⢷⣿⢿⢿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣽⣻⠀⠀⠀⠀⣤⣾⣷⣯⡄⠀⣠⣴⣾⣿⣿⣿⣿⡓⠯⢟⢣⢃⠧⡙⣌⢒⠻⣾⣶⢾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⢷⡯⣝⡳⣎⣿⢖⡳⣞⢾⣱⢧⢺⣿⣾⢿⣽⣷⣯⣿⣷⠀⠀⠀⢿⡇⢶⡩⢖⡳⢬⡛⡧⢾⣿⣶⡿⡇⠎⡿⢻⣾⣿⣿⣿⣿⣿⣿⣯⣿⣻⢿⣟⢿⣼⡽⠉⠀⠀⠀⣾⡿⣏⠿⣹⢿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣬⣆⣛⠻⠷⡎⢎⣱⣨⡽⠛⣸⣿⣿⣿⡿⠀⠇⠅⣒⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣜⡿⣧⡛⣧⣛⡧⡟⣧⣛⡼⣇⢿⣸⡿⣟⣿⡼⣧⢿⣿⢧⡀⠀⠀⢸⡿⣄⠻⣜⢣⢇⣻⢧⣿⣟⢧⣿⣻⣧⣧⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠧⣿⣿⣿⢿⣧⡀⠀⠀⠀⢻⣿⣻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⣇⠘⠠⠀⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡽⣽⣧⣛⢶⡱⣏⢷⣓⢮⢳⣏⡷⡚⣿⣿⣟⡿⣿⣿⣞⡿⠁⠀⠀⠀⠹⣧⣛⣾⣞⣞⣛⡶⢯⢎⡭⢳⣷⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡀⠈⢿⣾⢯⣟⣿⡄⠀⠀⠀⠙⠓⠟⢾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣟⣷⣿⣿⣟⣿⣿⣿⣿⣷⣼⣿⣿⡟⣿⢻⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢻⣽⣓⢮⣳⢹⡏⣞⡼⣋⢧⡟⡶⢭⣟⣿⣯⢿⣳⣯⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠫⣜⡣⢞⠼⣩⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠹⣿⣾⣻⢽⡄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡼⣧⣟⡾⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣟⣾⢹⡞⣼⢣⡟⣼⢳⡝⡮⣟⡝⣮⢿⣾⣿⣟⣷⢯⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣾⣟⣷⣟⡟⠁⠀⠀⠀⣀⣀⣀⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⢯⣗⢣⣟⣿⣿⣿⣿⣿⠇⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⢾⣽⡺⣼⣱⢻⡼⡥⣏⢾⡱⢿⡜⣎⢿⣾⣿⡾⣽⣻⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢣⣾⣿⣾⠏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡿⣿⣿⣯⣾⠷⣮⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡯⣟⣯⣿⡵⣓⢎⢷⣣⣛⠼⣣⣛⣽⣺⣙⣾⣟⣾⣿⣟⣿⣿⣽⢷⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣷⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⣟⢻⡅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⣿⣺⡽⣻⢯⣿⣻⡽⢯⣿⣻⡽⢯⣟⡽⣾⠽⣾⣿⣾⣻⣾⣿⠏⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣽⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⣎⠳⢻⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣽⣿⣿⣿⣿⢿⣽⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣼⡳⣟⡽⣯⢶⣯⣽⢻⡶⢯⣽⡻⢾⣝⡷⣻⣳⣿⣿⣿⠵⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣾⣿⣻⣿⡿⣿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⡏⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣷⣿⢻⣟⣿⣿⠏⠀⢿⣯⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢧⢿⡽⣽⡞⣯⢶⢯⣟⣽⡻⣞⣽⡻⣾⣹⣷⣿⢿⣷⡀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⢿⣻⣿⣟⣿⣿⢿⣻⣽⣾⣿⣿⣽⣿⣟⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣻⣿⡷⣏⡷⣼⣺⣿⠀⠀⢈⣷⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢮⢻⣞⣳⠿⣭⡟⣯⣞⣷⣿⣽⢾⣻⣽⣿⣟⣯⣿⣟⣧⡀⠀⠀⣀⣼⣿⣿⣿⣟⣿⣿⢿⣿⣿⣟⣿⣿⣻⣿⣿⡿⣿⣷⣿⣿⣽⣿⣿⣽⣿⣯⣿⣿⣷⣿⢿⣿⣯⠀⠀⠀⠀⠀⠀⢠⣟⡿⣿⠾⢛⣋⣾⣿⣟⣿⡿⣿⣯⣿⣶⣿⣿⣶⣾⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠠⣞⢯⡽⣭⢯⡽⣭⢯⡽⣭⢯⡽⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣟⡿⣻⢽⣛⡟⡿⣿⢿⣻⡽⣏⡿⣽⢿⡿⣧
⢸⡝⣮⢳⡳⢞⡲⣭⢶⡹⣎⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡾⣵⣛⢮⡳⣝⡳⣭⢻⡽⣻⣯⣷⢯⡿⣽⣻
⡹⣞⡵⣫⠽⣭⢳⢳⣎⢷⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠄⠁⠀⠠⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣽⠶⣭⡳⣝⢮⣳⢭⡳⣝⢧⡻⣞⡿⣿⣿⣽
⣱⢏⡾⣱⢻⣜⡫⣗⢮⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠩⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⢿⣿⣿⣿⣿⣿⣿⡝⣶⡹⣎⢷⡹⢮⡝⣮⡳⣝⢮⣝⡳⣯⢿
⢼⣫⢞⡵⣫⢶⡹⣎⠷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⠹⣿⣿⣿⣿⣷⡹⢶⡹⣎⢷⡹⢧⣛⠶⣽⡹⣞⡼⣳⡝⡾
⢎⡷⣫⢞⡵⣫⠷⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣮⡝⣧⢻⡜⣧⣛⢧⣏⡟⣶⡹⣎⢷⣣⢟⡽
⢺⡵⣫⢞⡵⣫⢗⡧⣟⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣾⣧⣛⡶⣹⢞⡼⣹⢶⡹⣎⢷⡹⣎⢷
⢣⣟⡱⣏⢾⡱⣏⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠟⡉⢠⢹⣿⣿⣿⣿⣿⣿⣷⣹⢎⡷⣹⢎⡷⣹⢎⡷⣹⢞
⣹⣮⢷⡽⣞⡷⣽⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡹⣫⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⣻⡜⣧⢻⡜⣧⢻⡜⣧⢟
⢽⣻⢯⣿⣻⢟⡿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠿⠻⠟⠿⠿⠿⠿⠆⡀⠀⠀⠀⠐⢶⣿⣿⣿⡤⠿⣋⢿⣿⣿⣿⣿⣻⣿⣿⣧⢻⡜⣧⢻⣜⣧⣻⡜⣯
⢺⣭⡟⣶⢫⣯⢟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣴⣶⣾⣿⡿⣷⡦⢅⡐⢀⠀⠀⢈⠩⢉⠒⠠⢈⠒⠠⠡⢻⣿⣿⣿⣷⣻⣿⡗⣯⢞⡵⣫⢿⣿⣿⣿⣳
⣻⢮⡽⣞⢯⠾⣽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⠷⢒⡋⢡⠐⡌⠠⠂⠀⠒⠠⢈⠐⠂⢈⠂⡁⠄⢻⣿⣿⣿⣷⣻⡿⣜⢯⡞⡽⣿⣿⣿⣿⣿
⣽⢿⣳⣟⣾⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠛⡍⠒⠄⢂⠈⠄⠨⢁⠊⠄⢃⠄⠀⠈⠐⡀⠀⠀⠀⠀⠀⠌⠸⣿⣿⣿⣿⣿⡿⣎⢷⡹⣽⢿⣿⣿⣿⣿
⢼⢯⢿⡽⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡐⠠⠁⠊⠄⠈⠀⠁⠀⠌⢌⠢⢌⠀⠀⠁⠄⠣⡐⡀⠄⠡⢈⢸⣿⣿⣿⣿⣿⣿⡹⢮⣝⢾⣻⣿⣿⣿⣿
⢺⡝⣾⡽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡀⢁⠀⠀⠀⠀⠀⡐⢬⢢⢙⠄⡂⠀⡀⠈⠔⠠⠑⣈⠡⠌⢸⣿⣿⣿⣿⣿⡮⣝⢯⡞⣭⣿⢿⣿⢿⣿
⣹⠽⣶⣻⢿⣻⢾⣽⣻⡟⣿⣿⣿⣿⣏⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⠱⡀⠆⠠⠀⡀⠄⢂⠘⠄⢃⠛⢋⠒⠓⠈⣁⠰⣀⢆⠠⠀⠌⢸⣿⣿⣟⢿⡹⣞⡽⢮⣝⡳⣽⣛⢾⣫⢟
⢼⡻⣵⣿⣻⢯⣿⣽⢯⣿⡜⣿⣿⣿⣿⣯⣞⣿⣿⣿⣿⣿⣿⣿⣿⣧⢣⠘⡄⢣⠐⢄⠊⠄⡈⠄⠂⢌⣠⢦⢥⡲⣼⣛⠯⠐⢂⠐⡈⣼⣿⣿⡾⣭⢷⣻⡼⣏⢾⡱⢧⣛⣮⢳⣫
⢺⣽⣳⣿⣽⣻⢾⣿⠟⢻⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⢌⠣⠌⡐⢈⠂⠌⢂⠳⢞⠿⢯⡛⢮⠳⡙⠦⢁⠢⢁⠂⢨⢐⣿⣿⣿⣿⣞⣷⣳⡽⣎⢧⡛⢧⡻⡜⢧⢳
⣹⣞⣿⡷⣯⣟⣿⣿⣏⠄⢋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢦⠑⡈⢄⠢⠈⠄⡘⢠⠊⠤⢉⠢⢁⠌⡐⠀⠆⢂⠀⡲⣼⣿⣿⣿⣿⣿⣿⣳⡽⣎⢷⡹⣣⢳⢭⢣⢏
⢼⣻⣯⣿⢷⣿⣿⣿⣿⢏⠠⢑⡚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡳⣈⠆⡌⢡⠂⢌⡀⠣⢘⠠⢂⠅⢂⠌⡐⢁⠂⢄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢮⣷⡹⢧⣛⢮⣓⢮
⢺⣿⣿⣿⣿⢿⡽⣯⡟⡌⡐⢂⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⢎⡴⣁⢚⡤⣐⠡⠊⠤⡁⢌⡀⠆⡐⢠⣎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣯⣾
⣻⣿⡿⣟⡾⣯⢟⡷⣏⠐⡐⡈⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢶⡹⢶⣩⢒⡬⣀⠒⡤⢑⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢼⣳⠿⣝⣯⡽⢾⣹⠇⣈⠰⢀⠣⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣛⠟⡻⠛⡌⠓⡌⠄⠃⠄⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢺⣽⣫⣿⠾⠛⢛⢋⡐⠠⠂⠍⡁⠃⠀⠀⠀⠀⠠⠀⠉⠋⢛⢿⣿⣿⣿⣿⣿⣷⠣⠄⡑⠌⢊⠡⠁⠌⡐⠠⢈⠠⠈⡔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⠋⠁⠀⠀⣰⠎⢠⠀⠡⢁⢂⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⠕⡨⠐⡈⠐⠠⠉⠄⢠⠁⠄⡐⢢⠞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⣴⡿⣁⠂⠌⡰⢁⠂⡁⠂⠄⠐⠈⠐⡈⠄⠁⠐⠠⢶⣾⣿⣿⣿⣿⣷⣭⣐⠡⠄⠡⠀⠌⣀⡄⠄⠂⠄⠡⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⢰⣿⡛⠤⢌⢂⠡⠂⠌⠠⢁⠀⠀⠀⠀⠄⠈⠠⠀⠀⠈⠚⣿⣿⣿⣿⢷⠠⠌⠉⠛⠙⠋⠉⠀⠀⠀⡀⠀⠡⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢾⡟⠬⡑⢂⠌⠄⠃⠄⠀⠂⠀⠀⡀⠄⢀⠢⠄⠠⢄⢄⣠⣿⣿⣿⣿⣯⣂⠡⠈⠐⠀⠀⠀⠀⡀⠀⢀⠠⣒⡭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡞⢨⠑⢌⠂⢌⠠⢁⠈⠀⡐⠠⠀⠀⠈⠀⠄⢈⠀⠺⠪⢿⣿⣿⣿⣿⣿⣯⡃⠆⣀⡄⣈⣤⣐⠀⠒⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⢀⡬⡐⢣⠘⠄⢊⠄⠂⠄⡈⠠⢀⠡⠀⠄⠠⢁⠂⡀⠠⠄⢰⣽⣿⣿⣿⣿⣿⣟⠧⠃⠀⠀⠀⠉⠉⠈⠀⠀⠈⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠉⡝⡤⢑⠢⠉⠌⡄⠨⢀⠡⢀⠂⠄⢂⠁⠂⠀⠀⠐⡈⠍⠹⢻⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠁⠀
⠀⠈⠢⢃⡂⠍⡐⠠⢁⠂⠂⡄⠒⡈⠄⠒⡀⢠⠐⣨⠐⣈⣸⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⢿⣿⣿⣿⣿⣻⣿⢿⣿⠏⠛⠁⠀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠑⠚⣯⢧⡄⠀⠀⠀⢶⡚⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⡤⠄⡀⠀⠘⡿⣇⠀⠀⢺⡏⠐⣿⣶⠶⠶⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣤⡞⠋⠁⠀⠀⠀⠀⠀⠀⢠⡆⠹⣿⣧⡄⣿⡇⠀⢸⣶⠆⠀⠀⢸⡗⣧⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡟⠛⠓⠶⢯⡙⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢛⣿⣿⢿⠀⠀⢸⣧⣤⣀⣼⡷⠋⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠗⣲⠹⣿⡇⠀⠀⠀⠀⠉⢿⣥⢤⡤⡖⡿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠒⣾⣿⣿⢽⣿⠟⠀⠀⠀⠀⠀⡄⠚⠃⠃⣿⠀⠀⠀⠀⠀⠀⣿⣏⠉⠁⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠉⠁⠀⣰⡟⠁⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠘⣷⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣄⣀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠰⡿⡁⣄⡆⠐⠊⠿⣿⣿⡿⠀⢠⣿⠁⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡉⠀⠹⣻⡀⠀⠀⠛⢿⡶⣼⡅⢀⡦⠊⠓⠁⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⠃⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣆⠀⠹⣷⠀⠀⠀⠀⠀⣯⣗⡦⡄⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⡿⣏⡯⠀⠀⠀⠀⢠⡟⡺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⡷⣄⠙⠳⣦⡠⡾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⡟⠍⠀⠀⠀⣶⡯⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠁⣱⡧⣖⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡏⠀⣠⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣶⣯⠜⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡗⣿⠀⠀⠀⠀⠀⠀⣾⣔⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣿⡄⠀⠀⠀⡠⢯⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣽⢄⣦⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣭⣟⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣞⠀⠀⠀⢀⠀⣠⡐⣲⣌⣹⣷⠿⠕⠚⠉⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⡮⠖⠋⠀⣰⡟⠋⠀⠀⠀⠀⠀⣔⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡤⡖⣒⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣔⢍⡟⠁⠁⠀⠀⠙⢥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣗⠋⠀⠀⠀⠀⠀⠀⠀⢙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢐⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣯⡟⠉⠉⠉⠛⠣⡖⣠⣀⠀⠀⠀⠀
⠀⠀⡇⣟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⡃⠀⠀
⠀⢀⡃⡗⠀⠀⠀⠀⠀⠀⢀⣴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⢐⢁⡃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀
⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠈⠛⠦⡤⣄⣄⣦⣆⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀
⠀⣘⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⡠⢩⡮⠟⠁⠀⠀⠀⠀⠀⠀⠰⠥⠽⢦⡀⠀
⠀⣃⡅⡅⠀⠀⠀⠀⠀⠀⠀⣸⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡆
⠀⣥⠇⠆⠀⠀⠀⠀⠀⠀⠀⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇
⢀⡧⡁⠇⠀⠀⠀⠀⠀⠀⠀⠛⢿⣄⣀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⢠⣎⠏⠁
⢸⡝⠄⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢄⡵⠝⠋⠉⠁⠀⠀⠀⠀⠀⠉⣷⡀⠀
⠸⣧⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⣔⣡⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⠀⠀⠳⡤⡑⢦⣀⡀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠀⠀
⠀⠀⠀⠀⠈⠉⠃⠋⠏⣓⢃⡫⣝⢿⠦⡦⡶⠖⠶⠶⠶⠶⢷⣟⠯⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣠⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀
⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⡿⡀⠀⠀⠀⠀⠀
⠀⠀⠘⢻⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢹⣿⠃⠀⠀⠀⢹⣗⣀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣼⣿⠏⠀⣠⡴⠟⠛⠛⠋⠉⠉⠓⠲⣄
⠀⠀⠀⣸⠃⠁⢸⣿⠏⣿⣿⣿⣿⣿⣿⠁⣿⣿⠟⣽⣿⢿⡃⣿⣿⣿⣿⡏⣻⣿⣿⣿⡟⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⡿
⠀⠀⠀⠿⠶⢮⣄⠈⠁⢺⣿⣿⠀⠻⢃⣀⢉⣁⣠⡉⠁⠘⣿⡿⣁⣾⣷⡾⠿⠿⠻⣿⠁⠀⠀⢿⣶⠶⠛⠛⠛⠛⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠙⠳⠶⣿⣽⣿⣿⣷⢦⣭⣍⣩⣿⣷⣤⡴⠿⢻⣿⣿⠏⠀⠀⠀⠀⢻⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⣰⣿⠛⠋⠻⠛⢀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⣼⡃⠀⠀⣨⡿⠶⠶⠶⠶⠶⣶⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⣰⣿⣿⣦⣤⣤⣶⣿⣿⣦⣻⣼⣷⣀⣀⣀⣠⣤⣿⡀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⡏⠏⠙⣿⣇⠀⣴⡟⠛⠷⣦⣤⣀⣀⣀⣴⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢏⠉⠀⠀⠀⠀⠉⠛⣶⣯⠀⠀⠀⠀⠀⠉⠙⣿⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣾⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢖⢶⡶⠶⠲⠒⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠁⠰⠛⠚⢶⣾⣿⣿⣿⢶⣶⡶⣷⣶⣶⣶⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢳⣶⠶⠶⢾⣿⣿⣿⣿⣤⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⢽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣠⡴⠟⠛⠲⠦⣬⡳⡬⠃⣈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣾⡾⠃⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠋⠙⠛⠻⣍⣻⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠿⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣍⣙⠒⠲⠶⠶⠶⠶⠶⠒⠛⠉⣁⣠⠼⣏⠿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠈⠑⠦⣍⡙⠓⠒⠶⠲⠶⠖⠖⢒⣋⣩⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠁⠀⠀⠉⠉⠁⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⡀⢀⡤⠒⢦⠀⠀⠀⠀⣀⠔⠋⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀⣀⣀⡀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣿⠊⢄⣠⡿⠁⠀⢀⠞⠁⠀⠀⠀⠰⠛⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠙⢷⡄⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⣹⠠⣠⡟⠀⢉⠑⠧⡀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⢯⡁⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⣆⢸⡁⣶⣿⠦⣤⠟⠀⠀⠀⣄⢁⡀⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢙⣧⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣇⣇⣜⠁⣽⠀⠠⣼⡼⠶⣷⣿⣦⡖⠠⠤⢄⣇⣁⣤⣤⣤⡦⠶⠾⣿⣿⡆⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⠟⠋⠀⠉⢀⣴⠋⠀⠀⡸⡅⠀⠻⣿⡿⠇⠀⠀⠀⣿⠀⠻⣿⡿⠃⠀⢠⣾⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣰⡿⢀⣀⣤⠤⠞⠁⠀⠀⢎⠀⠙⠢⠤⢀⣀⣀⣀⠤⠞⠉⠓⠤⣀⣀⣠⢤⣾⡷⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢾⡠⠂⠀⠀⠀
⠈⠒⠤⠽⠿⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠉⠀⣀⣠⡀⠀⡟⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠙⢿⣻⠒⡦⠤⣀⠀⠀⠀⠈⠙⠦⠖⠛⠒⠂⣀⣤⣶⣿⣿⠉⠀⢠⡇⠀⠀⠀⠀⢠⡇⠀⣱⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⠀⢟⠳⣶⠤⢼⠬⠽⡶⠶⠶⡶⠶⢶⠾⠿⡗⣺⠽⢋⠎⠀⠀⣼⠀⡄⠀⠀⠀⢸⠃⢀⡅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠑⣄⠉⠒⠦⢄⣀⠀⠀⡇⠀⣸⣠⠴⠋⠁⣰⠃⠀⠀⣼⠃⠀⠀⠀⠀⠀⣽⢦⣁⠰⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠⡾⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⣠⠇⢼⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⠲⢦⣤⣤⣤⣤⡴⠶⠛⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⢸⠀⡞⠉⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠾⣆⣹⡦⠤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠤⠤⠤⠤⠔⠒⠚⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣶⣶⣦⣄⠀⠀⠀⣡⣤⠤⢶⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⢀⣿⣿⣧⠀⣼⣿⡇⠀⠀⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣖⠾⠟⠋⣸⣿⣿⢸⣿⡇⠈⠛⠿⣷⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⡽⠋⠀⠀⠘⣿⣿⡟⠀⣿⠉⠀⠀⠈⢿⡻⣿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⢀⠀⠀⠀⠀⢀⣹⣿⠁⠀⢿⣄⠀⠀⠀⠀⣀⠀⠁⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⠉⠉⡉⢉⣉⡉⠤⠃⠀⠀⠘⠌⣉⣉⠉⠉⠉⠉⣉⡡⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠋⠁⠙⠻⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡌⣹⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⢿⡄⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢘⠀⠀⠀⠩⡇⣴⣿⣿⣿⣷⡄⠙⣿⠿⠿⡛⠟⡈⠄⣟⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣂⠀⠀⠀⠀⢸⠀⠚⠛⠉⠉⠀⠀⠏⠁⠀⠀⠀⠐⣣⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢐⣚⡸⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⠈⢏⣯⣶⣤⡐⣟⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠈⠁⢆⠀⠀⠀⠀⠀⠐⢠⣴⣿⣿⣶⣦⣶⡿⢿⣿⢛⣱⣿⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠑⣪⡻⡹⢏⡯⡤⢴⣟⣣⣹⣿⡿⣎⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⠙⠻⢗⠁⠀⠀⠀⣀⣀⣰⣿⡟⣿⡐⢻⠿⢟⡛⣡⣽⣿⣟⡟⠀⢹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣼⣿⣿⣿⣿⣿⣷⡈⠻⢿⣷⣶⣿⣿⣿⡿⠋⠀⠀⣼⣿⣿⣷⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⠻⣿⣿⡛⠀⠀⠐⡬⠪⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠆⠀⠀⠀⠀⠀⠤⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣰⣾⣿⠽⣫⣳⢦⢀⡍⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀
⠀⡴⣷⡂⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⠏⠀⠂⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀
⢸⡇⣿⡁⠀⠀⢠⠩⣕⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⠔⠄⠠⠱⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀
⣽⣧⠿⣇⠀⡀⢎⣵⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢞⢿⣿⡌⠀⣴⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀
⢿⣿⣞⢮⣙⣛⣻⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⣾⣿⣿⡤⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀
⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⡿⡽⡽⣷⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣽⡹⣱⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠨⠿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡵⣹⣿⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠉⠛⠻⠓⠛⠈⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡵⣽⣿⢯⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣫⢯⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡻⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡢⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢔⣶⣒⠒⠒⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⡡⠔⣶⡿⠛⠛⠁⠉⠉⠐⠢⣤⣭⡲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠔⢡⠖⠁⠀⠘⠁⠀⡀⠀⠀⠀⠀⠀⠀⠛⠛⢷⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠊⢎⠀⠀⠙⢦⡀⠀⠀⡰⠃⡐⠁⠀⠀⠀⢠⣮⠴⠒⠿⣄⠀⠀⠀⡠⠤⢤⡀⠓⡄⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⠀⡰⠁⢰⠁⠀⠄⡀⠀⣶⠃⣠⡤⡄⠙⡄⠀⣼⠞⠉⠙⠻⣇⠸⡄⠀⠑⡀⠀⠀⣠⠚⠛⠛⡗⢄⠀⠀⠀
⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⢠⠃⠀⠀⠁⠀⠀⠤⣁⣸⢸⣧⣿⢹⠀⣷⠀⣿⣞⣿⣧⠀⠘⡆⠀⠀⠀⢳⠀⡞⡁⠀⠀⠐⠁⠈⡆⠀⠀
⠀⠀⠀⠀⠘⣀⠀⠄⡤⠤⣾⣼⡀⠀⠀⠀⠀⠐⠂⠒⠌⠹⣿⡷⠋⢠⡟⠀⠈⣿⣯⡽⠁⢀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀
⠀⠀⢠⡴⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠊⠉⠱⡒⠄⠪⠱⠶⠋⠀⠀⠀⠈⠣⣤⡴⠞⠁⠂⠀⠀⢀⣇⣧⣤⣄⠀⢀⡸⠀⠀⠀⠀
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⡆⠀⠀⠀⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠨⣻⠭⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠩⡲⣄⠀⠀
⢰⠁⠀⠀⠲⣀⡠⠔⠂⠀⠀⠐⠒⠲⢖⣇⠀⠀⠀⠀⠀⢹⣧⡉⠐⠒⠤⠤⠤⢤⣤⠖⠊⠁⠀⢰⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢧⠀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢿⣿⣶⣤⣄⣀⣤⣾⠇⠀⠀⠀⢀⣼⠞⠛⠉⠉⠉⠑⠒⠠⢄⠔⠀⠀⠀⠇
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠀⠀⠀⠀⠀⠀⢢⠙⡟⢿⣿⣿⡿⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀
⠘⡆⠀⠀⠀⠀⠀⢲⠊⠁⠀⠀⠈⠑⢳⢮⡀⠑⢠⡀⠀⠀⠀⠀⠙⠳⠤⠿⠛⠁⠀⠀⠀⠀⠘⣄⣀⢤⠤⠤⠤⣀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠘⢆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡜⠻⡦⡀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠊⠁⠀⠐⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠜⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡤⠀⠀⠀⠠⡴⠊⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡔⡿⠞⠓⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣔⡿⡏⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣲⣒⣆⡀⠀⠀⠀⣠⣶⡻⣿⣦⠀⠀⠀⠀⣠⣺⣯⡛⢗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠬⡯⡎⠀⠀⠤⠄⠠⡀⡤⣺⣄⠀⠀⠀⠀⠀⣷⠏⠉⡋⢯⠀⠀⢀⢟⠇⠀⠀⣸⡏⠀⠀⠀⣿⠋⠀⢀⣯⡷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀
