⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢰⣿⣷⡄⣀⠠⠖⠉⠉⠉⠉⠉⠐⠒⠄⣀⡀
⠀⠀⠀⣼⣿⣷⣄⡀⠀⠀⢰⣿⣿⣿⣷⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣆⣀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠟⠛⠛⠉⢉⠔⠈⠀⠀⠀⠈⠁⠢⡀⢰⣿⣿⣿⣿⡇⠁⠦
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠜⠈⠻⣿⣿⡿⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠀⠀⠀⠤⠤⢤⡀⡔⠁⠀⠀⠀⠈⣡⣴⣶⣶⣶⣤⣵⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢀⠆⠻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠄⠠⠤⠚⢤⣀⣀⣀⣠⠔⢹⡀⠀⠀⠀⡘⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠲⠴⢖⡏⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⡿⢿⠿⠏
⠀⠀⠀⠀⢠⠁⠀⠀⠀⡤⠊⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⢸⠀⠀⠀⢀⠞⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀
⢀⣤⣶⣾⡏⠀⠀⠀⠑⢄⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢤⣠⠤⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⢃
⠀⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠷⠒⠒⠦⡀⢀⣀⠠⠤⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⡀⡆
⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣾⠆⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣶⣤⣤⡤⠤⠤⠤⠐⠒⠉⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠋⠁