⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣿⠁
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⣾⣟⡇
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠈⠻⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⢠⣠⣤⡀⠀⠢⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⡀⠀⣠⣾⣏⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠟⠋⠈⠀⠀⠈⢻⣦⣼⡀⠀⠀⠀⠀⠀⠀⠉⢻⢽⣿⣾⠟⠀⠈⠀⠀⠀⠀⠀⢠⠊⢀⡠⠔⠀⠀⠀⠀⠀⣴⠟⠉⠘⠆
⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣤⣀⠀⠀⠀⠀⠀⢸⡀⢻⡏⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠙⢷⣦⣀⣄⠀⠀⠁⢨⡃⠀⠀⢀⣤⡶⠟⣽⡃⠀⠀⠀⠀⠀⠀⠀⢘⣴⠏
⠀⠀ ⠀⠀⠀⠀⢠⣿⠟⠉⠉⢹⣿⡀⡀⡀⠀⠀⠀⠀⠀⣿⡄⠘⣿⠿⢿⣿⣦⣀⠀⢹⠀⣠⡿⠋⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⣦⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⠹⡀⠀⠀⠀⠉⢩⣿⠗⠀⠀⠀⠀⠀⢸⣷⢸⣿⠀⠀⠉⠻⣿⣷⣶⣾⠋⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⠃⠉⣻⣿⡂
⠀⠀⠀ ⠀⠀⠀⠹⣷⣱⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡆⠀⣠⣾⡿⠛⠻⢿⣦⣄⣀⣼⠇⠀⠀⠀⠀⠀⠀⠐⢿⣷⣀⠀⠀⢀⣤⡞⠉⠁
⠀⠀⠀ ⠀⠀⠀⠐⠿⣿⣶⣤⣠⡿⠛⠳⡂⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣼⠟⠋⠁⠀⠀⠈⠈⢹⣿⣿⣤⣄⡀⠀⠀⠀⠀⠀⠘⠛⢿⣧⠀⣹⣿⡇
⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡽⠛⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⢿⣷⣄⣠⡀⠀⠀⠀⠀⢠⠿⢿⣻⡟
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡞⠉⠀⠈⣿⡄⠀⠀⠀⠀⢀⣀⣿⣷⠀⠀⠈⣏⠉⠙⢿⡄⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠐⠊⠉⠉⠈⠉⠛⣻⠿⠿⠿⠿⢿⣿⣾⣷⣶⣶⣶⣾⢿⣿⡿⠛⠿⠿⠿⠿⠛⠛⠛⠛⢷⡖⠢⠄⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠈⠋⣿⣇⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣼⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣰⠏⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳⠄