Donkey Emojis & Symbols

⠀⠀⠀⠀⢠⠞⣧
⠀⠀⠀⠀⣼⠀⢸⡄⠀⠀⠀⣠⠞⣹
⠀⠀⠀⢀⡇⠀⠈⡇⠀⢀⠞⠁⢠⡇
⠀⠀⠀⢸⠇⠀⠀⡇⢠⠏⠀⠀⡼
⠀⠀⠀⢸⡀⠀⢰⢇⡏⠀⠀⣸⠁
⠀⠀⠀⣈⠷⠶⠺⠾⣀⢀⡼⠁
⠀⢀⡞⠁⠀⠀⠀⠀⠈⢯⢳⡀
⢀⡞⠀⢴⠀⠀⠀⣀⠀⠈⣇⢹⣀
⣸⠁⠀⠀⠀⠀⠀⠉⠀⠀⢹⣆⠈⢧⡄
⣏⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠉⢷⣄⡀
⡏⠀⠀⠆⢩⠝⠲⢤⡀⠀⡟⠀⠀⠈⠓⢤⡀⠉⠛⢦⣀
⢳⠀⠀⠀⠀⠀⠀⠀⠳⣴⠃⠀⠀⠀⠀⠀⠀⠘⠂⠀⠭⢉⡂⢤⣀⡀⢀⡀⠤⠤⠤⠤⢤⣄⡀
⠀⠳⣄⠀⠀⠀⠀⣀⡴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠉⠓⠚⠋⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠃⠀⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠀⢸⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆⢸⡍⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⠴⡞⠁⢸⡄⢸⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢻⠀⣧⠀⠈⡇⢸⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢻⠀⠀⡇⢸⡆⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡄⠀⣇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠇⠀⢻⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣍⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣺⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧⣿⣿⣭⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⣿⣿⣷⣤⣦⣈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣯⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣻⣿⢿⣿⣿⣿⣿⣿⣴⣿⠉⠀⠈⠉⠙⠛⠲⣾⡾⠁
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⢻⣏⣉⣯⣻⣿⣿⣿⠇
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⠛⠻⢟⣿⠏⠁⠀⠈⠻⡜⢯⢷⣯⣾⡿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⠁⢛⢆⡠⢄⣄⣀⣀⣿⠮⠅⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣺⣿⣿⣷⣏⣷⣿⣖⣴⡆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠿⠛⠙⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⣾⢼⣿⣿⣿⣿⣿⣿⠛⠉⠙⠛⠻⠿⠒⠂⠀⠀⠀⠉⠉⡟⢉⢀⣼⡇
⠀⠀⠀⢻⣿⣿⣿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⢟⣿⠅
⠀⠀⠀⣸⣿⣿⠋⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢸⣿⠇
⠀⠀⠀⣿⣿⠃⠀⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⢿⠃
⠀⠀⠀⣿⡏⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠙⣷⣄
⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣆⠀⠀⠉⠋
⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢱⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡠⠓⠉⢉⠤⠐⠀⠀⠀⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡰⠁⡠⠊⣀⠤⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⢡⠞⠊⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣠⠚⠀⠁⢀⣤⠂⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠐⠣⠎⠀⠀⠀⠀⠀⠌⠀⠈⠢⡐⠧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢔⣠⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠿⢿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠓⠤⣀
⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠑⠂⠄⣓⠀⢤⡀⢀⣀⡀⠤⠤⠄⠀⠀⠐⠒⠀⠐⠀⠠⠄⣀
⠀⡀⠤⠊⠣⡈⠢⣀⠀⠀⠀⣀⠀⠀⠤⠐⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⡎⡠⠠⡀⠀⠉⠢⣀⠑⢢⠊⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢄
⢃⠉⠉⠀⠀⢀⡔⠀⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⡀
⠀⠑⠠⠤⠴⣀⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢆⠘⡄
⠀⠀⠀⠀⠀⠡⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡒⡄⠀⠀⠀⠀⢀⠦⠤⠀⠀⣀⡀⡀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⡁⠈⠲⢀⠀⠀⠀⠰⡀⠀⠀⢠⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢣⠀⠀⠀⠑⢄⠀⡇⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⡘⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠂⡇⠀⠀⠰⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢠⠁⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠈⡄⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠃⠀⠀⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠘⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠒⠰⠂⠉⠉⠉⠈⠃⠀⠀⠀⠀⡐⠊⠉⠉⠐⠃⢀⠐⠓⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⡔⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡀⠀⠀⠀⣤⡤⢠⣤⡦
⠀⠀⠀⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠄⠀⠀⣿⡇⣸⣿⡇
⠀⠀⠀⣿⡿⢹⡹⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠒⠀⠀⣿⣿⢹⣿⡇
⠀⠀⠀⠸⡇⠈⠳⣄⠙⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢽⣿⣿⡭⡀⠀⠀⣿⡟⢸⣿⡇
⠀⠀⠀⠀⢻⡀⠀⣸⣧⠀⢻⣿⣇⢀⣷⣀⠀⠀⠀⠀⣴⣿⣿⢸⣿⣿⣷⠀⠀⠀⣹⡇⣸⣿⡇
⠀⠀⠀⠀⠀⢳⡀⣙⣿⡿⠃⢿⣿⣾⣻⣿⣶⣤⣾⣾⣿⣿⡏⠘⢿⣿⣿⡏⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠹⣿⡿⠿⡆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣸⠿⢻⣧⣤⣆⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⡆⠛⣿⣿⣿⣿⣿⣧⣭⣝⡿⢿⣿⣿⣄⠀⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠟⣹⣿⠛⠋⠉⠉⢩⣤⣤⡆⠠⠌⠛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣿⠁⣾⣽⠃⢀⣼⣿⣿⡷⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⠛⠁⣰⡏⢿⣿⡟⠀⠀⠀⢀⣀⢀⠀⣤⣤⣿⠆⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⢸⣿⣦⣠⡟⠅⠀⠀⠀⠿⡿⡟⣿⣿⣟⠁⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣦⡷⣻⣿⡟⢆⠀⠀⠀⠠⠒⠋⠙⢿⣿⣼⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⣿⣿⠶⠷⠄⠀⠀⠤⠤⠤⣬⣷⣿⣿⣿⣿⣿⣿⣇
⠀⠠⣤⣤⣤⡦⠀⠀⣤⠄⠀⢠⡠⠠⠀⣤⡤⠀⠀⠀⠀⠂⠀⠀⢼⡂⠀⠬⠻⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⢠⣿⡿⢿⠃⠀⠀⣿⠀⠀⠀⠉⠀⠀⣿⡧⠀⠐⠐⠀⠐⠀⠀⢸⡇⠀⢰⠄⠈⢻⣿⣿⣿⣿⡿⡿⠼⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⢤⡀⠀⠀⠘⣯⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣶⣶⣤⣶⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣾⣯⣿⣷⣽⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡒⠒⠔⠖⠶⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣯⡟⣛⠗⣪⣿⣿⣿⣽⣿⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⢂⠀⡴⡆⢤⠀⠀⠀⠈⠁⢉⡓⠒⠒⠲⠶⠶⢶⣶⣾⠟⢟⣫⢳⠐⣿⣿⣿⣿⣿⣿⣿⣿⡝⣶⣽⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠕⠀⣖⠟⢉⡲⠀⠠⠄⠘⠃⠂⠈⡄⣀⠄⢠⢂⣤⡟⠉⣆⣽⣻⣌⡾⣿⢿⣿⣿⣿⣿⣿⣷⣦⣠⣿⣾⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣜⢶⢻⡿⣡⡘⢃⠖⢈⠋⠄⠀⡈⠀⠠⠀⠠⢀⡌⣾⠑⡈⣾⣿⣿⣿⡟⢹⠘⣿⣿⣿⣿⣟⣿⣿⣿⣿⡜⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣞⣿⣧⠏⡔⡬⡀⡁⠗⠀⠀⠀⠀⠀⠘⠀⣾⢀⡏⠈⢡⣿⣿⣿⡿⢷⡄⣽⣿⣿⣿⠿⢿⣿⣿⣿⠛⠩
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⣹⡿⣿⣤⣰⣋⡐⠀⠀⠀⠀⠂⠐⢠⣿⣿⢼⡇⠃⢠⣿⣿⣿⣷⣾⠿⢟⣭⠟⠁⠀⠀⠉⠿⠿⣧⣼⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠘⣿⠟⣿⣿⢿⣷⣿⣦⡄⡄⣇⠄⣾⣿⣿⣞⠅⠰⠃⣹⣿⣿⣿⣇⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠷⠁
⠀⠀⠀⠀⠀⠀⠀⡎⡜⢿⣇⣧⣿⣿⣤⡉⠘⠛⠏⠑⠇⠃⠛⠐⠼⣿⣿⣧⡄⢊⢶⣿⣿⣿⣿⠟⡾
⠀⠀⠀⠀⠀⠀⠌⢀⠃⢹⡿⣛⣿⣿⠏⠀⠀⠀⠠⠤⣀⡀⣀⠀⠀⠙⣿⣿⣯⡄⠈⠁⠀⠠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⠀⠀⢀⢤⣤⡒
⠀⠀⠀⠀⠀⠸⠁⠀⠀⠘⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡔⠀⠀⠈⣟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣦⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣱⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣾⢿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠾⠚⠛⠦⠄⢸⡟⣿⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠊⠙⠲⠖⠒⠒⢂⢠⠤⣀⠀⠀⢠⣟⡇⠀⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠭⠛⠟⢶⠘⣟⣷⡀⠂⢻⣟⡧⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⠌⠇⠑⠒⠶⠒⠃⠛⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠇⢀⡔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡘⡰⠋⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⢟⠔⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⠒⠁⠁⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠤⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⣠⢎⠑⣄⠀⠀⠀⣠⠞⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠹⢄⡀⠈⣠⠖⠋⠀⡇⠀⠀⠀⠀⠀⠑⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠒⠒⠒⠒⠒⡋⣏⠁⠀⠀⠈⠙⠲⣴⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⠀⠀⠀⠀⢀⡇⣸⠀⠀⠀⠀⠀⠀⠈⠧⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣍⣁⣀⡭⠖⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣤⠤⠤⡖⠊⢃⠀⠀⡀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⢘⡀⠀⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⢰⠁⡇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣨⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⢸⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡤⡀⠀⢋⠢⡀
⠐⡘⢄⢸⡀⠱⡀
⠀⠘⢄⠙⡇⠀⢣
⠀⠀⠀⠑⢼⡀⠈⡦⢒⡠
⠀⠀⠀⡲⢮⠈⠀⠀⠀⠈⠑⠢⠤⣂⠀⠀⣀
⠀⠀⡘⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠷⠤⢤⣀⠀⠀⠀⠀⠀⢀⡤⠴⠤⣄⡀
⠀⢀⠃⠀⣀⡀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠖⠞⠋⠀⠀⠀⠀⠙⢶⡄
⠀⡼⢀⠀⠼⢀⠤⠊⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠹⣸⠀⠶⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣸⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠲⡀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡄⠀⠀⢀⡇⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡇⠀⡇⠉⠒⠒⠒⠒⠚⠉⠘⡄⢸⠙⢦⡀⠈⠣⡄⢣⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⠀⠈⢳⢀⠎⠈⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⠀⠀⠀⢸⢨⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠫⣠⠛⢀⠜⠀⠀⠀⠀⠀⢀⠔⠃⡞⠀⠀⠀⢠⢆⡨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣀⠔⠁⠉⣹⠄⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠣⠤⠐⠃

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⣇
⡏⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿
⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸
⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣸
⢻⠀⢀⠀⢻⡆⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡿
⠸⡆⠀⠀⠘⣷⠀⠀⠀⠀⠀⡎⠠⠀⠀⢰⡇
⠀⢷⠀⠆⠀⢿⡀⠀⠀⠀⢠⡇⠀⠀⠀⡾
⠀⠘⣇⠈⡄⣸⡇⠀⠀⠀⢸⠁⠂⡔⢰⠃
⠀⠀⠘⣆⢱⣹⠇⠀⠀⠀⠸⠸⣸⢡⠇
⠀⠀⠀⠈⠂⣿⡖⠀⠛⠳⢶⣤⡃⠊
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠠⣔⢌⢳⡈⠲⡶⢦⣄⡀⣀
⠀⠀⠀⠀⣏⡴⣿⡤⠴⠖⠘⡎⠧⠃⠀⠙⣼⣮⠙⠮⡳⣔⡔⣔⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡴⠶⠶⠶⢶⣄
⠀⠀⠀⠐⠟⠀⢠⠄⢤⠄⠀⠁⠀⠀⠀⠀⠘⣿⠳⡀⠈⠚⠞⠜⡎⢆⠱⣌⠉⠉⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠆⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢘⢦
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢱⣧
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢿⡇
⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣽⠇⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡏⠀⠀⠀⣸⢧
⠀⠀⠀⠀⠉⠀⡀⢢⠀⠴⠛⠩⠵⠋⠁⠀⠀⠀⠀⠀⠀⢰⠀⡰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⠎⠀⠀⠀⣼⢃
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⢘⡇⠀⠐⠒⠒⠶⠦⢤⣤⣤⣤⣤⣴⣶⠶⡿⣧⠀⢀⠀⠀⠀⢰⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢰⡇⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠃⢸⠀⢸⠀⠀⠀⠸⣿⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⣼⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⢸⠀⢸⡇⠀⠀⠀⠘⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡿⠀⡟⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠇⠀⢸⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⢀⠁⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⣾⠀⠀⠸⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠦⣤⡿⠀⡈⠠⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠾⠆⠀⣠⠛⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⣟⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⠏⣿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⡟⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢤⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣸⠇⠀⣸⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡟⢶⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢳⡀⠙⢦⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⡇⠀⢠⡏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣷⠀⠈⢳⡄⠹⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⡼⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠘⢧⡀⠀⠹⣄⠙⣧⡀⠀⠀⣤⡀⠀⢸⡇⣸⠀⣰⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠈⢷⣄⠀⠹⣆⠘⣧⠀⠀⠀⠉⠁⣸⡗⠛⠚⠛⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠙⣦⡀⠹⣆⠸⣇⠀⣿⠀⡼⠋⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⢦⣹⣆⢻⡄⠋⣸⠃⠀⣠⣀⡀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡈⠻⢆⣧⣤⣿⡀⣈⣹⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡟⠁⠀⠈⠙⣿⠻⠟⠋⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠿⣿⡀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠀⣠⡴⣿⠙⠲⠶⠴⢖⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠀⠀⠠⠞⠁⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⢀⡟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡿⠀⠀⠀⡼⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠃⠀⠀⣼⠃⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡾⠋⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢰⡏⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣹
⠀⣠⣄⣴⠞⢻⢻⡄⣠⡀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⢘⠁⣿⡷⢇⢠⡸⣿⠋⡇⠀⠀⡈⠙⠶⢦⣤⣤⠴⠒⠁⠀⠀⠀⠰⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⢀⡎⢹⡏⠰⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⣿⡿⠀⢸⠀⠁⡟⠀⢰⡄⠘⢹⣆⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡇⠀⠸⣆
⠀⣿⠃⠀⢸⠀⢰⡇⠀⠸⡇⠰⠜⢿⠁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠹⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡟⠀⠀⢸⠀⢸⡇⠀⠀⣷⠀⢠⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢸⡇⠀⠀⣾⠀⢸⡇⠀⠀⢿⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣽⠏⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⢸⠀⠀⠀⣿⡄⢸⡇⠀⠀⢸⠀⢸⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣴⣟⡉⠉⣩⠟⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⡇⠀⠀⠀⡿⢣⢸⡇⠀⠀⢸⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⢧⣀⡈⠙⣉⣠⠞⠋⠀⠀⠀⠙⠳⢦⣤⣄⣀⣤⣤⣶⠟⠋⠁
⡇⠀⠀⣠⠇⠘⣾⡁⠀⢰⣾⠀⢸⡀⠀⠀⢸⠀⠀⠀⢠⣄⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⡇⠀⣸⠟⠀⢀⣾⣇⠀⣿⣉⡀⢸⡇⠀⠀⢸⣾⠁⢀⣿⣿⡟
⡇⣸⠇⠀⣠⡾⠛⢿⣰⠟⠁⠈⠘⡇⠀⣼⣿⡏⠀⣼⡿⢻⡇
⣷⡏⠀⠸⣇⢳⡀⠀⠻⣄⠀⠀⣀⣡⠀⡏⢸⠁⢰⠇⡆⠸⢧⣀⡀⣀⣀⣀⡀
⠀⢹⡆⠀⠿⢞⣛⣛⣦⡬⠶⠛⢾⣿⣼⢃⡎⠀⠹⢶⡃⢀⣀⣀⠤⣭⡽⢿⣏
⠀⢸⣧⡴⠞⠋⠁⠉⠻⢦⡀⠀⠀⠙⢧⡘⠳⣄⠀⠀⣿⣽⠶⠖⠶⢶⡇⠀⠈⢳⡄
⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⣷⣠⣏⣠⠞⠉⠀⠀⠀⠀⠀⠙⢢⡄⠀⠙⣆
⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠛⠋⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠛
⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠖⠛⠋⠁⠀⠀⠈⠳⠦⣤⣀⣀⣀⣀⣀⣀⣠⣤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣞⣾⠻⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣄⣸⠿⣯⣤⡀⠹⣿⣧⣤⡀
⠀⠀⠀⠀⠀⢠⡾⣿⡅⠉⣩⣶⣿⣿⣁⠀⠀⠛⢿⣷⡄
⠀⠀⠀⠀⢤⠀⠹⣿⣷⣾⣿⣿⣿⣯⠷⠀⠀⠂⣩⡙⠻⣷⣦⣄⣀⠀⠀⠀⠀⠀⡀⢀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠈⠓⠀⠛⠋⠁⠀⠈⣿⣿⠀⢂⡴⠚⠉⠀⠀⣸⠟⠉⠂⠋⠀⠡⡟⠀⠉⣘⠆⢿⣿⣿⡟⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣤⣵⡀⠀⠀⣼⣿⣦⣄⣀⡀⠀⠀⠀⢀⢠⣼⣻⣿⣯⡺⡀⣴⣌⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣥⣄⠐⠀⣸⣿⣿⣿⣿⣧⢹⢶⣷⣾⣿⣿⠋⣿⡿⢠⠽⣷⣟⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⢋⣀⠀⣿⣿⣿⣿⣿⡿⣾⣷⣿⣾⣿⣿⢘⡇⢐⠀⣸⣿⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣦⡲⢿⡿⢧⣼⣸⣿⠿⠿⣿⢿⣿⣿⠸⣿⣾⣼⣻⣿⠃⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⡵⠟⡏⠉⠁⠀⠀⠄⠂⠂⠛⠻⣿⣿⣧⣿⣿⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣳⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠘⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢠⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠟

⡤⡀⠀⠍⠢⡀
⠐⡐⢄⢸⠀⠱
⠀⠘⢄⠙⡄⢀⢃
⠀⠀⠀⠑⢴⡀⠈⡆⢐⡀
⠀⠀⠀⠲⢯⠈⠀⠀⠀⠈⠑⠢⠴⣀⠀⠀⢀
⠀⠀⡈⣄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠶⠦⢤⡀⠀⠀⠀⠀⠀⣠⠴⠶⠤⣄
⠀⢠⠁⠀⣀⡀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠖⠒⠛⠁⠀⠀⠀⠀⠙⢦⡀
⠀⡜⢀⠀⠎⣀⠔⠋⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢳⡀
⠀⠰⣼⠀⠛⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⢁
⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢀⡞⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢲⠀⢸⣅⠀⠀⠀⠀⠀⠀⣠⡞⠉⢳⡀⠀⠀⢸⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠘⡄⠉⠓⠒⠒⠚⠋⠁⠱⡀⠇⠑⢤⡀⠘⢦⡀⡆⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠳⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠀⠀⠈⠆⡐⠁⠑⣤⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⣴⠋⢠⠃⠀⠀⠀⠀⠀⡠⠚⠒⡇⠀⠀⠀⠸⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⣤⠊⠀⣈⡽⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠘⠒⠒⠊
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣶⣼⣴⣸⣠⣤⣤⠒⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣸⠿⠟⠋⠉⠉⢻⡯⠻⢷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢄⣀⡀⣀⠀⠀⠀⣀⣠⠤⠤⠶⠤⠤⠞⠋⠉⠀⠔⠛⠁⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠋⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠠⠄⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣰⡾⠋⠈⠣⣤⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠈⢢⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡆⠀⠀⠀⠀⠀⣠⣖⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠳⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠠⠀⠀⠀⣠⠏⠻⢷⣦⣄⣀⣀⣀⣠⣽⡧⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢼⣵⠃⠀⡞⠀⠇⠀⢰⠋⠀⠀⠀⠈⠉⠉⠉⠉⠁⢸⠁⠀⣸⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡜⠃⣴⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠱⡉⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣾⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⠀⠰⡈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠠⣄⠀⢺⡌⠀⢠⢀⢱⠘⣆⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠏⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⠀⠀⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣿⠀⢰⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣴⠀⣿⢀⣿⣯⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣸⡇⣼⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣸⣯⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣦⣼⠃⠼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⠀⠐⠙⡿⠻⡿⡿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣾⡿⡋⢿⡄⠀⣤⣀⡠⠄⠀⠀⣀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣿⣿⠋⠀⠀⠀⢠⡖⢿⡿⣷⠓⢲⡦⠙⣿⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⢀⣿⠓⢶⣶⣿⣿⣿⣳⡄⠈⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⠿⠋⠀⠀⠀⠀⠀⣼⣿⣴⣍⢿⡩⣿⠚⡿⣿⡀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣤⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣶⡶⠛⠉⣩⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⢎⣷⡺⣷⡙⣧⡿⢶⣴⠿⠿⠆
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⣬⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡹⣿⡉⠿⢩⣽⣟⣴⣙⡟⢃⡀⠀⠢
⠀⠀⠀⠀⠀⣼⢃⠀⠀⠀⠀⢌⣿⣷⣭⣄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⢧⡱⢎⡿⠦⣿⣯⣴⣿⠉⠀⠘⣁⡀⠀⠑⡀
⠀⠀⠀⠀⢸⡏⣞⣢⡆⠀⡀⠀⣾⣿⣿⣿⣷⣶⣄⣀⣀⣀⣠⡇⠀⠀⢻⡄⢸⡆⠀⠀⠀⣶⣶⣾⣿⢪⢱⡟⠁⠀⠀⠙⠛⠧⡘⡆⠐⠿⠇⠀⠰
⠀⠀⠀⠀⣿⡧⣻⡿⠀⠀⠇⠀⢻⣿⣿⢿⣿⣿⣿⣿⣿⢿⣽⠃⠀⠀⠘⣿⡀⢻⠀⠀⠀⣯⣿⡼⢿⡌⣾⠁⠀⠀⠀⠀⠀⠀⢁⠹⢄⡀⠀⡀⠁
⠀⠀⠀⠀⣿⡴⣏⡇⠀⢠⠀⠀⠘⢯⣿⣷⣿⣿⣿⣿⣿⡇⣿⣗⠀⠀⠀⢸⡇⠀⠀⠀⣰⣿⣿⣿⣿⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢹⣇⢟⡇⠀⠸⡄⠀⠀⠀⠙⠺⣽⣿⣿⡿⣯⢳⣿⢸⡄⠀⠀⠀⢧⣠⡄⣴⣙⠟⢪⣽⣏⣿⢻⡇
⠀⠀⠀⠀⢀⣿⡘⢇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢸⡟⣏⣿⣶⡀⠀⠈⠉⣥⣾⠇⠀⠸⡷⠛⡃⣸⠇
⠀⠀⠀⠀⢸⣿⣿⡽⠄⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢽⣿⣣⣾⣻⣶⡞⢶⡟⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⣸⢻⣿⣇⡇⠀⠀⠈⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⣮⡽⡻⢢⣭⡽⣕⡾⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⣿⣻⣿⣇⣇⠀⠀⢀⢿⣇⡍⠉⠉⠓⠶⠲⠦⠤⢤⡟⣣⠹⢿⡯⢱⡿⠀⠀⠀⠀⠀⢰⡏
⠀⠀⢀⣴⣿⣿⡇⢷⣸⡄⢀⡎⢸⣧⠇⠀⢀⠜⠀⠀⠀⠀⠀⢻⣿⡇⣿⡟⣻⢷⠒⠚⠓⠀⢌⡿⠁
⠀⣠⣿⣿⣿⣿⣇⣾⣿⣿⣾⢠⣿⣷⡄⡔⠁⠀⠀⠀⠀⠀⠀⠸⣿⡿⣸⣿⠏⢸⠀⠀⠀⣷⠟⠁
⠀⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣿⠀⢀⣾⣷⢸⠋
⠀⢸⣿⣿⣿⠃⠀⠻⣿⢿⡏⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⠀⣼⣿⣯⣼
⠀⠀⢻⡟⠃⠀⠀⠀⣿⣿⡇⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟⠀⣿⣿⣿⣿
⠀⠀⠈⠀⠀⠀⠀⠀⣿⣿⣧⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡄⠀⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⢠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠻⣿⣿⡏⠀⠸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠿⣿⣿⡿⠇
⣶⣶⣶⣶⣶⣶⣴⣶⣤⣤⣦⣶⣴⣴⣶⣦⣤⣤⣤⣤⣴⣦⣴⣦⣤⣤⣤⣦⣦⣴⣤⣤⣤⣴⣶⣤⣶⣤⣤⣤⣤⣴⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶
⣿⣭⣭⣹⣭⣽⣯⣭⣭⣯⣍⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣭⣼⣿⣿⣭⣽⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠤⠶⣄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠈⢄⠠⠀⣤⡶⠿⠀⣪⣍⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣱⠄⠩⣠⡀⠀⠈⠉⠓⠾⠛⠂⠀⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠉⠛⠧⡀⠀⠀⠀⠀⠀⢤⣌⣡⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⢰⢤⣴⣴⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠺⢷⣌⠻⢷⣦⣬⣀⠀⠀⠀⢁⢀⠸⠀⠀⠀⠙⠛⣿⣿⢿⢻⣳⠂⣾
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠓⢹⣿⠛⠛⠛⠛⠒⠂⠉⠹⠀⠀⠀⠀⡀⡙⣿⣅⣾⢱⣼⠇
⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠐⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⢰⠰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠶⠛⠁⠀⠀⠀⢶⣶⡄⡄⣄⢠⡠⡀⣈⢑⣂⣛⠥⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣆⣦⠤⢮⢹⡜⣿⣺⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠯⠽⠞⠓⣿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠈⠀⠀⠀⡀⠀⠈⠁⠈⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠖⠒⠉⢉⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠙⠻⡏⠀⠀⠀⠀⢀⣀⣀⠀⠀⠓⢢⣄⠀⠈⠑⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⡀⠀⠀⠉⠲⢤⡀⠈⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⢀⡀⠁⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠉⠁⠀⠀⠀⠈⠙⠲⠶⠶⠶⠶⠶⠶⠛⠛⠉⠉⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠸⠇
⠀⠀⠀⠀⠘⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡐⠲⠃⡠⠀⠀⠀⢹⠇
⠀⠀⣦⣄⠀⠀⠀⠉⠙⠛⠫⠧⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠐⠀⠀⠀⣀⠤⠚⠀⣀⢸⠀⠀⠸⠗⠀⠀⠀⣾
⠀⢄⡉⠛⠋⠶⠴⣦⠀⣿⠒⠒⠞⠋⠀⠀⠀⣀⣀⡀⠉⠂⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⡜⠉⠀⠳⣴⠁⠀⠀⠀⡔⠁
⠀⠈⠛⠷⠶⢠⣤⣄⠠⠏⠀⠀⠀⠀⠀⠒⠂⠀⠀⢁⣀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⢀⡤⠈⠀⠀⠐⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢹⣆⠻⠀⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠉⠀⠀⠀⢀⠀⠀⠀⠐⠒⠤⠄⡀⠀⠀⠀⠀⢡⣾⡏⠁⠀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠓⠒⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⢻⣿⣿⣿⠷⢤⣀⠀⠀⢀⠀⠀⢚⡄⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠉⠛⠿⣶⣬⡟⠃⣀⡠⠤⠟⠀⠀⠀⡠⠀⢌⡁⠀⠀⠀⠘⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⢰⠀⠀⠠⠛⢛⡶⢶⡊⠀⢹⡄
⠀⠀⠘⢦⣀⣀⣀⡀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣠⠀⠀⠀⠘⡏⠀⠀⣸⠁
⠀⠀⠀⠀⠉⠙⠛⠓⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠤⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠹⢄⣄⣀⣤⡑⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⠙⠛⠛⠛⠛⠻⠿⢿⣿⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡭⠶⠶⠶⠶⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠉⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠉⠁⠀⠀⠀⠛⠛⠛⠲⠶⠶⣤⣤⣀⣀⠢⣄⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣁⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠉⠁⠀⠐⠒⠛⠲⠶⢦⣤⣈⣉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢼⣶⣄⡀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠉⣭⣉⣙⠛⠲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣬⣍⣛⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠉
⠀⠀⠀⠀⠰⠋⠠⠖⠚⠲⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣶⡄⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠓⠶⣤⣀⠈⠙⠳⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠷⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠄⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⡿⢿⣼⣴⣶⣎⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠶⠛⣩⡅⠀⠀⠉⠃⠉⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠉⠒⠢⠤⠠⠤⠤⠴⠚⠋⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⣠⠄⠀⠀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣄⢀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠋⠀⠀⠀⠹⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠘⡆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠘⣆⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⢠⠀⠀⠀⣰⠻⢿⣤⣀⡀⣀⡀⣀⣸⡧⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⢠⣮⡆⠀⡼⠀⠇⠀⣼⠃⠀⠀⠈⠉⠉⠋⠉⠉⢸⠁⠀⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠛⠀⡔⠃⣴⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⠙⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠰⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣾⠃⠸⠀⢀