⢸⣿⣧⡅⠀⠀⠈⠁⠉⠉⠉⣻⡫⡄⠀⠀⠀⢸⣯⠉⠉⣼⠇⠀⠀⠈⣾⣇⣰⢿⠍⠀⠀⠀⣾⡯⠭⠿⡝⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠚⠀⠀⠀⠀
⠘⢿⣽⣃⠀⠀⠀⠀⠀⠀⠀⠀⣡⠷⡁⠀⠀⠀⠀⠈⠉⠋⠃⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀
⠀⠀⠻⢷⣷⣄⠄⢤⣢⡆⣿⣶⠿⡏⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡪⡁⠀
⠀⠀⠀⠀⠀⠉⠛⠏⢿⡷⡾⠯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠼⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡄⠀⠀⠀⠀⠀⠀⠀⢨⡵⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠀⠀⠀⢷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡅⠀⠀⠀⠀⠀⠀⠀⠐⣫⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣸⡁⠀⠀⠀⠀⠀⡀⡔⠶⣦⠀⠀⠀⠀⢨⡠⢃⡠⣴⡒⡦⠀⠀⠠⢪⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡰⠇⠀⠀⠀⠀⡰⠽⠷⢲⠀⡷⠀⠀⠀⢠⡁⡎⠏⠀⠀⢍⠯⠀⠀⢂⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡛⠉⡂⠀⠀⠀⢺⠖⠀⠀⠀⡁⠏⠀⠀⠀⠘⠇⢌⠁⠀⠀⠀⣿⠁⠀⠀⣽⣻⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⠀⠀⠀⠀⠀⠀⡜⡘⠌⠠⠃⠀⠀⠀⡦⠷⡇⠤⡤⢋⠁⠀⠀⠀⢈⠊⢶⠀⠀⠀⣌⡇⠀⠀⠀⠀⡟⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⣏⠣⡀⠀⠀⠀⠎⢧⡣⠅⠁⠀⠀⠀⠀⠣⢄⣛⡋⠒⠀⠀⠀⠀⠀⢠⣗⡇⠀⣠⠎⡂⠀⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠑⠞⠶⡒⡣⠟⠍⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠿⠭⠒⠁⠀⠀⠀⠀⣼⠯⣷⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢴⣖⠲⠶⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⣩⣴⠚⢿⣟⣿⣻⣟⡿⣶⣬⣉⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣯⣻⡿⣿⣷⣌⣿⣞⡷⣯⣟⡷⣯⣿⡿⣿⣄⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣾⣯⣿⣽⡿⣾⣟⡷⣯⣟⡷⣯⣟⣷⡿⣟⣿⣽⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⣿⣻⣟⡾⣽⣳⢿⣟⣷⢯⣟⡷⣯⡿⣽⣿⣟⣿⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠟⠺⠷⠯⣟⣷⣯⣟⣾⣟⡿⣾⣽⡿⣽⣿⣟⠾⠟⠛⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢩⣴⣾⢿⣶⣶⣤⣑⣛⣿⠯⠿⠷⢯⣿⣛⣥⣴⣶⣶⣶⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠹⢿⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⡈⠙⠷⣦⣩⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⣠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⢶⣤⣤⣭⣟⣻⠿⣿⣿⣿⣿⢿⣟⣯⣵⣶⣿⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣽⣻⣿⠿⠿⠿⠷⠾⠶⠿⠿⠿⢿⣽⣾⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣯⣿⣷⣼⣉⣉⣩⡶⠩⠄⡈⢉⣵⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⣿⡿⣽⣧⡳⣕⢲⢒⠒⢆⡠⣲⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠝⠻⢯⣿⣷⣶⣶⣶⣶⣾⣿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⠀⠀⠀⠀⢀⣀⡤⢾⣇⠀⠈⠢⡀⠉⠉⠉⠉⠉⠛⠉⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢺⣀⣤⢖⣺⣭⣶⢾⡿⣿⣷⣤⡀⠈⠂⠄⡀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡇⢒⠁⢷⣾⢿⣽⣳⢯⡿⣽⣳⢯⡿⣿⣶⣦⣤⣠⣅⣠⣴⣶⣿⢿⣻⢿⡽⣯⣟⡿⣿⣿⣲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡾⠿⠾⠽⠾⠤⠥⠬⢿⣟⡾⣽⢯⣟⡷⣯⢿⣽⣳⢯⣟⣿⡻⠏⢿⣯⢷⣯⣟⣯⢿⡽⣷⢯⣟⡷⣯⣟⡿⣶⣦⣭⡙⣳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢟⣾⡏⠀⠀⠀⠀⠀⠀⢀⠈⣿⣻⣽⣻⢾⡽⣯⣟⡾⣽⣻⢾⠟⠁⠀⠈⠙⣿⢾⡽⣞⣿⡽⣯⣟⣾⣻⢷⣯⣟⡷⣯⡟⣱⡿⣷⣮⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