⢻⣶⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢻⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣿⡟
⠀⠀⠣⡀⠀⠀⠀⠑⢄⢀⣀⣀⣀⣀⣀⣀⠤⠒⠉⠀⠀⠀⢠⠟⠀
⠀⠀⠀⠑⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢤⠊⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠀⠀⢮⣽⠀⠀⠀⠀⠀⠰⣭⡇⠀⠀⠈⢆⠀⠀⠀⠀
⠀⠀⠀⠀⢃⠠⢄⠈⠁⠀⠰⠶⠀⠀⠀⠈⠀⡀⣀⠀⠸⡀⠀⠀⠀
⠀⠀⠀⢸⠠⣀⣠⠇⠀⠀⡠⠐⠒⡄⠀⠀⠨⡀

⢀⣠⣤⣤⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣶⠶⣶⠄⠀⠀⠀⢀⣤⣄⡀⢀⡀
⠈⢹⡟⠀⠀⠀⠀⣧⡤⠀⢠⡟⢻⣆⠈⢿⡄⠀⢀⣴⠿⣦⠀⠘⣷⠀⠀⠀⠀⣀⣴⠿⣦⡄⠀⢠⡿⠁⠙⢿⣬⣿⡀⠀⢀⣴⠟⢷⡄⠸⣦
⠀⠸⣧⣤⣤⣶⠀⠃⠀⠠⡟⠁⠀⠹⠃⠸⠗⠀⢸⣇⠀⣸⠇⠀⢻⡆⠀⠀⣛⣯⣥⣤⣤⣤⡄⠸⣧⣄⣠⣾⠿⢿⡇⠀⢸⣇⠀⢸⡿⠛⣿
⠀⠀⠀⢠⡞⠛⠛⢻⡆⠀⠀⣷⡀⠀⠀⢀⣀⠀⠀⠙⠛⠋⠀⠀⠘⠃⠀⠀⠉⣿⠶⠾⠷⣦⠀⠀⠀⢉⣭⣤⣠⣶⣦⡀⠀⠀⠙⠛⠛⠁⠀⣿
⠀⠀⠀⠘⠛⠿⠿⠟⠃⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠛⠁⠘⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉

⢀⣠⣤⣤⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣶⠶⣶⠄⠀⠀⠀⢀⣤⣄⡀⢀⡀
⠈⢹⡟⠀⠀⠀⠀⣧⡤⠀⢠⡟⢻⣆⠈⢿⡄⠀⢀⣴⠿⣦⠀⠘⣷⠀⠀⠀⠀⣀⣴⠿⣦⡄⠀⢠⡿⠁⠙⢿⣬⣿⡀⠀⢀⣴⠟⢷⡄⠸⣦
⠀⠸⣧⣤⣤⣶⠀⠃⠀⠠⡟⠁⠀⠹⠃⠸⠗⠀⢸⣇⠀⣸⠇⠀⢻⡆⠀⠀⣛⣯⣥⣤⣤⣤⡄⠸⣧⣄⣠⣾⠿⢿⡇⠀⢸⣇⠀⢸⡿⠛⣿
⠀⠀⠀⢠⡞⠛⠛⢻⡆⠀⠀⣷⡀⠀⠀⢀⣀⠀⠀⠙⠛⠋⠀⠀⠘⠃⠀⠀⠉⣿⠶⠾⠷⣦⠀⠀⠀⢉⣭⣤⣠⣶⣦⡀⠀⠀⠙⠛⠛⠁⠀⣿
⠀⠀⠀⠘⠛⠿⠿⠟⠃⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠛⠁⠘⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉

⢀⣠⣤⣤⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣶⠶⣶⠄⠀⠀⠀⢀⣤⣄⡀⢀⡀
⠈⢹⡟⠀⠀⠀⠀⣧⡤⠀⢠⡟⢻⣆⠈⢿⡄⠀⢀⣴⠿⣦⠀⠘⣷⠀⠀⠀⠀⣀⣴⠿⣦⡄⠀⢠⡿⠁⠙⢿⣬⣿⡀⠀⢀⣴⠟⢷⡄⠸⣦
⠀⠸⣧⣤⣤⣶⠀⠃⠀⠠⡟⠁⠀⠹⠃⠸⠗⠀⢸⣇⠀⣸⠇⠀⢻⡆⠀⠀⣛⣯⣥⣤⣤⣤⡄⠸⣧⣄⣠⣾⠿⢿⡇⠀⢸⣇⠀⢸⡿⠛⣿
⠀⠀⠀⢠⡞⠛⠛⢻⡆⠀⠀⣷⡀⠀⠀⢀⣀⠀⠀⠙⠛⠋⠀⠀⠘⠃⠀⠀⠉⣿⠶⠾⠷⣦⠀⠀⠀⢉⣭⣤⣠⣶⣦⡀⠀⠀⠙⠛⠛⠁⠀⣿
⠀⠀⠀⠘⠛⠿⠿⠟⠃⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠛⠁⠘⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉

⢀⣠⣤⣤⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣶⠶⣶⠄⠀⠀⠀⢀⣤⣄⡀⢀⡀
⠈⢹⡟⠀⠀⠀⠀⣧⡤⠀⢠⡟⢻⣆⠈⢿⡄⠀⢀⣴⠿⣦⠀⠘⣷⠀⠀⠀⠀⣀⣴⠿⣦⡄⠀⢠⡿⠁⠙⢿⣬⣿⡀⠀⢀⣴⠟⢷⡄⠸⣦
⠀⠸⣧⣤⣤⣶⠀⠃⠀⠠⡟⠁⠀⠹⠃⠸⠗⠀⢸⣇⠀⣸⠇⠀⢻⡆⠀⠀⣛⣯⣥⣤⣤⣤⡄⠸⣧⣄⣠⣾⠿⢿⡇⠀⢸⣇⠀⢸⡿⠛⣿
⠀⠀⠀⢠⡞⠛⠛⢻⡆⠀⠀⣷⡀⠀⠀⢀⣀⠀⠀⠙⠛⠋⠀⠀⠘⠃⠀⠀⠉⣿⠶⠾⠷⣦⠀⠀⠀⢉⣭⣤⣠⣶⣦⡀⠀⠀⠙⠛⠛⠁⠀⣿
⠀⠀⠀⠘⠛⠿⠿⠟⠃⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠛⠁⠘⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉

⢀⣠⣤⣤⣤⣤⠀⡀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣶⠶⣶⠄⠀⠀⠀⢀⣤⣄⡀⢀⡀
⠈⢹⡟⠀⠀⠀⠀⣧⡤⠀⢠⡟⢻⣆⠈⢿⡄⠀⢀⣴⠿⣦⠀⠘⣷⠀⠀⠀⠀⣀⣴⠿⣦⡄⠀⢠⡿⠁⠙⢿⣬⣿⡀⠀⢀⣴⠟⢷⡄⠸⣦
⠀⠸⣧⣤⣤⣶⠀⠃⠀⠠⡟⠁⠀⠹⠃⠸⠗⠀⢸⣇⠀⣸⠇⠀⢻⡆⠀⠀⣛⣯⣥⣤⣤⣤⡄⠸⣧⣄⣠⣾⠿⢿⡇⠀⢸⣇⠀⢸⡿⠛⣿
⠀⠀⠀⢠⡞⠛⠛⢻⡆⠀⠀⣷⡀⠀⠀⢀⣀⠀⠀⠙⠛⠋⠀⠀⠘⠃⠀⠀⠉⣿⠶⠾⠷⣦⠀⠀⠀⢉⣭⣤⣠⣶⣦⡀⠀⠀⠙⠛⠛⠁⠀⣿
⠀⠀⠀⠘⠛⠿⠿⠟⠃⠀⠀⠈⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠛⠁⠘⠛⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