⠀⠀⠀⠀⠀⠀⠲⠄⠘⠆⠀⠰⠠⠱⠘⠆⠠⠀⠀⠀⠀⠀⢀⠈⠀⠃⡀⠀⡰⠛⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⢿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣛⣻⣿⢿⣻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⠾⣿⣻⣿⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⣯⣿⣿⣿⣿⡀⠀⢀⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⠙⢧⣰⣇⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣁⠈⠙⠛⠛⠋⠉⣴⡶⠂⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿⣿⠇⠀⠀⠀⠀⣀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠴⡄⣶⣶⣾⣷⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⢹⢘⢁⣴⠀⠀⠟⢻⣾⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⣿⣿⣿⣿⣿⡖⠾⠘⠈⠉⠀⠀⠀⠈⠙⠻⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣿⣿⣿⣿⣿⣿⡛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⡗⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣿⣿⣿⣿⣷⣜⠀⠀⠀⠀⠀⠀⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣶⣿⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⢿⣿⣿⣿⣧⣤⣶⣶⣶⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⢶⣿⣿⡿⠛⣿⣿⠛⠛⢷⠶⠶⠶⢦⣤⣀⡀
⠀⠀⣠⡶⠻⠉⠈⠀⠀⠠⠆⠁⠀⡀⣀⠉⠀⠀⡀⣿⠿⠓⠒⠶⠤⠉⠛⠷⣦⣀
⠀⣸⠟⠀⠪⠀⠀⡀⠀⠀⠀⠀⠈⠀⠉⠀⠠⠨⠀⠀⢀⣤⡴⠶⠛⢛⡛⠛⠛⠛⠿⢶⣄
⠀⣿⡌⠀⠀⡁⡜⡍⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⡩⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠠⠙⣧
⠀⢻⣷⣾⡆⣠⢰⢸⢰⢾⡜⡎⢀⢀⢬⠡⠠⣸⡏⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢻⠟⠿⢿⣿⣾⣿⣿⣿⣿⣧⣿⣾⣀⠸⣿⡇⠀⠀⠀⠀⠅⠀⠁⠀⣀⣀⣀⣀⡀⠀⣾⠃
⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣶⣿⠿⢛⡉⠉⠉⠙⠻⣄
⠀⠀⣸⠇⠂⠀⠀⠀⠀⠐⠀⠄⠐⠂⠦⠄⡈⠉⠙⢷⡰⡠⢠⣿⣿⠟⠁⠀⠀⠁⠀⠀⢀⣠⣽⡷⠟⢛⡉⠉⠩⠛⠳⣄
⠀⢀⣿⢀⡀⠰⠀⠃⠰⠀⠐⠀⠄⠀⠀⠀⠀⡄⠀⢨⣷⠀⣼⠿⡇⡄⠠⠀⠀⠀⢉⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⢂⠀⢸⡇
⠀⢼⣯⣼⡗⣆⢀⢀⠈⢡⠀⠀⠀⠀⠀⠀⢰⢀⡖⢾⢹⠀⢸⡆⢡⡱⠀⠀⠀⠀⣾⢻⡇⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠙⠿⢿⣿⣿⣿⣷⣼⣰⡄⣴⡇⣀⠀⢸⢨⢻⣿⣿⠀⠀⠻⣿⣿⣶⣤⡐⠀⢿⡸⡄⠄⠠⠀⢀⠀⠀⠀⠀⠈⠐⠘⣇
⠀⠀⠀⠈⠉⠉⠛⢿⣟⣿⣿⣧⣿⣧⣿⣷⣧⣾⣿⣿⣯⠀⠀⠀⠈⠻⡏⠙⡇⠀⡈⠻⢿⣦⣄⡀⠀⠀⣀⠀⠁⠒⠂⢀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠩⠭⠭⠭⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⡹⠀⠀⠀⣀⣠⣿⣦⣵⢣⡀⠀⠀⢻⠛⢻⠀⠀⠒⠃⠀⠀⠀⠀⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠲⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⣝⣂⣀⣸⣷⣼⣇⢀⠀⠀⠀⠀⠀⠀⠀⠐⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⣛⣻⡟⠛⠛⠛⠛⠛⢻⣿⣿⣦⣓⡀⠀⢀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠒⠀⠀⠀⠶⠰⠒⠆⠐⠐⠂⠐⠐⠰⠀⠀⠂⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣤⠀⠀⠀⢸⣿⠿⡿⠉
⠀⠀⢀⣶⣿⣿⣷⣶⣶⣶⣿⣿⣿⡿⣿⣧⠀⠀⠀⢠⣶⣿⣿⣶⣶⣶⢲⣿⣺⣿⣿⣾⣦⠀⠀⠘⠘⠀⠓
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠁⠀⠀⠀⢸⢏⣿⣿⣯⣷⡿⣟⢿⣿⠛⠀⠈⠁⠀⠀⢠⣤⣤⣶⠷
⠀⢀⠜⣿⢿⣿⡟⠛⠛⠿⣿⣟⠀⠀⠀⠀⠀⠀⢀⠜⣿⢿⣿⠝⠛⠚⠻⣿⡃⠀⠀⠀⠀⠀⠀⠀⡟⠉⠏
⠀⠈⠀⡏⠘⢻⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠘⡇⠘⢯⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢗⠀⠈⠳⠄⠀⠀⣇⠷⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠧⠀⠀⠀⣇⠧⠀⠀⠀⠀⠀⠀⠈⠿⢻⠃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠤⠀⠀⠀⢻⣞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⣿⣧⣶⣷⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⣾⣿⣷⣾⣿⣿⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠪⠉⠑⠙⠙⠒⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⡿⢉⣅⣫⣾⣿⣿⢶⣿⣿⡏⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢉⢆⣴⠏⡐⢆⠀⢀⣄⠀⢀⠌⠉⠉⠉⠋⠉⣹⠟⣟⢋⡩⢇⢻⣸⣿⣿⣿⣿⣿⣿⢿⠷⢻⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⣁⣸⣭⢁⡄⢁⢀⣣⢈⠉⠀⠀⡐⠠⠂⡐⠡⣺⠏⢀⣳⣿⣽⡾⣻⡟⣿⣻⣿⣿⣿⣿⣿⣴⣿⠻⣮⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠎⣏⣿⢥⡃⠈⠎⠀⢈⡀⠀⠀⠀⠐⢀⡜⣰⠇⡿⠨⠆⣿⣿⣿⣿⠇⠳⣸⣿⣿⣿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣾⡘⠸⢣⠴⡘⠀⠀⠀⠀⠀⠈⣠⣾⢠⡇⡀⠸⣿⣿⣿⣏⣿⢸⡿⢿⣿⠛⠉⠻⣿⣿⣧⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⡶⢿⣽⣿⣷⣷⣶⣢⡀⠀⠀⣀⢘⢰⣿⣿⣻⠇⢀⠜⣿⣿⣿⣿⡟⢋⡷⠋⠀⠀⠀⠀⠈⠉⠙⢿⣘⣟⡶
⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⢳⢸⣯⡝⠻⠟⡿⡿⢟⡇⢗⢳⠈⢺⣿⣿⡗⠁⡨⣀⣾⣿⣿⣿⡾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡴⢸⠀⣿⣾⢿⣿⣿⠗⠀⠀⠁⠈⠁⠀⠈⠀⠉⢻⣿⣿⡥⠛⠙⠋⠓⢛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠁⠆⠀⢸⣞⣾⣿⠋⠀⠀⠀⠀⠉⠙⠃⠐⠀⠐⠀⠙⣿⠋⠁⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢯⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠈⣿⡇
⠀⠀⠀⠀⠠⣦⠾⠦⣠⠈⣷⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠒⠒⠦⡦⠤⠤⠆⢀⣀⠀⠀⠀⢀⡿⡇⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠓⢞⡻⠿⣥⡘⣟⣧⠐⠈⣿⣛⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠿⡉⠇⠢⠬⠭⠔⠒⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡶⠃⡝⠀⣰⠏⢀⣾⠀⠀⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡍⢰⡇⢸⣇⡠⣿⣞⠈⠛⠲⠖⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⡏⢸⣇⣾⡶⠚⢿⣥⣈⠉⠛⠛⣲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡙⢆⠀⠀⠀⢰⢹⣷⠚⢯⣈⡛⠷⣤⣌⠉⣩⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⠣⠀⣠⡾⢤⣽⣿⣶⣬⡽⠗⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠒⠚⢣⡻⠋⠉⠉⠉⠉⠉⠉⠉⠙⠻⠗⠒⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣁⣤⣴⣤⠀⣀⣀⣠⣧⣡⣤⣶⣦⣄⣤⣤⣤⠄⠐⢶⣾⣿⣗⣒⣌⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠁⣻⡿⢛⣿⡿⢻⣦⣨⣉⡉⣉⣉⣉⣉⣉⡉⠁⠀⠀⡘⢿⡻⡻⡟⠭⡛⢧⡢⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⡜⣁⡵⠛⠁⠔⢅⢈⠀⠙⠀⣿⣿⣿⡇⢿⡳⡈⣦⢠⡨⠢⠑⣌⢀⠀⡠⠀⠙⣆⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢈⢪⢊⠀⠀⠀⠈⠃⠀⠀⠀⢡⠟⣷⣿⡇⠈⠀⠡⠸⣧⠱⡁⠱⠈⠆⠂⠑⠁⠀⠈⢧⠀⢡⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡇⠀⠀⠀⠀⢹⠒⣧⠀⠁⠈⠀⠀⠀⠀⠀⠘⣧⢠⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠃⠁⠀⠀⠀⠀⠀⠠⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⡇⠀⢠⠀⢀⠃⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⢰⠃⠀⡜⠀⢸⠀⠀⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⡈⡆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⡄⠸⢀⠀⠀⢸⠸⢰⠀⠠⠀⢳⠀⠆⡄⢀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣧⢣⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⢸⢀⡇⡇⣸⠀⢀⡏⡇⡞⠀⠀⠀⡞⡘⢰⠁⡸⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣯⡆⠀⢀⢸⣧⠀⡄⡄⣿⣄⠀⡇⣼⠀⢰⠀⣸⡘⢸⠀⢁⡏⢀⣿⢻⢡⠇⣰⢠⣜⢡⢁⠇⢠⢇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢄⢄⢂⢻⣆⢥⢱⢸⣿⣸⢁⣹⣄⣸⣿⣿⡇⣸⣸⣸⢻⡸⣟⡟⣼⢀⡿⣞⣿⢇⣎⢀⢟⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣞⣧⣻⣿⣾⣿⣾⣿⣿⣼⣿⣿⣿⣿⣿⡇⣇⣇⣿⣿⣿⢹⢡⣿⣾⣿⣿⢏⠞⣠⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣷⣯⡾⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡿⠿⠋⠁⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡶⠶⠶⣶⠖⠂⠤⠤⠤⠤⠄⠠⣤⣤⡀⠀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠋⠑⠂⠲⠶⠶⢶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⢠⡄⠀⠋⠙⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠀⠀⠀⠀⠀⠇⠀⠄⡇⢸⢀⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣿⣇⠀⠀⠀⠀⡀⠁⠀⠀⣁
⠀⠀⠀⠀⠀⠀⣿⣿⡿⣧⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢸⡷⣿⣿⡆⠀⠀⠀⡀⠂⢣⢸⠀⢨⠀⢸⠁
⠀⠀⠀⠀⠀⠀⣿⣿⡧⢿⠀⠀⠸⣿⣿⣿⣆⠀⠀⣀⣀⣀⣤⠀⠀⠀⠀⣆⠘⠧⣰⣟⡇⠀⠀⠒⠞⠛⠘⠰⠄⠸⠀⠸
⠀⠀⠀⠀⠀⠀⣿⣿⣯⠉⠁⠀⠀⢳⡟⠷⣟⣷⡀⢹⣿⣿⡗⠀⠀⠀⢀⢹⡗⠂⠀⠻⡇⠀⢀⠠⢠⠀⡄⠄⠠⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠈⢿⣸⣿⣿⣷⣘⣿⣿⣧⡀⠀⠀⢸⣌⠗⠀⠀⡄⡀⠀⠠⠀⢸⠙⡇⠃⢸⠀⠸⡀⠐⠄
⠀⠀⠀⠀⠀⠀⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠀⡼⠉⠚⠀⣼⣄⡼⠂⠀⠈⠈⠀⠀⠓⠈⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠛⠈⣿⣿⠟⢻⣿⣷⡶⠟⡀⣀⠀⣾⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⣼⣿⣿⡟⠁⠀⠈⠛⠁⣿⡿⢛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⣾⣿⣿⣷⣶⣤⣤⣄⣸⣿⣿⣌⡛⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠈⣿⣿⣿⡿⠿⠟⠛⠻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⣤⣌⢂
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣀⣤⣤⣴⣤⣾⣿⣿⣿⢹⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣇⣁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠛⠟⠉⠋⠉⣁⠍⣿⢋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡷⢰⣖⣛⣍⣵⣾⣿⣿⡄⠀⣠⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⢠⣾⣧⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣄⣠⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡤⣾⠋⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣼⣷⣿⣯⣿⢉⣿⣿⣿⣿⠛⠛⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⠛⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⢉⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢸⡷⣿⣷⢠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠟⢹⡇⢠⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢩⣯⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⡇⢾⡏⠀⢽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣈⣿⣿⣿⣯⣿⣿⣿⡿⠿⠿⠿⠿⠿⠷⠶⠛⠓⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡿⣿⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⢟⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣯⣿⠛⠉⠛⠛⠿⠧⣄⣶⡇
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣛⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠿⣿⣿⡟⠁⠀⠙⢿⡻⣿⣿⣿⣿⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣛⣯⣠⣄⣄⣀⣸⣿⠿⠼⠁⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣙⣿⣿⣿⣿⣿⠋⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⣇⣤⣴⣿⠁
⠀⠀⠀⢿⣿⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢿⣿
⠀⠀⠀⣿⣿⠏⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿
⠀⠀⠀⣿⠏⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣷
⠀⠀⢠⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠐⢿⣄
⠀⠀⠸⣿⡀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠘⠛⠃
⠀⠀⠀⠸⠿⠂⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⣄⠠⠀⠀⠀⠀⠀⠀⠀⡼⠟⢂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠞⠾⠿⢟⣛⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡟⠀⠀⠀⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠀⠀⠀⠀⢀⣴
⠀⠀⡆⠆⠂⠐⠂⠚⠛⡛⠉⡃⠻⠁⠀⠀⠀⣠⣆⣿⣶⣾⣿⣷⣿⡇⠀⠀⣿⣿⠀⠆⢐⣶⣿⣿⣧⡀⠈⠻⣧⣌⣣⣌⣿⣿⡇⠀⢴⣿⣷⣿⣇⣴⣿⡿
⠀⠀⠀⡰⠞⠀⠐⠂⠚⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡈⣻⣿⣿⣿⣿⠇⠀⠀⣿⣿⠻⡞⢿⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀⡀⠙⣿⡇⢰⣿⠿⡻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⣿⣿⡤⢼⣿⣿⣿⣿⣏⠛⠛⠻⣦⡙⠊⠀⣼⣿⡇⢸⣿⣿⣶⣿⣯⣶⣶⣶
⣿⣿⡿⠛⣿⣿⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢙⣫⣽⡟⢻⣿⣿⣿⣿⣿⣿⠘⣿⣮⢉⣼⣿⡇⡈⢻⡿⠋⠀⠀⠀⠀⠐
⡿⠋⠀⣲⣿⣿⢧⣄⠈⠙⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡁⡆⠀⢠⣿⣿⣿⡄⣼⣿⣌⡏⢻⣿⣦⣿⣿⢿⣿⣿⡧⡂⠀⣅⠀⠀⠀⠀⣼⡶⠇
⢀⡤⢿⡏⢹⣿⣿⣿⣷⡄⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⣇⢸⠀⡼⠏⢻⡏⣄⣼⣿⣿⣷⣀⠙⠛⠛⢁⡼⣿⣿⣗⠀⢠⡿⣷⣤⣴⣾⠟⠁
⠰⠳⠎⠁⠸⣿⠟⢿⠟⠛⢺⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣧⣿⣼⣬⠃⠰⠖⠻⠛⣿⣿⣿⣿⣿⣉⣿⣶⣾⣿⠀⢹⣿⣗⠀⣾⡇⢸⡙⢩⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠀⠈⣿⡧⢸⣿⣇⣀⣉⣉⣀⣀⣀
⣿⣿⣿⣿⠿⣿⢿⣿⣿⢿⡿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣤⡀⢸⣧⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣯⣤⣥⣧⣧⣤⣥⣥⣧⣴⣦⡘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣇⣀⡽⠿⠇⠉⠉⣩⠟⠁
⣿⣿⣿⡏⠉⠏⠫⠛⢫⡏⢻⣟⡟⠝⠛⡝⠻⠉⣟⣯⢋⢋⡍⡙⢋⢹⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣻⣯⣙⣀⣹⣿⣿⠏⣿⡄⠀⠠⠾⠷⠶⠶⢶⣦
⣿⣿⣿⡿⠿⠿⣿⣿⢿⠿⡿⣿⢿⠿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣧⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣧⣤⣴⣬⣼⣤⣧⣷⣧⣥⣧⣧⣬⣴⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡀⣿⡏⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⠀⠀⠀⢀⡶⠂⣴⠆
⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⡇⢹⡇⠀⠀⠀⠀⠀⠀⢰⣇⠆⠀⠀⠀⣼⠃⢰⡏⠐
⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣿⡃⠀⣷⠀⠀⠀⠀⠀⠀⣸⢋⣤⠀⣶⢂⣿⠀⣸⠇⢰⠶⠄
⠀⣿⣧⣙⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣸⣷⡆⣿⡆⠀⠀⠀⠀⠀⢸⠃⠈⠀⠉⠀⠙⠐⠘⠂⠈⠁
⠀⢹⡆⠻⣿⡍⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠉⣿⣧⣾⡇⠀⠀⠀⠀⣠⣄⢀⠀⣀⠀⡀⢠⡤⡄⢀⣄⡄⠀⣠⣤
⠀⠘⣧⠀⣸⣧⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⣻⣿⣿⠇⠀⠀⠀⠸⣇⠈⢙⠀⢿⠀⡇⢸⣀⠀⢈⣀⡀⠀⢸⡅
⠀⠀⢹⣿⠻⣿⡇⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣀⣀⣿⢛⡏⠀⠀⠀⠀⠀⠈⢷⠀⣿⠈⣼⠁⢸⠁⠀⢸⠁⠀⠀⢸⡇
⠀⠀⠀⢻⣷⣿⣷⠂⠀⡙⣿⣄⠀⠀⠀⣠⣴⣶⣤⣤⣶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠦⠾⠀⠟⠀⠻⠀⠸⠤⠤⠰⠦⠤⠀⠸⠇
⠀⠀⠀⠀⠹⣿⡿⣷⣄⣸⣿⣿⣷⡾⠿⠛⠻⠛⠉⠀⣀⣤⠿⠋⠉⠉⣻⣦⡀
