⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁

⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁

⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁

⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁

⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁

⣿⡇⠀⣿⣿⠀⢠⣿⣿⡆⠀⢻⣷⠀⣿⡏⢸⣿⠿⠇⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀ ⢠⣶⣦⠀⠀⠀⠀⠀⢿⣦⣿⡄⠀⠀⠀
⣿⡿⠿⣿⣿⠀⣼⣏⣸⣷⠀⠘⣿⣴⡿⠀⢸⣿⠿⠇⠀⠀⢀⣿⣇⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣾⣿⠀    ⠀⠟⠉⠀⠀⢾⣧⣼⡷⠀
⠿⠇⠀⣿⣿⠰⠿⠋⠉⠿⠆⠀⠹⠿⠃⠀⠸⠿⠿⠗⠀⠀⠸⠿⠉⠙⠿⠄⠀⠀⠀   ⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠙⠋
⣿⣷⡀⢸⣿⠀⣿⡇⢀⣶⡿⠿⠆⢸⣿⠿⠇⠀⠀⢻⣷⠀⣾⣿⣷⠀⣾⡟⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡇⣴⠿⢸⣿⠿⠇ ⣿⣷⡀⢸⣿ ⣿⠿⠻⣶⡀
⣿⡟⢿⣾⣿⠀⣿⡇⢸⣿⡀⠀⠀ ⢸⣿⠿⠇⠀⠀⠘⣿⣴⡿⠘⣿⣴⡿ ⢸⣿⠿⠇⢸⣿⠿⠇ ⣿⡷⡇ ⠀⢸⣿⠿⠇ ⣿⡟⢿⣾⣿ ⣿⠄⠄⣿⢸
⠿⠇⠈⠻⠿⠀⠿⠇⠈⠻⠿⠿⠇⠸⠿⠶⠆⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁  ⠸⠿⠿⠗⠸⠿⠿⠗ ⠿⠇⠻⠿⠸⠿⠿⠗ ⠿⠇⠈⠻⠿ ⠿⠿⠿⠟⠁