Butcher knife Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣿
⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠉⡳⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡟
⠀⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⡜⠀⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠂⣸⠇
⠀⠀⠀⠈⢿⢯⡆⠠⠀⡀⠀⠠⠂⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⢠⡟
⠀⠀⠀⠀⠈⣿⣯⡀⠀⠠⠀⠀⠀⠀⢦⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⡀⠀⠃⢠⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⡀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢀⡼⠁⣀⡟⠃⠈⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣆⠀⠀⢠⠀⠀⠀⠀⢀⠙⣆⠀⠀⢀⡴⠋⠀⠀⠋⠁⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⣨⣧⣠⠞⠁⠂⠀⠁⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠊⠀⣠⢴⣏⠠⡄⠙⢶⡄⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠶⠋⠀⢀⡽⣗⡄⠀⠈⠻⣷⣴⣦⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠘⣿⣄⠛⠀⠙⢮⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠀⣠⡾⠋⠹⣷⡄⣠⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⣼⠋⠀⠀⠀⠘⣧⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⠠⠄
⠀⠀⠀⠀⣠⠤⠶⠶⠒⠛⡓⠉⠉⠉⠉⣉⠉⢹⣇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢧⣀⣀⣶⣤⣤⣭⣤⠤⠤⠶⠾⠖⠛⠛⢶⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠄⠀⠀⠀⠐⠀⠐⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡎⡡⢬⡉⠓⠂⠀⠀⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠚⠋⠛⠁⠉⣩⠉⠉⠉⠉⠉⡉⠉⠉⡙⠓⠲⣆
⠀⠀⠀⠀⠀⠀⡸⠀⠓⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠶⠖⠒⠒⠶⠤⠦⠤⠦⠴⠶⠴⣷⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⡠⠠⠄
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠂⠂⠀⠊⠀⠈
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⢠⡠⠠⠄⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢁⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⡟⢉⡷⠀⠀⠀⠱⣄
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠣⡀
⠀⢀⡴⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⢔⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠳⣄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠈⠢⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢁⣤⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠽⣷⡀⠘⠒⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠑⢄⠀⠀⢀⡠⢖⡥⠊⠀⠀⠙⣝⢄⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠈⣳⢔⣫⠖⠉⠀⠀⠀⠀⠀⠈⠳⡱⣄⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡳⣄⠀⠀⠀⢀⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡓⢄⠀⠫⠽⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⢄⣠⣴⠟

⠀⠀⠀⢀⣀
⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⣿⣿⣿⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⢠⣿⣿⣷
⠀⠀⣿⣏⣿⠀⠀⢸⣷⣿⣏⢋⣿⣿⡇⠀⠀⢀⣤⣤⣴⣶⣶⣦⡄⠀⠀⢰⣿⣿⡀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿
⠀⠀⣿⣇⣿⠀⠀⢸⣿⣿⣯⢵⢽⣿⣿⠀⠀⢸⣿⣿⡍⠝⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡧⢼⣿⡄
⠀⠀⣿⡍⣿⠀⠀⢸⣿⣿⣿⢂⣺⣿⣿⠀⠀⠈⣿⣿⣿⠌⣻⣿⣇⠀⠀⢸⣟⣛⣿⠀⠀⠀⢹⡟⡻⢿⠀⠀⠀⣿⠭⢿⠀⠀⢠⣿⣆⢹⣿⡇
⠀⠀⣿⣎⣿⠀⠀⢸⣿⣿⣿⡒⣾⣿⣿⠀⠀⠀⢻⣿⣿⣤⣼⣿⣿⠀⠀⢸⣯⠽⣿⡇⠀⠀⢸⣿⠒⣿⠁⠀⠀⣿⡗⣻⠀⠀⢸⣿⣞⣽⣿⡇
⠀⠀⣿⠏⣿⠀⠀⢸⣿⡿⣥⡼⣿⣿⡿⠀⠀⠀⢸⣿⣟⣓⣺⣿⡿⠀⠀⢸⣿⣃⣿⡇⠀⠀⢾⣥⡬⣿⠀⠀⠀⣿⡟⣿⠀⠀⢸⣿⡯⣽⣿
⠀⠀⣿⣿⣿⠀⠀⢸⣿⣷⣝⣋⣾⣿⡇⠀⠀⠀⢸⣿⣧⣛⣫⣿⡇⠀⠀⢸⣞⣛⣿⡇⠀⠀⢸⣬⣵⣿⠀⠀⠀⣷⣿⣾⠀⠀⢸⣷⣾⣿⣿
⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⠛⠛⠛⠃⠀⠀⢸⣿⣿⠿⠃⠀⠀⢸⣿⣿⡿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⡏
⠀⠀⣿⣿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⣿⡏
⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⢿⡿⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⢸⣿⡇
⠀⠀⡀
⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⡐⡄
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⣶
⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⢹⣿⡇⠀⠀⠘⣿⡄⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⣶
⠀⠀⠀⢸⡷⣿⡀⠀⠀⠀⢸⣏⡇⠀⠀⢐⣿⣇⠀⠀⠀⢸⣿⢘⣷⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⡆⠀⠀⠀⢸⡏⣿⠀⠀⠠⣆
⠀⠀⠀⢸⣯⢽⡇⠀⠀⠀⢸⡇⣏⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣞⣿⠀⠀⠀⣿⢯⣇⠀⠀⢰⣟⡇⠀⠀⠀⢸⡯⣿⠀⠀⠀⣿⡆⠀⠀⠀⣆
⠀⠀⠀⠈⣿⢸⡇⠀⠀⠀⠸⣇⣿⠀⠀⠘⣿⣿⠀⠀⠀⢸⣷⣊⣿⠀⠀⠀⣿⣙⡇⠀⠀⢸⣿⣇⠀⠀⠀⢸⡟⣿⠀⠀⠀⣿⣷⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣿⣼⡇⠀⠀⠀⢶⣿⣿⠀⠀⢀⣷⣿⠀⠀⠀⢸⣧⣤⣿⠀⠀⠀⣷⣾⡗⠀⠀⢸⣿⡇⠀⠀⠀⣸⣷⣿⠀⠀⠸⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⢾⣿⠇⠀⠀⢸⣿⡿⠇⠀⠀⢸⣿⠏⠀⠀⠀⠀⣿⡿⠁⠀⠀⢸⣿⡇⠀⠀⢸⣿⡏⠀⠀⠀⢀⣿⡿⠀⠀⢠⣿⡇
⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢨⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣻⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⡇
⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢻⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⡆
⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⠟⠙⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⣠⣴⣤⡀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢤⣤⠐⠒⠒⠒⠒⠐⠀⠠⠉⠉⠉⠩⠉⡩⠋⠉⠉⠉⠉⠉⠩⠉⢉⠉⢉⢍⠉⠉⠙⡏⠉⣟⢉⡉⢉⣭⠽⠝⣴⠶⢖⣂⡠⢀
⠀⠈⠓⠯⣲⡶⣦⣀⢀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⠔⠁⠀⠀⠀⠀⡇⠠⡇⠀⠈⠨⠶⡃⠠⡠⢀⢼⣯⠶⢥⣴
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⣶⣶⣶⢠⠄⣥⣦⣤⣤⣤⣤⣤⣤⢤⣤⣤⡄⣴⣶⣤⣆⣇⡠⠟⠒⠉⠉⠙⠲⠯⠾⠷⠿⠾⢥⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈





⠀⠀⠀⡰⠊⢉⠙⠒⠢⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⠤⢤⡤⢤⡤⣠⢄⡤⣠⣄⣀⣀⣠⠤⣀
⠀⠀⢠⠇⢸⣁⣱⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠕⠁⠩⠉⠉⠉⠉⠉⢩⠏⣛⡛⠷⢚⣭⣟⡻⠿⠒⢝⣫⣿⡯⢽⣓⠫⣝⣳⡕⡄
⠀⠀⣸⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⣁⡬⣛⣽⣏⣡⣴⣪⣬⡥⢼⣷⣾⣿⣪⠽⢿⣿⡿⡰
⠀⠀⡏⠀⠀⢀⡠⠊⠔⡡⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠾⠓⠋⠙⠚⠋⠟⠿⠮⠭⠥⠚⠛⠉⠉⠙⠻⠵⠃
⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇
⠀⢸⠁⠔⠁⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡀⢀⢰⠁
⠀⢸⢀⣀⣀⣄⢀⣄⣀⣄⢀⣀⢁⣀⣀⣀⣀⣀⣘⣁⣀⢊⣀⢘⢑⢁⢚⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⢶⣿⡶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣉⣉⠤⣉⣉⣛⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⣤⣤⣤⠄⠀⠀⢰⣿⡇⠀⠀⠠⢠⣤⣤⣤⠄⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⠛⣿⣿⣿⡏⠀⢸⣿⣿⣿⡟⠛⠛⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣿⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠀⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠛⠙⢿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠉⢻⣿⣷⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣶⣿⠟⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢛⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠋
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣤⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⢀⣾⣿⡿⢿⣿⣿⣿⡿⠟⠁
⢾⣿⣿⣄⣠⣿⡿⠋
⠘⣿⣿⣿⣿⠟⠁
⣀⣈⣛⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⣛⣟⣝⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣟⣿

⠀⠀⠀⠀⠀⢀⣠⠤⠤⡀⣠⠄⠴⡖
⠀⠀⠀⠀⠀⣠⣅⠈⣠⣷⣧⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠟⠿⠋⡅⠀⠀⠀⢤⠤⣤⠤⣴
⠀⠀⠀⠀⣴⣿⣿⣯⣯⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠃⠀⠀⠀⢠⣂⣤⣒⣬⠀⢀⡀
⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⡷⡷⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿⣿⠿⢿⣿⠀⢸⣇⡾⢀
⠀⠀⢰⣿⣿⣿⢷⠻⣿⠿⠃⠀⠀⠊⠉⠹⢦⡠⢚⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⠀⢹⡇⠘⠛⣷⠟
⠀⠀⢸⡿⠋⠙⡏⢹⠁⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⣨⠅⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠤⠄⠂⡇⢠⠇⢠⡆⢀
⠀⠀⠈⠀⠀⠀⠭⠖⠂⠀⠀⠀⢨⢋⡎⠀⠀⠀⠈⣿⣟⡂⠀⠀⠀⠀⠀⠀⠀⠸⡧⠐⠀⠂⠀⣇⣌⠀⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⠁⠀⠀⠀⠐⢘⢷⠁⠀⠀⠀⠀⠀⢰⣄⣀⣧⣂⣀⡠⠼⠃⠀⠀⠙⠷⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠩⠀⡈⢀⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⡆⠠⠐⢰
⡎⡤⣤⣀⣮⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡄⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠸⣄⢀⡏
⠄⠀⠈⠛⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⠁⠀⠀⣿⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠖⠚⠛⠋⠁⠡⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠁⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⡎⠀⠀⠀⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠶⠖⠖⢊⠂⠀⠀⠀⠀⣤⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⣤⣻⣿⣈⣘⣈⢤⠼⠀⠀⠀⠀⡟⣉⠐⣶⠞⡋⢹
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠈⠆⠀⠀⠀⠀⠀⣘⢮⣽⣋⠀⠈⠀⠈⠀⠀⠀⠀⢀⣧⣈⣰⣿⣄⣁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠢⣀⠠⡀⠀⠀⠀⢠⣍⣛⣾⡋⠙⠛⠛⠟⠁⠀⠀⠀⢸⠘⠋⠀⠀⠈⢿⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠑⠃⠀⠀⠀⠼⠛⠋⠙⢿⡶⡶⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⣸⡼
⠀⠀⠀⠀⡀⢠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠔⢠⠀⠀⠀⠀⠀⠀⠈⣿⠀⠉⠩⠅⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⣀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠉⠒⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠋⠀⡠⠐⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠉⠒⢄⠑⠌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⠁⢀⠎⠀⡀⢀⠄⠀⡐⠢⢀⠁⠢⢄⡈⠑⠂⠀⠠⠈⠢⠈⠄
⠀⠀⠀⠰⠢⡞⢂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢈⠔⠁⡠⠊⠀⠀⠀⠑⠢⠄⡀⠁⠒⠠⠤⠤
⠀⠀⠘⣅⠳⠉⠀⠈⠈⠀⠀⠀⠀⠀⠀⢠⠀⠈⠠⠔⢊⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠠⠄⠀⠂
⠀⠀⠘⢌⡀⠀⠀⢀⠔⠲⠄⠀⠀⠀⠀⡘⡆⡰⠂⠉⠀⠀⠀⠘⠃⠀⠀⢀⡀⠀⠀⠘⠃⠀⠀⠀⠀⢀⣈⠅⠐
⠀⠀⠀⠀⠈⠑⡊⠁⠀⠀⠈⠢⡀⠀⠀⢡⠈⠂⢧⠀⠀⡠⠄⠀⠀⠀⠠⣀⣠⠄⠀⠀⡠⠠⡀⠀⠀⡌⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠒⢤⠏⠀⢀⢀⠧⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢀⠜⢠⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠉⠒⠮⣀⠀⠈⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠲⡖⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢇⠀⠈⠁⠒⠀⠀⠀⠀⠒⠈⠁⢀⠑⢦⠀⠀⠀⢡⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣬⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠀⠤⠤⠤⠀⠀⠠⠔⠁⠀⠀⠑⠄⠀⠀⢱⣊⣥⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠋⠿⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠰⢻⠸⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢣
⠀⠀⠀⠀⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣴⢤⣤⣤⡀⠀⠀⠀⠀⣀⣀⣀⠤⠄⠀⠀⠠⠃⠀⠀⠀⠀⢃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠀⡠⠒⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠉⠛⠿⢿⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⡿⠿⠛⠉⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⢀⡟⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢻⡀
⠀⠀⠀⠀⠀⣼⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⣧
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠸⣇
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⢀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⡀
⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠿⠿⠿⠿⠆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠿⣶⣶⣶⣶⣶⣶⣶⣶⠿⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⡄⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡹⢙⡲⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢚⡃⠔⠊⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⠂⠁⠁⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣞⣘⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣇⡌⠉⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢠⢢⠀⢀⣤⠟⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡴⠊
⠀⠀⠀⠀⠀⣠⣶⠟⠁⡔⡆⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢀⣴⡽⠋
⠀⣠⣾⠿⠗⠁⠀⠀⢀⢴⡿⠋
⡼⡵⠣⣖⠆⠀⣠⣾⠟⠉
⢳⡀⠀⠀⠀⢸⡟⠁
⣀⣉⣳⣶⣶⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠒⠉⠀⠈⠑⠴⠋⠁⠉⠑⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⠁⠀⠀⠀⢁⠄⡐⡠⣠⢀⡄⠠⢂⠆⡄⢀⠀⠈⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡠⢀⠔⡡⡡⢪⢊⠔⡡⢊⠔⡱⢁⠎⡴⡡⢣⢂⠄⡈⠱
⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⢐⠔⡱⢡⢊⢜⠔⡡⢊⠔⡡⢃⠌⡰⢁⠎⡔⡑⡡⢊⢜⠄⡈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⣪⢊⢔⡕⣡⣋⠞⡡⢋⢞⡰⢃⠎⡰⡡⢊⢎⠔⡱⣡⢊⢎⠔⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠔⡡⡣⣻⠚⠫⠙⠺⠻⠉⠈⠙⠛⠻⣜⣑⣁⡬⢦⠐⠡⡣⢊⢊⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢆⠀⢊⢔⣎⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡦⠰⢕⡡⠳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣅⣐⡹⠿⠁⡠⠒⢀⠐⠒⠀⠀⠀⠀⠀⠔⢒⠐⠒⠤⠀⠑⡤⠩⡊⠎
⠀⠀⠀⠀⠀⠀⠀⡏⢦⡈⢿⡢⡤⢲⠽⠏⠡⢕⢦⠀⣀⠀⡴⣪⠽⠫⠝⣦⣀⢄⡷⢊⡝⢧
⠀⠀⠀⠀⠀⠀⠀⠳⣴⠃⠈⠘⢣⠇⢶⡰⡶⠂⡇⡿⠶⡞⡜⠑⢖⢲⡖⠜⣿⠋⢠⢿⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠃⠀⠀⠢⡓⠤⠍⠤⣊⡼⠁⠀⠰⡙⠦⣈⣉⡠⣊⠏⠀⠰⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡶⡇⠀⠀⠈⢙⠉⠉⠁⠀⠊⠈⠁⠈⠑⠒⢒⠚⠁⠀⠀⢸⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠁⢰⠐⠒⠂⠂⠐⠖⠒⠄⠤⡄⠑⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠝⡝⡹⡻⡻⢫⢃⢂⢞⠃⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⢯⣎⠌⡔⡱⣱⣡⣣⠎⠀⠀⢠⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉⠚⠚⠚⠚⠃⠀⠀⢀⣤⣢⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠤⠀⡀⠀⠀⣤⡤⠤⣨⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⠶⠤⡤⡤⡤⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢎⢜⠔⡑⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡤⠃⠀⠀⢪⢊⢔⠵⢤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⡁⠙⢄⠑⣄⠀⠀⠀⠱⡿⢁⠞⢀⣎⢍⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡊⠕⡡⢀⡱⣤⡑⠦⣀⣀⠔⢁⣴⢟⠕⡡⢊⢔⡄⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠋⠴⠋⠔⠡⠊⠕⠩⢳⠦⡥⠚⠕⡱⠛⠊⠁⠙⡧⡪⢲⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡄⠀⠀⠀⠀⠀⡞⠻⣽⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣶⣗⠀⠀⠀⠀⠀⢲⣿⠆⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡰⠋⠁⠀⠀⠉⣛⡼⢢⣀⠀⠩⣿⡄⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠐⢷⠙⢿⣯⡷⠶⣦⡁⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢒⣶⠶⠖⠉⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⡾⠿⢻⣢⡇⢸⡟⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠸⠀⠀⠀⠀⠀⠀⡇⠀⢼⣴⣋⣽⣟⠮⠇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⢠⣾⢎⣱⠆⢿⣦⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠦⠤⠖⠀⠀⠶⣤⣤⣴⠄⣿⠸⠞⡋⣽⣸⢷⡄⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⡶⠟⣩⡥⢨⠃⠀⠀⠈⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡧⢹⡟⢿⣇⢈⠀⠀⠀⠀⢹⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡹⢷⡎⢳⣸⡏⣼⠁⠀⢤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡏⢺⣿⢸⠃⣶⢻⣤⡀⢀⣿⠟⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⣎⢻⣎⡷⠁⣯⢸⣹⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣷⣿⢀⡿⡁⡄⣿⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣷⢻⡿⢷⣄⢷⠙⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⣸⣿⣼⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢈⣡⣿⠏⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣻⠛⠋⣻⠏⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣾⣿⣷⣾⣿⣏⢠⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⢻⡿⣰⣿⣏⣸⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠉⠈⠁

⡿⢿⡿⠿⡿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠄⠂⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢠⠀⡄⣠⢠⢀⡆⣰⠀⡔
⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⢤⡐⢄⠳⠙⠈⢁⡀⠀⢀⠀⢀⠈⠈⠀⠃⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀⠐⢤⡙⠦⠉⢀⣤⠒⠀⣐⠂⢲⡐⡐⢈⠉⡑⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠉⠀⡴⡉⠇⠈⠢⢉⠘⢀⡀⠄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠘⠠⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⡟⢱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣼⣦⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠦⠤⠤⢤⡤⠤⣤⡴⡾⠀⣰⣩⡵⣾⡿⠄
⠀⠀⠀⠀⠀⣀⡤⠴⢒⣿⣿⣿⢿⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣡⣋⣿⣛⣩⣣⣼⣐⣎⡵⣧⡿⠵⠓⡀⣠⢚
⠀⠀⠀⠀⠀⢏⠛⣠⠟⠉⠉⢳⣾⠱⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠯⠉⠛⠛⠛⠻⠵⠷⣾⣁⡀⢲⣾⡽⢺⠄
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢉⠀⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡠⡆⢏⢛⠡⣔⠓⠀⠌⠀⣚⠩⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠘⡷⠶⠶⠟⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⣠⣶⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣦⣤⡀⢾⣧⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣴⠾⠷⠤⣄⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣨⣿⣁
⠀⠀⠀⢀⣿⣿⢻⣿⣿⣿⣿⠻⣿⣿⠇⠀⠀⠀⠈⠃⠀⠀⠀⢸⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⠉⠉⠓⠦
⠀⠀⠀⢸⣿⠃⢈⣟⣛⣛⣏⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢻⣿⣿⣿⡇⠻⠿⠃
⠀⠀⠀⠘⠛⠀⣼⣿⣿⠛⠛⠂⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⣿⡇⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⣴⠀⠀⣿⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⡇⢸⣿⣦⣤⣴⣿⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠈⠀⢠⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠐⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢷⡈⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡄⠙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣌⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠋⠉⢠⠖⢶⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠄⠀⠀⠀⠐⢄⡼⠁⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⡀⠀⢰⣿
⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠀⣰⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢀⠏⠀⣾⡏
⠀⠀⠀⠀⠀⢻⣿⣿⢳⡄⠀⣼⠁⠀⠀⢈⢡⣤⢜⡟⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢀⡘⠃⣸⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣭⣿⣧⠀⠁⠐⠊⠀⠂⠌⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣄⡏⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣧⡀⠀⢠⢆⠀⠀⠀⠀⠀⢿⣢⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣰⣦⣄⢑⠛⠁⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀⠈⠀⠠⢀⡀⠀⠀⠉⠁⠀⢀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣈⣻⠿⠈⠈⠃⢠⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣻⡀⠠⠴⠋⠀⢄⠀⠀⠀⠀⢾⠆⣼⢷⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢀⣽⡷⢯⠀⠀⠐⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣾⡀⢲⢘⠆⣿⡀⡀⠀⠀⢼⣀⣶⡊⢻⣆⠀⠀⠀⢠⡾⣋⣼⠀⣘⠀⢷⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠸⡗⠀⠀⠀⠀⠁⠀⡇⢃⣹⣧⣀⣴⠟⣡⡽⠁⠉⠺⠁⠀⠀⠈⣸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣦⠀⠀⢁⡴⠂⠀⠀⠀⣨⡴⠋⣁⠈⠻⣧⣀⠉⠀⠀⠀⠀⠀⠠⢄⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣷⣄⠀⠀⠀⣠⠶⠛⠿⣶⣄⡛⠃⠀⠘⢿⣧⣀⠀⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡶⠛⠁⠀⠀⢀⡼⣿⣳⡀⠀⠀⠀⠹⣿⣷⣼⣷⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣰⠟⠀⠈⢿⣷⣄⠰⣶⠀⠈⢷⡌⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠟⢁⣼⡿⣿⣦⡀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢀⡀⢀⣴⡿⠋⠀⠈⠻⣿⣦⢠⣦⡄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠛⢁⣾⠏⠀⠀⠀⠀⠀⢹⣿⠀⠉⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⡿⠏⠀⠀⠀⠀⠀⠀⠀⠻⣷⣴⣶⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠘⠋⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣐⡈⢷⣤⣀⠀⠀⠀⠀⠀⠀⠹⣇⣀⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠟⠿⠉⠛⠷⣬⡿⣿⣷⣿⣦⡷⣶⣄⣈⣿⡁⢸⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⢤⠚⡟⠋⠙⠻⣷⡌⠉⠙⠋⠀⢫⣼⣿⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⣤⣽⣶⣤⡶⠊⠉⠁⠀⣀⡀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡷⣄⠀⣸⣿⣷⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡷⠈⠲⢿⡇⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⡉⠁⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⢀⣿⣿⣼⣿⣿⡿⠯⢇⠀⠀⠀⠀⠹⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⢀⠀⣸⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣀⣧⣀⣀⣸⣿⡿⢷⣿⣶⣶⠾⣷⠀⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⣿⣿⠟⠉⣿⠃⠚⠻⠟⠁⠀⢿⡀⣼⡿⠙⣿⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠈⠁⠀⠘⢿⣤⠀⠀⠀⠀⠀⠘⢷⡿⠁⠀⣿⠀⢻⣿⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣿⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⣦⣄⢀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⠀⠲⣾⣿⣷⠀⠀⠻⣆⠀⡇⠀⠀⠀⠀⠙⢟⣉⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⠘⣿⣿⣿⣧⠀⠀⠈⠲⣧⡀⠀⠀⠀⣠⣿⠉⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣸⣿⣿⣿⣇⠀⠀⠀⠀⠈⠓⠄⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠹⣿⣿⣿⣿⣿⣿⢆⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢹⣿⣿⣿⣿⣿⡎⢷⡀⠀⠀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠸⢿⣿⣿⣿⣿⣷⠈⣿⡄⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⢹⣿⣿⣿⣿⡆⣿⣷⠟⣼⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢿⣿⣿⣿⣷⣽⡏⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣻⣼⣿⣿⣿⣿⡟⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⢃⣼⢿⣿⣿⣿⣿⡟⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⠟⠡⠾⠍⠿⣿⠟⣶⢹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠄⠤⠶⢒⣶⡟⣼⡿⣿⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⢤⣴⢁⣿⢟⣼⣿⠃⠙⠲⣇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠱⣾⣏⠚⠛⠋⠀⠀⠀⠀⠳⠾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⣶⣶⣶⣦⣴⣶⣶⣶⣤⣶⣶⣴⣦⣴⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣶⣤⣶⣶
⣿⣿⣿⡻⠛⠛⡿⠋⢛⠛⠛⡛⠟⣛⡿⢟⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣾⣿⣶⣿⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠔⠉⠀⠑⠊⠈⠐⠠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠂⢉⠀⡀⠀⢀⢤⡄⢴⠀⠂⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡂⠀⠐⢀
⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠰⡁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⠤⠄⠄⠀⢨⡀⠀⠐⠄
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠀⠘⠤⡄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⡂⠈⡂⠀⠀⠠⡠⣀⠄⠀⣀⡠⠂⠄⢀⠈⠙⠂⠀⠀⠀⠀⠠⣀⡀⡄⠆⠀⠀⠀⡀⢀⢩⠎⣁⢤
⠀⠀⠀⠀⠀⠁⠀⠈⠒⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠑⠠⡀⠸⣀⢄⢀⡄⠀⠀⠐⠁⠀⠀⠀⠈⠂⠈⠀⠡⠦
⠀⠀⠀⠀⠀⠀⠆⠐⠖⠊⠁⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⣀⠈⠂⠀⠀⡀⡠⠜⢹⠁⠀⠀⠀⡠⠄⣀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠑⠠⠠⠀⠀⠀⠀⠈⠃⠀⠀⢀⡀⠀⠀⠉⠀⠀⠈⠈⠀⡄⠄⠂⠀⠀⡠⠊⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠐⣉⠆⠀⠀⠀⡀⡠⠀⠀⠀⢎⡁⠀⠀⡜⠀⠀⢀⠄⠊⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⡠⢪⠠⠔⠊⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠓⠄⣈⠐⠂⠤⠀⠀⠀⠠⠄⠂⡁⠔⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠁
⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⢷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⡀⠐⠤⠋⠉⢉⢲⡀⠀⠀⠀⠀⣠⠤⠔⠒⠒⠒⠒⠒⠦⠤⣄
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⢈⠀⠀⠠⠄⠀⠀⠀⠀⠠⠌⠐⢄⡰⠋⠀⠄⠀⠀⠐⠀⠀⠤⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣠⡴⠞⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠷⢏⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠗⠚⠀⢵⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠶⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠿⠛⠶⠲⣤⣤⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣥⣀⠶⣀⣴⠿⠟⠉⠀⣴⠋⠀⢀⡴⣀⣤⣤⣤⣀⣀⠉⠈⠁⣼⣿⡿⣄⡉⢛⣛⣋⣁⣈⡀⣀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠘⣷⠀⠀⠘⢤⣯⡍⠉⠉⠉⠉⠀⠀⠀⣿⣿⠀⣽⠁⠈⠉⠉⠉⠉⠁⣬⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷⠀⠶⣶⡶⠞⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⠏⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣋⣿⣋⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣿⣿⣿⣷⡄⠀⣼⣶⣾⡟⢻⡶⠶⣶⡉⢹⡄⠀⠀⠀⠀⣾⠃⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⣰⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣯⠙⠿⣤⣀⣀⠀⢀⣙⣃⣀⣸⣿⡇⠸⠇⣸⠋⣿⠛⢿⣦⠄⠀⣴⣿⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⢰⠆⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠈⣿⡟⣷⠀⠈⠙⠻⢿⣿⠏⠉⢉⣴⡿⠁⢦⡸⠇⢀⣿⣤⠀⢿⡀⠀⠈⠙⠃⠀⢀⡄⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⡗⡇⠀⠉⠀⠀⠀⠀⠴⠶⢿⣿⠁⣰⣿⠃⠀⣼⣿⣶⣦⣴⣧⣀⣀⣀⣀⣀⣼⠃⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢠⣿⡏⣀⣠⣏⣉⠉⢉⣉⣹⣏⡉⠉⠉⠉⠁⠀⠀⠀⠀⣠⣟⣀⣀⣀⣀⣀⣀⣀⣘⣧
⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢰⣿⣇⠀⠀⢀⣶⠀⠀⢀⣼⠏⠀⢠⡿⠿⣿⣿⣿⡟⠛⠛⠛⠛⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡟⠛⠛⠛⠛⣋⡹
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⡟⢀⣤⡿⠁⣠⣴⠟⠁⢀⣴⣿⠃⠀⠀⠿⠛⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠃
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣿⣿⣿⣿⣯⣴⡾⠟⠁⣠⡴⠋⣽⠁⠀⢀⠇⢰⡇⠙
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⡿⠟⠋⣉⣁⠴⠖⠛⠁⢀⡼⠃⠀⣠⡟⠀⡆⢹⠄
⠀⠀⠀⠀⠀⢠⣿⠛⠃⠀⣸⣿⣤⣴⣿⠋⠁⠀⣀⣠⣴⣟⣁⣤⣾⣏⣤⣿⡼⠃
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢻⡟⠋⠉⠉⠉⢙⡟⠙⠋⠛
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⣿⣟⣿⣿⡟⣠⡟⠀⠀⠀⠀⢀⣿⠀⠀⠀⣠
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⣿⣿⣿⣿⣯⣼⡿⠀⠀⠀⠀⢠⣾⠃⠀⠇⠀⣿⡆
⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⣴⢿⡏⢀⣶⠀⢠⣿⡇
⣴⢓⣀⡀⢀⣿⡇⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⣀⣴⣿⣯⡆⢀⣾⠃⠀⣾⣿⡇
⠙⠿⣿⣿⣾⣿⣧⠸⣿⡅⠙⠛⠉⠀⣀⣤⣾⣿⣿⣿⠟⢀⣾⡟⠀⢠⣿⣿⠁
⠀⠀⠘⢿⣿⣿⣿⠀⠙⢿⣶⠶⣾⣿⣿⣿⣿⣿⣿⠋⣠⣾⣿⠁⠀⣸⡟⠃⢰⠃
⠀⠀⠀⠈⣿⣿⡏⠀⣰⣾⠟⣀⣤⣿⣿⣿⣿⠟⢁⣴⣿⣿⠇⠀⢸⣿⡇⠀⡂⢀
⠀⠀⠀⠀⠙⠿⣷⡤⢟⠁⠘⢿⣿⣿⣿⠟⢁⣴⣿⣿⠿⡏⠀⠀⣿⣿⠇⠀⡇⢸
⠀⠀⠀⠀⠀⢀⠛⢡⣾⣷⣄⠀⠙⢿⣁⣴⣿⡿⢃⠘⣦⠀⠀⣾⣿⣿⠀⢸⣧⠀⣶
⠀⠀⠀⠀⠀⠈⢰⣾⣿⣿⣿⣷⣄⠀⠙⣿⡏⠡⡎⢱⠁⠀⣸⣿⣿⡇⠀⢸⣿⠀⢻
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⣧⣠⠇⠀⣰⣿⣿⣿⡇⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠋⠀⠛⢦⡄⠈⠻⣧⣄⢻⣾⣿⠘⠇⠀⠀⢿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣶⠟⠀⣰⠃⢙⣦⡀⠈⠻⣿⣡⠙⣤⠀⠀⠀⢸⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣁⣀⡾⠁⢠⣿⠋⡹⣧⡀⠈⢿⣦⡟⠀⠀⠀⣸⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⣰⣿⠋⡀⠙⢠⡿⢦⡀⠙⢷⡀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⣀⣾⣿⠁⣠⠉⡄⣿⠁⣾⠛⢦⡀⠙⣷⣀⣿⠀⠀⠀⠈⣅
⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡿⠁⣰⣏⣿⢱⡏⢀⠋⠀⢼⠙⢦⡀⠹⢿⡀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⢀⣾⣿⣿⠇⣸⠃⣿⠀⠀⡻⠀⠀⠙⢦⡈⠛⣦⡀⢸⣿⡄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⡿⢠⡟⢀⠀⠀⣼⡇⠀⠀⠀⢸⠻⢦⡈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢻⣿⠟⣁⣴⡟⣿⣿⣿⣿⡇⣸⠃⢾⠀⢀⡿⠀⠀⠀⠀⣿⠀⠀⠙⢦⡘⢻⣷
⠀⠀⠀⠀⠀⠀⢾⣯⣾⣿⠟⣸⣿⣿⢹⡟⠀⣿⠀⢸⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⢨⡿⢦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣿⣿⠃⣿⠃⣼⡏⢀⡏⠀⢸⠃⠀⠀⠀⢀⠃⠀⠀⠀⢸⡇⠸⣿⣦⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣼⡟⠀⣿⠀⢸⡇⠀⡎⠀⠀⠀⠀⣸⠀⠀⠀⠀⣿⢱⠀⣿⣏⠙⢠⡙⢧⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⢰⣿⠁⢸⡟⠀⡘⠁⢠⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⢸⠇⣿⢸⡄⠀⠙⢦⡙⠂
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣠⣿⡏⠀⣿⡇⢠⡇⠀⣸⡏⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇⢸⠀⡇⢸⡇⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠁⢸⡿⠀⠈⠇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⡇⢸⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⣾⡇⠀⣴⠀⠀⣿⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡇⠀⡇⠈⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⠀⠀⢀⣿⠀⠀⠀⣰⠸⡇⠀⠁⠀⠹
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣆⢸⣧⠀⣿⠀⠀⠀⠀⠘⢣⣄⠀⠀⠻⣄⠰⣆⠀⢇⠀⢿⡀
⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⢼⣿⣿⣯⣀⣼⡆⠀⠀⠀⠀⢀⣼⣷⣀⣀⣙⣶⣿⣆⣸⣧⣄⣻⣄
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣶⣶⣶⣶⣶⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣥⣬⣭⣭⣤⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠟⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀⣀⣀⡀⠀⠤⠤⠤⠤⠄⠀⠀⠀⠀⠂⠀⠀⠰⠖⠂⠀⠠⠤
⠀⠀⠀⠀⣤⠤⠶⠶⠒⠒⡒⠊⠉⠉⠉⣉⠉⢹⣇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢇⣀⣀⣶⣤⣤⣭⣤⠤⠤⠶⠾⠚⠛⠛⢷⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠄⠀⠉
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠤⠤⠤⠄⠀⠀⠀⠒⠀⠐⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡎⡡⢬⡉⠒⠂⠀⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠒⠒⠒⠒⠒⠒⠚⠋⠛⠋⠉⣩⠉⠉⠉⠉⠉⣉⠉⠉⡙⠓⠲⣆
⠀⠀⠀⠀⠀⠀⡸⠀⠳⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠶⠖⠒⠲⠦⠴⠶⠶⠦⠴⠶⠴⣷⣄⣠⠇
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡠⠠⠄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠂⠂⠀⠊⠀⠈
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠁

⠀⠀⣼⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢛⣿⡿⠁⠁⢸⣿⣿⡄
⠀⠀⢿⣿⣿⣿⣿⡿⠤⠾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢡⣾⡟⠀⠀⠀⠀⣿⣿
⠀⠀⠸⣿⣿⣿⣿⢹⣦⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣵⣿⣟⡄⠀⠀⠀⢸⣿⣿⡀
⠀⠀⢀⣼⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣾⣿⣿⣿⠀⣾⣿⣦⣟⣿⣿⡇
⠀⠐⣿⣿⣿⣿⣿⣿⣿⣦⣘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⢽⣿⣿⡿⢿⣿⣿⡆
⢀⣄⣽⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⢾⣿⣿⣿⣿⣿⣿⡿⠋⠀⢹⡟⠻⠾⠛⠀⠙⣿⣿⠻⠃
⠀⢹⣿⣿⣿⣿⣿⡇⣾⣿⡟⣼⡟⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠘⣿⣦⣤⡄