⠀⠀⠀⠀⠀⠈⠙⢾⣿⣿⠿⢿⣧⣤⣦⡀⠀⠀⢀⠘⣿⣧⡀⠀⢼⣿⣿⣿⣷⠀⠀⡰⠋⠻⢀⡇⠀⣷⢰⡏⠉⠀⡟⠈⠁⢸⢠⠃⢰⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣟⣁⣀⠀⠀⣰⣿⣥⣖⠠⡤⠿⠿⣿⣿⣇⣀⠈⠙⠛⠛⠂⠀⡇⠀⠀⢀⡗⠒⣿⢸⡗⠂⠀⡷⠒⠀⢸⢇⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⣿⣿⡏⠉⠀⠀⠀⠀⠈⠛⠻⣿⣷⣤⣿⣆⠀⠀⢣⡀⣰⢆⡇⠀⣧⢸⡇⢀⠀⣇⠀⠀⢸⠈⣆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⠁⢀⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣄⠀⠀⠉⠉⠀⠁⠀⠁⠈⠉⠉⠁⠉⠉⠁⠈⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣌⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢀⡀⠀⠀⠀⢀⢠⣶⣦⡤⢶⣤⣄⢠⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⣷⡀⢠⣤⣿⣾⣿⣿⣿⣿⣿⣇⣾⣿⣿⠁⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠹⣿⣿⣶⣙⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣦⣾⣿⣗⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣄⣹⣿⣿⡇⢹⣿⣿⣿⣿⡟⢋⣙⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢸⣿⣿⣟⣹⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢃⣿⡿⠛⠛⠋⠹⣿⣿⡼⣟⣿⠇
⠀⠱⠏⠀⠀⠀⠘⠇⠀⠀⠀⠀⢀⠀⠀⠀⣠⣿⣿⠛⡿⢿⣿⣿⣿⣿⣿⣾⠧⣾⣿⠇⠀⠀⠀⠀⠀⢻⣷⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡆⠁⠌⢿⣿⣄⡞⠻⠿⠛⣛⣉⣭⣴⣾⣿⠏⠀⠀⠀⠀⠀⠀⢸⡏⠘⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣄⡀⠀⠀⠀⠀⣠⣄⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⣿⡇⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⣛⣛⣭⣭⣛⣛⣒⠶⢤⣄⡀⠀⠀⢀⣠⡤⠶⣒⣛⣛⣭⣭⣛⣓⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠵⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢭⣓⣚⡭⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠈⢦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣉⠉⠀⠀⠀⠺⠿⠆⠀⠀⠀⠀⠈⠈⠀⠘⠀⠀⠀⠘⡇⣷
⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢆⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣟⢹
⠀⠀⠀⠀⠀⠀⠀⣷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠛⠀⣇⠀⠃⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣀⡔⠹⣄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠉⠛⠋⠉⠀⠀⠈⠙⠛⠉⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⠇⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸
⠀⠀⠀⠀⠀⣀⡤⢶⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡶⢤⣀
⠀⠀⠀⣠⠞⠁⣠⢼⠇⡇⠀⠀⠠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣄⠈⠳⣄
⠀⠀⣼⠁⢀⡞⠁⢸⢰⡇⠀⠀⠈⠒⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⡇⠈⢳⡀⠈⣧
⠀⢠⡇⠀⢸⠀⠀⢸⢸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠀⢸⡄
⠀⠘⡁⠀⠸⢦⡀⢸⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⡇⢀⡴⠃⠀⢈⠃
⢀⡞⠁⠀⠀⠀⢧⣀⣳⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣞⣠⡼⠀⠀⠀⠈⢳
⣼⠀⢀⣴⡦⣄⣀⣠⠇⠙⢮⣑⡢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢔⣫⡵⠋⠸⣄⣀⣠⢴⣦⡀
⡇⠀⢸⠇⣧⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⣶⠶⡶⢶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠚⠋⠉⠁⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡟
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⢰⣇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⡽⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣾⢷⣿⣯⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣱⠿⡖⢷⣭⣿⣷⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⠉⣵⢿⡟⣿⣿⣿⣿⡷⢄⣀⡀⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢻⣷⣾⣿⢸⡇⣹⣿⣿⢿⣷⣄⠘⣧⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⠇⢸⡄⠀⠀⠀⡀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⣄⠀⡠⠛⠉⠈⢻⣿⣿⣿⣿⠉⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠀⠀⠀⠀⠀⣹⣿⣿⡟⠀⠀⢀⣼⠀⣠⡀⢀⣴⣾⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⡿⠷⣀⣴⣿⣿⢀⣿⣿⣿⣿⡿⠿⢿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠈⠙⠿⣿⡎⠉⠁⠀⢠⡄⢸⡨⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢸⠀⠀⠀⠀⠀⠋⢈⣷⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣴⢷⠀⠀⠀⠀⠀⢸⡾⠏⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣷⠀⠀⠀⠀⠀⢸⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⢿⣿⠆⠀⠀⠀⢀⣿⡷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠈⣿⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠻⠶⠦⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⢠⣶⣦⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⣸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣄⣀⡀⣀⣐⣶⣶⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⠟⠛⠛⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠛⠿⣿⣿⣿⣿⣿⣷⣴⣶⡄⣠⠀⠀⠀⢀⣴⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠠⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣾⠛⠷⣿⣿⣿⢟⣩⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣄⠙⢿⣶⣦⡈⢷⣮⣭⣛⢿⣿⣶⣆⡀⢺⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣦⣄⣈⣛⠳⠄⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣷⣿⣻⣿⣿⣏⣿⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣧⣿⣿⣿⣿⣛⣛⠻⣿⣿⡿⢸⣿⡛⢋⡁⢹⣿⣿⣿⣿⡝
⠀⢤⣤⣤⣀⡀⠀⠀⢀⣾⡟⣿⣿⣿⡄⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣷⣮⣻⣇⣿⣿⣷⣯⣛⣀⣹⡿⣿⣿⣷
⠀⠀⢽⣿⣿⣿⣷⣶⣾⠟⠀⠸⣿⠙⢿⣦⡀⠀⠉⠻⢿⣿⣿⠟⣿⣿⣿⣿⣷⣿⣿⣿⠻⡿⠻⣿⣿⣿⠻⣿⣿⣿⣿⢿⣿⣿⣧⣜⣿⠿⢇
⠀⠀⠀⠊⠹⠿⠛⠋⠁⠀⠀⠀⢻⣷⡀⣿⠙⠶⣤⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⠀⣸⣿⡟⠀⠘⣿⣿⣿⣷⣦⣿⢻⣿⠏⠀⠆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡏⠀⠀⣸⣿⣿⣿⠶⢦⣼⣿⣿⣿⣿⣿⣄⠤⣾⣷⣴⣿⣿⠃⠀⠀⠈⠛⠿⣿⣿⣿⡟⠃⡦⣀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⢰⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣶⡀⠿⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⠘⣿⣿⣏⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠈⣿⣿⡀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢸⣿⣷⡀⠀⠀⣼⣿⣿⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠈⢿⣿⣇⠀⢀⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⣿⣿⣷⣌⣿⡿⠋⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⡀⠀⠀⠙⠛⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⣠⠖⠋⠉⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⢀⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡞⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣄⣿⣥⣶⠾⠭⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣸⣿⣿⣿⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⡤⠶⠛⠳⠦⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠿⠟⠛⠿⢿⣿⡿⠿⠋



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠉⠉⠉⠉⠉⢛⣓⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⣀⣀⡤⠤⠼⠓⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠖⠋⠁⣀⣠⠤⠖⠒⠋⠉⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠛⢓⣢⣤⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠠⠾⠕⠒⠚⠉⠁⠀⠀⠀⠀⣀⡴⠖⠋⠉⠁⠀⠀⣀⣠⠴⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠒⢤⣀
⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣀⡠⠴⠒⠊⠉⠁⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠛⠒⠒⠮⠷⣄
⠀⠀⠀⠀⠀⢻⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠤⠽⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢷⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⣀⣀⣠⠤⠤⠖⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠶⠶⠶⠦⠤⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣀⠤⠀⣠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⢶⣇⣔⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠶⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣥⣔⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠧⣄⣤⣀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠺⠷⠶⠶⠶⠾⠗⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⠀⢐⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠓⡞⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣃⠀⠐⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠉⠉⣿⣿⣿⠿⠿⠟⠛⠉⠉⣀⣠⠉⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡀⢀⣀⣰⣤⣤⣴⣶⣾⣿⣿⠏⣿⠀⠀⣾⠘⣸⣿⡄
⠀⠀⠀⠀⠀⠀⣧⠀⣠⣇⠀⠦⣇⡀⠁⠰⠤⠄⠒⠦⠝⣿⠿⠟⠛⠛⠿⡋⡁⠐⠿⢄⣡⣿⡄⠞⠀⠈
⠀⠀⠀⠀⠀⢸⡿⠰⠋⠉⡠⠆⢁⠉⠁⠈⠀⠰⠆⠒⠀⢀⠀⠂⠀⣧⠀⠈⠈⠐⢲⡦⡀⠈⠱⠔
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⡰⠀⠁⠀⠀⠀⡆⠀⡀⠀⣸⣴⣿⡀⠠⠄⠀⠀⠀⠀⠀⢰
⠀⠸⠀⠄⠀⠀⠀⠀⠀⠰⣶⣶⣶⠀⠀⠋⠀⠲⠸⣿⠘⢋⠄⠉⠉
⠀⠀⠀⠀⠀⠂⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡟⡿⣿⣿⣿⡟⣰⣶⣶⣶⣶⣿⣬⣭⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⢦⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠻⣿⣿⣟⣣⣍⣡⣽⡇⣿⣹⣩⢹⣿⣿⣿⣟⠿⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠟⠟⠻⠟⠛⠛⠿⠿⠟⣾⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣷⡀⠳⡱⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣶⡟⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⡿⠋⠁⠈⠋⠀⠀⠀⢀⡜⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⡿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠱⠶⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠫⣽⢰⠂⠈⠀⠐⠒⠛⠉⠛⠶⡶⠦⠤⢤⠤⠤⣴⠶⠶⢾⠻⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⣄⡀⠀⣀⠀⠋⠙⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠱⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠙⠲⢟⢠⣀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡗⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠙⠀⠀⠀⠰⢀⣿⣧⣴⠀⡐⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠹⣾⡮⡤⠀⠀⠂⣺⣿⢿⣾⣾⣿⣼⣧⡀⠀⡀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⣯⣧⡀⠀⠀⣿⣟⡂⠀⠀⠉⠉⠀⠂⠀⠁⠀⠀⠀⢀⣿⢸⠇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣸⠙⡇⠀⢹⣿⣷⠀⢠⢻⠉⠙⠻⠶⠮⣤⣤⣤⠤⠶⠶⠶⠶⠶⢿⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⣸⡇⠀⠀⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢻⣾⡇⢀⡿⠉⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠊⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢻⠁⣼⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣇⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠘⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣶⡇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⣷⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣬⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠜⢆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⢸⠸⡆⠀⠀⠁⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⢐⣀⡀⡼⢠⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠉⠉⠑⠎⠓⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣀⡀⠄⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠹⣆⢀
⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⠢⠤⢀⠀⡀⠀⠄⠀⠐⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠈⠀⠀⠰⠂⠀⢀⠄⠐⠚⢡⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⠂⢈⠳⣦⣄
⠀⠀⠀⠀⢗⠀⠠⠐⠠⠊⠀⠀⠀⠀⠡⠀⠐⠀⠀⢄⠀⠀⢠⠀⠒⠀⠀⡍⠀⠁⣀⢠⠁⢁⠤⢤⠁⢂⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠐⠼⠀⠐⠊⠑⠂⡀⣋⢀⠬⠤⠤⠄⠀⡒⠩⡄⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠠⠄⢀⣠⢞⣈⣨⠭⠭⠥⠤⠖⠃⠁⠁⠈⠈⠀⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡁⠀⡃⠄⠀⠒⠂⠂⠀⠀⠀⢀⡀⣄⠀⠀⠀⠀⠀⠄⠀⠘⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣁⠀⠀⠀⠀⠀⠀⠈⠝⠉⢀⡾⢂⠀⠀⠠⠊⠀⠀⠀⠀⠈⠄⠂⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⣹⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⢸⡎⠀⠈⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⠰⢸⠀⠀⠠⢢⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣙⣻⢀⣄⣀⡀⠀⠀⠀⠀⠀⢀⡔⣶⡄⠀⣤⣀⡔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠙⠛⠋⠫⣀⡤⠃⠀⠀⠀⠀⠀⠄⠝⠙⠁⠐⢦⡭⠃⠀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⣄⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⢻⣿⣿⣿⣿⢿⣾⠟⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠚⠯⣎⣿⠈⠟⢛⣛⣹⡇⠀⢸⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣫⣾⣿⣟⢻⣿⣿⣷⣤⣄⠉⠉⢀⣰⣿⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡆⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠻⠗⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⣿⣦⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣟⠾⣄⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⡏⠻⢿⣿⣷⡀⠀⠈⢙⠛⠿⠻⣻⡏⣿⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⡇⠁⢀⠸⡿⢿⣿⣿⣿⣿⣧⣼⣿⣿⣇⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣃⣿⣻⣟⣿⣿⠿⣷⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠇⢸⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠀⠀⠸⠉⢉⣽⠟⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⡔⢻⣿⣦⣀⣙⣿⣇⠈⠀⠀⠀⠀⠀⠁⠺⢷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠂⠀⠀⠀⠀⠀⢰⠁⣼⣿⣿⣍⠻⠿⣿⣤⣳⣶⣦⣄⠀⠀⠀⠘⢿⠇
⠀⠀⠀⠀⠀⠀⠀⡝⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣫⣷⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⢫⠟⠟⢻⠟⠡⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠿⢿⣿⠿⠟⠛⠋⠁⠀⠀⢈⠈⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣰⣾⡼⡋⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡛⠯⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⡿⠁⣀⣠⢉⠐⠀⠀⠂⠀⠀⡀⠀⣹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠛⠛⠁⠈⠛⢻⡶⠂⠀⠈⣙⢿⣶⣿⣷⡀⢂⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⣬⣧⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣄⡀⠈⠓⢘⣆⣀⣿⣾⣿⣿⣿⣷⡈⣄⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣷⣄⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⢷⣌⠳⠀⠀⠀⠀⣠⣾⣿⣿⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠄⠐⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢁⣀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠔⠒⠉⠉⠁⠒⢤⡀
⠀⠀⠀⠀⢀⠠⠤⠀⠐⠺⡏⣁⡠⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠤⢄⡀⠙⢧⠀⠀⠔⠁⣀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠑⢺⡤⢞⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠤⠄⠈⠑⠤⣀⡀⠀⠀⢀⡠⠔⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡉⠉
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠊⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⢀⡀⠠⠄⠤⠠⢌⡁⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠙⡄⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠄⠒⠊⠁⠀⠰⢦⡀
⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠆⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠐⠒⠂⠤⢹⣄⡀
⠀⠀⠀⠀⠈⠲⠀⠤⠤⠠⠤⢧⣞⡠⠀⠐⠒⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢤⣤⣇⣀⠈⠉⠐⠲⢄
⠀⠀⠀⠀⠀⢀⡠⠐⠂⠀⢀⣨⡧⠔⠂⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠀⢾⡂⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠠⢗⡀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠠⠠⣀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⠛⢛⠒⠢⠤⡀⠀⠀⠀⠀⠀⣠⡤⠶⠲⢤⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⣀⣠⣤⣨⡾⠳⠦⣄⠀⣏⢮⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣈⣆⠀⢀⡤⠻⢿⡄⠀⠀⢸⡿⠓⠦⡀
⠀⠀⠀⠀⠀⠀⢿⡦⡊⠁⠀⠉⠟⠛⠀⡀⢀⠸⡆⠸⣷⠇⠀⢠⣴⣟⣗⡆⠀⠀⢨⣽⣿⠋⢀⡾⠆⠀⠀⠃⠀⠀⢸⠀⠀⣠⡿⡄
⠀⠀⠀⠀⠀⠀⠈⣷⡇⠀⠀⡸⢀⠀⠀⠈⠳⣿⠂⠀⢨⠀⠀⠀⠈⠏⠁⠀⠀⠀⠀⣹⠏⠀⣎⠀⣈⡶⠤⠾⠶⠶⠛⠒⠾⢧⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣠⣜⣇⣑⣐⣀⣤⠟⠀⠀⠘⠳⢤⣤⣴⠀⢀⣀⣠⣤⡬⠏⠀⠀⠰⠜⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣴⣾⠛⢻⣿⣮⡵⣄
⠀⠀⠀⠀⠀⢀⡤⠤⡤⠀⡶⢤⣤⠖⠒⣶⢶⣶⠶⠋⢉⣩⣟⡲⠚⠉⣹⢒⣳⣶⠾⠉⠓⠒⢆⠀⢠⠓⠒⠉⠉⢻⣿⡟⠉⠙⠇⠀⢷
⠀⠀⠀⠀⠀⣏⡀⠠⠴⠋⠛⠁⠤⠒⠛⠛⠉⠀⠐⠚⠙⠉⡉⢀⣒⢉⡋⢉⡉⠀⢀⠀⣀⢄⡼⠀⠸⡀⠀⠀⠀⠟⠀⠙⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠙⠛⠛⠒⠓⠒⠓⠻⠿⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠶⣤⣤⣀⣤⣤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⢒⡲⠶⠶⠖⢒⣢⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣠⠤⣤⣀⣀⣀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣎⢀⣷⡦⣰⣯⣄⣀⡴⣮⢬⣉⣀⣀⣀⣱⡄⠀⠀⢀⠤⠂⠉⢡⣫⠟⠋⢁⣴⡫⠿⡋⢀⡴⡿⠟⠋⠁⠢⡀
⠀⠀⠀⠀⠀⠀⣾⢸⡟⠻⣆⠙⠽⢧⡌⠛⠷⣌⣀⠈⠳⢤⡈⠉⠙⢦⠀⢺⣠⠀⠀⠟⠁⠀⠀⣸⡿⠁⠀⠀⠚⠉⠂⠀⠀⡀⠩⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣄⣘⣤⣄⠈⠻⡀⠀⠈⠛⢅⡂⠀⣙⣦⠴⠋⠀⠀⠙⠷⣆⣀⠀⢀⣤⡅⠀⠀⢀⣀⣀⠀⣀⣤⣯⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠓⠒⠚⠑⠒⠛⠚⠉⠉⠉⠁⣀⣀⣀⣀⣠⣤⣀⡈⠉⠉⠙⠛⠒⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⡠⠒⢗⠖⢛⠍⡭⠊⢡⠔⠂⠈⠛⡆⠀⠀⠀⠀⠀⣀⣤⡤⠀⡒⢢⣤⢄⡀
⠀⠀⠀⠀⠀⠀⣰⢇⡴⠊⠛⢄⠙⣆⠀⠀⠀⢀⠎⢰⠫⠊⡠⣣⣿⣴⠞⠁⠀⠀⠁⢠⠃⠀⠀⢀⢔⠟⢛⣽⠛⡄⡦⢠⢘⡦⠙⣆
⠀⠀⠀⠀⠀⠀⡏⣼⢇⣀⡤⠤⠶⢿⡀⠀⠀⣾⢾⡇⣾⠸⡃⡇⠘⣷⠀⠂⠀⠀⠂⠘⠀⠀⣴⠃⡆⢠⡋⣂⡬⢔⡥⠂⢼⡗⠀⢼
⠀⠀⠀⠀⠀⠀⣇⠸⡃⣌⣉⣓⣶⠶⡈⢦⠀⠹⣌⠣⡱⠄⠳⡘⢷⡝⡆⠀⠠⠀⠀⢰⠀⢸⠁⡀⠑⢀⣀⣀⣠⠵⠂⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠘⢦⢷⣅⠙⠈⠀⠀⢸⠋⢧⠀⠈⠱⡌⣎⢆⠘⡀⠃⡇⠀⠀⠀⢁⡎⠀⠘⣷⡈⠲⣦⣤⣤⣤⣤⡤⢴⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡁⠗⠰⠖⢁⡰⠃⠀⠀⠀⠸⣌⣘⡄⡇⡄⢿⡄⠀⡠⠊⠀⠀⠀⠈⠑⠲⠼⠿⠾⠷⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠓⠋

⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣶⣤⣼⣿⡏⠉⢻⣿⣿⣿⣿⣿⣿⣷⣦⣴⣦⡀
⣼⠏⣶⠀⠀⠀⢀⣀⣀⣠⣴⡷⢿⣿⡿⠟⠙⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠏⢸⣷⡄⠀⠀⠉⠙⠛⠟⠻⣦⣼⣿⣿⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⣷⣀⡀⢀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⠛⣿⣿⣯⣌⣭⣼⣅⣤⣤⣿⣿⡿⠛⠋⠁
⣠⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣽⠿⣶⡆⠀⠀⠀⠀⠀⣿⣸⣿⡟⠙⣻⡏⠙⢿⣿⣿⣦⣠⢶⣿⢦⣾⣿⣿⣿⣿⡿⠛⠿⣟⢿⣿⡇⠀⠀⠀⠀⢠⡶
⠇⠀⢨⠀⠀⠀⠀⠀⠀⢻⠛⠿⣾⣶⣴⣿⢶⣟⡿⣫⡿⡷⢶⣿⣾⣃⣾⣿⣿⣿⣦⣰⣶⣯⡗⣿⠃⠀⠀⠀⠀⠻⣷⡄
⣤⠀⣸⠀⠀⠀⠀⠀⠀⠈⣴⣶⣾⣟⣿⡗⠻⠉⠛⣿⣿⣧⣐⣮⣿⣿⠿⢛⣡⣶⡿⠟⢩⣿⡛⣻⠄⠀⠀⠀⠀⠀⠙⣿⣄
⠇⢀⣸⠆⠀⠀⠀⠀⠀⠀⢺⣿⠽⡛⣻⢌⠷⣶⣶⣾⣿⣿⣿⡿⣛⣿⣷⣿⣿⣙⣔⣿⣟⣿⣫⢽⣆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣼⣿⠀⠀⠀⠀⠀⢀⣤⣩⣷⣰⡷⣿⣿⠟⢛⣉⡉⢾⣿⣿⣿⣷⠎⠉⠙⠿⠿⣶⣿⣶⣿⣶⣸⣏⡀⠀⠀⠀⠀⠀⠀⠙
⢰⣿⣿⢠⣾⡇⠀⠀⠀⢽⣿⣯⣤⣤⡿⣇⡀⠩⢏⣀⣤⣼⣿⣿⣿⣿⣿⡆⢦⣤⠽⡿⠻⣟⣿⣿⣿⡏
⣼⣿⣇⣿⣿⠃⠀⠀⠀⠀⠀⠙⠲⣽⣿⣟⣿⣧⣼⣿⣿⣿⣿⡟⠛⠛⠉⢀⠐⣂⣤⣤⣶⢾⠟⡁⠀⠀⠀⠀⠀⠀⠀⢦
⣿⣿⣿⣿⡿⠀⠀⠀⠀⢰⣷⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣯⣤⣤⣴⡿⢿⣿⢿⣽⣿⠗⠀⠿⡿⠀⠀⠀⠀⠀⠀⢀⣸⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁⠰⠂⠀⣿⠈⠓⣿⣟⣿⡏⣈⢿⣿⢩⣿⣴⣶⣋⣿⣿⡇⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠐⠛⠀⠀⠂⣿⠀⣴⣿⣿⣿⣿⣿⣸⠀⣠⣿⣿⣿⡟⠉⢸⣇⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠚⢁⣬⡙⠛⣿⣿⣿⣿⣿⣿⠀⣿⣿⡿⠿⠏⠀⢸⡟⢻⠿⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⢀⣤⡀⠀⠀⠀⠀⠃⠀⠸⣿⠃⠀⢿⣿⣿⠀⢻⣿⣤⣿⠟⠁⠀⠀⠀⢸⡇⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⢸⣿⣿⠀⢸⡿⡿⢉⣷⣷⡞⠁⠀⠸⠁⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠸⠿⠿⠀⠸⡇⠀⠀⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣻⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠀⠰⣈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃⠀⠀⠀⠣⡀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⡀
⠀⠀⠀⠌⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⠀⡇⡇⠀⣠⣤⣀⣄⣀⠀⢰⢏⡾⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⡀⠀⣀⠀⠀⠃
⠀⠀⠆⠀⣇⢧⠀⣿⣿⣿⣿⣿⣷⡏⣘⠃⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠈⠑⠃
⠀⠀⠀⠀⣇⢾⠒⣿⣿⠿⠟⠿⠿⠐⡞⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠂⠁
⠀⠀⠘⣤⠋⢂⠄⠅⠀⣀⡁⠀⠀⠀⠶⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⣼⣴⣶⢦⠤⠄⢀⣀⣀⠠⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡿⠖⠤⡏⠀⡆⣋⢭⡝⠓⠈⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣧⠰⡾⠀⠀⢳⠁⣤⣵⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠟⠀⠀⠀⠀⢤⡄⠀⠀⠀⠒
⠀⠀⢰⣗⠈⠁⠀⠀⠐⢏⡈⠑⣠⡿⠙⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⢓⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠑⢦⠀⠀⠤⣴⠀⡌⣿⡀⠀⠀⢰⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠣⣀⢈⡄⢈⡀⡏⠉⠀⢘⡆⡰⠈⡼⠀⠈⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⢻⡇⠀⠀⣿⡖⡛⡹⣇⢀⠀⣇⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠛⠇⡔⢠⣳⣟⣀⣰⣿⠀⠁⢻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠂⠀⠀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠿⠟⣠⣀⣘⣼⠉⠛⠛⢉⣍⣂⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠉⠀⠒⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠃⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠔⣴⣤⣦⠀⡆⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠉⠛⠉⠂⠃⠘

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⣶⣶⣶⣶⠶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢤⣤⡤⠐⠒⣒⣶⣤⠤⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⡠⣺⠉⣀⠔⡪⢁⡠⢤⣤⣤⣄⣀⣀⡒⠋⢉⣉⠤⠬⢭⣶⠤⣀
⠀⠀⠀⠀⡀⣼⢃⠞⡱⠊⡔⠁⠼⡳⠄⢒⣒⣒⣚⣛⡳⠦⣄⣐⠀⠀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⢇⠀⠁⠊⠀⢸⠀⠀⠤⠒⠉⠁⠀⠀⢀⡠⠤⠤⠤⠬⠍⣒⣤⣀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠸⠀⠀⠀⠀⠤⠶⠤⠤⠒⠒⠉⢉⣉⣉⠀⠠⢀⣈⡑⠦⡁
⠀⠀⠀⠀⢀⠤⢀⠔⠀⠐⠢⣀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⠤⠒⠒⠉⠉⠉⠛⠋⠺⠶⣄
⠀⠀⠀⠀⠇⢠⡁⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠈⠁⠀⠀⠀⢀⡠⠤⠀⠀⢈⣉⣁⣒⠢⢬⡳⡄
⠀⠀⠀⠀⢗⡸⣈⠑⠢⣄⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠘⠋⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠚⢆
⠀⠀⠀⠀⠀⠑⢨⡛⠓⠺⣗⠤⠤⠤⠤⣔⡇⠠⢄⡀⠀⠀⠀⠀⠀⠀⠶⠶⢀⣀⣈⣉⡁⠒⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⣟⠿⠿⢭⣴⠞⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠔⠒⠁

⣿⣽⣿⡿⠁⡙⣿⠉⠙⢾⣶⢠⡌⢷⣿⡹⣿⡈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀
⣿⢋⠻⣷⣜⣻⠿⢦⢠⣬⡹⣏⠸⠀⠛⢻⣾⡉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠏⠛⠙⠛⠛⠵⠛⠂
⢿⣮⣦⣿⢿⣿⢀⣤⣹⣏⣷⡌⠹⡄⠀⡠⠻⠇⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⡾⠟⠉⠁
⣿⠛⠙⣿⣄⡏⢨⣒⠙⠯⡻⣧⢀⠘⠆⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⢀⠤⠒⢀⣐⡂⠀⢀
⣿⣟⣘⠹⢿⣇⠀⣬⠇⣨⣥⠜⠊⠣⣹⡘⢻⣳⡀⠀⠂⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⢇⣤⠊⢻⣦⣨⣕⢢⡘⣦⡀
⣿⠿⠿⣷⣄⣹⢧⣿⢸⡟⠃⠀⣿⡖⣈⠻⣄⠀⢡⣄⠀⠓⠀⠐⠙⠀⠀⠀⠀⠀⠀⢠⡟⠑⣿⣿⣧⡀⠙⢿⢿⣧⡈⢿⣷⡀
⣾⣿⣯⠛⣻⣿⣦⣾⣿⣇⢀⡀⠠⣾⠟⠓⠌⣦⣄⠛⠳⣄⡠⠤⠀⠀⠀⠂⠀⠀⢠⡿⠂⣠⢿⣯⡻⢷⣦⣄⠘⢿⣿⣎⢃⣅
⢿⣿⠿⢾⣿⣿⣿⣿⣿⣮⣑⠁⠀⣷⣦⡀⠀⢀⠙⣮⣆⠘⠇⢀⣬⡄⢺⠀⠀⠀⣾⠇⠀⠘⠺⣿⣿⣿⣿⣿⣿⡿⠿⠆⠀⢨⣀
⣦⠈⢿⡛⠿⣿⣿⣿⠟⠋⠛⣿⡲⢦⣬⣙⠂⢿⢃⣿⣿⣿⣦⡠⡛⢁⣼⡇⠀⢠⣿⠀⠀⠀⠀⢹⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⣿⡯⢸⣿⣦⣿⣿⣿⡄⢰⣷⣼⣿⣿⣿⣿⠿⠦⣌⡁⢄⢹⣿⣿⠞⠛⢧⣅⢻⣿⣿⠄⠀⠀⠀⠈⢻⣆
⠋⣀⣾⣿⡟⠋⠉⠻⣿⢾⡿⣿⣏⠁⢨⣿⠿⠷⠆⠉⠀⠺⢿⡿⣄⣶⣸⣿⣕⣹⣿⡧⢀⠀⠀⡀⠀⠻⣆
⣿⣿⣿⡏⠀⢉⣕⡀⢸⣦⡈⠫⠻⢯⠻⣧⠀⠼⣢⡤⠶⠚⠋⠉⠙⠨⣟⢷⣼⡟⣿⣿⣶⡗⠆⠈
⣿⡿⡿⠇⠀⢘⢛⠃⢸⣿⣿⣿⣤⣀⣉⡩⠻⠿⢿⣇⠲⣆⠀⠿⢱⣄⣵⣿⣿⣿⣾⣿⣿⣭⠒
⣻⠤⠀⣨⡦⢄⢡⣴⣿⣧⠞⠛⢿⣿⣾⣇⠀⢴⣷⣼⣿⣮⣷⣶⠿⠋⣿⣝⡿⠿⣿⣿⣿⡳⢆⠠⠀⠀⠀⠄⢀⠀⠀⠀⠀⠁⠀⡀
⣿⣶⣶⣿⣀⣼⣿⣿⣿⣷⣶⣷⣮⣿⣿⣿⣧⣬⣥⣾⣿⣿⣛⠃⢶⣤⣯⣼⡇⢴⣹⣿⣿⢦⡤⠴⠌⠁⠀⠐⠀⣀⠀⠀⠂⠀⠀⠁⢀
⣿⣿⣿⢿⣿⣿⣿⠿⠿⣿⣿⣿⡝⢾⣿⡟⣫⣿⡻⢿⣿⣿⣿⣦⣨⣽⣿⣛⣷⣾⣿⣿⣿⡟⠲⣴⠮⢥⠉⠙⠀⣀⣀⣀⠛⠒⠀⢱⠞⠀⡀
⣿⣿⣿⣿⣿⣿⠏⢀⠤⠈⢻⣿⣿⣾⣟⣾⠟⢯⣽⣿⣿⣿⣿⣿⣿⣿⡆⢀⣤⣬⣿⢻⣿⣿⣿⣀⣀⣀⡷⠶⠶⢁⣀⡠⠗⠖⠂⢉⡀⣠⠇
⣿⣟⠿⣿⣿⣿⠀⢸⣿⣦⠀⣿⣿⣿⣯⣶⣿⣶⣾⣿⣿⣟⡏⣾⣿⣽⣧⡘⠟⣳⣿⣽⣿⣿⠈⠛⠛⠉⢱⣤⡤⠖⠉⠃⣀⢀⠀⠈⠁⠀⣤⣶⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠸⡗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣘⣗⠷⠿⢣⠇⢸⡠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣟⠂⠁⠀⠀⠀⠀⠉⠘⢉⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡛⢩⡴⢀⡠⢀⠀⠀⠀⠀⠚⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⢀⣛⣉⠿⠛⣏⡔⣄⣄⡰⣭⡿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⢀⠔⣵⠯⣴⡚⠃⠘⠉⠼⣋⡻⡍⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⡞⠀⢀⢾⣶⢾⠄⠀⠀⣴⡒⢝⢾⠈⡆⠀⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⡠⡞⡇⠀⢈⠀⢁⡌⠀⠀⢸⠛⠉⣷⠀⠀⢹⠦⣀⠀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡠⠴⠒⠋⠁⡰⢡⠇⠀⠈⣒⡫⠀⠀⠀⡸⣀⣠⠃⠀⢀⠎⢣⠈⠑⠢⣄⡀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡴⠋⠀⠀⠀⢀⡜⣡⠎⣀⣠⣤⢤⣄⣀⠀⠀⠑⠈⠀⠀⢀⠾⡀⠀⠣⡀⠀⠀⠉⠓⢄⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡜⠀⠀⢀⣠⣴⠯⠾⠕⠊⠁⠀⢀⣠⠎⠁⠉⠲⣄⠀⠀⠀⡸⠀⢣⠀⠀⠙⠢⢄⡀⠀⠀⠙⢦⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢁⠴⠚⠉⠀⣯⠆⠀⠀⠀⠀⠐⡾⠍⠀⠀⠀⠀⠈⠳⡄⠀⡇⠀⠈⢣⡀⠀⠀⠀⠀⠉⠓⠲⢄⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⢀⡇⠀⠀⢶⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⡤⢇⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢻⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢠⠎⢇⠀⠀⠀⠀⢰⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⡤⢸⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⢦⡀⠀⠀⣾⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠦⣀⢻⠤⠀⠀⠀⠀⠀⠀⠀⣠⠞⡄⠀⠀⠀⠀⠀⠀⠀⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⠀⠀⠀⠀⠐⣜⣿⡓⠒⠂⠐⠒⠒⠂⠉⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⢹⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡆⠀⠀⠀⠀⠈⢳⣌⠑⠢⠤⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⡆⠀⣇
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⣾⡘⡄⠀⠀⠀⠀⠈⡌⠱⡦⣄⠀⠀⠀⠀⠀⠀⢰⢱⡀⠀⠀⠀⠀⠀⠀⢱⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣰⠫⣅⠉⠙⠢⣄⠀⠀⡠⠊⠀⠈⡄⢹⠀⠘⡄⠀⠀⠀⠀⢸⡄⢻⠆⠁⠀⠀⠀⠀⠀⠘⡆⢧⠀⠀⠀⠀⠀⠀⠘⡀⢸⣄⠀⠀⣀⠤⠒⠘⢁⣈
⡇⠀⠈⢣⡀⠀⠈⠓⠉⠓⠀⠀⠀⢳⠘⡇⠀⢸⣄⠀⠀⠀⠈⣷⠀⢇⠀⠀⠀⠀⠀⠀⠀⢱⡘⡆⠀⠀⠀⠀⠀⠸⡇⠀⠈⡤⠞⠁⠀⢠⡔⠁
⢧⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠞⢻⠁⠀⡎⠺⠒⠋⠀⠀⠋⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⣆⠀⠀⠀⠀⠀⠻⠀⠀⠁⠀⠀⢠⠎
⠈⠢⡀⠀⠀⠈⠣⡀⠀⠀⢀⠼⠓⠀⠀⠀⠀⠘⣦⠔⣂⡀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢦⠀⠀⠴⢊⡜⣳⠀⠀⠀⢀⡎⠀⠀⠀⡴
⠀⠀⠹⡄⠀⠀⠀⠈⠑⠈⠁⠀⢀⣠⠤⠔⢒⠟⠁⠀⠀⠉⢀⠎⠀⡞⠒⠶⠤⠤⠤⠤⠤⠤⠔⠚⢳⡀⠱⣤⠀⠁⠠⠛⠒⢤⡠⠞⠁⠀⠀⣺⠁
⠀⠀⠀⠙⠦⣀⡀⠀⣀⡠⠔⠊⠁⠀⠀⢰⠃⠀⠀⠀⢀⡜⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠳⢤⡀⠀⠀⠀⠙⣤⢤⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠹⣤⡠⠤⠚⠁⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠒⠦⠤⣀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀⠀⣀⠀⠀⣀
⠀⠀⠀⠑⡢⣀⠄⢀⠀⠀⠀⠀⠀⠀⢠⡁⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠇⣆⠀⠀⡎⢹⠀⠀⠀⠈⠻⡺⠟⡃⠰⠋
⠀⠀⠀⠁⠜⠀⠒⠐⡆⠀⠀⠀⠀⠀⠈⢿⡌⠇⠠⠀⠤⢂⣀⠈⠉⠀⠀⠀⠂⣸⣀⣸⡇⠈⠀⠀⠀⠀⠈⠁⠈⠅⣠
⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡰⠿⠃⠀⠀⠀⠀⠀⢘⢻⣿⣿⢟⠄⠀⠀⠀⠀⠀⠑⠀⠈⠻⠀⠀⠠
