⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠩⠄⠀
⠀⠀⠀⠀⠀⠀⠀⡟⠟⠩⡄⠀⠀⠀⡀⠠⠔⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣗⣮⣱⡷⢶⣿⣷⣠⠀⠀⡇⡇⠀
⠀⢀⣠⣤⣶⣾⣿⠍⡿⣽⣸⣻⣼⣶⣿⣶⡿⠷⠇
⢸⡿⢓⣯⣿⣿⣿⡾⣧⣾⣿⡟⠛⠉⠉⠀
⠘⠿⠾⠿⠛⠋⠉⣇⢸⡚⡇⡇
⠀⠀⠀⠀⠀⠀⣼⣯⣵⣮⡍⠓⢄⠀
⠀⠀⠀⠀⠀⢰⣿⡛⡫⣻⣿⡄⠀⢢⠀
⠀⠀⠀⠀⠀⠰⣿⣏⣽⣿⣿⣧⠀⠀⡆⠀
⠀⠀⠀⠀⠀⠀⠙⣾⡏⣿⡼⣿⣿⠆⠈⢻⣢⢄⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡹⠈⠃⣯⣘⢦⣀⡌⡿⠀⠈⢢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⡆⡄⠉⣷⣿⢷⣇⠃⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠸⣿⠿⣾⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠟⠉⡟⠀

⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠧⠤⡄⠀⢠⠤⠼⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⡖⢶⣀⠀⡇⠀⢸⠀⣀⡖⢲⣀⠀⠀⠀
⣀⣀⡀⠧⡄⢠⠽⠀⡇⠀⢸⠀⠧⡄⢠⠼⢀⣀⣀
⡇⠀⣇⣀⣉⣁⣀⣀⣧⠀⢸⣀⣀⣉⣁⣀⣸⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⡏⠉⡭⣭⠉⠉⡇⠀⢸⠉⠉⣭⣭⠉⢹⠀⢸
⠉⠉⠁⣖⡃⠚⣶⠀⡇⠀⢸⠀⣖⠓⠘⢳⠈⠉⠉
⠀⠀⠀⠀⠧⠾⠀⠀⡇⠀⢸⠀⠉⠧⠼⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡖⠒⠃⠀⠘⠒⢲⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⣾⣿⠛⣿⠛⣿⠻⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣤⣿⣤⣿⣤⣿⡇⠀
⠀⠀⢀⣴⠀⣿⣿⠟⢋⠉⠙⠛⣿⡇⢸⣦⡀⠀
⠀⢠⣿⣿⠀⣿⠇⠐⠀⠀⠀⠀⢸⡇⢸⣿⣿⡆⢀⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀
⠀⢸⣿⣿⠀⣿⣧⠈⠠⠀⠀⠃⣼⡇⢸⣿⣿⡇⠘⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀
⠀⢸⣿⣿⠀⣿⣿⣿⡶⠤⢶⣾⣿⡇⢸⣿⣿⡇⢸⣿⠿⣿⠿⣿⠿⡿⢿⣿⡇⠀
⠀⢸⣿⣿⠀⣿⣿⡏⠀⠀⠀⢸⣿⡇⢸⣿⣿⡇⢸⣿⣄⣿⣀⣿⣠⣧⣸⣿⡇⠀
⠀⢸⣿⣿⠀⣿⣿⡇⠀⠀⠀⢸⣿⡇⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠀⠈⠉⠉⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⢦⠗⢑⠘⠢⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢂⠀⠀⢌⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠰⠘⠀
⠀⠀⣐⣄⡀⠀⠀⠀⠀⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣀⣴⢄⠀⠀
⡠⢾⠟⠊⠂⠉⠤⠀⠐⠶⠿⠀⠀⠯⠤⠤⠤⠾⠓⠉⢈⡻⡂⣄
⠻⢓⣄⠀⣀⠠⢀⣀⣀⣀⣠⠈⢡⣄⣀⣀⣐⣀⡤⢀⠀⣔⡻⠋
⠀⠀⢎⠿⠋⠁⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠉⠻⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢸⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠘⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡝⡄⠀⢺⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡶⡲⢀⣤⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠽⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡏⠉⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠉⠉⠀⠀⠉⠉⢹⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠒⠒⡆⠀⡖⠒⠃⠀⠀⠀⠀
⠀⡿⡀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡜⡇
⠀⡇⡇⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⠇⡇
⠀⢧⠘⢴⠲⣄⠈⠉⠉⠀⢀⡴⢲⠞⢰⠀
⠀⠈⠳⡄⠳⠌⠳⡀⠀⡴⠋⠴⢁⡴⠁⠀
⠀⠀⠀⢸⠀⠀⠀⡱⢸⠁⠀⠀⢸⠀⠀⠀
⠀⠀⠀⡞⠀⠀⠀⡇⠀⡇⠀⠀⠸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⠑⠄⠀⠀⠀⠀⠀⠀⡠⠐⠉⡆⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠢⠤⠤⢀⡠⠊⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⢠⠊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀
⠀⢠⠁⠀⠚⠿⠁⠀⠀⠀⡠⣒⣤⠀⠀⠀⠀⠀⠀⠀⢣⠀
⠀⡇⠀⢀⣀⣀⠀⠀⠀⠀⠑⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⡄
⢠⠀⠀⢻⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⡄⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠱⠀⠈⠉⠙⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