⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⠛⠁⠙⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣀⣀⣤⣾⣿⣿⣿⣿⣶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣖⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣾⣿⣿⠛⠻⣿⣿⡿⠛⠛⠛⠛⢿⠿⢿⣿⣿⠋⠁⠀⠹⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣸⣿⡷⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⣿⣿⡃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣿⣿⠀⠀
⠀⠀⠀⣀⣠⣶⣿⣿⠟⠻⠛⠻⠛⠀⠀⠀⠀⠀⠺⣿⣷⣦⡀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣟⠀⠀
⢀⣴⣾⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢻⣿⣿⣴⣿⣿⠇⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠘⠻⢿⣿⣿⡄
⣿⣿⠟⠋⠀⠀⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠹⣿⣿⣿⡋⠀⠘⠿⠟⠀⠀⠀⣾⣿⣧⣀⡀⠈⠛⠟⠁⠀⠀⠀⢹⣿⡟
⠉⠀⠀⠀⢸⣿⣿⠿⠿⠿⣿⠇⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⢻⣿⡿⠁⠀⠀⠀⢰⣾⣿⣿⣿⠿⠿⣿⠗⠀⠀⠀⠀⠀⢀⣴⣾⣿⠗
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠀⠀⢸⣿⣧⡄⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⡀⣀⣤⣴⣿⣿⡿⠟⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠿⣿⣿⣥⡀⠀⠀⠀
⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⠆⠛⢻⣿⣦⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀
⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣾⣿⣿⡇⠀⠀
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠻⠟⠁⠀⠀
⣿⣿⣄⡀⠀⠀⠀⠀⠀⢠⣠⣤⣤⣠⣶⣿⣿⣿⣦⡄⠀⠀⣠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠋⢠⣿⣿⢇⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀
⢸⣿⣿⣯⡉⠉⠉⠉⠉⢉⠀⣀⣤⣤⣶⣿⣿⣿⢋⣿⣿⣿⣿⡇⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⡀⠀⣹⣿⡇⠀⠀⠀⠀⠀
⠀⠉⠻⣿⣿⣿⣶⣶⣶⣶⣿⣿⡿⠛⠛⢛⣽⣷⣾⣿⠟⣸⣿⣇⣴⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠹⣿⣿⣴⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣿⣿⣝⣉⣉⣡⣤⣤⣶⣿⣿⠿⠟⠁⠀⠙⠿⠻⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