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠞⠀⠀⠀⠀⠀⠀⠀⢨⣾⠛⠻⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠
⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠐
⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠖⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠄⠲⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⢰⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢰⡆⠀⢰⣇⣀⣼
⠀⠀⠀⠀⣀⣀⡀⠀⠀⣴⣿⣿⣿⡄⠀⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⡁⠀⢀⣿⣿⣏
⠀⠀⢠⣾⣿⣿⣿⣷⣾⣿⣿⡿⢿⣿⡄⠀⠀⠀⣿⣿⣿⡄⠀⠀⣀⣤⣄⣀⠀⠀⣠⣴⣿⣿⣿⠇⠀⠀⣿⣿⣿⣷⣤⣄⣀⣀⣤⣤⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠀⣠⣴⣤⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣀⢼⣿⣿⣿⣿⡿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢿⣿⣿⡇
⠀⠁⢸⡟⢿⠃⢸⡇⠸⡇⠀⠀⠀⠀⠦⢸⣿⡿⢿⣿⡿⠀⠀⠋⣿⡿⠃⠀⠈⠁⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢻⣿⡇⠆
⠀⠀⢸⡇⣼⠀⢸⡇⠀⣷⠀⠀⠀⠀⠀⠀⣿⠁⢸⣿⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣟⡇⠀⠀⠀⠀⢠⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢤⣤⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡤⡤⠤⣀
⠀⠀⠀⠀⠀⡀⢤⠒⠋⢹⡖⠂⠈⢳⡌⢂⠙⣿⠣⡀⠀⠀⠐⡟⠡⠔⣛⣫⣶⣦⠀⠀⢀⠎⠀⣀⠤⠜⠀⠧⣀⠀⠡⡀
⠀⠀⡠⠒⣭⢄⠸⡍⠳⡈⢳⡀⠀⠀⢻⡌⡄⠘⣄⡇⠀⢸⠀⠃⢠⠊⠉⠉⢉⣈⣁⠀⣸⡀⠚⠀⠀⡄⢠⠀⠀⠱⠀⡧
⠀⠰⠁⠀⢿⠀⠂⠹⣆⢱⡈⢷⡀⠀⠘⡇⣧⣶⠟⠀⠀⠘⢧⡀⠐⠔⠒⠉⠉⢉⡟⠀⢿⣧⡀⠀⠀⠸⠂⠀⠀⣀⣴⠇
⠀⢠⡀⠀⠈⠓⠄⣦⣘⢦⣧⣀⣷⣶⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⠴⠚⠁⠀⠈⠻⣿⣷⣶⣶⣶⣾⣿⡿⠋
⠀⠀⠉⠛⠓⠒⠛⠛⠛⠛⠛⠋⠉⠀⡠⠒⠀⠁⠀⠠⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢉⡩⠭⠟⠫⢤⣀⣀
⠀⠀⣠⠒⠫⣅⠉⠉⠱⣶⢤⠀⠀⡌⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠀⠀⠙⡿⠉⠱⡀⠀⠀⢀⣴⡙⠀⠀⠀⠀⢨⠀⢨⣉⠵
⢀⣞⠣⠄⢈⢮⡀⠀⣠⡇⢠⠳⡄⡇⠁⠀⠀⠀⠀⠀⣸⠀⣸⠶⢦⣄⡰⠁⠀⠀⣷⠀⣰⡋⠀⠘⢎⢂⠀⠀⣸⠀⠊⠁
⠠⠁⠀⠉⣷⣿⣿⡾⠛⠶⠾⢤⠁⠘⢄⣀⣀⣀⣠⠴⠃⠀⡇⠀⠀⠘⡇⠀⠤⠞⡿⠠⠀⠬⢷⣤⠼⠿⠶⠛⠁
⠘⠦⠒⠛⣉⣁⠀⠄⡠⠠⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠰⣤⡀⠀⠰⣄⠀⠚⠀⠀⠀⠀⠤⠶⠾⠥⣄⡀⠈⠙⠲⣄
⠀⠀⣴⠍⠁⠀⠀⠀⠀⠀⠛⣯⠀⠀⠀⠀⠀⠀⠀⠤⡤⢤⣤⣤⣭⣉⠉⠁⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠙⢲⡀⠀⠈⡆
⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⠈⠢⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢲⣧⡤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡴⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⡱⠀⠀⠠⠁⠀⢀⠀⠀⠀⠀⠀⢹⠁⠀⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠑⠦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣸
⠀⠀⠀⠙⠢⠤⠴⠄⠂⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠒⠒⠋⠀⠀⠀⠀⠘⠓⠢⠤⠤⣄⣀⡀⠀⡼⠖⠉
⡶⠒⢶⢶⡶⠶⠶⣶⢶⠶⠶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⠶⠶⡶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢊⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠈⡁⠀⠀⠀⢀⡄⣠⡀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣀⠀⠀⠀⢸⡷⠋⢻⣀⡴⣏⠀⢀⡞⠹⠀⣴⡻⠀⠀⠀⠀⣼⣷⠀⡶⠖⠰⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡟⠀⠀⠀⣀⠀⠀⠀⠉⠀⠙⠒⠉⠧⠤⠒⠻⣤⠔⠀⠘⢛⡟⢻⡄⠻⠶⡆⠳⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠓⢰⣤⣧⠰⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⠀⠀⢀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠰⠶⠶⠶⠤⠤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡴⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠶⠦⠀⠀⠀⠀⣿⣿⣿⡀⡼⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣾⣿⡿⠀⠀⠀⠀⠀⠰⠖⠒⠀⠈⣿⢻⣿⣷⠁⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⡇⣿⣼⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡧⠀⠀⠀⠙⢁⣴⣿⣇⢢⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢿⠙⢿⠀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡧⢿⡀⠀⠀⠠⠿⢿⣿⣿⣼⣷⡄⠀⠀⠿⠀⠀⣽⣿⡇⠀⠘⢷⣾⣧⠀⠀⠀⢀⣴⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⡀⠀⠀⢘⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣤⡀⠀⢋⣽⣿⡁⠠⠄⣘⣿⡏⠘⠐⠂
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⢄⠀⠐⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⡿⣻⣿⣷⣄⣿⣭⢽⣿⣦⣤⣥⣟⣛⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣶⣄⣴⠏⠀⠰⣿⣿⣿⠗⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⡷⢿⣷⣾⣿⠏⠀⠀⢿⣼⡗
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠹⣿⠏⠀⣀⡴⠋⢻⣿⣿⣿⣿⡿⠁⠈⠁⠈⠻⣿⣿⡿⠃⢸⣿⡿⡋⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡷⣤⡆⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡸⣿⠾⣷⡶⣾⣼⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣹⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢿⣷⡶⣶⣿⣄⣰⣷⡶
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣘⣋⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣠⣦⣤⣾⣤⣷⣾⣷⡼⡀⠀⣼⣿⣦⡌⢻⣿⣿⣿⢀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣹⡇⠀⢿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣛⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⣿⢿⣼⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣸⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠝⠀⢀⣠⣾⣥⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠉⠁⢻⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣛⣿⣿⡿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣏⣁⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣷⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣿⣧⣤⡙⢿⣿⣿⣿⡇
⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣄⣼⣿⠿⠿⠟
⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡉⢻⣿⣟⣻⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠛⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠰⣄⠀⠀⠀⠀⠉⠙⢷⣄⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠿⠶⣄⣰⠀⠀⠀⠀⠹⣧⠀⢠⡾⠻⣆⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠉⠛⢶⣤⡀⠀⣿⣰⠟⠀⠀⠉⠛⣳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠠⠶⠛⠉⠙⢦⣼⡏⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣄⣀⣀⣀⣀⣀⣨⡿⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣽⠃⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⣿⠀⠀⣾⠁⠀⠀⠀⣀⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢶⡇⠀⢰⣧⡤⠶⠛⠛⠉⠉⠉⠀⠀⠀⠉⠉⠉⠛⠲⢦⣀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣷⠀⣿⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿
⣿
⣿
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠦⣤⣤⣤⣤⣤⣤⠴⠞⠛⠁
⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣽⣿⣿⣿⣯⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣥⣬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣶⣶⣿⣿⣷⣶⣾⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠒⠢⢄⣀⡠⠐⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠤⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⡀⣺⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢸⢀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢶⣦⡀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⣠⣾⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⢻⣿⣇⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⡴⠀⢻⡄⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠢⢙⣿⣿⡿⠁⠀⠀⢀⣠⠤⠤⠤⣤⠀⠀⠈⠉⠉⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠙⠷⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣠⠏⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⢹⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣀⠠⠤⠒⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠉⠉⠑⠤⣄⣀⣀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠄⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢰⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣠⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡁⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠠⠓⢤⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠄⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠁⡀⠀⠀⠀⠀⠀⠀⢰⠤⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠃⠀⠀⠀⠀⠀⠀⢚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣅⠀⢀⠀⠀⠀⣠⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠙⢄⠀⠀⡄⠀⢰⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠀⠙⠦⠠⢄⣀⣀⠤⠤⠔⠃⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠀⠀⠒⡂⠐⠒⠦⠤⣋⣉⠉⠩⠉⠙⠒⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣚⣋⡀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠉⠓⢦⣀⣀⠀⢄⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠌⠠⠒⠔⠲⠈⠍⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡀⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡴⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡈⣀⢈⣥⣤⣀⡀⣀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⢠⡈⠛⠀⡠⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠽⠚⠁⠉⠀⠀⠐⠉⠍⠉⠉⠙⣛⠓⠚⠣⠦⣄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠨⢆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠈⠑⠫⣢⡀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠈⠀⡀⠀⠅⢪⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠤⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⢈⡹⣷⣌⠂⠄⠀⢁⠀⠀⠆⠄⠆⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⡀⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⠀⠀⠀⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠻⣦⠀⡀⢂⡴⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⣴⡋⠐⠂⠠⠀⢀⡀
⠀⢀⣴⡾⠛⠉⠉⠉⠨⠉⣉⠉⠈⠛⠀⠛⠷⢶⢤⢬⣀⡀⠁⠀⠀⠠⠀⠐⠂⠀⠀⡀⢂⠂⠠⢳⡧⠐⠃⠀⠀⠐⠀⠂⠀⠀⢀⢀⡨⠞⢁⣀⠀⠐⠀⠀⠉
⢠⣨⠁⠀⡀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠍⠐⠛⠿⢶⣤⡀⠀⠀⢀⠀⠀⠀⡩⠂⣾⠷⠔⠐⠶⠳⠶⠾⠶⣶⣷⣶⣾⣿⣶⣶⠶⣶⣶⣶⣷⣶⠖⠂
⢺⠉⠙⠳⢦⣤⣐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠡⠀⢛⢶⡀⠈⠡⠀⠀⢀⣴⡽⠲⠲⠒⢒⠳⠶⠖⠛⠛⠻⠿⠏⢻⣿⣿⣿⣿⣿⠟⠋⠉
⠈⠉⠁⠶⢄⡀⠉⠛⠶⢤⣀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠄⢳⣿⡻⣷⠖⣞⣿⢫⠾⠟⠛⠛⠿⠏⣛⣛⠛⠛⠛⠒⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠒⠲⣄⠈⠉⠓⠶⣠⡀⠀⠀⠀⠀⠀⠀⠆⠈⠤⠀⣀⣎⣼⠤⠩⠀⠀⠉⠑⠒⠒⠢⠥⠒⠒⠠⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣤⣀⣙⠣⠗⠶⠒⢒⣲⣖⣼⡿⡛⣡⡮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⠶⠤⢴⣂⣲⣧⣴⠟⠛⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⣠⢄⣦⠤⠶⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡂⢰⠐⠱⠞⣁⡀⠀⡄⢘⡓⠀⠈⢡⣔⠒⠣⢴⣦⡴⠶⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣼⡀⠀⠾⠃⣀⠀⠉⢰⡆⢀⠙⠛⢀⡘⠂⢨⡄⠆⠈⠁⡀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠉⠙⣁⠠⠆⠈⠋⠰⣦⠀⢠⡀⠁⣠⡄⠁⠠⠦⠀⣀⠀⠘⣂⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠰⠃⠀⠀⠀⠀⠈⠁⠀⠈⠁⣀⠀⠀⠀⠈⠁⠐⠄⠙⠢⡀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠤⠄⠁⠀⢠⡄⠀⠀⠀⠀⠤⣤⡀⠀⣶⡀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠪
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢔⠄
⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⢰⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠚⠦⣄⠀⠀⠶⠃⢀⠀⠀⠀⠀⠚⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣶⠄⠀⠀⢠⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⢀⡉⠀⠀⠀⣶⣿⢿⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣽⣿⣾⣿⡇⠀⠀⠈⠉⣦⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠘⠁⠀⠀⠀⣿⣿⣾⣿⣶⣾⣷⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⠿⣳⠃⠀⠰⣆⢠⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠀⠀⠀⠀⠀⠹⣝⡿⠿⢿⣣⠟⠄⠀⠀⠀⠀⠀⠀⠁⠉⠒⠒⠋⠁⠀⠶⠀⠋⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣃⣴⠀⠙⠦⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠠⠿⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⢦⡀⠀⣈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠉⠀⠀⠀⢀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠢⠤⠀⠀⠀⠀⣠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠛⠃⢰⣮⡐⣶⣤⠤⢀⣄⢀⠀⠀⠀⠀⠀⡀⠀⣢⡀⠀⣠⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣠⣄⣾⡟⠀⢨⣄⠈⠛⡃⠀⠀⠉⠀⠀⠀⠀⠁⠀⠸⠋⠀⠐⠿⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⢿⠏⡉⠀⣀⣀⠙⠃⠈⠛⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠂⠀⢴⡶⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⠁⣈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠠⢤⡄⠲⣄⠋⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡈⠃⠀⠟⠞⢡⠞⠃⠐⠓⣀⡀⠠⠀⠀⠀⠀⠀⠀⣐⠚⠂⠐⢶⣔⣆⠼⢏⡀
⠀⠀⢀⡀⡄⠀⣆⠈⣀⠛⣡⠿⡄⠀⠀⣤⠀⠐⡁⠞⠀⠀⠁⠀⠐⡀⢀⠆⠀⠈⠉⠀⠉⠁⠆⠀⠈⠀⠀⢀
