⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣴⠂⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⠀⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸⣤⣇⡼
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠃⠀⣀⣀⣠⣤⡤⠶⣿⠁
⠀⠀⠈⠛⢻⣽⢿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠉⠀⠀⠀⡿
⠀⠀⠀⠀⠙⠛⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢰⠇
⢴⡇⠀⠀⡴⠊⣿⣿⠁⠘⣿⣿⡇⠀⠀⣀⣤⣴⣶⣾⣷⣄
⢸⠀⠀⣠⠃⣼⡟⢱⠀⣸⣿⣿⣧⣶⣿⣿⣿⡿⠟⡿⢻⣿⣆
⠀⠉⠉⠁⣼⠏⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣦⣽⣿⣧⡀⠀⠀⠀⠀⣀
⠀⢤⡶⠾⠃⠀⠀⠀⠉⠛⢿⣿⣿⣿⡿⠿⠟⠛⠉⠟⠉⠛⠛⠿⠿⠷⠶⠾⠟⠁

⡀⡀⡀⣰⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⣆⡀⡀⡀
⡀⡀⣸⡏⣻⣦⣤⣤⣤⣤⣀⡀⡀⣀⣤⣤⣤⣤⣴⡟⣹⡇⡀⡀
⡀⡀⣸⡇⡀⣹⡆⡀⡀⡈⡙⣷⡾⡋⡁⡀⡀⣰⣏⡀⣸⡇⡀⡀
⡀⡀⣾⡛⡛⡋⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡙⡛⡛⣷⡀⡀
⡀⡀⣿⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣿⡀⡀
⡀⡀⡙⣧⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣼⡋⡀⡀
⡀⡀⡀⡘⣷⡄⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⡼⡃⡀⡀⡀
⡀⡀⣀⣀⣈⡻⣦⡀⡀⡀⡀⡀⡀⡀⡀⡀⣀⣴⡟⡁⣿⣦⡀⡀
⡀⣾⡋⡉⡉⡻⣮⡻⣦⡀⡀⡀⡀⡀⣀⣴⡟⡁⡀⣠⣿⣬⣷⡀
⡀⣻⣄⡀⡀⡀⡈⣻⣌⣻⣦⣀⣀⣴⡟⡁⡀⡀⡀⡉⣱⡟⡛⡀
⡀⡀⡉⡛⡶⡶⡶⡞⡛⣯⣈⡉⡉⡁⡀⡀⡀⡀⣀⣴⡟⡀⡀⡀
⡀⡀⡀⡀⡀⡀⡀⡀⡀⡀⡙⡷⣦⣤⣤⣤⣤⡶⡟⡁