⢠⣿⣿⣿⣿⣿⡿⠧⢸⣿⣷⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⣼⠈⡆⠀⠀⠀⠀⠀⠈⠈⢿⣷⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⢹⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣰⣦⡀
⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠏
⣿⣿⣿⡗⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣹⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⡇
⢿⣿⣿⣿⣿⣿⣿⣿⣟⡼⢿⣿⣿⣷⣼⣧⣿⣿⣿⣿⣹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣤⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⡏⠀⢻⡀
⠀⢹⣿⣿⣿⣿⣿⣿⡿⢇⣼⣿⣿⣿⣿⣿⣿⣯⣿⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢹⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢰⠇⠀⢸⣇
⢀⣼⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⡄
⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡆⠀⠀⠀⢙⣧
⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⢰⠁⠀⠀⠀⢸⡼
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡼⠀⠀⠀⠀⠀⡇⢀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠇⠀⠀⠀⠀⠀⢹⠀⡀
⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣬⣰⡀⠀⠀⠀⠀⠀⢸⡆⢁
⠑⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣦⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡇⠘⡆
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢊⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣱⠀⠧
⢶⣟⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠸⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣷⣿⡿⣿⠿⠿⣿⡿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠿⠛⠳⠉⠁⠁⢀⣀⣠⣈⠀⠸⣿⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣣⡀⣤⣠⣶⣾⣿⡿⠿⠟⠛⣻⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠘⣷⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡖⢛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠅⠀⠀⠀⠠⠄⠀⠀⠀⣀⡀⠀⠙⢿⢾⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣷⣦⣀⠠⠀⢀⣴⣶⣾⣿⣿⣇⣾⣿⣿⣿⢀⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⠈⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡟⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣄⡠⠤⠈⠉⠉⠀⠀⡴⠂⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣃⣀⣀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⠶⠦⠀⠀⠀⠀⠀⢀⣠⠞⢡⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣤⡀⠀⠀⢀⣤⡾⠋⠀⠀⡸⠃⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣏⠹⣿⣿⣿⣿⣿⠏⠀⠀⠀⡰⠁⠀⣿⣿⣿⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠀⠘⢿⣿⣿⡏⠀⠀⢀⠞⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠀⠿⠎⢻⣿⠀⢀⡔⠱⠾⡆⠀⣿⣿⣿⣿⣹⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡆⠀⠀⠈⣿⣾⡟⠀⠀⠀⡇⣸⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇⠀⠀⠀⠸⠟⠀⠀⠀⠀⠗⠋⠁

⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⣼⣤⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⡆⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠄⠀⠀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣏⣹⡏
⠀⠤⠤⢼⣿⣿⠥⠤⠀⠀⠀⠀⠀⣿⣿⣿⠂⠀⠀⠀⠀⠤⠼⢿⣿⣿⠿⠤⠄⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⣾⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠺⠿⠿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣽⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡋⠉⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣿⡿⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣶⣿⣿⣿⣧⣤⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠉⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠿⠇⠀⢰⣿⠿⢿⣷⡄⢰⣿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⣿⡇⣾⡏⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣴⡦⠸⣿⣄⣴⣿⠃⢻⣿⣤⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠈⠛⠋⠁⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣴⣿⣶⣄⠀⣿⣿⠀⣠⣾⣷⣦⡀⣿⣇⠀⣸⣷⠀⣴⣿⣿⣦⠀⣶⣿⢿⣷⡄⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣼⣿⠀⠉⠉⠀⢿⣿⠀⣿⣧⣼⣿⠃⢹⣿⠀⣿⡏⢸⣿⣧⣾⡟⠀⣿⣿⣴⣿⠇⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢻⣿⡀⠀⣀⠀⢸⣿⠀⢻⣿⣋⣁⠀⠘⣿⣾⣿⠁⠸⣿⣏⣁⣤⡀⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠈⠻⢿⡿⠿⠃⠸⠿⠀⠈⠻⠿⠟⠁⠀⠙⠿⠋⠀⠀⠙⠿⠿⠛⠁⠻⠟⠀⠻⠟⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠃⠀⣠⣤⣄⡀⠀⢠⣴⣶⣤⡀⠀⠀⠀⣶⡆⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢀⣀⣿⣧⣤⡄⢸⣿⠉⠻⣿⡄⢸⣿⢉⣿⡷⠀⠀⠀⣿⡇⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠘⠛⢻⣿⠛⠁⢸⣿⠀⠀⣿⡇⢸⣿⣿⡟⠁⠀⠀⠀⣿⡇⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⢸⣿⡄⠀⠘⣿⣶⣾⡿⠁⢸⣿⠛⣿⡦⠀⠀⠀⢻⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣶⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠲⡄⠀⠀⢀⣠⠞⢛⣛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡘⠄⣠⢎⡵⠿⠋⠉⠛⢦⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⣦⡉⠞⣁⣤⣀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢠⠂⣀⠀⠀⠀⠀⠠⣏⣉⢉⠉⠙⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠃⢰⠁⠐⠩⠵⣶⠶⡯⠄⠤⡤⣼⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣽⣦⡘⢼⣆⠀⠀⠈⠁⠊⠁⠀⠀⠛⠻⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠋⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠐⢀⢀⣤⣠⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡇⠈⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠙⠃⠀⠀⠀⠠⣦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖⠀⠀⠀⠀⠀⠀⠀⢀⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠄⢶⠿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⢾⣀⠀⢀⣨⠉⠑⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠱⢤⣋⣛⣉⡕⠋⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣇⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣟⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠉⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣴⣿⡿⠃⠈⠻⣷⣄⠀⠀⠀⠀⣠⣾⠏⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠙⢷⣦⣠⣾⠟⠁⣠⡾⠋
⠀⠀⠀⠀⠀⣠⣾⣿⠋⠙⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣤⣾⠋
⠀⠀⠀⣠⣾⣿⣿⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⣠⣾⡿⢿⣿⣿⣿⣿⣿⠟⠁
⣰⣿⣿⣇⣀⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⡿⠋
⠘⢻⣿⣿⠟⠋
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠘⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠙⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠈⢎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠘⢮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⣿⣿⣿⣏⣹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣕⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣥⣤⣆⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣁⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠿⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠒⠋⠉⠉⠁⠀⠐⠐⠒⠠⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣈⣉⠐⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠒⠂⠠⠄⣉⠁⠐⠢⠀⠀⣁⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢬⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⢻⡉⡹⠒⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⡏⢸⠀⠸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⢧⠇⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠒⠊⠁⠀⠀⠀⣱⢾⠀⠀⢆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠈⠲⢤⣈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠚⢁⡃⠀⠀⠀⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⠀⢀⣀⣀⡀⠈⢭⣽⣟⣗⣒⣒⣛⣋⣉⣉⡠⠤⠔⠒⠉⢹⠀⠀⢸⠀⢹⠀⣀⣀⣤⣤⣄
⠀⢀⠴⠒⠒⠶⢤⣀⠀⢠⡇⠀⠀⣀⠸⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠣⡸⠋⠁⠀⠀⠀⠀⢳
⢰⠃⠀⠀⠀⠀⠀⠈⠑⠾⠀⠀⠀⡸⠀⠀⠀⡠⠚⠉⠉⠁⠲⣄⠀⠀⠀⠀⢀⡴⠒⠀⠀⠒⢦⡀⠀⣾⢾⠠⡐⢮⠆⠀⠀⠀⠀⣠⠞
⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢸⣁⣀⣀⣀⣀⣀⣨⡆⠀⠀⠀⣌⣀⣀⣀⣀⣀⣀⣱⠰⠿⠿⠣⡍⠛⠀⠀⠀⠀⠛⠓⢤
⢀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢱⠤⠼⠤⠤⡼⣤⣤⠇⠀⠀⠀⣧⣄⣧⣀⣀⣿⣀⣸⠁⠀⠀⡂
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⣀⣠⠴⢫⠖⠚⠒⢢⠳⣄⣀⠀⣀⣠⠔⠁⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠀⠶⣶
⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡏⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠳⣄⣀⣀⣠⡴⠞⠋⣿⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⡦⣤⣄⣀⣤⠴⠞
⠀⠀⠈⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠈⠐⠠⠤⠄⣀⣀⣀⠠⠤⠔⠊⠁⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠗⠂⠤⣄⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠴⠒⠉⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⢩⡇⠀⡀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢯⣤⠿⣄⡼⠃⠀⠀⠀⠀⠀⠀⠘⣧⡴⠳⢤⠼⠓⠖⠋

⠀⠀⠀⠀⠐⡌⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⡔
⠀⢀⠀⠀⠀⠈⠁⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠀⠀⢀
⡄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⢀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠈
⠀⠀⠑⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠔⠁
⠀⠀⠀⠀⠑⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⡀⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠐⠀⠀⠀⢀⠄⠐⢎⡲⠊⠐⢊⠆⠀⢄⠀⠀⢀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠗⠁⠀⡠⠊⡀⢀⠊⡉⠢⡀⠀⠑⢂⡡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⡀⠀⠈⠀⠀⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡈⠀⠀⠀⠀⠀⠈⡈⡡


⠀⠀⠀⠀⠠⡄⠤⠄⣀⣀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠸⠨⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠂⢸⢠⠍⠀⠀⠀⢠⠄⠀⠀⠈⡌⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⠂⠚⠉⠉⠂⠢⠀⠂⠉⠁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠠⠤⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⢬
⡀⢀⣀⣐⠠⠄⣄⣀⣠⣀⣀⣀⣀⣉⣉⣀⣀⣁⣀⣁⣀⣀⣀⣀⠞⢀⣀⣀⣀⣀⣀⣀⠀⡀⢀⣀⢀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠉⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⣀⣤⠾⣦⣀⣙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣨⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠯⠶⠀⠰⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢷⡴⠀⢀⠶⢴⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣿⣁⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡈⢧⡀⠺⣂⣼⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⣚⡉⠄⠂⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣸⠛⠶⢿⣿⠺⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡜⣿⡏⠀⠀⠀⢧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⠋⠀⣀⣨⡿⠗⠚⣷⣶⠖⠋⠉⠉⠉⢉⣉⣤⣴⣿⡿⠀⠀⠀⠀⠘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠛⣿⡛⠦⣭⣥⡴⠶⢟⣽⣏⣴⣿⣿⣿⠿⠿⠟⢻⢛⠁⠀⠂⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⡇⠹⣮⡳⣤⡉⠀⠀⠚⠁⣿⡿⠋⠁⠀⠀⠀⠀⠀⠘⠀⠀⠈⠴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣰⡿⠁⠀⣌⠙⠦⣀⣤⣶⡀⠀⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⠉⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣧⣿⣄⢨⡳⣦⣙⢿⣿⣧⢸⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⢰⡏⣸⡟⢹⣿⣿⣆⢳⣬⣛⠷⣽⣿⣿
⠀⠀⠀⠀⠀⠀⡾⢡⣿⠀⠘⡇⢻⣿⡜⢿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⣼⢱⣿⠇⠀⠀⣧⠈⢿⣿⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⡇⢸⡿⠀⠀⣸⡟⡄⠢⡉⠉⠉⣩⣾⣿⠟⣇
⠀⣴⣶⡄⣿⢀⣾⠃⠀⠀⣿⣷⡜⠀⠙⣶⣾⣿⠟⢡⢸⣿⡆
⠀⠙⣿⢠⠇⣼⠃⠀⠀⢸⡏⠘⢿⡄⠀⠈⠉⠀⣴⡏⣼⣿⡀
⠀⠀⢸⠇⣼⠃⠀⠀⠀⣾⣿⣦⡀⢙⡁⠀⢠⣾⡟⢰⣿⣿⡇
⠀⠠⣋⣼⣿⠀⠀⠀⠀⣿⠋⠙⠿⠋⢀⣴⣿⠟⣰⣿⡿⣿⡇
⠀⠀⢻⣿⣿⣀⣠⣶⡀⣿⠀⠀⠀⣠⣾⡿⠃⣰⣿⣿⢣⣿⣿
⢷⠾⠿⢿⣿⡏⠉⠈⠁⣟⠀⢀⣼⣿⠟⢠⣾⣿⣿⡏⣼⣿⣿⡇
⠀⠀⠀⠘⣿⣧⠀⠀⢸⣿⣴⣿⡿⢃⣴⣿⣿⣿⡿⢠⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⡄⠀⢸⣿⣿⡟⣵⠟⣹⣿⣿⣿⢃⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣧⠀⢸⣿⡟⢸⡏⢠⣿⣿⣿⠇⣾⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⢹⡜⡄⢸⣿⣇⣿⠀⣾⣿⣿⠏⣼⣿⣿⣿⣿⠀⣿⡄
⠀⠀⠀⠀⠀⠈⣷⢁⢸⣿⣿⡏⢰⣿⣿⡟⣰⣿⣿⠿⣿⡟⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢹⡎⣸⣿⣿⢃⣿⣿⡿⣱⣿⣿⡿⠀⣿⡇⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠈⣷⢿⣿⣿⣼⣿⠏⣰⣿⣿⣿⠇⠀⢹⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡞⣿⣿⣿⡟⣴⣿⣿⣿⡟⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢻⣿⣿⣾⢿⣿⣿⣿⣡⠀⣧⢠⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣿⡿⢃⣿⣿⣿⣷⡏⢸⣿⣿⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⢀⣾⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⠀⠀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠉⠉⠉⠒⠦⢀⠀⣀⡤⠔⠂⠉⠉⠙⠛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠋⠀⠀⠀⠀⠀⠸⠿⢷⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⣁⠀⠀⠀⠀⠀⢈⡀⠀⢠⡾⠦⣄
⠀⠀⠀⢀⣴⠋⠀⠈⠓⣤⠄⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⢆⣠⠊⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⡄
⢀⡴⠛⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⢰⠁⠀⠀⠀⣀⣀⣀⣨⣇⣀⣀⡀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣾⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⡋⠉⠉⠛⠿⠇⠀⠀⢩⠈⠛⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⡟⠀⠀⠀⠀⣀⠄⠀⠀⠐⠺⠓⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢀⡾⡀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳
⠸⡆⠀⠀⣌⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠳⣄⠀⠀⠀⡠⠊⠀⠉⠂⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⢦
⠀⠹⣄⠀⠟⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈
⠀⣠⠞⠳⠄⠀⠀⠀⠀⠀⠀⠀⠈⠗⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠸⡏⠒⠒⢠⡤⠤⠤⠤⣤⠐⠒⠂⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠀⢀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⢾⡀⠀⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣶⠚
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠢⡀⣨⠀⠀⠀⠀⢸⠀⠀⠀⢀⡿⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⢀⣀⣸⡀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠘⢿⣤⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠈⠉⠻⣏⣁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣹⠆
⠀⠀⠀⠀⠀⢠⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡄
⠀⠀⠀⠀⠀⢀⡟⠛⠒⠛⠛⠛⠛⠛⠚⠛⠒⠚⠛⠛⠛⠒⠒⠒⠛⠛⠛⠒⠛⠛⠓⠒⠛⠛⠛⠛⠛⠛⠛⢻⡀
⠀⠀⠀⠀⠀⠈⠳⢶⡶⠦⠤⠤⠤⠤⢦⡤⠶⠤⠴⠤⠤⠤⠤⠤⠤⠴⠤⢴⡤⠴⠦⠤⠤⠶⠶⠶⠶⠶⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⡼⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡃⣀⠴⠞⠋⠁⠀⠀⠈⠳⢦⡀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠙⠳⣄⠀⠀⠀⠀⢀⡰⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡴⠚⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⡿⠀⠀⠀⠀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⢀⣤⡤⠀⢕⣚⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠐⣽⡛⡙⠀⠙⠻⣟⡓⠈⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠲⠶⣶⣿⣿⣶⠶⠒⠒⠀⠀⡀
