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⛓♡🏳️🌈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⢤⣴⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠿⣿⠟⠋⠙⢿⣿⣵⡄⠀⠀⢰⣿⣿⣯⡀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠸⣿⣄⡀⠀⠀⠀⠀⠀⠱⡄
⠀⣀⠀⠀⠀⠀⣿⣿⡇⠀⠓⠂⠀⠠⠠⣀⣿⣿⣿⣦⣴⣿⣿⣿⣿⡇⢠⣤⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣦⣤⡀⠀⠀⢳
⣾⣿⣿⣦⣤⣀⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠁⠀⠀⠘
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡛⠛⠛⠛⠛⣉⣠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣤⣀⣀⠀⢀⣀⣤⢠⣄⣀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠐⢆⠀⠀⠀⠘⢿⣿⣿⣿⡿⠋⠀⠹⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣯⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠿⣿⠇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠞⠀
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣦⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⡿⠿⠿⠛⠋⣹⣿⡇⢰⡏⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⣿⣶⣤⣀⣀⣀⣀⣀⣤⣾⣿⣿⢧⣄⣱⠀⠀⠉⠓⠲⢦⡤⣄⣀⣠⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⡄⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠛⠻⠿⠿⠿⢻⡀⠀⡐⣿⡧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠈⠳⠖⢱⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠴⠚⣏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⢤⣤⣀⣠⣤⣀⡀⢀⢀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠻⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⡆⠀⣼⢿⣿⠷⣦⣄⣀⣴⣶⣶⣬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣧⣾⣿⡂⡍⠙⣸⣿⣟⡙⠄⠦⠈⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣶⣿⠿⣋⡙⢻⣿⠾⠟⢿⢿⣿⣿⣷⠀⠀⢹⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠏⠁⠀⠈⠉⠉⠛⠲⠦⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⣤⣼⡏⠉⠛⠲⢤⣄⣀⡴⠾⠛⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣼⡄⠀⠀⠀⠀⠈⣿⣇⢿⣿⡿⣷⣄⡐⣲⣿⡟⠻⢶⣭⣷⡿⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢷⣄⠀⠀⣼⠋⠙⠷⣶⡶⠟⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣈⠳⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠉⢹⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡇⠀⠀⠀⠀⡐⣠⣶⣶⣄⠀⠀⠀
