⠀ ⠀⠀⠀ ⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣶⣶⣶⣦⡄
⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀
⠀⠀ ⠸⣿⣿⠟⠉⠀⠀⠉⠛⠛⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⡢⣫⠓⣞⡨⡄⢲⣢⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡄⢚⡱⡎⢸⠐⢸⠐⣱⢧⢍⡻⠷⡾⢬⣕⣒⠤⣀⠀⠀⠀
⢀⡤⣫⢱⣏⡇⡧⣈⠬⡼⠤⠙⡦⣼⢩⣽⡶⠫⣤⡞⣣⣴⠍⣢⣄
⠈⢙⣿⣤⢇⡇⡇⣿⠁⣇⣸⠀⡗⣸⠭⢭⣭⡇⣝⡷⣋⣼⣹⡏⠀
⠀⠸⣿⣿⠠⡇⡷⠯⠐⢳⡖⢡⡓⢸⢚⣓⠶⠇⡻⡘⠺⣴⡚⡇⠀
⠀⢰⣿⣿⡐⡇⡗⢠⡉⠰⢠⢛⠄⣹⠸⣏⡳⡆⣷⡌⢸⡥⠞⡇⠀
⠀⠸⠷⢿⣅⡇⡏⣼⡆⡁⢺⡘⠄⢲⠹⣌⢳⡦⠏⣾⣫⡶⠽⠃⠀
⠀⠀⠀⠀⠀⠉⠁⠛⠧⣅⣺⡐⠌⡢⣝⢬⣼⠓⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀ ⣴⠞⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⡇⠀⠀⠀⠈⢻⣄⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀
⠀⢹⡇⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠉⢳⡆⠀⠀⠀
⢀⡬⣷⡀⡴⠛⢳⣼⡏⠀⠀⠀⠀⢀⡌⣿⠀⠀⠀
⢸⡀⣤⣟⣳⠚⠘⡿⣧⡀⠀⣀⣠⡾⠃⢿⣄⠀⠀
⢠⣧⣴⠾⠙⠓⠒⠃⠈⠛⠛⠛⠉⠀⠀⠀⠙⣧⠀
⣾⠃⠀⢀⣤⡶⠒⠛⠛⠛⠛⠒⠶⣤⡀⠀⠀⢹⣆
⣿⠀⢠⡟⢡⣤⠀⠀⠀⠀⠀⠀⢠⣤⡙⣦⠀⢸⡏
⠻⣆⢸⠀⠿⡿⠀⠀⢠⣤⠀⠀⠸⠿⠇⢸⢠⡾⠁
⠀⠉⠛⠷⣤⣄⣀⣀⣑⣒⣁⣀⣀⣤⡶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡤⣂⣭⣭⣅⠢⡀⠤⢀⣀⣀⠂⠾⡿⠛⢿⣦⢡
⠀⠀⡌⢰⡿⠉⠉⠙⣡⣶⣿⣿⣿⣿⣿⣷⣦⡀⣸⡿⠸
⠀⠀⢃⠸⣿⡤⢀⣾⣿⡿⠛⣿⣿⣿⣿⠛⢻⣿⣄⢶⠁
⠀⠀⠀⠁⢒⢠⣿⣿⣿⣇⣀⢟⡛⠛⠛⡠⢼⣿⣿⡄⡆
⠀⠀⠀⠀⠸⢸⣿⣿⣿⣿⢱⡿⣷⡦⢴⠇⡇⣿⣿⠃⠇
⠀⠀⠀⠀⠀⠣⢙⠻⢿⣿⣧⣝⣲⠾⢗⣫⠼⢛⠅⠉⠀
⠀⠀⠀⠀⠀⡀⠤⣃⡒⣬⣭⣭⣭⡭⠭⢴⣦⠑⠠⣀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠄⣪⣴⣿⣿⡷⢸⣿⡟⣵⣾⣿⣷⣮⢣⢻⣶⣭⠒⣂⣔⢂⠀
⢀⢊⣴⣾⣿⣿⣿⣿⠇⡿⠟⣃⡛⠿⣿⣿⣿⡏⡆⢿⡟⢸⣿⡤⠆⡄
⢨⠨⡀⠀⠉⢿⣿⠟⡌⡴⢙⡀⣏⠙⡌⣿⣿⣿⢸⠈⣤⢸⣿⡇⠀⡇
⠀⠑⠬⠑⣒⠪⢄⠺⡇⣿⠉⠀⠀⠉⡇⡿⠿⣣⢏⣼⣿⣿⣿⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠢⠙⣄⠀⠀⢠⢃⡛⠩⠀⠈⠩⠭⠭⠭⠍⠑⠁

⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀
⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⢻⡀⠀⠀
⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒
⠀⠀⠈⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀
⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀
⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⣶⣤⣴⡶⠶⠶⠟⠛⠉⠀⠀⠀⠀