⣼⠋⠀⠀⠐⠒⠒⠒⠂⠒⠊⢿⣷⢯⣟⣯⣟⡷⣯⣟⣷⠟⠁⠀⠀⠀⠀⠀⠉⣿⣻⡽⣾⡽⣷⢯⣷⣻⣟⡾⣽⣻⡝⢰⣿⣽⣳⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⣿⣇⠀⠀⢀⢀⢀⣀⣀⣐⣈⣸⡿⣯⣟⡾⣽⣻⢷⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣷⣻⡽⣟⣾⣳⢯⣟⣷⡟⢀⣿⡷⣯⣷⣻⢾⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣷⣿⣿⡀⠀⠁⠉⢉⡁⠀⠀⠈⣿⣟⡷⣯⣟⡷⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣻⣟⡾⣽⣯⣟⣾⠁⢸⣯⣟⡷⣯⣟⡿⣞⣿⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⢻⡇⠀⠀⠂⠒⠒⠒⠒⢺⣿⡽⣯⢷⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣯⣟⣷⣻⢾⠃⠀⣾⣿⣽⣻⢷⣯⣟⣯⣟⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⣼⣿⡟⠈⠧⠤⣤⣤⣤⣤⣤⠤⠞⣿⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣳⢯⡏⠀⡀⣿⣿⡾⣽⣻⢾⡽⣾⡽⣾⣿⣄⠀⠀⠀⠀⠀
⠀⢠⣟⣿⣀⣤⣴⡿⣿⢿⣆⠀⠀⠀⠀⣿⢘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡿⠀⢠⢰⣿⣟⣿⣯⣟⣯⣟⣷⣻⡽⣿⣿⣆⠀⠀⠀⠀
⠀⣼⣿⠹⣿⣽⣳⣟⣿⣟⣿⣷⣄⠀⣼⣿⡾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡅⠀⠎⢸⣿⣟⡾⣷⣟⡾⣽⢾⣽⣻⢷⣻⣞⣷⡀⠀⠀
⢀⣿⣿⡆⣿⣞⣷⣻⡿⣾⣟⣾⣿⢿⣿⣿⡿⣽⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡘⠀⣾⣿⡿⣽⣻⢾⣟⣯⢿⡾⣽⢯⡿⣽⣿⣧⠀⠀
⢸⣿⣿⣿⣿⣽⢾⣿⡽⠟⠊⠉⠀⠸⣷⣿⣟⡷⣯⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣻⣇⢀⡏⢻⣿⣯⣟⣯⢿⣾⢿⡽⣯⡿⣽⢷⣻⣿⡆⠀
⢸⣿⣿⣽⣻⣿⠛⠁⠀⠀⠀⠀⠀⠀⢹⣿⢯⡿⣽⣻⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣷⣻⢾⣟⣿⣼⠀⠀⠻⣿⣽⡾⣯⢿⣯⣟⡷⣟⣯⣿⣳⢿⣿⠀

Nhiều mẫu tại đây 👉 1001+ Icon CUTE

Nguồn Gốc, Ý Nghĩa Biểu Tượng Like Facebook

Biểu tượng Like Facebook ra đời để người dùng có thể bày tỏ cảm xúc nhanh với một bài viết, hình ảnh hoặc bình luận mà không cần phải gõ tin nhắn dài. Nút này xuất hiện từ khá sớm trong quá trình phát triển của Facebook và dần trở thành một trong những biểu tượng quen thuộc nhất trên mạng xã hội.

Về hình ảnh, biểu tượng Like thường gắn với bàn tay giơ ngón cái lên. Đây là cử chỉ quen thuộc trong đời sống, mang ý nghĩa đồng ý, thích, ủng hộ hoặc công nhận. Khi đưa vào Facebook, ký hiệu này được đơn giản hóa để người dùng ở nhiều quốc gia đều dễ hiểu và dễ dùng.

Ý nghĩa của biểu tượng Like Facebook thường gồm:

Thể hiện sự yêu thích với bài đăng, ảnh, video hoặc bình luận
Phản hồi nhanh mà không cần viết chữ
Tạo tương tác xã hội, giúp người đăng biết nội dung của họ đang được quan tâm
Gợi cảm giác kết nối, vì chỉ một cú nhấn Like cũng đủ cho thấy bạn đã xem và có phản hồi tích cực

Về sau, Facebook mở rộng thêm nhiều biểu cảm khác như Yêu thích, Haha, Wow, Buồn, Phẫn nộ, nhưng nút Like vẫn là biểu tượng cơ bản và phổ biến nhất. Vì vậy, khi nhắc đến Facebook, nhiều người vẫn nghĩ ngay tới hình ngón tay cái màu xanh như một dấu hiệu của sự đồng tình và tương tác.

Nếu dùng trong bài viết, cap hoặc tin nhắn, biểu tượng Like Facebook còn mang nghĩa vui vẻ, thân thiện và gần gũi. Nó không chỉ là một nút bấm trên mạng xã hội, mà còn trở thành một kiểu ký hiệu quen thuộc trong giao tiếp online hằng ngày.