Gerontology Emojis & Symbols

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠢⡀⠀⠀⢠⠒⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠸⣀⣠⠇⠀⠀⠠⣀⡠⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢄⢢⡇⠀⠀⠀⠀⢸⠔⡠⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⠬⣶⡀⢀⣶⠕⠊⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⡆⡇⠀⡇⢸⠀⣌⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⡀⠀⠄⡇⡇⡇⠀⡇⢸⠀⢸⢹⢹⠉⠁⢀⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠱⡠⢉⡀⠉⠁⠀⠁⠈⠀⠈⠉⢀⡉⢀⠎⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠣⠤⣈⠉⠑⠢⡄⢠⠖⠈⠉⣁⠤⠜⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⣀⡀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠎⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡆⡆⡶⢰⢂⠰⠀⣂⣦⣶⡶


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⠀⠀⢨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⡀⡸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠚⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠠⠀⠀⠀⠀⠀⠐⠀⢰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠆⢤⣀⣒⢉⣀⣴⣋⣸⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⢠⡔⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⠬⠙⠉⠣⠘⠛⠃⢸⠀⠀⠀⠈⡠⠔⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠘⠄⢰⠊⠁⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠷⢤⠀⠀⠀⠘⠂⠀⠀⠀⠊⢤⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢈⡀⠈⠀⠀⢠⢷⡀⠘⣆⠇
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐⠀⠀⢠⠀⠀⠀⢠⣵⠂⢍⠇⠀⠀⠀⠀⠀⠠⠀⢨⡥⣤⠀⠀⢁⠀⢸⠈⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠀⠘⠀⠀⠀⡿⢤⣀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡆⠀⠀⠀⠀⠀⠋
⠀⠀⡔⢂⠐⠁⠀⠀⠀⠀⢸⠀⠀⠰⢀⠄⢠⡇⠐⣽⠏⢸⣀⣀⣀⣀⡤⣤⣤⣍⡵⡄⣷⠀⠀⠀⠀⡀⠙⡀
⠀⠀⠈⠉⠀⠀⠀⣄⡀⠀⠘⠀⠀⠐⠊⠀⡰⣇⢸⣿⡆⣼⠧⠄⠖⡹⠈⠙⢿⡿⡍⢁⡿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⢄⠀⡀⠀⢀⠲⠜⠛⣆⡈⣸⡼⡀⠀⠀⠀⠀⠀⠈⠻⠗⠽⠁⠀⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠆⠆⠀⠰⠀⠀⠀⠆⠆⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣤⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⠶⠒⠂⠀⠀⠀⠀⠉⠉⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⡀⢀⡀⢤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢲⣶⠰⠀⠀⠀⠀⠀⠀⠀⣾⡀
⢠⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠤⠀⠀⡨⢸⡛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⠁⠀⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡯⣿⣧⡤⠀⠀⠀⠀⠁⠘⠓⠂⠀⠄⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⢻⣿⣿⣿⣿⣿⣏⣻⣵⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⡇⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⡿⢷⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠙⠂⠀⠀⠰⠀⠀⠀⠀⠸⣿
⠀⠀⢀⡀⠀⠀⢠⡴⠞⠉⢀⣤⣶⡿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⢸⡯⣽⣿⣟⣿⡇⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⣿
⢰⠄⠈⠁⠶⠓⠀⠀⠀⠀⠀⠈⠉⢸⣿⣿⣿⡇⠀⠸⣿⡿⣿⡿⠿⢿⡿⠀⠀⠀⠀⣿⣯⣻⣿⠿⣿⠷⠀⠢⠷⠆⠶⠶⠿⢶⣶⣿⣷⡖⠀⣶⣾⣗⡂⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⠀⣿⡗⣿⡇⠀⠀⡇⠀⠀⠀⠀⣾⣿⣿⣿⢤⣤⡼⠷⣶⠰⠄⢤⢤⣦⣬⡟⢷⣯⡀⢸⢿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣷⣾⡇⠀⠀⠀⠀⣻⢿⣿⣿⣾⣶⣦⢠⡇⠀⠠⡄⠴⡿⠿⠿⠀⠽⠿⠮⠘⠯⢻⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⣿⠘⡏⠀⠀⠀⢹⡟⢿⡇⠘⠿⡇⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⢀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠠⠇⠀⠀⠀⢴⡇⠸⠧⠀⠘⠇⠀⠀⠀⠀⢸⣷⡿⣿⣶⢾⣻⢿⡇⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⠿⠛⠋⡅⠀⠀⠀⠀⠀⠱⠀⠀⠀⠲⡀⠙⢦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣉⠁⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⣄⠨⡀⠅⠀⠀⠻⣦⡀⠸
⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣯⣵⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠁⢌⠂⢠⡀⠀⠈⠇
⢀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠳⠆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣧⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡁⢰⣷⠄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣴⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣾⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⠟⣿⡆⣿⣿⣸⣿⡇⠀⠀⠀⠀⢸⡿⠃⣿⡟⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⣿⣿⣿⣿⡯⠤⣿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⡇⠀⣿⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣟⢿⣿⠟⠀⣴⡏⢻⣭⣿⣿⣿⣿⠶⠀⠀⢀⣿⠀⠀⣧⠀⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠙⠁⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠁⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣭⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣯⣿⣯⣽⣿⣭

⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢁⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⣷
⠀⠀⠀⢀⠤⠚⣩⠋⠀⠰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠐⡤⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⢠⡅⠀⣰⠃⠀⠀⡃⠀⠐⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠈⠉⠁⠀⠀⠁⠀⠠⠀⠈⠀⠈⢿
⠀⠀⠘⢣⢰⠇⢠⡀⠀⡇⠀⢁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⢼⡦⠄
⠀⠀⠀⠈⡞⠀⠈⠢⢀⡹⠀⠸⠀⢠⣀⣀⣈⣤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⢰⠀⠀⠀⢸⡡⠛⠄
⠀⠀⠀⣸⣀⡀⠀⠀⠀⠀⣶⣀⠀⠀⠁⠀⡗⣿⠀⠀⠀⠈⠁⠒⠐⠂⠀⠀⡦⠆⠀⠀⠘⠀⠀⠀⠀⠃⠸
⠀⠀⠀⢘⡀⠈⠑⠂⢄⡀⢘⠈⠁⠀⠐⠒⠷⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃⠀⢸⠀⠐⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠾⠇⠐⠀⠀⠀⠀⠀⡆⢸⡆⣶