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⣸⣄⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣼⡟⠁⢫⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢀⣀⠘⣏⠉⠉⣯⠉⠉⠀⠀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⠁⠀⠀⠈⢟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠷⠞⠛⠉⠉⠉⠹⠿⠶⢿⣗⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣿⣆⣀⣀⣀⣈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣛⣻⡦⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⣸⠟⠶⢶⣴⣿⠟⠋⠉⠛⠛⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⣿⠿⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⣤⣀⠀⠀⠀⠀⠀⣀⣤⡶⢿⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠿⣧⣴⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠛⠛⠟⠛⠉⠁⠠⠀⠀⠀⢀⣩⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠋⢁⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠉⠀⠈⠙⣷⣈⡉⢙⠛⣿⠋⠉⠉⠉⠀⠀⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⠀⢐⣾⠏⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⢿⣀⣀⣀⣀⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⣧⡀⠀⠀⠀⣠⡾⢋⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⠹⠷⠶⢤⣤⣤⣴⣟⡻⠶⠶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣤⣤⠶⠞⠋⠉⣿⣷⣦⠀⠙⢢⡀⠀⢀⣠⣄⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⢶⣤⣴⡶⠞⢛⡟⠛⠳⢶⣤⣤⣸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡆⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⣸⣷⣤⣤⣄⣀⣴⠞⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡙⠁⠀⠀⠀⠀⡠⠋⠔⠁⢀⠞⢠⠋⠁⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡼⠋⠀⠀⠀⠀⠀⠀⢧⠎⠀⢠⠁⡠⠁⠀⠀⠀⠀⠀⡂
⠀⠀⠀⣠⠶⣤⣀⡏⠙⠁⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡴⠛⠃⠀⠙⢟⠷⣦⣀⠀⠸⣿⣿⠇⡠⠐⠒⠒⠀⢄⠀⠀⣴⣿⣿⣷⠀⠀⠀
⣿⠀⡰⣲⣦⠀⠀⠥⣪⢝⠳⣦⣄⠀⠌⠡⢀⠴⡀⠀⡀⢡⠀⠻⣿⣿⡿⠁⠀⠀
⡏⠀⠱⠿⠟⠀⠀⠀⠀⠉⠛⠖⠉⢿⢦⣄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⡀⢴⠄⡔⠀⠢⢄⡀⠀⠀⠀⢸⢸⢸⢻⢶⡶⠶⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⢄⡑⠒⠊⡠⣤⣄⡀⡏⡗⠂⠄⡸⣼⣸⢸⢸⢸⢑⡺⢧⠀⠀⠀⠀⠀⠀⠀⠀