⠀⠀⠀⠀⣤⠀⠛⠀⠀⠀⠈⠙⣋⠴⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⣸⣇
⠀⠀⢀⣠⠟⣠⡀⠀⠀⠀⠀⠉⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣠⣾⣧⠀⠀⠀⢰⢹⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⠌⡀
⠀⠀⢾⢸⠀⡏⣇⠀⠀⠈⠁⠒⠒⣹⡆⠀⠀⠀⠀⢀⡴⠋⠀⢠⣾⣿⠟⠁⠀⠀⢀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢈
⠀⠀⠈⢄⠁⢀⡸⠂⠀⠀⠀⠀⢀⠏⠳⠀⣀⡠⠖⠁⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⣾⠀⣸⡇⠀⠀⠠⣴⣶⢋⡴⢚⠟⠉⠀⠀⠀⢀⣾⠟⠁
⠀⠀⡏⢋⣧⡹⡷⡀⠀⠀⡼⢣⠏⢠⠏⠀⠀⠀⠀⠀⠾⡡⠂
⠀⠀⠑⠀⢊⢻⡆⡅⠀⡼⢡⡟⢀⣿⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⠶⠀⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⣶⣶⠶
⠀⠀⢀⡇⢌⡆⢻⢠⠀⡿⢸⠁⢸⢻⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⣀⠞⢡⡏⡇⣀⣠⢷⣇⠸⡀⠀⠈⣆⠀⠀⠀⠀⠃
⡾⠁⢠⠟⢰⡠⠵⣚⡿⢿⠀⢧⠀⠀⠘⣄⠀⠀⢸
⠁⠀⡞⠀⠸⠗⠊⠁⠀⢸⡆⠘⡆⠀⠀⠈⢦⡀⢸⡇
⠀⠀⠁⠀⠀⠀⠀⢀⡴⠋⢹⡄⠘⡄⠀⠀⡀⠻⣼⠁
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣠⢿⡄⠰⠀⠀⢷⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢳⠀⠄⠀⠸⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⠃⠐⠀⠈⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⡎⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⡠⠔⠁⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⢀⡀⠀⠀⠀⠀⠙⡆⠀⢀⡠⠒⠉⣀⠴⠊⠁
⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠈⠂⠁⠀⡀⠔⠀⢀⠷⣞⠁⣀⠴⠊⠁
⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⢀⡠⠚⠁⠀⠀⠉
⡴⠀⠀⠀⠀⠘⠛⠀⠀⠀⡠⠔⠉⠀⣠⠔⠉
⡇⠈⠢⢄⠀⠀⠀⡀⠔⠉⠀⣀⠔⠋
⠱⣄⠀⠀⢡⠄⠀⠀⣠⠔⠊
⠀⠈⠓⢤⣸⡤⠒⠉
⣿⣿⠛⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠤⠄⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⡠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠐⠠⢁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢠⠊⠀⡀⠀⠀⠀⠀⠀⠠⢀⠈⠀⠂⠄⡑⢌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠃⠠⠊⠀⢀⠄⢀⠄⢄⠐⠠⢈⠐⠂⠤⠈⠀⠀⠂
⠀⠀⣀⡖⢜⢂⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣊⠔⢁⠔⠁⠀⠀⠁⠂⠄⣈⠐⠂⠠⠄
⠀⠀⡱⠝⠈⠀⠁⣀⠀⠀⠀⠀⠀⡀⠀⢐⠈⠄⠊⢀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠉⠁⢐⣐⢃
⠀⠀⠈⠂⢄⡠⠂⠀⠑⢄⠀⠀⢐⠩⠚⡀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠈⢀⠀⠀⠀⠔⠊⣸
⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠑⢄⡠⠂⠀⠑⡄⠐⠤⠃⠀⠀⠉⠊⠀⠀⠀⠀⠃⠀⠴⡀⠈⠣
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠁⠂⠜⡁⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠀⠐⠖⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠁⠐⠀⠀⠐⠀⠉⢀⠍⠢⡀⠀⠐⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢒⠶⣷⣄⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠐⠐⠂⠐⠒⠁⠀⠀⠐⢄⠀⠘⣵⡾⢗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢂⠈⠀⠘
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⠆⠀⠀⠀⢂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠠⠂⠉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⡔⠶⢶⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠳⠤⠞⠁⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢀⡴⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⢶⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠳⣄⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⣀⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣽⣯⠀⠀⠧⠼⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⣠⠖⣩⠞⠁⠀⢻⡳⡄⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⠀⣀⡴⣋⡴⠋⠀⠀⠀⠀⠀⠙⢮⢢⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⡠⢟⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⣠⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠧⠼⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⣀⣀⣴⡿⠋

⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦⣀
⠀⠀⠀⠀⣠⣶⣿⣿⡿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠻⣿⣿⣷⣦⡀
⠀⣀⣴⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣤⣿⣿⣿⣿⣿⣷⣄⡀
⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⡟⢹⣿⣿⣙⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠏⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠘⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡟⠀⠀⣠⣶⡿⠻⣿⣿⣿⣿⣿⡿⠿⣷⣦⡀⠀⠘⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣾⠿⠋⠀⠈⠻⢿⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⣸⣇⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠈⠻⢤⣄⣀⣀⣀⣤⣴⣾⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣷⣦⣤⣀⣀⣀⣀⡤⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢧
⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⠈⢧
⠀⠀⠀⠀⠀⠀⡰⠁⠀⡇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢸⠀⠈⢆
⠀⠀⠀⠀⠀⣰⠃⠀⠀⡇⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠀⠀⠘⣆
⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠀⠀⠀⠘⡆
⠀⠀⠀⢠⣇⣀⣀⣀⣀⣇⣀⣀⣀⣀⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣀⣀⣀⣸⣀⣀⣀⣀⣸⡄
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢠⠎⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⣰⡧⠴⠚⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠝⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⠠⠀⢀⡀⠀⠀⣀⠀⠀⠀⢀⡤⠚⢛⣥⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠛⢁⡆⠁⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣀⣀⣀⠀⢠⣀⣀⣠⣤⣶⣾⣿⣿⣶⣾⣿⣿⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠛⢛⣛⣿⠛⣥⣤⣿⣿⣿⣿⡟⠛⠻⣤⡈⠉⠋⠉⣹⠷⠖
⠀⠀⠀⠀⠀⠀⢀⠤⠈⠝⠋⢹⡏⠉⠳⢤⣉⣭⣩⣷⠳⡌⠑⢦⣀⣙⠛⣳⠈⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⢩⣿⣿⠷⣀⣒⣤⠬⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡅⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢿⣿⣿⣿⡿⡽⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⡀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣘⣿⣿⡿⠖⠁⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠀⣸⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣤⣶⣶⣿⣿⣿⣷⣄⣤⣴⣶⣶⣿⣿⣿⣿⡿⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠈⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣼⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⣶⣾⣾⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⣼⣿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢈⣿⠛⠉⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠾⠃⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦⣤⡀
⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⢀⡴⠞⠉⠡⠚⠀⠈⣉⡛⠦⣤⠖⣛⢶⣄
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡾⠁⠀⠀⠀⠀⠐⠞⣉⡉⠉⣻⣆⣌⢩⣟⢳⡄
