⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠉⠉⠉⠉⣉⣉⠑⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠢⠤⣀
⠀⠀⠀⠀⣠⠖⠉⠀⢠⣶⣶⣾⠟⠛⠛⠋⠛⠋⠉⠓⠄⠙⠒⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠤⠖⠉⠠⠒⠺⠟⠻⠶⠾⢷⣤⣤⡀⠉⠲⣄
⠀⠀⣠⠎⠀⣀⣾⣿⣿⠃⢀⡤⠖⠚⠉⠉⠉⠉⠑⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠈⠉⠐⠲⠬⡉⠙⣿⣿⣆⠈⠳⡄
⠀⡰⠁⠀⢸⣿⣿⠇⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢹⣿⣿⠀⠘⣆
⢰⠃⠀⢰⣿⣿⠉⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⢀⣀⣀⣀⣈⠉⠲⢄⠀⢀⡤⠊⠁⣀⣀⣀⡀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢹⣿⡷⠀⠘⡄
⡎⠀⢀⣼⣿⡿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣦⡀⠙⠛⠯⡛⠾⣟⢿⣿⣿⣷⣤⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⣿⣷⡀⠀⢣
⡇⠀⠀⣹⣿⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⠀⠈⢷⣿⣿⣿⣿⣿⣦⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⡀⠀⢸
⡇⠀⠈⢙⣿⣯⡀⣇⠀⠀⠀⠀⠀⠀⡠⠋⢀⣼⣿⣿⣿⣿⣿⡿⠿⠿⣿⡿⠿⠛⠉⢇⠀⠀⠈⠀⡠⠫⠿⢿⣿⣿⣿⣿⣷⡄⠑⡄⠀⠀⠀⠀⠀⡎⢠⣿⣏⠁⠀⢸
⢣⠀⠀⠛⣿⣿⡃⠘⢦⡀⠀⢀⡠⠎⢀⣴⣿⠟⠋⠉⠉⠁⠀⠀⢀⣠⡆⠀⠀⠀⣀⢈⠑⠢⠤⡪⡀⠀⠀⠈⣇⠀⠀⠉⠻⣿⣦⡈⠢⢄⣀⣀⠜⣀⣸⣿⡏⠁⠀⡞
⠘⡆⠀⠈⣻⣿⣿⣷⣀⡈⠉⣁⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⣴⠋⣿⡿⠀⠀⠀⠀⠈⠛⠄⠀⠀⠦⠃⢠⣿⠃⠀⢣⠀⠀⠀⠈⢿⣿⣷⣦⡀⣠⣤⣿⣿⣿⡍⠀⣰⠃
⠀⠘⣄⠀⠉⠿⣿⣿⣿⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠉⠀⠀⠉⠁⠈⡆⠀⠈⡆⠀⠀⠀⢸⠏⠀⠀⡸⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⡟⠓⠀⡰⠃
⠀⠀⠈⢦⡀⠀⠋⢹⠻⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⡶⢾⣿⣿⠛⠀⠀⠘⠀⠀⠀⠸⣞⣿⣿⠳⠀⠀⠀⠀⠀⠘⢿⣿⢿⠻⠛⠇⠀⢀⠜⠁
⠀⠀⠀⠀⠙⠦⣀⡀⠀⠁⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠑⠤⠛⠋⠠⢀⠀⠀⠀⠀⠀⠀⠈⢯⣭⢖⠀⠀⠀⠀⠀⠀⠈⠻⡆⣀⣀⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⡦⣀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢳⣡⠀⠑⠲⠤⣄⡀⠀⠀⣙⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡜⣩⠤⡀⠈⠑⠦⣀⠀⠀⠀⠙⠦⠴⠲⢄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠃⠀⢀⣤⡤⠶⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⢠⣶⠦⣄⠀⠀⠑⠠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢯⠶⠲⠶⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢹⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⠓⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠈⢉⡿⠀⣀⡄⠀⠀⠀⠀⠈⠉⠛⠛⠉⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢿⣇⢸⣿⣷⡖⠀⠀⠀⠀⠀⠀⢀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠻⣿⡻⣷⣄⠀⠀⠀⠀⢀⡼⣠⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃⠙⣿⣿⠀⣴⣾⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣼⢻⣿⣦⣻⣿⣿⣿⣿⣷⣤⣂⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⢿⡿⣿⣿⠻⢿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