⠙⠳⢮⣝⣫⣍⡒⠭⣛⠷⣧⣄⠀⠀⠙⠛⠿⣾⣼⠀⠀⢸⡆⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠈⠙⠻⢿⣦⢤⣍⣒⠭⣛⣖⣤⣀⣀⡀⠉⠂⠄⣀⣇⠐⠄⠤⠑⠂⠚⠀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠸⡏⠁⢀⠄⠂⠀⠙⠳⣤⣀⡟⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡇⠠⠁⠀⠀⠀⠀⠀⠐⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀
⬛️⬛️⬛️⬛️⬛️
⬛️⬛️⬛️⬛️⬛️⬛️ ⏹
⬛️⬛️⬛️⬛️⬛️⬛️🟦🟦 ⏹
⬛️⬛️⬛️⬛️⬛️🟦🟦🟦🟦 ⏹ ◽️◽️◽️
⬛️⬛️⬛️⬛️⬛️ 🟦🟦🟦🟦 ⏹ ◽️
⬛️⬛️⬛️⬛️⬛️⬛️⬛️⬛️ ⬛️⬛️⬛️ ◽️
⬛️⬛️⬛️⬛️⬛️⬛️⬛️ ⬛️⬛️⬛️ ◽️
⬛️⬛️⬛️⬛️⬛️⬛️ ⬛️ 🟨🟨🟨🟨🟨
⬛️⬛️⬛️⬛️⬛️ 🟨🟨🟨🟨🟨
⬛️ ⬛️ 🟨 🟨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣟⡉⠀⠀⠀⠀⠀⠀⣀⣤⣭⣽⣶⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣿⠽⠧⣅⡘⣭⠽⢷⣄⠀⣠⣆⠰⠿⠾⠃⢀⣀⣈⠛⣦⡀⠀⠀⠀⠀
⠀⠀⢠⣾⡟⣡⣶⢶⣌⢻⢁⣶⡛⣻⣷⠏⠹⣆⠀⠀⠀⠈⣿⣽⣷⢬⣷⡄⠀⠀⠀
⠀⠀⣾⣽⣤⣿⣟⣫⡿⣞⡿⢿⣟⣿⡏⣼⢧⡙⢷⣄⠀⠀⠿⠛⠁⠀⠈⢻⣄⠀⠀
⠀⢠⣿⣫⡀⠀⠉⢿⣶⠛⠛⠦⡤⣴⣷⡿⠞⠃⠀⠙⠛⠶⣦⣤⡤⠤⠶⠚⢻⠇⠀
⠀⣸⣟⣿⣧⣼⣷⣼⡇⡐⢴⣺⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢲⢇⣾⠀⠀
⠀⢹⣏⣩⣿⣯⣽⣿⣡⣾⢾⣿⡯⠄⠲⣤⣄⣎⣱⠀⢀⣀⡀⠀⠈⢿⡯⠞⣹⠀⠀
⠀⢘⣿⣥⣾⣿⢿⣩⣏⣿⢿⣼⣧⠀⠀⠀⠘⠻⡀⠀⣸⣶⣃⠀⠀⢸⣧⣤⡟⠀⠀
⠸⣿⣟⡳⢭⣿⡀⠉⢩⡷⠶⠾⠾⢷⣤⣄⣀⠸⣿⠏⠈⠁⠉⠛⢢⣸⣿⡟⢻⣇⠀
⠀⠀⣻⣾⣏⣼⡇⠀⠀⠀⠀⠀⢀⡀⢀⣨⠿⠿⢷⣤⣀⣀⣀⣀⣤⣿⣷⣀⣦⠭⠿
⠀⣿⡍⣙⡥⠾⣧⠀⠀⠀⠀⠈⠀⠉⣲⠬⠆⠀⠀⠈⢻⣟⣹⣿⣯⡉⠿⣿⡁⠀⠀
⣿⣥⣴⣀⣶⡶⠿⣆⠀⠀⠀⠰⠄⠁⣳⠀⠀⠀⠀⠀⠀⢻⣇⣼⣧⠙⡂⢶⡏⠀⠀
⠀⠀⠈⠋⣼⡟⢹⢿⣷⣦⣤⣀⣞⣉⣁⣀⣠⡄⢠⣦⠀⢸⡟⠉⠙⠾⠻⢦⡿⠀⠀
⠀⠀⠀⠀⢸⣧⣾⣾⠛⠃⠀⠉⠉⠉⠉⠉⠀⠻⣼⠿⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣦⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣾⡿⠛⠛⡉⣉⣉⡀⠀⢤⡉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣤⣾⡿⢋⣴⣖⡟⠛⢻⣿⣿⣽⣆⠙⢦⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠻⠻⠶⣦⣄⠀
⠉⣿⢸⠁⣸⣥⣹⠧⡠⣾⣿⣿⣿⣿⣧⡈⢷⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣾⣿⣿⣶⣦⣈⠈⠻⣤
⠀⢹⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣫⠀⠙⣿⣿⣿⣿⣷⡄⣽
⠀⠀⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡊⠙⠉⠉⠉⠓⠲⠤⡀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣦⣴⣿⣶⣶⠀⠠⠀⣰⣤⣿⣦⠀⠀⠀⠀⠉⠙⠛⠻⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠃⢀⣄⠀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⢀⣀⣠⣴⡿⣿⣦⣀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠉⠉⠉⠉⠉⠑⠋⠙⠻⡢⢖⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣏⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣳⣻⣟⡿⣷⣦⡀⠀⠀
⠀⢀⣾⣿⣳⡟⣿⣻⣿⣿⢿⡿⣿⣝⡷⣯⣟⡷⣯⣟⡆⠀
⢀⣿⣟⣾⢷⣻⡵⣯⣷⣻⢾⣽⣳⣾⢷⣻⡽⣿⣳⢯⣿⡄
⢸⡿⣽⣟⡾⣯⢷⣻⣯⣟⡾⣽⣻⢿⣞⣯⢷⣯⢿⡾⣽⡇
⢺⣟⡷⣿⡽⣯⣟⡷⣿⢾⣽⣳⣯⣟⣿⣞⡿⣞⡿⣿⣳⡇
⢹⣯⢿⣽⣻⢷⣯⣟⣿⣻⣞⣷⣻⢾⣽⣾⣻⣽⣿⣿⡟⠀
⠈⢿⣿⣻⣿⣟⣾⣽⣾⣷⣻⢾⣽⣻⣾⣿⣽⢿⣞⡏⠀⠀
⠀⠈⠻⣿⣯⣿⣟⣯⣿⢿⣿⢾⣻⣿⢯⣿⣟⣾⠟⠁⠀⠀
⠀⡀⠀⠀⠉⠉⠙⠿⠾⠿⠛⠿⠯⠿⠛⠉⠉⠁⠀⠀⠀⠀