⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠎⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢰⠱⠁⠀⠀⠆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⣰⣿⡄⢨⠁⢀⠔⠁⠀⠀⠀⠀⠐⠀⢦⠇⠀⠄⠀⠰⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⢀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣿⣿⣧⣇⡀⡌⠀⠀⠀⠀⢀⣤⢄⡀⣈⠂⠐⡨⠒⢛⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠓⠠⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠡⢺⠀⠀⠀⠀⠀⠊⠀⠘⢣⠡⠀⡰⠁⠀⡘⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⣄⣴⣿⢻⣿⣬⡕⠀⠀⣠⠄⠂⠉⠀⢀⠞⠁⠐⠅⠀⠔⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣼⡿⠋⠀⠙⣿⣇⣼⠘⠁⠀⠀⠀⢠⠋⠀⢀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢀⣴⣶⣿⣿⠟⠁⠀⠀⠀⠙⢻⣿⣷⣶⣄⡠⢢⠃⠀⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠚⠉⠉⢹⣿⡇⠀⠀⠀⠀⠀⣸⣿⡉⠉⠉⠃⢀⠣⢒⡀⢱⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡮⠥⠔⢦⡁⠙⣿⡆⠀⠀⠀⣸⡿⠁⢀⠎⣴⠉⣷⣄⠀⢋⠜⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣆⠀⠀⢻⣶⣾⣿⠀⠀⢰⣿⣷⣾⠏⠀⢁⣴⣿⣿⣶⣅⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠉⢀⣆⣨⣿⡇⠘⢿⣷⣶⣼⣿⣿⡟⠀⠀⠘⣿⣿⣿⣤⣶⣿⠟⠁⢾⣿⣄⣤⡈⢑⣧⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠟⠛⠛⠛⠀⠀⠀⠈⠙⠛⠛⠿⠃⠀⠀⠀⠙⠟⠛⠛⠉⠁⠀⠀⠈⠛⠛⠛⠻⣿⣿⣿⣶⣄⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠟⠛⠉⠉⠉
⢀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣈⠻⣿⡛⠻⡿⠿⣧⠀⢀⣤⣶⣶⡾⣿⣿⡄⠀⠀⠀⢰⣿⡿⡶⣶⣦⣄⠀⠀⣾⠿⣿⠟⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢾⣿⣦⣿⡿⢋⣤⣴⣿⢿⣷⠀⠀⢠⣾⣿⣷⡀⠠⡙⣿⣷⣴⣿⡖⠀⠀⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡝⢿⣿⠉⠉⡴⠋⡁⢸⣿⠀⠀⢸⣿⠄⠈⡿⣄⠫⣸⣿⡟⠁⠉⠉⠁⠉⠁⠀⠀⠀⠰⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⢠⠛⠉⠉⡱⠊⠀⠀⣉⠗⠙⡉⣘⣁⣹⣷⠀⠀⢠⣿⠇⠀⠇⠈⠀⠘⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢀⡴⠽⠁⠀⢀⠷⠑⠀⢸⣿⠀⠀⢸⣿⠀⠌⠀⠀⠀⠀⠀⠀⠈⠓⠂⠤⠤⠀⠠⠖⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢽⠀⠀⢀⡇⠀⠀⡆⣸⡟⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⡠⣹⠂⠀⢸⠀⢀⡔⠁⢸⣷⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⡌⠀⠄⠀⠑⠘⡀⠉⠀⠀⣸⣿⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠚⠆⢂⠀⠀⠀⠀⠁⢄⢀⣰⣿⠇⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡡⠂⠠⠄⠂⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⢢⠀⠀⢠⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠄⠀⠀⠈⠂⠄⢸⡏⠀⢸⣿⣷⣦⡀⠀⣠⣴⣾⣿⡁⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠁⠙⠋⠹⣿⠙⢿⣿⣼⣿⡟⢹⡿⠋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⢘⣿⣿⣿⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