⠀⠀⠀⠐⠈⠀⠁⠀⠉⠀⠉⠀⠛⠦⡀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⢢⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠠⠀⢠⡀⠀⠀⢰⡀⠧⠷⡀⢠⡄⠀⢀⡀⠀⠀⠔⠀⠒⠂⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠶⠶⠖⠚⠛⠻⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⡄⣠⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⡖⠶⣼⣧⣸⡟⠁⡤⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡃⠀⢈⠸⢻⣿⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⠇⠀⠠⢌⣧⣿⡀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⢳⡀⠋⣠⢻⣿⣯⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⣿⣇⠀⠀⢠⣿⠿⢷⣤⣾⠣⣹⣆⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⡏⢹⠚⡽⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⢿⣦⠀⣈⣍⠓⠲⣿⣛⠀⠀⡙⣻⡶⢤⣤⣤⣤⣄⡽⢦⡀⠀⠀⠀⣇⡏⢰⡇⢸⠿⣿⡟⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣄⠈⠀⠘⠛⣶⣤⣀⣉⣉⡽⠇⣿⡇⠀⢷⡀⠀⠀⠀⠈⣿⠀⠀⢠⢿⠇⠀⣷⠘⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢻⡧⣄⠀⠀⢨⣿⢹⡅⠀⡠⣴⡝⢷⣄⣼⠇⠀⠀⠀⠀⣸⠃⠀⢈⡿⣆⣀⡿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⠀⢹⣾⣁⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⠞⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡞⠙⠦⣤⣄⠀⢀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠞⠀⠀⠀⠈⠛⠶⠟⠁

⠀⠀⠀⠀⠀⠀⣔⠲⠶⠶⠶⠒⠒⠶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢆
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠤⡀⢠⠄⠐⠀⠠⠍⠉⠛⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠠⣄⣀⣀⠉⠰⠆⠄⠈⠙⠲⢄⠀⠀⠀⠀⠀⢷⠀⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢤⡀⠙⠛⠟⠷⢦⣤⣐⠀⡀⠀⠙⢦⡀⠀⠀⠈⣄⡀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⠤⣄⣀⣈⣐⣇⣀⠀⠀⠉⠲⣾⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡉⢁⣤⣤⣿⣶⣄⠀⢤⡟⠉⠙⢻⡛⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣿⣿⣿⡿⠟⠉⠀⠀⠀⣄⠀⠀⠙⣦⠘⢿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣿⣿⣿⣿⠿⠿⠟⠛⠉⠉⢀⡀⠀⠀⠀⠀⢣⣾⡷⠀⠀⠸⠃⠈⢻⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⢀⣠⣶⡶⠟⠀⠀⠀⣰⠀⠮⠐⠃⠀⠀⠀⠀⠀⠈⠀⠘⣆
⠀⠀⠀⠀⠀⣀⡠⠞⠉⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠻⡄
⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣄⠀⠸⡆⠀⠀⠀⣀⣀⠀⠀⣀⠀⠘⣄
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⢀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⢀⡄⣀⣤⣤⣉⠳⡄⣯⣤⠄⣌⠄
⣸⠁⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠙⠻⣿⡷⠀⠁⠸⡆⠊
⡇⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢿⡿⣿⣿⣿⣄⡀⠚⣆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⢢⡀
⢷⡀⠀⠀⠀⠀⣠⠐⠁⢀⠀⠀⠰⣄⠀⠀⠀⠀⠁⠀⠁⠙⣿⣿⣿⣿⣷⡀⠀⠀⣱⣿⣿⣿⣿⡃⠲⢤⣀⠀⡀⠀⠀⢉⣿⣼⠇
⠈⢷⡈⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⡗⠀⣼⠛⢿⣿⣿⣇⣀⠃⢰⠌⡹⣆⠀⢀⡶⠐⠋
⠀⠈⢧⡈⠢⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⡰⠖⠂⠒⠬⣳⣿⣿⣿⣿⣿⠀⠠⢿⡆⢈⠉⣿⡿⠛⠲⢄⠀⢑⡾⠒⠋⢀⡤⠖⠒⠒⠶⣄
⠀⠀⠈⠳⣄⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠶⠦⠤⠀⠋⠉⠉⠉⠉⠛⢦⣌⢦⡑⠠⢄⣻⡇⠀⠀⠀⠈⠁⠀⠀⣴⠞⠲⠶⠃⠀⠀⠸⠶⢦
⠀⠀⠀⠀⢹⠂⠀⠀⠹⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠉⡚⠶⢦⡏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶
⠀⠀⠀⠀⠈⢧⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣜⣠⠴⠶⠶⠦⢤⣤⣤⣄⣤⠴⠞⠋⠀⠀⠀⣀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣄⠀⠀⠀⠀⠀⣠⡤⠶⠒⠛⠉⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠋⠁⠀⠀⠀⠀⣠⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⢦⣄⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠤⠾⠛⠉⠀⠀⣠⡴⠂⠁⢀⡠⠞⠁⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠷⠦⣤⣀⣤⣤⡤⠴⠶⠖⠛⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡠⠶⠂⠀⠀⠀⠀⠀⠀⢠⣧⠆⠀⠀⠀⠀⠀⣠⠤⠀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠈⠣⠄⠠⡆⠀⠀⠐⠀⠀⡠⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢘
⠀⠀⠀⠀⠀⢠⠀⠀⠐⠦⠀⠀⣷⠀⢀⠀⠀⠘⠁⠀⠐⠋⠀⠀⠙⡆⠀⠀⠀⠀⢸⣠⠂⠀⠀⢀⠀⢀⠔⠊⠁⠸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⠀⠀⠛⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠐⠁⠀⢀⡀⢰
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡀⢀⡤⠀⠀⢧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⢀⡄⡀⠀⠰⣦⡤⠊⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠻⠷⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣀⡆⠀⠀⢿⣇⣀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠻⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⢤⡠⠄⠀⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠐⢄⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠠⠀⠀⠰⠆⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡀⣠⠀⠀⠀⠀⢷⣄⡀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⣿⣿⢛⠿⠛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣖⣧⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠟⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⠀⣼⣧⣤⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⡰⠁⢰⣿⣿⣆⡈⢢⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡠⣱⠈⣁⠀⠸⣿⠿⡄⢳⡀⢳⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢰⣿⡇⠀⠀⠀⠀⠀⢀⢠⡃⠓⣈⠉⡄⡆⠀⣴⢷⡈⣇⢘⡇⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⢠⣿⣀⣀⠀⢀⡤⠐⢛⠓⢋⠉⠭⠀⢷⣙⣿⣅⠚⢷⡋⠉⠙⠻⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣸⡚⣛⣭⣛⣛⣛⠻⠶⠖⢶⠶⠖⠋⣹⣙⢷⡂⡈⠙⢦⡈⢧⡘⢶⡄⢠⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣠⢽⣇⣿⣿⡿⣿⣿⣿⡀⢇⠀⡱⠁⠰⢶⣿⣦⢳⡘⢦⡀⢳⡀⠙⣶⣶⣦⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡶⠾⢿⢻⣿⣿⣿⣿⡿⠁⠀⣼⢃⢰⠀⠉⣿⠋⠣⣱⡄⠙⠢⣁⣆⣿⣿⣿⣽⡟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⣗⣠⣿⡿⠋⠛⢿⣿⣇⢀⣾⠊⢁⣱⣶⠟⢡⣴⣷⣿⣿⣧⣄⣸⢸⣿⣿⣟⣋⣒⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⣉⣾⠋⠀⠀⠀⢀⠞⢿⣿⠁⢸⣞⠋⣁⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠉⡛⢻⢏⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⡿⣇⠀⠀⣀⠔⠁⠀⠰⡜⣿⠂⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣯⣩⣬⣅⣤⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠹⣿⣶⠃⣰⣿⠟⠿⠿⠿⠿⠿⠛⠋⠁⢸⣿⣿⡿⢿⣿⣿⣧⠻⣟⠀⠀⡀⢀⡀⣀⣀⣀⢀⣀
⠀⠰⠴⠶⣶⠶⠦⢤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣏⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠙⢻⣿⣷⡌⠀⠸⢿⣿⣿⣿⣿⣿⣉⣍
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠉⠉⠉⠙⠉⠀⢠⢾⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠉⣿⡆⠶⠚⠛⠋⠉⠛⠛⠛⠛⠻
⠠⠾⢿⡿⣣⣶⠶⢧⡤⣴⢦⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⢇⡼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢠⣾⢟⣤⡤⠤⠄⠀⠀⣿⠀⣠⠤⠶⣦⣦⡴⠶⠤⣤⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣾⠁⣿⠀⠔⡐⠒⠛⠃⠉⠉⠁⠀⠐⡿⠁⠀⢀⠀⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠐⠚⠚⠻⠏⠉⠙⠋⠛⠛⠙⠉⠁⠀⠀⠁⠀⠀⠀⠈⣿⢰⢸⠇⣀⣤⣦⠽⠷⠖⢀⢰⣳⣋⣡⣷⣶⡶⠾⠿⠟⠃⡸⢼⠃⠀⠒⠀⣐⣀⣩⣿⠿⠶⠴
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡧⠱⠟⢋⡉⣁⣀⠀⠀⢀⡈⠨⣡⣌⠁⠀⠀⠀⠀⠀⠀⠐⠑⠞⠐⠋⠉⡉⠉⠉⠀⠀⣠⣄⣠
⠀⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣀⣠⣤⣀⣀⣀⡀⠀⠓⠛⠓⠒⠛⠉⠉⠉⠉⢉⡉⣉⡉⣉⣉⣉⣀⣀⣀⣤⣄⠲⣤⢶⣶⡽⢓⣈⣾⣿⣿⣾⣶⣾⣿⣿⣿
⣀⣉⣉⣉⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣁⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣈⣁⣈⣉⣀⣁⣈⣀⣀⣀
⣿⣿⡏⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⣀⣀⠔⠐⡐⡠⢶⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠐⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⢛⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣼⣧⣤⣼⣿⣛⣲⢶⣄⣀⣀⠀⢠⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢋⠙⢀⣠⠟⠋⠁⠀⠹⣄⠀⠀⠀⢉⣉⣻⣷⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡱⣧⣇⢀⣀⣀⠀⠀⠈⠙⠛⠛⠉⠉⠙⠻⢿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠊⠉⠁⠀⠀⠸⣿⡀⠀⠀⠀⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⢹⡌⠿⣿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⣾⣿⣾⣷⣿⣷⣿⣷⣦⡄⠀⠀⠀⠀⢝⣷⣤⡀⠀⠀⢣⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠴⢿⣿⣿⣦⡀⠀⠐⠤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣰⣶⣾⣿⣿⣿⣿⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢢⣄⢄⣄⣄⣆⢀⡀⡄⣠⣠⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠟⣿⣼⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡏⡞⠘⢸⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠃⠈⠀⢸⢸⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⢸⠿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⢨⡀⠀⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢹
⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠘⣷⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⡘
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡆⠀⠈⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠁⠀⠰⠀⢸⣯⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢀⢈⠈⡇⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠘⡌⠸⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠄⡆⠄⡆⡇⡇⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠠⠀⢰⢐⡰⣻⢡⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣧⢻⣧⣧⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠉⠉⠉⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠷⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠉⠛⠛⠳⢾⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠶⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣽⣶⣿⣭⣭⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⣤⣴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠀⣿⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢿⠀⠀⢠⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣠⣾⠃⠀⠀⣠⠟⠁⢀⣠⡄⠀⣼
⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠱⣄⠀⠻⣄⠀⠀⠀⢠⣿⣧⠀⠀⠀⣿⠹⣧⠀⠀⠀⣴⠟⣿⠀⢠⡞⠁⢀⡴⠋⠀⡇⠀⡟
⠀⠀⠀⠀⠀⠘⣇⠀⠘⡄⠀⠘⢷⣦⣽⣦⠀⠀⣸⡇⢿⡄⠀⢰⡟⠀⢿⡄⢀⡾⠃⣸⡇⣠⠏⠀⢀⠞⠀⠀⣰⠁⢰⠇
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⡀⠀⠈⢻⣍⠻⢷⣤⡿⠀⠈⣷⣠⡾⠁⠀⠈⠻⠟⠁⠀⢿⣤⣯⣤⣠⣯⣀⣀⣠⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠱⣄⠀⠈⢿⣧⡀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣽⡿⠛⠋⣹⠋⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⣈⣧⡴⠾⠛⠁⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⢧⣄⣸⠀⣠⠞⠁⢠⡾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⡿⠿⠿⠶⠶⢾⡾⠃⠀⢀⣴⣿⠀⢠⡿⣦⠀⠀⣴⠞⠳⠶⣤⣍⣻⣿⣁⢀⣴⠟⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⣀⣴⣟⣠⣴⠶⠛⠁⢹⡆⣾⠁⠘⣧⣸⡏⠀⠀⢠⣤⣌⠉⢙⣿⠿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠿⠋⡉⠀⠀⢀⠀⢸⣿⠃⠀⠀⠘⣿⠁⠀⠠⠀⠀⢄⠀⢸⡇⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡅⠀⠘⠀⠀⣴⣆⣧⠈⠏⠀⠀⠀⠀⠙⠀⢼⣰⣦⠀⠀⠀⢸⣧⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⢌⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣟⡄⠌⠀⢸⣿⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⠳⠶⠶⠶⠶⠞⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢀⣴⠾⠛⠋⠉⠉⠉⠉⠙⠛⠷⣦⣀⠀⠀⠀⢠⣿⠀⠀⣀⣀⣀⣠⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⣼⠇⠀⠀⠈⠻⣯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⡀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣶⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠁⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠛⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⣽⡇⣿⡶⠶⡶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⡟⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠷⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⡟⠉⠀⠀⠀⣀⣀⣀⣀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠇⠈⠉⠙⠙⠛⠋⠛⠉⠉⠉⠀⠀⡇⠀⠀⠀⢸⡏⠉⠉⠙⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⣧⣄⡀⠀⠀⠀⠀⠀⢀⣀⣴⠟⢩⠇⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠉⠛⠻⠿⠿⠿⠟⠛⠋⠁⣠⠏⣴⢶⣤⣀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣀⠀⠀⠀⢀⣀⣤⡞⠁⠀⢿⡄⠈⠙⢷⣄⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⢸⣧⣀⠀⠘⣧⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⢷⣄⠹⣧⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⢷⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠒⠊⠉⠉⠉⡉⣉⢉⠉⡉⠉⢒⠒⠒⠠⠤⢄⣀⡀
⢀⢶⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠕⠘⠚⠻⠲⠀⠀⡹⡆
⢸⠏⠑⠫⢔⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧
⣿⠀⠀⠀⠀⠈⣑⠊⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢟⡸⣧
⢻⡄⢀⡀⠀⢸⡹⡷⡀⠀⠉⠑⠫⠖⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⡆⣡⣿
⠀⡇⠘⠗⠀⠈⠧⣀⡅⠀⠀⠀⠀⣠⡀⠉⠑⠛⠵⣖⡤⣀⡀⡰⣵⣝⣷⡛⣿⣿
⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠁⠀⣠⢲⡶⣄⠈⠙⠺⣻⡇⢹⡿⢁⡿⣿
⢸⡆⠀⣠⣤⡀⠀⠀⣾⣹⠼⠟⡆⠀⠀⢸⣷⠅⠀⢈⠀⠀⠀⣿⣼⡎⠟⢛⢳⣿⡶⢶⣖⠒⠂⠠⠤⠤
⢸⡇⢸⣿⡟⠚⡆⠀⠙⢇⣀⠰⠁⠀⠀⠀⠙⠤⠴⠊⠀⣠⠶⡿⠙⡕⡀⣸⠛⣿⡛⢉⣉⠉⣉⣉⣈⡁⠉
⢸⡧⡀⠙⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠠⣷⣵⠂⢸⣷⡟⣏⣿⡿⠔⠀⠤⠦⠤⠔⠂
⠀⠙⠪⣕⡤⣀⠀⠀⠀⣴⢦⠀⠀⠀⣾⣶⡵⠛⠆⠀⠀⠉⠓⣔⣳⣿⣷⣿⣿⣃⣉⣉⣉⣭⡭
⠀⠀⠀⠀⠙⠳⢽⣦⣀⠈⠊⠀⠀⠀⠙⢏⡀⣀⠇⠀⠀⠀⠀⣿⠄⠦⢶⡿⠷⠺⠿⠖⢳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⢿⡏⣿⠍⠉⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣒⣄⡀⠀⠀⢠⡶⡄⠰⣷⢁⣼⣽⡯⠍⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⣤⡀⠉⠀⠀⠈⡿⣿⣟⣓⣒⣐⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣦⢄⡀⠀⣧⡯⠌⠥⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣿⠛⠛⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⣀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠁⠀⣀⣙⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠏⠀⠙⠛⣄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢷⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢸⡆⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⢷⠀⠀⢀⢬⣅⠈⠁⠈⠰⠷⠿⢿⡟⠀⠀⣾⠇
⠀⠀⠀⠀⢰⠟⠉⠀⠀⠀⡼⠀⡠⠋⠀⠀⠈⠀⠀⠀⠀⠀⠒⠃⠀⣰
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠞⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠀⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠧

⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⣀⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⠃⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠙⠚⣿⣿⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣯⣼⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⢿⣿⣿⣸⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⣆⣠⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠐⠂⠀⠀⠤⢀⣀⣈⣀⣛⣛⣛⣛⡋⠙⠛⠛⢛⣀⣀⣉⠩⠤⠄⠲⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣦⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⠭⠙⠉⠉⠙⠓⢄
⠀⠀⠀⠀⣀⣤⣤⡤⣤⣴⣷⣿⣽⣿⣿⣿⣿⣻⡿⣿⣇⠀⠀⠀⠀⣀⠤⠒⣒⢀⣴⡂⠁⡡⠋⠁⠀⠀⠐⠲⠢⢄⠀⠂
⠀⠀⣰⣿⣿⣷⣾⣷⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣼⡏⠀⠀⠀⡼⠁⠀⠀⠀⠈⠁⠠⢊⠀⠘⠀⠀⠀⠀⠀⠄⠈⡀
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⡀⠶⠄⠀⠀⠐⠁
⠀⠀⠘⢿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⠀⠀⠀⠈⠙⡄⠀⠉⠀⠂
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⢐⣠⡀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⣿⣿⣶⣢⣴⣦⣄⣀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⣀⢀⠈⠉⠳⠛⠀⠂⢤⢴⣶⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣭⣼⣿⣿⡆⠀⠀⠀⠀⠀⠈⠃⠀⠀⠨⠉⠖⢄⡀⠀⠀⠀⠛⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣟⣿⣿⢿⣿⣿⠿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠆⠤⢤⠤⢤⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠑⠀⠀⠀⠂⠠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠄⠀⠁⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⣿⣿⣿⣷⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡇⢠⡄⢸⠀⠀⠂⡛⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠛⠸⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠨⣛⣦⣷⣾⣴⡀⢰⠟⠋⠁⡈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈

⠀⠀⠀⣤⣶⣶⣶⣄⣄⣦⠤⣤⣤⡤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⣿⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠛⠋⠉⠋⠉⠛⠉⠙⠛⠿⠟⠻⢟⣿⣿⣶
⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⢀⠄⡰⠈⠉⠙⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡤⣸⢠⠇⣤⠀⠀⢹
⠀⠀⠀⣿⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⡀⠀⣀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⣿⡇⠈⣿⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡇⠐⠀⢠⢃⠀⠄⠀⠄⠀⣽⠀⠈
⠀⠀⠀⣿⡇⠀⣿⠁⣉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠛⢿⠃⠐⠀⠘⠘⠁⠦⠀⠤⠄⠻⠀⠠
⠀⠀⠀⣿⡄⠀⠸⣇⠉⠀⠀⠙⢦⡀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣿⠟⠀⣴⠀⡐⠒⠀⠀⡄⠒⠂⠒⠀⡀⢠⠄
⠀⠀⠀⣿⡇⠀⠀⠱⣌⠻⡛⠀⢹⣷⣄⣴⣾⣿⣶⣄⣰⣿⣿⠁⣠⠞⠁⠀⢃⢀⠨⠉⡇⡉⠀⠉⠀⠃⠀⠑⡐
⠀⠀⠀⣿⡇⠀⠀⠀⠈⢳⣷⣿⣿⣿⣿⠟⠉⠋⠉⣻⣯⠿⠶⣿⣧⡀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠈⠀⠀⠀⠉
⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣿⠗⠛⢻⣿⣷⣠⢼⣿⣥⠀⠾⣿⠉⠉
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⠸⣿⢗⡼⣫⠁⠀⠀⠉⠉⠛⢲⣿⣦
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢀⣀⣀⣀⣀⠀⡀⠸⣿⡇
⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣶⣿⣿⣿⣿⣿⣿⣿⢰⣮⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣿⣿⠀⣀⣀⣀⣀⣀⣀⣀⡸⣿⣿⢏⣿⣿⣿⣿⣿⣿⣽⣿⡄⣿⣿⣷⠿⣿⡿⢻⠻⣿⣷⠶⣤⣤⣤⣴
⠀⠀⠀⣿⣿⣿⣟⣉⢀⣼⣿⢋⣿⡞⣮⠙⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⠃⠀⢼⡇⣟⠀⡇⠄⠐⣿⡏⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠀⠀⣠⣿⠀⠋⠁⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡷⠀⠀⢼⡇⣿⠀⡇⠀⢸⣿⣷⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠃⠀⣿⡅⠀⢿⣆⠀⣹⠞⣿⣿⣿⣿⣿⣿⡿⡏⢿⣻⡇⠀⠀⢹⣇⣿⣽⡇⠀⢸⣿⡇⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣡⣘⡟⡿⠆⣤⠖⠶⠉⠁⠈⠀⠀⣿⣿⣆⡑⢃⠈⢹⡇⡀⠠⢾⡯⣿⣿⠇⠀⣸⢽⣅⣿⣿
⠀⠀⠀⣿⣿⣿⣿⢤⠀⣄⣧⡀⠀⠉⠠⠀⠀⠀⠀⠀⢿⣿⣿⡇⣿⣿⣸⡇⣱⠶⢿⡷⣿⠡⣇⡄⢹⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡛⠀⣿⣿⡤⡖⠀⢸⣀⠀⠀⠀⠀⣾⣿⣏⣷⣿⣿⣿⣿⡟⢰⣾⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿
⠐⠶⣾⣿⣿⣿⣿⣧⠦⣿⣿⣿⣿⣶⣿⣟⠃⢄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⣿⣿⣿⠿⠷⠿⠿⠾⠿⠟⠛⠿⠓⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠄
⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣤⣸⣿⣯⣴⣿⣧⣶⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄⢒⡀⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡿⠿⠿⠛⠛⠛⠷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡟⠂⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⣿⡇⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿⣛⡃⠀⠀⠤⠄⣹⣿⣏⣹⣿⣷⣦⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⣷⠀⠀⠰⢾⡗⠿⠛⢶⣶⢂⣄⡀⠀⠀⢠⠈⡄⠀⢻⣿⠀⠀⠀⠙⠛⠻⣿⠧⠜⠿⠃⠘⢻⣽⣯⠈⡶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⣿⡀⠀⠀⠀⠀⠀⣀⡀⠉⠑⠈⠁⠀⠀⢨⠈⡁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠛⠄⠀⠀⠠⠂⠈⠻⠓⠿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣆⢸⣷⣶⣆⠒⠀⢈⣭⣿⡁⠀⠀⠀⠀⠀⠸⡔⢰⡀⠐⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣅⣶⣶⡄⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠹⣾⣿⣿⣷⣷⡿⢯⣉⠁⠒⠀⠀⠀⠀⠀⢘⡚⠾⣇⠀⣿⣿⣿⣿⢶⡚⢼⠗⠀⠀⣀⣠⣾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠹⣿⣿⣿⣿⣷⣤⣿⡁⠀⠀⠀⠀⠀⠀⠰⣂⠏⢻⣶⣾⣿⣿⣿⣿⣇⣯⣤⣶⣾⠿⠿⠿⠄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣜⢿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠠⢾⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⣷⣶⣄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⣄⠀⠘⣿⣆⢻⣿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢾⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⣆⣨⣽⡟⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠀⠉⠻⣧⢿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⠹⣿⣿⣌⢻⣿⣿⣿⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣧⠀⠀⠀⠀⠀⠀⢸⣷⡄⠀⠀⠀⡿⣿⣷⡆⢻⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣇⠀⢀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠈⠽⢿⣿⡄⢻⣿⠀⠀⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠠⣼⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣷⣾⣷⣠⡄⢀⣀⠀⣴⣿⣿⣿⡿⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠠⣤⡉⠙⠻⣿⢿⣿⣿⣿⣿⡏⠛⠾⢿⣿⣟⡭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣆⠙⠿⣿⣦⡈⢷⣶⣮⣟⣿⣿⣷⣄⠘⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣷⣤⣬⣭⣓⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⣿⣿⣯⣿⢿⣿⣽⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⡙⢿⣿⠇⣿⣯⣩⣤⡀⣿⣿⣿⣿⣿
⠀⠳⣶⣶⣦⣤⡀⠀⣰⡿⠹⣿⡿⣷⡄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣼⣟⢿⣿⣿⡄
⠀⠀⠚⣿⣿⣿⣿⣿⠟⠁⠀⢹⣧⠙⢿⣦⣀⠀⠈⠛⠿⠿⠋⣿⣿⣿⣿⣿⣿⣿⡟⠙⠋⠙⣿⣿⡏⠻⣿⣿⣿⣯⡻⢿⣿⣶⣿⠛⡓⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢿⣷⢸⠇⠉⢻⣶⣤⣄⣀⠀⢻⣿⣿⣿⣿⣿⠟⠀⣠⡆⢠⣿⣿⠁⠀⠙⢿⣿⣿⣿⣿⣭⣿⢋⠀⡉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣸⣿⣿⡿⠉⠛⠛⢿⣿⣿⣿⣿⡗⠋⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⠛⢿⣿⡏⢀⠞⣴⠈⣠⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠰⣿⣿⣿⠃⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⣉⣵⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠙⣿⣿⡀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠸⣿⣧⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠈⢻⣿⣦⡀⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠇⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣤⣤⣀⠀⠈⠉⠑⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢸⣵⣿⣿⣿⢇⠀⢰⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⣤⣤⡀⠀⠉⠹⠿⠗⠃⠀⠘⣞⢷⣝⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⢴⣶⣤⡀⠈⠉⠁⢀⣤⠶⠶⠶⢦⣄⠀⠈⠙⠚⠭⠉⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠘⠻⣿⡿⠏⠀⠀⢰⣿⣶⣿⣿⣿⣿⣿⣷⠒⠒⢒⣛⡉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣠⠔⣋⣀⣀⣀⣤⠤⠤⠴⠖⠒⠒⠋⠉⠉⠻⢿⣿⣿⣿⣿⠿⣫⠂⠀⢿⣿⣷⡄⠀⢸
⠀⠀⠀⠀⠀⣾⠉⠉⣽⣂⡀⠀⠀⣠⢖⣒⣒⡂⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠀⠀⠀⠈⠙⠋⣀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠿⠇⠀⠘⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢔⣂⡀⠀⠀⢀⡴⣫⢷⣶⣿
⠀⠀⠀⠀⠀⣿⣀⣀⡠⢄⡀⠀⠀⢿⣿⣿⣿⢿⡟⠀⢀⡤⢤⠤⠀⠀⠀⣿⣿⣿⡆⠀⡞⡾⣱⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣝⢦⠀⠀⠙⠛⠚⠋⠀⠀⠋⣾⣿⣿⣷⡀⠀⠙⠒⠋⠀⠀⡜⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⢀⣀⣀⣀⡤⠬⠥⠤⠶⠒⠒⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⠿⠓⠒⠒⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⠃⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢻⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡇⠀⢷⡄⠀⠀⠀⠀⠀⠀⢼⣧⣀⢋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡿⡄⢀⣿⣦⣤⠴⠿⠟⠛⢛⠿⠛⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡿⠛⠫⢤⡄⠀⠀⢈⣧⡀⠰⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣶⠀⢸⡟⠃⠀⠈⠙⠧⢴⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⣴⡞⠁⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡜⢿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⡄⠀⣀⣀⢠⣠⣶⢠⣿⡇⢸⡿⣿⣷⣿⣹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣿⣷⣽⣿⣿⣿⣿⡟⠛⣴⡾⣿⣸⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣟⢁⣿⣿⣿⣿⣿⣶⣿⠇⣿⣿⢁⣠⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠛⢀⣿⣿⠿⣿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠙⠛⢿⣿⣏⠄⢀⣿⠀⠀⠀⠈⣷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣬⣭⣥⣴⣶⣿⡇⠀⠀⠀⠀⠙⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢧⠀⠀⠀⠲⠆⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣟⣻⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⠶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⠀⠀⠀⢠⣿⢁⣶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠛⠁⠄⠤⠒⠰⠂⠂⠖⠂⠠⠄⣀⠀⠀⠀⢻⣷⠀⠀⠀⣿⠃⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⢿⣧⣤⣼⡏⣼⣧⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢶⣦⡀⠀⠀⠀⠀⢀⠀⠈⠀⢑⡘⢅⠀⣾⢠⡇⠀⠀⠉⠉⠉⠙⠛⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠶⣤⣤⣤⡠⠤⠔⠊⠁⢈⠢⡛⣿⣸⣄⣤⠴⠊⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠡⢂⢀⠄⡴⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⡔⡡⠃⠀⠞⠈⠀⠡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠌⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⡜⠀⠀⠀⢀⠀⠘⢠⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⡜⠀⢀⡍⠀⢠⠁⡆⠀⢀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠘⠀⠀⠀⠁⡄⢸⠃⡇⠘⠀⠀⠀⢸⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⢰⠀⡀⠀⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢠⠈⡄⡇⠀⠀⠇⠀⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⡀⢃⠓⢀⠠⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠅⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠸⡄⠀⠄⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠂⢳⠀⡀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢧⠁⠐⡀⠀⠈⠆⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠈⠆⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⢀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠻⠿⠶⠾⠟⠛⠉



⢀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡟⣉⡻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