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⢿⠃⢰⡄⣆⢀⣀⠀⣰⣿⡼⢿⣟⣿⣿⣻⣿⡠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⠖⠛⠉⠀⠀⠀⠀⠨⣑⡶⠙⣿⢯⣛⠀⢿⡆⠹⣯⢿⣾⡯⢻⢈⢷⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⡋⠀⠀⠀⠀⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠙⠛⢫⠙⠓⠋⡠⠚⢋⠉⠛⠿⢧⣿⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⣧⠄⣼⠁⠀⠀⠁⠀⠀⠀⢙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠿⠷⠶⠤⠄⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠃⣠⠟⠸⢿⠀⠐⠃⠀⠀⠀⠀⣸⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⣤⡴⠾⠃⢠⣀⡌⠛⢦⣀⣀⣀⣤⠶⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣶⣤⣄⡀⠀⠉⠋⠛⠀⣼⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⡘⢙⣛⣏⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠙⠶⣄⣀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⢀⡿⢿⠟⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⢲⢄⣿⡇⠙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠃⠚⢪⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢷⠶

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣽⣭⣿⣼⣯⣯⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣶⣶⣿⣿⣷⣷⣾⣶⣿⣷⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠂⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⢠⣾⣴⣾⣿⠀⠀⢀⣰⣿⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣽⣿⣿⣅⣤⣾⣿⠿⡏⠀⠉⠀⠨⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢽⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⢿⣿⣽⡿⡇⠀⢀⣀⢀⠀⠠⣤⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣸⣿⣿⣿⣧⠈⠛⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢹⡇⠀⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡷⠀⢿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣠⢾⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠙⢿⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣻⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⢿⣤⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠃⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠘⠿⠏⣽⣿⡻⢷⣄⠀⠀⢈⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣷⣦⣬⣙⣛⣧⣤⣶⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⠿⠟⠛⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠿⣿⡉⣹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢧⡼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠰⠾⠿⠿⣿⣿⡀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠸⣧⡜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣶⣦⣄⠀⠙⢿⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣠⣾⣿⡎⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣛⣛⠟⠛⢲⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠛⠋⣙⣛⠋⠱⣿⣷⣶⡄⢙⣦⣀⡀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⡿⠀⠀⣈⣯⣄
⠀⠀⠀⠀⠀⣀⡀⢠⣿⠃⠾⠏⠉⠀⠀⠉⠉⠁⠀⠀⠀⣿⠿⠃⣠⠿⣿⣦⡀⠀⠀⠀⠀⠀⢴⣾⣿⣧⣤⠘⢿⣿⣿⣿
⠀⠀⠀⠀⢺⣿⣧⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣶⠾⣏⡀⠀⢹⣿⣶⣤⡀⠀⠀⠀⣿⠛⣿⡟⠀⢸⣿⣽⠋
⠀⠀⠀⠀⠀⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⡀⠻⣿⣿⣿⣿⡉⠹⣿⣦⣤⣤⣿⠄⠘⠟⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠈⠻⣿⣿⠓⣴⡿⠋⠙⠻⣿⣶⣿⣦⠀⠀⢀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢿⣦⣀⣀⣀⣀⡀⠀⠉⠀⢀⣀⣴⡾⠛⢱⣿⠋
⠀⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠸⠿⠛⠉⢛⣿⣿⣿⣿⢟⣿⠟⠀⠀⠀⠸⣿⣷⡄⢠
⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⣤⡜⣿⣿⣏⠀⢀⡀⢶⡄⠀⣠⣤⣿⣿⣧⠈⢷⡀
⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⢰⣾⣿⡟⢻⠿⣿⣿⠀⢹⣿⠀⠁⣼⣿⣿⠿⣿⣿⣷⡀
⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡟⠉⠿⠃⢠⣿⣿⣄⣿⣿⡇⠠⣿⣿⣏⠀⠙⣿⣿⣿⡆
⠀⠀⠀⠀⣿⡇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠘⣷⣆⠀⢴⣦⠿⣿⢿⣿⣿⣷⣤⠹⢿⣿⠀⠀⠙⣿⣿⣇⠀⡀
⠀⠀⠀⡄⠸⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣩⣟⣷⡌⠰⣥⣶⣿⠋⠉⢻⣦⣌⣁⠀⠀⠀⠈⢿⣿⣦⠀⠆
⠀⠀⠀⡇⠀⠃⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠛⢿⣿⡅⠴⠿⠷⠾⠿⠟⠷⣦⣙⠁⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣶⣾⣿⣿⣆⠠⢶⣴⠶⣶⣶⣿⣿⣷⣄⡀⠀⠀⠀⠀⢻⣿⣿⣾⢆
⠀⠀⡇⠀⡖⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣿⣟⣷⠏⣥⠷⣶⣭⣠⣄⠀⢿⣿⣿⡏⠁⠀⠀⠀⠀⠈⢿⣿⣿⡼⠃
⣤⣴⣷⣴⣧⣀⣀⣀⣀⣼⡇⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⣹⡇⠀⠀⢸⣿⠀⡿⣧⣠⣿⣶⣿⠛⢻⣿⠀⢸⣿⣿⣅⡀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠘
⠉⠉⠙⠿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣾⣿⡿⠟⠂⠘⠇⢰⠀⠙⠋⠁⢀⠉⠀⣾⡟⢠⣾⠋⢻⣿⡟⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢠⡅⠀⢠⡄⠀⠐⣿⣿⣿⣿⠋⠻⡟⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣠⡘⣷⣎⣿⣿⡿⠋⡉⢠⣦⢿⡆⠀⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣧⡀⢀⣼⣿⣿⢻⡎⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⢻⣷⡀⠈⣿⣿⣿⠋⣿⣿⣾⡇⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡘⢿⣦⡝⠛⠀⢸⣿⣿⠀⣿⣿⣿⣧⡀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠻⣦⡽⣷⣤⠀⢿⣿⣿⡀⠙⢻⣿⠟⠁⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⡠⠌⠳⠿⣿⣿⡆⠀⢿⣿⠀⣸⣿⡄⠀⣤⣿⠃⠀⠀⠀⠠⣶⣦⣄⣀⣼⡟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣏⣙⣷⣶⢠⣀⣿⣿⣷⠀⢸⣿⣿⠟⠋⣁⡀⣿⣯⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠛⢿⣿⠁⠈⢋⣿⣿⣿⡀⢸⣿⡇⠀⢸⣿⣽⢿⣿⣧⡀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⢸⣿⣄⠀⠈⣿⣿⣿⡇⠸⣿⡆⠀⢸⣿⠁⣸⡿⣿⣿⣷⣤⡀⠀⠸⣿⣿⡏⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⢻⣷⡀⢹⡇⢻⣷⠀⣿⣿⣶⢎⡹⠃⣿⡇⠈⣿⠟⢿⣿⣷⣀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⢸⣿⡄⠉⣿⡆⠙⠈⣿⡀⣿⣿⠋⡀⠃⠰⣿⡇⠀⢹⣷⣈⣿⡿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣹⣿⠀⢸⣿⣧⠀⣿⣿⡇⠀⣿⣿⣿⠇⠀⠻⠀⠀⣿⣧⠀⠈⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡆⠸⣿⣿⡄⢻⣿⠇⠀⣿⣿⡏⢠⡇⢀⠇⠀⣿⣿⣧⣤⣿⣿⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⠀⢿⡟⢁⣿⡏⢠⣴⣿⣿⠀⣿⠀⣿⡀⠀⣿⣿⡿⠛⣯⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣠⣯⣤⣾⡿⣷⣿⣿⣿⠁⣾⡇⠀⣿⣷⠀⢻⡟⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⠏⠀⣿⡿⠉⠛⢰⣿⣿⣧⠀⣿⠆⠀⣠⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣾⣿⠃⠀⠀⣾⣿⣿⣿⠀⣿⣀⣠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⢿⣿⣿⣿⢠⣿⣿⣫⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⣴⣶⡟⠻⣿⣿⢸⣿⣿⣿⡿⠁⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠉⠉⠀⣰⣿⣿⣿⠏⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣤⣾⡿⢿⣿⣿⠟⠀⠛⣿⣿⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⣾⣿⡿⣿⣿⡿⠛⣿⣿⣿⠟⠀⠀⣼⡿⣿⣿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣀⣼⡟⠁⢸⠃⠀⠀⣸⣿⠟⠀⢀⣼⣿⣷⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⣶⣿⣿⣏⣀⣠⣾⣷⣶⣶⣿⡟⠀⠀⣼⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢿⣿⣿⣿⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⢿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣟⣠⣶⢠⣿⣷⡘⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⢀⣿⣿⣿⢿⣿⣿⡏⠀⣾⣿⣿⣿⣿⠃⢸⣿⣿⣧⣾⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⣼⣿⠟⣡⣾⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣇⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣿⣶⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⠤⠼⠛⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⠿⠟⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣧
⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢰⣿
⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⡿⢟⣄⠀⢀⣶⣝⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⣛⣛⠛⠛⠃⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡺⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠨⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠘⠛