⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣦⡀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⣚⣥⣤⠀⠀⢀⠔⠒⠒⠲⠦⡀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣦⣤⣤⣀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢎⣾⣿⠟⠁⡠⠖⣡⣶⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⡇⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⡔⣱⣿⠟⠁⡠⠊⣠⣾⣿⡿⠟⠁⠀⢀⠌
⠀⠀⠀⠀ ⠀⠀⡀⠀⣼⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠉⠀⠀⠀⠀⠉⠀⠘⠛⠛⠁⠀⣀⠤⠚⠁⠀
⠀⠀⠀⠀ ⠀⠀⠣⡀⣿⣄⠣⠃⢻⣿⡿⢛⢛⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣿⡆⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠁
⠀⠀⠀⠀ ⠀⠑⠤⣈⠽⣿⣿⣿⡿⢿⣤⣈⣁⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀ ⠑⠒⠒⠒⠉⣻⣿⣿⣿⣿⣿⣿⠿⠤⠤⢊⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁ ⠀⠀⠀⠀⠀⣰⠁⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ 
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠘⢄⠉⠒⣲⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠛⠁⠐⠂⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ 
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⠉⠒⣿⣿⡛⢿⣿⣿⠀⠀⠀⢠⣶⣦⠀⠀ ⠀ ⠀⠀⠈⢧⣠⣾⣷⣦⣠⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⡇
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣿⡿⢸⣿⣿⠀⠀⠀⠸⣿⣿⣾⣿⠀⠀ ⠀⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠟⠛⠉⠁ ⠀⠀ ⠀ ⠀⠈⢿⣿⣿⣿⣿⣯⡉⠉⠉⠒⠲⢤⡔⠁⠀ ⠀ ⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠻⣿⣿⡿⡋⠉⠓⠦⡄⠀⠀⠉⢫⠉⡆⠀⠀⠀ ⠀⠀⠀
⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⠀⠀ ⣠⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⠀⠀⠀⠀⠈⢢⠤⠤⠜⠀⠀⠀⠀⡗⠁⠀⠀⠀⠀⠀ ⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡿⢿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠙⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡖⠒⠒⠤⣀♡