⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣾⠇⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠉⠉⠉⠁⠀⠉⠉⠙⠷⢄⣴⡾⠛
⠀⠀⠀⠀⠀⡀⠀⡼⠋⠀⠀⠀⢀⣤⣶⣶⠶⢄⠀⠀⠈⢳
⠀⠀⠀⠀⠀⢻⣿⡃⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⢰⠟⠁⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⣻⡋
⠀⠀⠈⠙⠹⡟⠂⢀⠀⠀⣀⣤⣤⡈⠁⢀⣴⣿⣶⣄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⢤⣧⠀⠘⣧⣰⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠀⠀⣾⠁
⠀⠀⠀⠀⠊⠀⢀⠀⠘⠿⣿⣿⣿⠟⠀⠈⠛⠿⠟⣿⠃⠀⢠⡾⠷⠤⠞
⠀⠀⠀⠀⠀⠀⢀⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠞⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠐⠛⠀⠈⠑⢄⣠⣄⡀⡀⠀⠀⣀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠉⠙⢻⣦⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