⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⢻⣷⣾⣿⣾⣾⢹
⠀⠀⢄⣼⣂⠀⠀⠀⠀⠀⠀⢻⡉⢻⣿⣿⠿⠿⣿⠿⣿⠆
⠀⠀⠨⣿⣿⠀⠀⠀⠀⢀⣀⣾⢾⣾⡿⠇⣲⣦⡄⠀⠸⡯
⠀⠀⢠⡟⡟⠀⠀⠘⠻⣿⣿⣿⣿⣿⣷⠀⠉⠙⠓⠀⠀⣑⣄
⠀⡰⠁⡾⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠀⠀⠐⠤⣄⣀⣹⡝
⠘⢰⠏⠀⠀⠈⠙⠿⣿⣿⣿⢸⣿⣿⣿⠀⢨⣿⣗⡒⠒⠉
⢠⡞⠀⠀⠀⠐⠛⠛⣛⣿⣾⢸⣿⢸⣿⠀⠘⠿⢦⡤⡀
⡼⠀⠀⠀⠀⠀⠀⢠⠊⠁⢹⡇⢻⣅⠈⠇⠀⠀⠀⢸⣧⡇
⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣭⡀⠈⠇⠀⡀⠀⠀⡀⠈⠿⡄
⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣶⣄⡀⠈⢆⡌⠀⣠⣿⣷
⣻⡀⠀⠀⠀⣀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠈⢀⣾⣿⣿⣿
⠈⠙⣻⠛⠉⠀⡇⠀⠀⠀⠛⢿⣿⣿⣿⠿⠛⢛⠛⠿⠟⠋
⠳⢶⠀⠀⠀⠀⢘⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠔⠁⡜
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⣤⣤⣤⢠⠎⠀⠀⡜
⠀⢸⠀⠀⠀⠀⠀⢡⠀⠀⢸⠈⡿⠁⠸⠀⠀⡜