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⣀⠆⢀⠃⠀⠀⠀⠸⡀⠀⠀⠀⢀⠀⣇⠂⡘⠀⠀⠀⠀⠀⡇⢸⡇⡏
⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠠⠃⢠⠎⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡟⠒⠃⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠆⢀⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⢹⡻⡄⠀⠀⠀⠀⠀⢀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡝⢲⠉⣆⠤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠃⠑⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⠶⠾⠷⡒⢉⣣⠄⠘⠘⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⣀
⢀⣴⣿⣿⣷⣄⠈⠙⠻⠿⠟⠛⠁⢀⣴⣿⣿⣶⡄⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠈⠛⠿⠿⠟⠋⠁⣠⣾⣿⣿⣦
⣾⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣿⡿⠛⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣸⣿⣿⣿⠿⠋⠀⠀⠈⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠋⣥⠤⠤⠙⠿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⢋⠥⠤⣄⠀⠀⠀⣠⠤⠬⡻⣿⣿⣿⡀⠀⠀⠀⠀⣾⣿⠟⣁⣀⣁⠀⠀⡁⣈⣀⣈⡙⣿⣿⣿⡄
⠀⠀⢰⣿⣿⠴⢚⣷⠦⠀⠀⠀⠖⣺⡶⠄⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣠⢖⣶⡦⠀⠀⠀⠴⣲⣶⢆⣺⣿⣿⡇
⠀⠀⢸⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠃⠀⠉⠠⠃⠀⠈⠢⠈⠁⠘⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣇⠀⠀⠀⣀⣒⣀⡀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⡒⡂⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣦⡀⠈⠫⠭⠝⠁⢀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣄⠈⠈⠛⠿⠟⠃⠀⢀⣾⣿⣿⣿⠃
⠀⠀⠀⢹⣿⣿⣿⣿⠑⠂⠤⠐⠊⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠒⠠⠤⠄⠐⢺⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣄⠀⠀⠀⣠⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣶⣮⣿⣿⣿⣿⣿⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⠸⣿⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⣆⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠿⠁⠀⠹⠿⠿⠋⠿⠿⠃⠀⠙⠿⠟⠀⠀⠀⠇


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⡟⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣏⠀⠀⠀⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⢰⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⣸⣿⡀⠀⠀⢿⣷⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢸⣿⣇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠉⠉⠉⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⡋⠀⠘⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠉⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⠂
⠀⠀⠀⠀⠀⠀⣴⣿⠟⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠟⠁⠀⠙⠄⠈⠉


⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢄⣄⠀⠀⢀⠇⢻⢄⡀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠈⠑⠲⣆⠀⠈⣆⣈⣉⣙⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠒⠁⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢰⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢉⢿⠆⢀⣀⣀⣀⡤⠞⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡬⠾⢄⡀⢸⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣾⢀⣀⠀⠈⠉⢀⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⠓⠦⣄⣀⡀⠔⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡌⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⣀⣤⠶⠋⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⡇⡇⠀⠀⠀⢸⠀⠈⢰⡒⠒⠋⠉⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⢣⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⣾⠀⠀⠀⡟⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢿⠀⠀⢀⡇⠀⠀⠀⡇⠀⢀⡇⠀⠀⠀⠀⠀⢀⣀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⢸⡄⠀⢸⡇⠀⠀⠀⠳⡞⠙⠓⡖⡶⠒⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⣀⣨⡇⠘⣄⣀⣸⠃⠀⠀⠀⠀⡇⠀⠀⡇⢻⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⡳⢀⡿⠥⠏⠉⢉⣷⠀⠀⢸⠀⢸⡃⣸⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠿⠇⠸⣧⣤⠾⠛⠋⠁⠀⠀⣀⣧⠸⣧⣁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠁⠉⠀⡏⠛⠷⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣶⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠠⠄⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⠔⠒⠒⠒⠚⠉⠉⠉⠃⡇⣠⠋⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠁⠌⢠
⠀⠀⠀⠀⠀⠦⠀⠀⡈⠀⠀⠀⠀⠀⢀⠀⠁⠀⡀⠀⠀⠢⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀
⠀⠀⠀⠀⡐⠀⠀⢀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠤⠃⠘⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣡⣀⠃
⠀⠀⠀⠀⠀⠐⢀⠃⠀⠀⠀⠀⠂⢄⢹⣀⢠⣄⡄⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠈⠆
⠀⠀⠀⡠⠀⠀⠈⠓⠀⠀⠀⠀⠀⠸⠋⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠈⠹⠁⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠤⢤⡤⠤⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣴⣶⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣡⢸⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣧⠀⢹⢸⠀⠀⠈⠆⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠙⢾⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠋⠀⠀⠲⠯⠂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣭⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢿⣅⠀⠀⠈⠹⣆⠀⠀⠀⣾⠋⠉⡉⠀⠈⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⢶⡿⠀⠀⠀⠀⣿⠀⠀⠀⢻⡶⠛⠛⠳⠶⣤⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠼⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠈⣷⣄⡀⠀⣠⡾⠃⠀⠀⠀⠘⣷⡀⠀⠀⣠⡟⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⢈⣿⠟⠉⢿⡀⠀⠀⠀⠀⠈⠛⣿⠟⠋⠀⢠⡄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣰⣿⠀⠀⠀⠀⠀⠀⢻⡿⠁⣀⠀⠘⣧⠀⠀⠀⠀⠀⣼⠏⠈⢷⡀⠈⢿⡄⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢹⡆⠀⠀⠀⣰⣏⠀⠀⠈⣷⠀⠘⣧⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡄⠀⢿⡄⠀⣴⠏⢻⡄⠀⠀⣿⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣷⠀⠈⣷⡾⠃⣠⣾⡇⠀⠀⣿⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠳⢾⡇⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⣶⠶⢻⣧⡾⠋⢽⡀⠀⢰⡟⠳⣾⡏⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢰⡆⠀⠀⠀⣿⠀⠀⠿⣤⡼⠏⠀⠀⢸⡟⠛⠛⣷⠶⠛⢿⠛⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣿⣀⣀⣀⣀⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢀⣀⣸⣇⣀⠀⢀⣿⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠉⣿⠉⠉⣹⠏⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣇⣿⣄⣀⣉⣉⣉⣉⣉⣿⣌⣀⣉⣹⣧⣀⣀⣀⣀⣰⣟⣛⣉⣀⣿⣿⣛⣉⣀⣿⣄⣀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠀⠀⠀⠀⠀⠀⢀⡴⢋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠘⣄⠀⠀⠀⢀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠉⠉⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠔⠒⠉⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠴⠊⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣄⡀
⠀⠀⠀⠀⠀⠘⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣻⢿⡿⣿⣿⡇⠀⠀⠀⠀⠉⠙⢒⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⢄⠀⠀⠀⠀⢸⡿⢛⡿⠛⣿⢻⡟⠃⠀⠀⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠑⢭⣶⣦⣥⡦⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠁⠀⠀⠀⠀⠀⣀⣀⣀⡤⣄⢀⡞⠁⠀⣰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠒⠛⠒⠒⠺⣿⣿⠇⠀⢹⢸⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢻⡴⠁⠀⣴⣶⡄⠀⠈⠁⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠀⠀⠀⠀⠀⠛⠟⠃⠀⠀⠀⠀⠀⠀⢼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠂

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⢠⡆⠀⠀⣤⣀
⠀⠀⢸⡅⠘⡆⢈⣿⠀⠀⠀⠀⣀
⠀⢀⡸⣧⢘⡋⠀⣭⡾⣣⡀⢠⣍
⠀⣹⠃⠿⠏⠉⢤⠋⣴⠛⢷⣄⠹⣦⡀
⠀⢨⡄⠚⣀⠀⢲⡟⣷⡆⢠⣽⣥⠜⢡⡄
⣄⠀⣴⢛⡻⢷⣾⣫⣽⠃⠀⠀⠀⠰⢎⡉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠿⠀⣠⡿⠁⣾⠙⠃⠀⠀⠀⠀⠀⠀⠘⣛⣿⠘⣏⠠⣿⡃⠴⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⣀⠀⠉⢸⠓⣻⡒⢦⠀⡶⠶⠀⠀⠀⠈⢙⣿⠈⡛⠛⢛⣁⠠⡶⠶⢀⣴⠂⠆⠀⠀⣴⣄⠀⠐
⠛⠃⠀⣮⣡⢉⣷⣦⣴⡇⢶⣦⡀⠀⠀⣸⠋⠾⠋⣀⠀⠻⠇⢰⡶⠈⠁⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠠⡿⣦⡉⣥⡼⢿⣶⣿⠿⣦⣼⡟⠀⣸⠋⢋⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠾⠇
⠰⠟⠀⠐⢿⠛⣿⣎⣿⣿⢿⡿⠾⢥⡿⠀⣰⣟⡸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⡾
⠀⢠⣶⡄⠘⠟⠀⣿⣬⣧⢾⣲⠗⣿⡇⠀⣸⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠆⢼⠟⢰⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣶⠆
⠀⠀⠀⠸⢇⣤⠀⠈⠛⢾⣯⣿⣾⠿⡗⠀⣁⠘⠃⠀⠀⠀⠀⠀⠀⠀⡶⠖⠀⠀⣴⠆⢰⡎⠁⠘⡁⢠⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⠐⠷⠾⠋
⠀⠀⠀⠀⠈⠛⢠⣤⠀⠀⠉⢸⡟⣶⣿⡆⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣿⠾⢀⣤⠀⠰⠆⠻⠛⠾⠛⠶⠆⠀⠀⠛⠋⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠈⣉⡉⠛⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⢠⣤⡴⠂⠘⠋⠐⠶⠖


⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠰
⠀⠀⠀⠀⠀⠐⠀⢀⡃⠈⠁
⠀⠀⠀⠀⠀⢠⡄⠀⠁
⠀⠀⠀⠀⠀⡀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠒⠂⠀⠐⠂
⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠘⠘⠃⠀⠀⠁⠀⠃
⠀⠀⢰⠠⠄⠀⠀⠐
⠀⠀⠀⣤⡄⠀⠀⠂⠒⠂
⠀⠀⢠⢀⡀⠀⠀⠀⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⡀
⠀⠀⠀⠖⠛⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠂⠴⢂⠀⠀⠀⠀⠀⢹⡿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠁⠀⠂
⠀⠀⠀⠀⢄⠿⡄⠀⠀⠀⠀⠀⠰⣆⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠘⡀⠻⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡀⠹⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠛⠂⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⣄⠘⢏⡀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠈⠷⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢆⣀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠁⠶⠀⡀⠀⠀⠀⠀⠈⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠃⠴⠤⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⢨⣤⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⣀⣀⣀⣄⡀⣀⠀⠀⠀⣀⣿⣎⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢠⣴⡾⢿⣻⣏⡹⠁⢙⠹⣿⣿⣿⣟⢧⣿⠇⣉⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠜⠛⢁⡀⠀⠙⠻⢷⡄⢸⣶⣗⣼⣿⣟⣹⣿⣶⣿⡏
⠀⠀⠀⠀⠀⢀⣠⠤⠒⢉⠁⢀⣶⡟⠢⠄⠀⠂⠀⠀⠙⢢⣍⣷⡄⠸⣿⢿⣿⣿⡟⠁
⠀⠀⠀⠀⢺⠟⣡⡴⠞⠋⠀⠀⠙⠃⣀⣀⣀⠀⠀⣀⣀⣴⡄⠙⣿⣾⣿⣿⣿⣯
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⣋⠻⣷⢿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠴⣶⣶⣤⢀⣀⠀⠀⠀⠀⢾⣿⣉⡀⣚⠛⢛⣿⣿⣿⡇
⠀⢀⣠⣤⣶⡿⠁⠀⠀⠀⠀⠈⠻⡹⠡⠤⠄⠠⢀⣤⣴⠉⢉⣿⣿⣷⣿⣿⣿⠟
⢺⣿⣿⡿⠛⠉⠀⢀⠀⠀⠄⠐⠀⠈⣗⢠⢀⣤⣭⠶⠋⣠⣼⣿⣿⣿⣿⣿⡟
⣘⣩⣵⣶⣾⣯⣥⣼⡤⣠⣄⡀⠀⡀⡿⣶⣿⣿⣷⠇⠀⢸⣿⣿⣯⣿⠛⠋
⣿⣿⠿⠿⠛⠛⠯⠿⣿⣷⣿⣿⡟⠉⠁⠀⣿⣿⡟⣁⣠⣿⣟⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢠⣿⣿⢟⣽⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠁

⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠾⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢶
⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⡿⢂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⣀⣀⡀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠎⣰⣝
⢷⠴⠀⣀⡤⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠘⠻⢆⢍⡶⠄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢭⣤⠉⢀
⢸⠀⠐⡉⠘⢻⣀⡄⠄⣿⠀⠀⠀⠀⠀⢸⡌⣌⠠⣓⡪⠸⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠧⠀⠀⠈⢫
⢸⠀⢀⠀⠀⢀⠃⠀⠀⣿⠀⠀⠀⠀⠀⢸⠈⠉⠙⡒⡗⢁⠆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠃⠀⢈⠃
⣸⠀⠀⠙⠢⠐⠆⣀⠀⣿⠀⠀⠀⠀⠀⣸⠀⠄⠀⠈⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐⠃
⡞⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⣖⠒⢀⣦
⡏⠈⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢻⣦⡞⢣
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠒⠊⠀⠀⣠⠒⠀⡀⢀
⡏⠀⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠐⡇⢀⠀⢡⣌
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠇⠀⠀⠘⠃
⢇⠀⠠⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠈⢇⠀⢤⡀⢀
⣹⠐⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡾⢷⠗⠂⠃⠀⠢⡀⠉⠀⢠⠆
⢇⠀⠈⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⠀⢀⡀⡇⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⣿⠀⣐⠀⠈⠍⠀⠀⠈
⢸⠀⠒⠀⠀⠀⠀⠀⠀⣸⠀⢐⠁⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠂⠠⠀⠁⠀⠀⠀⠀⢀⠔⠂⠄
⢸⠀⠁⠀⠀⠀⠀⠀⠐⣿⠀⢘⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠫⠀⠀⠀⠀⠀⠀⣠⠄⠴⠀⠰⠆
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡃⠀⢀⠀⠀⢺⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢇⠰⠶⠈⠀⠀⠀⡴⠀⠀⢄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠈⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠈⠁⠀⠈⠀⠀⠀⠟⢰⡎⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢮⣞⣌⠋⡆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣤⣬⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠉⠀⠀⠀⣀⠤⠒⠒⠋⠉⠙⠓⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣠⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⠀⠀⠀⠎⠀⢀⠀⠀⠀⠀⠈⠈⠡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣦⣿⣶⣿⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠀⠁⠀⠀⠀⠀⠚⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠹
⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⡀⣇⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⣤⠄⠃⠀⢀⡿⠛⢿⣿⣿⣛⠁⠀⠙⠀⠈⠣⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⡠⠏⠀⠀⠊⠀⢻⠁⠈⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠊⠀⠀⢀⠦⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠁
⠠⠤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁
⠐⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⢀⣀⠤⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣠⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣠⠤⡈⠙⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡭⠴⡏⠙⠁⠀⠣⢤⡀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⢁⣄⠈⣿⣿⣿⣿⣿⢸⣡⡆⡐⠀⠀⠀⠀⠾⠓⢞⠛⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢫⢶⣿⣿⣿⣾⠀⢀⡀⠙⡟⡵⠋⠁⠙⢿⡞⠉⣲⣶⣰⣦⡿⢀⣖⣦⡶⠒⣖⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⡏⣷⠛⠀⢹⣿⣿⡧⠾⣽⡠⡵⡙⠿⠛⠀⣹⠧⢰⣃⣴⣿⣿⡟⠉⢹⡙⢿⣙⢿⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣀⣀⡼⠀⢤⣼⣿⣿⣧⡀⠈⣏⡆⣝⣦⣤⣴⣥⣄⣀⠉⢻⣿⣿⣿⣶⣴⣷⣿⡿⣿⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⢹⠉⠉⠓⣶⣿⣿⣿⣿⣿⣿⣿⣇⢇⡿⣿⣿⣿⣟⣿⡇⢸⢛⣛⣛⢿⠿⢻⣿⣏⠁⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⣿⣶⣾⣿⣿⡿⣍⠻⣿⠟⣽⣚⢻⡿⣿⣿⣿⣿⣶⣇⡎⣿⡿⣣⢏⣴⡩⣿⣿⣷⣶⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣝⢿⠛⢫⣾⣮⡳⣶⣽⡖⢭⣼⣿⣭⡿⠿⣿⣿⢿⠧⠕⣋⣷⡟⠻⠞⣩⣽⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡼⡵⣾⢟⠕⠛⠛⠿⣿⣿⣿⣿⠟⠻⣶⣏⣂⠀⣉⣽⠿⠷⠮⢷⡼⡝⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣹⢭⡇⠀⠰⣄⠄⣹⢙⣿⣿⡀⣠⣜⢉⠍⠉⢻⣃⠀⠃⠁⢸⠇⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣷⡱⣄⡀⢀⡠⣫⣘⠛⠙⣷⣼⣜⠉⢠⠈⠚⡍⢓⠶⢶⣫⣼⡿⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⡟⢠⢠⣏⡝⠙⠟⡿⠷⠖⢿⡷⣶⠿⣟⣽⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡅⣸⣧⣀⢦⠇⣀⡄⠸⣋⣵⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡜⢀⣦⣼⣿⣿⣿⡇⢀⣳⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠈⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⠫⡻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣣⣯⣟⡿⠟⠛⠛⠓⠾⠿⣿⣷⣹⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⢛⡵⣻⣿⣵⠋⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⠤⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⣿⡁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠻⣽⣾⣄⣨⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣻⣦⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣀⣀⣈⡛⣁⣀⢀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠸⣿⡏⠀⠀⡄⣿⣿⣿⣯⠻⣿⠁⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡈⠁⠀⠀⢸⣿⣿⣿⣍⣀⣉⠦⠤⠀⠐⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣧⡙⠛⢆⢆⢻⣿⣿⣿⠊⠁⠀⠀⢀⣄⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣻⡿⣛⡷⣀⠆⠘⣷⡝⢿⡿⢀⠀⢀⣼⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣷⣤⡄⠙⢀⠀⠈⠀⢴⡞⢻⣥⡄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢹⣿⣿⣿⣿⣿⣷⠶⣿⡿⠋⣤⡀⣰⣿⣵⣦⣜⣷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⣿⣿⠇⠡⣼⠁⠀⠱⣤⡆⠁⠿⣿⣿⣿⣿⢻⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⣔⠛⣥⢠⣜⠁⣿⠇⠀⣴⣿⣿⡿⠁⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⣤⡀⢿⣿⡻⢿⡇⣿⣻⣝⢿⣿⣄⠼⣿⣏⣀⣠⡘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣆⣠⡿⠙⣷⣏⡁⡈⠃⢉⣽⡿⢁⠁⠸⡇⣩⣥⣤⡘⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣯⣹⡷⣿⣿⠗⣀⣹⣿⡷⠉⠻⠀⠈⠀⣤⢠⡞⣿⣿⣿⣿⣿⠷⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣶⣴⣮⣴⣿⣷⡼⠻⠿⢿⡟⠿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣛⡭⡽⢧⣈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣶⣧⣤⣿⢿⣿⣿⣿⣿⠃⡞⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠎⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠛⣱⣿⣿⠛⠛⠙⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠃⠀⣠⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠶⢦⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢧⣀⠀⢀⡾⠀⠀⠈⢷⡀⠀⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠛⢻⡇⠀⠀⠀⠈⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠜⠀⠀⢸⠀⠀⢹⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡀⠀⠀⠀⠀⣾⡆⠀⢸⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠻⣄⠀⢀⣠⣿⠃⠀⡿⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣄⠀⠙⢿⣿⣿⡿⠀⣸⣃⣀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣄⣈⣻⢃⣼⣋⡉⠉⠉⢻⡆⠀⣈⣹⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠀⢀⡼⠟⠋⠉⠀⠀⠀⠈⠻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⠀⠀⠀⣠⠊⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠖⠒⠒⢦⣰⠃⠀⠀⠀⠀⣀⡼⠋⠀⠀⢀⣠⠖⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⡇⠀⠀⠈⠒⠿⠧⠤⠶⠶⠚⠉⢀⡼⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢀⣠⣾⣥⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠈⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⢛⣾⠏⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⣎⢠⡞⠁⣠⡞⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠋⣰⣿⡛⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣴⡏⠉⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣾⡿⠛⢁⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣨⢀⣼⠋⢀⣴⣿⡏⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠄⠚⣉⢛⡶⠛⣶⢼⡿⠊⣡⣴⣿⣿⡟⣧⠨⣿⡇⠀⡀⠀⠀⠀⠀⠀⣰⠖⠃
⠀⠀⠀⠀⠀⡾⠙⢉⣉⠀⠀⠀⠀⢰⠂⠀⠿⡉⠁⢀⣇⠀⠀⣰⣿⣿⡟⢿⣷⡘⢧⢈⣱⠼⠏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢄⣀⠈⠉⠀⢁⡘⠲⠂⢾⣉⠳⣠⠁⢀⣿⣿⣾⢿⣿⣿⣿⣧⠈⠛⠗⣶⡟⠿⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⢻⣿⣿⣿⣾⢿⣿⡌⠙⢉⡿⢉⡉⠁⠀⠀⠲⠶⡆
⠀⠀⠀⠀⠀⢻⣆⢨⡑⢦⣀⠀⠀⠀⠀⠿⠛⡿⢎⢿⣿⣿⣿⣦⠉⠉⠀⡿⣠⡾⢧⠄
⠀⠀⠀⠀⠀⠈⢿⣿⣷⣀⡻⠅⠀⠀⠘⣤⡀⣿⣿⣿⣿⣿⣯⠛⠛⠀⣄⣜⠉⣠⡎
⠀⠀⠀⠀⠀⠀⠀⣇⠙⢿⡇⠘⣷⣦⣄⠠⣤⡬⠻⢻⠈⣟⣿⣶⡆⠰⣾⡟⠉⠿⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣸⣧⣦⣬⠛⠛⠛⢻⣷⣿⠛⣿⣿⠿⣯⠖⠈⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠙⠛⠛⢤⣤⣤⠛⢿⣿⣿⣿⣿⣿⡿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢈⣉⣁⣠⠙⠛⠿⣿⠏⠠⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠶⠒⠛⠛⠿⣷⡈⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣦⣤⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠎⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⣤⡤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢤⣤⡀
⠀⠀⠀⢀⡼⠋⣠⠴⠶⠶⣤⣉⠛⠳⠶⠖⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠲⠶⠞⠋⣉⣤⠶⠶⢦⣄⠙⣧
⠀⠀⠀⢸⡇⢸⣃⡀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⢀⣘⡇⢸⡇
⠀⠀⠀⠘⣧⠈⠉⠙⠻⣦⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢀⡴⠟⠉⠉⠁⣼⠃
⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠻⢦⣤⣤⡴⠏⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠹⢦⣤⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠤⠤⣄⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣫⣿⣿⣿⣿⣿⡹⣷⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⣿⣿⣿⣿⣿⣿⣿⣮⢠⠀⢠⣾⣿⡿⢟⣫⢿⡻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣥⣿⣿⣧⣽⣿⣿⠛⠀⢸⣿⣟⣛⣯⣵⣿⣿⣮⣟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣭⣭⣽⢻⣿⠃⠀⠸⠟⣿⣿⣤⣿⣿⣿⣤⣾⣿⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣝⠿⣦⣧⡾⢟⣵⣶⣦⡄⣀⣬⠻⣿⣟⣿⣛⣿⠟⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣿⣿⣿⣿⣿⣮⡷⡶⢖⣾⣿⣿⣫⣾⣿⣿⡼⣆⢽⣟⡫⣡⡟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣧⢻⣧⣽⣴⣿⢳⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣹⣿⣿⣿⣟⣿⣿⣿⣏⣿⣿⣿⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠁⠉⠉⠉⠁⠈⠉⠉⠈⠉⠉⠉⠀⠉⠁








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠿⠛⡿⠻⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠟⠑⠀⠀⠀⠀⠀⠈⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢀⣤⣶⡞⢻⡟⠹⣿⢟⣿⣷⣦⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢿⣲⣿⣿⢸⠇⠀⢿⣽⣿⣿⡿⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠙⠦⢭⣝⣛⣻⠁⠀⣸⡭⠽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⡿⠀⠀⠀⠀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠃⠀⠀⠀⠀⠹⢷⡄⠀⠀⠀⠀⢠⡇⠀⢠⠇⢀⣤⠶⠟⠋⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢴⣿⣿⣿⠛⣿⣶⣶⡄⢹⡄⠀⠀⢀⡞⠀⠀⡼⠀⢾⢉⠁⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠭⡏⠀⣯⣭⡭⠵⠋⠀⠀⠀⡼⠁⠀⢰⠃⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⢠⡏⠀⠀⠀⠀⢀⡿⢻⡶⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⠀⠀⠀⢀⡏⠀⠀⡾⠀⠀⠀⠀⢀⡞⠀⣸⠁⢀⣀⣤⠶⠚⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⡀⠀⠀⠀⣼⠀⠀⢠⡇⠀⠀⠀⢠⠏⠀⣰⠃⣴⢋⣉⣁⡀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠲⣄⠀⠹⡄⠀⠳⡄⠀⠀⡏⠀⠀⢸⠀⠀⠀⢠⠏⠀⠐⠃⠀⠘⢾⣿⣿⢿⣷⣦⣌⢻⡆
⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠈⠛⣦⡹⡄⠀⠙⣆⢸⡟⠀⠀⣾⠀⠀⢀⡟⠀⢠⡏⠀⠀⠀⢀⡬⠉⣨⠿⠿⠿⠞⠁
⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⢀⣀⡤⠞⠁⠹⡄⠀⠘⣿⡇⠀⣠⣿⡀⠀⣸⡇⡀⣾⠀⠀⣀⡴⠋⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠉⢧⠀⠀⠀⠀⢹⡤⠀⢸⣿⡄⡼⣾⣇⠀⣿⣱⡇⣿⣠⠞⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠳⣤⣤⣄⣀⢷⢷⠈⢿⡧⢃⢯⢿⡄⣿⢹⣃⣿⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣐⣭⣭⣽⠿⣿⢋⠘⣷⣁⣃⣾⠃⣿⣐⢋⣽⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢿⣘⣠⡟⠉⠉⠁⠀⠘⠿⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣶⡄
⣿⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠋
⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⠿⠟⠺⢿⣿⣿⣿⣿⣿⡿⠟⠛⠃
⣿⣿⣿⢎⡿⠏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠛⠛⠡
⣿⣿⣿⣾⡧⢰⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠰⢁
⣿⣿⣿⣿⣿⠂⠀⠀⠀⢈⡹⣧⣭⣻⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣧⡘⣦⡀⠀⠠⠠⣤⣤⣀⣀⡀⠀⢀⣀⡀
⣿⣿⣿⣿⠁⡐⢾⡇⠀⠸⣷⠀⠉⠙⢿⣿⣿⣿⣿⣿⣿⣯⣿⣋⣿⣷⣼⣷⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⣿⣿⣿⣿⣿⣇⠬⣿⠦⠀⠀⠃⣴⣤⢶⠿⢿⠿⢿⣿⣿⣿⣿⣿⡿⣧⣼⢻⡇⠀⠛⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣀
⣿⣿⣿⣿⣿⣧⣀⠀⠐⠒⠂⢰⣯⣾⣿⣦⡛⣿⣷⣍⢫⣙⠻⠿⣷⣿⣿⣋⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⡻⣿⣿⣿⠻⣿⢿⣷⣤⣀
⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣷⣬⠻⣿⣫⣅⣄⠀⠈⠁⠘⢻⡇⠀⠀⢀⡤⠀⠀⠈⠛⠿⣿⣮⡙⢿⣷⣍⠢⡉⠛⠻⢧⣄
⣿⣿⠟⠁⢀⡄⠀⠀⠀⠀⠂⠻⣿⡿⢿⣎⢿⣿⠤⣽⣿⢏⠀⠀⠀⠀⠀⣈⣤⠂⠹⡟⠁⠀⠀⠀⠀⠀⠀⠙⠻⢷⣽⣿⢧⡀⠀⠀⠀⠁⠁
⣿⣽⣶⡖⠉⠀⠀⠤⠀⠀⠀⠀⠈⠀⢛⣿⠇⠀⢸⣿⣧⡌⣦⠰⢀⣤⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠷⣥⣀
⣿⣿⣷⣤⡤⠶⠒⠂⠀⠀⠀⠀⠀⢠⣼⣿⡷⢀⠀⠘⣿⣳⣷⠿⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠓⠄
⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠊⠙⠻⠿⡇⠈⣿⣾⣿⠀⢹⣿⡿⠂
⣿⣿⣿⣿⡿⠿⠆⠀⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⡸⠀⣾⡿⣷
⣿⣿⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⢿⣿⣿⡇⢠⣿⡋⢻
⣶⣤⠆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡠⠣⠘⣸⠻⣇⣀⠛⣦⣼
⣉⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠘⠛⠛⠁⠐⠀⠈⢻⡦⣄⡀
⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢰⣆⣀⣀⡤⢠⣶⣾⣶⡅⠀⠁
⠿⠿⠿⠿⡓⠀⣠⣀⠀⠀⠀⣼⡂⡀⡄⠻⠿⣿⣤⣼⣿⣿⣿⣿⣧⣀⣀
⠒⠒⢒⠀⠀⠀⠉⠉⠀⠀⢠⣿⣿⠮⠀⠀⠀⠉⠀⠉⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠚⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⢀⡄
⠀⠀⢀⠀⠀⠀⠀⣠⣾⡤⠀⠰⠋
⣴⠞⠁⠀⢀⣴⣿⡟⠁
⠉⠀⢀⣴⣿⡿⠋⠀⠀⠠
⣠⣾⣿⣿⣿⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⢤⣀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⠇⠀⠈⠓⠦⣄⣀⡠⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⣤⣄⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣆⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠀⢸⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣠⠞⠋⠉⠉⠛⢦⡀⠀⢀⡔⠋⠉⠙⠀⠘⠇⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣰⢿⠁⠀⠀⠀⠀⠀⠈⣷⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣓⡒⠒⣾⠻⣼⡄⠀⠀⠀⠀⠀⢀⡿⠀⢻⠀⠀⠀⢶⠀⠀⠸⠇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠈⠓⢿⠀⠀⠙⢦⣤⣀⣠⡴⠞⠁⠀⢸⠀⠀⣠⣤⣤⣤⣤⣤⡶⠀⢸⠀⠀⠀⢀⣀⠤⢤⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠈⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⡜⠁⠀⠀⠀⠈⢳⡙⣆⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣰⠏⠙⠦⣄⠙⠦⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡁⠀⠀⠀⠀⠀⢈⡷⠞⢻⠖⣒⣚⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⡤⠞⠋⠀⠀⠀⠈⠳⣄⡀⠉⠓⠒⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⣄⠀⠀⠀⣀⡼⠁⠀⡼⠋⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢤⣈⣙⡿⠟⠋⣠⠴⢾⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⢀⡞⡇⠀⠀⠀⠀⠀⡄⠀⣀⣀⣀⣀⣠⣤⠶⠋⠁⠀⠈⢧⡀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⣽⠃⠀⠀⠀⠀⣼⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⣿⠀⠀⠁⠀⣰⡆⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣧⠏⠀⠀⠀⠀⠿⠁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⡏⡇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⠀⡾⣰⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⢸⠿⡇⠀⠀⠻⠋⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⢸⣄⡇⠀⠀⠀⠀⡀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⡇⠈⠛⠁⠀⠀⠀⠀⣇⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣽⣤⡀⠀⠀⠀⠀⠀⠘⠺⣇⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⠀⠸⡇⠀⠉⠓⠲⠶⠶⠶⠖⠛⠉⠳⣤⣀⠙⠶⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠿⣿⣿⣿⠟⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠛⠋⢁⣀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠀⣤⣉⡛⠃⠀⢀⣀⡈⠙⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠉⠙⣿⣿⡀⠀⠀⠘⠟⠋⠀⣴⢋⣍⡉⣰⡿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠇⠈⢉⣴⣯⡴⠀⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠐⠛⠲⠀⢀⣠⠞⠋⠁⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣀⠀⠀⠀⠈⢻⣿⣿⣦⣤⣴⣶⡿⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⢉⣀⣹⣄⣀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣠⡏⠈⠙⠛⠛⠉⢹⣿⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠿⠗⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠹⣆⣤⣤⠤⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⢿⣿⣿⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣷⠀⠉⢛⣿⢷⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠿⠶⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⣶⣤⣤⣀⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠈⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠁⠈⠀⠀⠀⠈⠂⠐⠊⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⡤⠚⠉⠑⠂⠤⠚⠁⠀⠈⠢⢄⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⡠⠄⠠⢤⡀⠀⠀⢳⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⢱⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⢰⠉⠉⡆⠀⠀⠀⢀⡀⠴⠥⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢄⡀⢀⡠⠊⠀⠀⢠⠁⠀⢠⠖⠉⠑⠢⡀⠈⠲⠖⠃⠀⡠⠊⠁⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⡔⠒⠤⠼⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⡜⠀⠀⠀⡠⠔⠢⢄⠀⠀⠀⢳
⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠙⠢⠤⣀⣀⠤⠔⠚⢣⠀⠀⠀⠙⠤⣀⣠⠔⠁⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⢣⠀⠀⠀⡆
⠀⠀⡠⠊⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢄⣀⣀⡠⠃⠀⠀⢠⠃
⠀⠸⠀⠀⠀⠀⡜⠁⠀⠈⠱⡄⠀⡔⠒⢢⠀⠀⠀⢈⠖⠐⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⡸⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⢣⠀⠀⠀⡆⠀⠀⠀⢀⠇⠀⠣⣤⠜⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠔⠊⠀⠀⠑⠢⠤⡄⣀⡤⠔⠊
⠀⠀⢸⠀⠀⠀⠈⠒⠂⠒⠉⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠸⣀⣀⣀⣀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⡇⠀⠀⡔⠒⢤⠀⠈⢆
⠀⠀⠘⠤⣀⣀⠤⠤⠤⢄⡠⠎⠀⢈⠗⠉⠁⠀⠀⠀⠉⠓⢄⠀⠀⠣⣀⠀⠀⣠⠃⠀⠈⠦⣀⠜⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⠤⠤⢄⠀⠀⠀⢳⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠁⠀⠀⠀⢱⠀⠀⠀⡇⢀⡤⠒⠂⠉⠑⠒⠤⣀⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢄⠀⠀⢀⠜⠀⠀⢀⡷⠁⠀⠀⠀⢀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉⠉⠁⠀⠀⢀⡾⠁⠀⠀⡴⠉⠀⠉⠲⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⣀⠤⠖⠁⢻⠀⠀⠀⡇⠀⠀⠀⢀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠒⠀⠒⠋⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⣷⠀⠀⠀⠀⣿⡏⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣀⣠⡤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⢀⣼⡿⠀⠀⠀⠈⣿⣇⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠶⣤
⠾⠭⠥⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠖⠒⠛⠛⠛⠓⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠁⠂⠤⠤⠄⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣤⣶⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠙⠻⣿⣿⣦⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠘⢿⣿⣿⣶⣤⠀⠀⠈⢳⡀⠀⠀⠑⢄⡀⡀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠾⠿⠿⠿⠿⠿⠿⠿⣿⣷⣦⣄⣈⠙⠻⣿⣷⣤⡀⠀⢳⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣶⣟⢿⠿⠃⠀⠀⢻⡄
⠒⠒⠀⡉⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣦⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠐⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⢺⣻⣿⠿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣰⢿⣯⡘⢿⣿⠺⣉⠛⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣶⣿⣏⢨⣹⣟⣿⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢯⣭⣥⣥⣽⠹⠯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⠂⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠐⠓⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣽⣿⣭⣁⡖⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⣀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⢀⢀⠀⠠⠤⠀⢀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠙⠛⠲⠦⢤⣤⣀⣀⣀⣀⡠⢤⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⢰⣿⣿⣿⠿⠛⠁⠀⣘⣽⣟⣁⣀⠙⣧⠀⠀⠀⠀⠀⠀⢄
⣸⣿⣿⠃⣁⡀⠀⣽⣿⣿⣿⣿⠉⠀⣅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠁
⣿⣿⣿⣿⠟⠀⡈⠻⣿⣿⡿⠷⠄⠀⠛⠂
⣛⣿⣿⡁⡰⣯⡾⢧⣶⣿⡿⠀⠀⠀⠀⠀⠂⣄⢀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⣿⣿⣾⠿⣧⣿⣵⣿⣿⣻⣶⣄⠀⠀⠲⣄⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠩⣾⠇⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⡟⢦⣽⣿⣿⠿⣿⡛⠛⠛⢦⣦⣴⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠢⣷⣄⠀⠀⠀⠀⠈⡆
⣿⣿⣇⣴⣮⠙⢿⡛⠿⢽⠲⣤⣤⣌⣻⠀⠀⠀⠀⠀⢀⠈⢻⣂⠐⠠⠤⡅⠀⠁⢻⠀⠀⠄⠄
⣿⣷⣽⠽⠟⠀⠠⠱⣦⡠⣐⠚⢿⣿⣿⣷⣦⣈⣀⡙⡟⠓⠎⠹⠏⠛⠛⠶⠄⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠛⠻⣿⣿⡷⡆⢀⠀⡤⠽⢾⣤⣨⣷⣻⣿⣿⣿⣿⣷⠀⠼⣷⣶⠛⢻⣛⣲⡶⠀⠉⠀⣩⡶⠀⠀⢀⡀⠀⠀⢠
⠀⢺⣿⣿⣣⠗⠀⠀⠘⢶⣶⣝⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠸⣿⣙⣉⣉⣭⣍⣀⠀⠈⣀⣯⣄⠰⠺⡇⠀⡶⢸⣇
⠀⠀⠈⠻⣿⣷⣷⡀⠉⢾⡿⣿⣿⣤⣿⣿⣿⣿⣿⡿⠆⠀⣰⣿⣿⠿⢟⣋⣥⡭⠀⣀⣠⠯⠋⠀⠀⡆⠀⢀⠰⠃⡄
⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣷⣾⠹⣟⣏⢸⠄⣀⣩⣤⣤⡠⠀⠁⢀⡊⠀⡀⣿⡇
⠀⠀⠀⢠⣿⣿⣿⡿⠿⣷⣿⣿⣿⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⣿⣿⣤⣞⣫⠷⠻⢣⠀⠀⡈⢁⣴⠃⢸⡇
⠀⠀⢠⣿⣿⣿⣿⢛⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⢿⣿⣾⣿⣿⡟⡥⣿⠀⠀⢛⠛⠹⢮⠉⠀⠀⠎⠀⠀⠀⢸⣿⡇⢸⡇
⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢸⣿⣿⣿⡿⣧⠸⡃⠀⠀⣭⣷⣄⡀⠀⠀⠀⠀⢰⣷⣶⣾⣿⣷⠘⡇
⠀⠀⠈⣿⣿⣿⣾⣋⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣹⣾⣧⣁⠢⣍⣙⣟⠻⣄⣠⣆⡀⣡⣿⣿⣿⡿⠿⠂⠈
⠀⠀⠈⣿⣿⣿⣿⣯⣿⣹⣿⣿⣿⣯⣿⣿⣿⣿⠿⣿⢹⣿⣿⣿⣿⣦⣠⣶⠈⣿⣟⣿⢆⣟⣿⣿⣿⣿⣿⡟⡇⠀⠲
⠀⠀⠀⢻⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣭⠭⣯⣿⣿⣿⠌⡍⠀⢻⣿⣦⡀⠂
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡭⢁⣿⠟⠛⠰⠇⠠⣈⣻⡿⠻⠟
⠀⠀⠀⠀⢿⣿⡿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠟⠁⠀⠀⠈⠉⠑⠚⠛⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠛⠛⠛⠓⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣉⡉⠉⠉⠁⣀⣀⣨⣽⡷⠤⠶⠶⠶⠶⠶⠶⠦⠤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⣉⣭⠶⠚⢫⣭⠁⠀⢴⠆⠀⣠⡀⠛⠃⡀⠀⠀⡀⠀⠀⠀⠈⠉⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠛⠉⠀⠴⠀⣀⡀⠀⠰⠆⠀⠀⠉⠀⠀⠀⠉⠀⡞⠀⠀⣰⢪⣍⢳⠀⠀⠀⠀⠈⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣅⠀⠛⠃⠴⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠙⠶⠷⠋⢀⣠⡴⠶⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⣶⣿⣯⣠⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠶⠶⠶⠦⠤⣀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠉⠁⢀⣤⠞
⠀⠀⠀⠀⠀⠀⢠⡾⢋⡿⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡖⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⣿⠔⢸⡇⠀⣠⢖⠚⠉⠁⠀⢀⣠⡤⠶⠒⠚⠛⠛⢯⣡⣄⣀⡴⠾⠶⠶⠶⠶⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠻⣞⣹⡇⠀⢿⡡⣂⡤⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠈⠉⠁⢀⡟⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⠀⣸⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡴⠃⠀⠈⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠶⠒⠋⠀⡀⠘⣦⡼⠓⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢤⠀⠹⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⣈⡛⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⡉⣉⠁⡄⢈⣉⣉⠙⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠉⠉⠀⠇⠀⠉⠁⢠⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⡀⠀⠲⠤⠖⠀⢀⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠟⠛⠫⠤⢤⠤⠝⠛⠻⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⡞⢸⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀⣇⡞⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢷⡀⠀⠈⠳⣄⣀⡤⣤⣀⣀⡤⠟⠀⠀⣰⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⣁⣀⠀⠙⠦⣄⣀⣠⠬⣟⠆⠀⠁⠀⢀⣠⠞⠁⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠉⠓⠲⢤⣍⡙⠒⠶⠶⠶⢒⣊⡭⠴⠖⠚⠋⠉⠉⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣴⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣢⣄⣀⣀⣀⣀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠂⠀⠀⠀⠒⠲⡄⠠⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⠀⠀⠀⠀⠀⢀⣴⡿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠚⠛⠚⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⡂⣀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠨⡟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢉⠙⠀⣽⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣠⢶⣦⡀⢻⡄⠙⢦⠀⠀⣦⠶⠶⠤⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠐⣹⡿⠋
⠀⠀⠀⠀⣤⣀⡀⠀⠘⠉⠑⠚⠁⠀⠈⢷⡀⠃⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⢀⡆⣴⠀⢸⡏⡀
⠀⠀⠀⠀⠈⠉⠻⢷⣾⣿⣴⣦⡄⡀⠀⠈⢿⡿⠃⠀⢀⡀⠈⠛⢿⡑⢦⡀⠀⢀⠈⣿⡜⠀⣤⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀⠁⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠈⠩⣆⠀⠀⠺⢿⣿⣃⠐⠛⠛⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿⣆⢀⠀⠀⠀⠀⠀⣰⣾⣿⣷⡤⠀⠀⠈⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢰⡇⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢯⠔⠓⠀⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈⣧⢹⣿⣿⠙⣿⣿⣿⣿⢻⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⠀⠀⠀⠀⠀⣿⢸⣧⣿⠀⣽⣇⣿⣿⡇⠿⣿⡤⣤⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢤⠀⠀⠀⠀⠀⢸⣿⣶⣿⣆⠙⣿⣿⠾⠳⠔⢐⠁⠈⡄⠆⢀⢀⣠⣶⣞⣽⡏⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠎⠀⠀⠁⠀⢺⣿⣟⣿⣷⣻⡟⠀⠠⠤⠞⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⡔⢿⠟⠻⠟⠙⠿⠉⠁⡀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠠⡄⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⣬⢁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣹⣿⣟⣦⣤⡬⠀⠀⠀⠀⠀⠇⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⣿⣿⣿⣿⡇⠀⠀⠈⠀⡀⠀⠀⡞⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡍⢻⣿⡇⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⡆⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣧⡄⣿⡇⠀⡀⠸⠀⠀⠀⡎⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠙⡃⣿⣿⢿⣿⡁⢰⠁⣼⠃⠀⠀⠉⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠐⣷⣿⣿⢹⣿⠇⣀⢰⡇⠀⠀⠀⠀⣠⠤⢴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢀⣤⣹⢿⣿⣿⣿⠆⣿⠼⠃⣀⠠⠔⠂⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣸⡜⣿⣿⣿⢻⣿⣿⣶⡿⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠙⠷⠲⠶⠶⠟⠉⠁⠚⢿⣿⣿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡁⠀⠈⣧⠀⠀⠀⣴⣄⠀⠀⠀⣼⠁⠀⢈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⣽⣶⠟⠁⠀⠀⣰⣿⣿⣦⠀⠀⠈⠻⣶⣯⠾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⢹⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠛⠹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⢤⣻⣷⣄⠀⠀⠀⠀⢀⣼⣏⠤⠴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠄⠀⠉⠉⠓⠦⢴⣚⡍⠉⠀⠒⢉⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣦⣤⣀⡑⠂⠈⠑⠂⠉⠓⠲⠿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢧⡠⢀⣩⣿⣷⣶⣤⣄⡀⠠⣀⠒⡴⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣿⡿⠟⠛⠉⠀⠈⠉⠛⠷⢶⣿⣣⠞

⠀⢀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡖⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣤⣌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡍⣿⣷⣤⣀⡀⠀⠀⣠⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⣴⠚⣻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⣸⣿⣷⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⣀⣿⣿⣿⣆
⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⢸⣇⣀⣽⣿⣿⣿⣿⣿⣿⣿⡿⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠻⠿⢿⣿⣏⢀⣼⣁⣀⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⣺⡇⠀⠀⠀⠀⠀⠀⠀⣴⢏⣸⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⡟
⠀⢀⡴⢶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣜⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⠟⠛⠁
⢰⣯⣘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣶⣤⡀
⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣆⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⣹⣿⣿⣿⣷⣦⣸⣿⣿⣿
⠀⠻⢿⣿⣿⣿⠟⠁⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣀⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣤⣤⣤⣶⣶⣿⣿⡿⠟⠉⠀⠀⠘⠿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠁⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉⠉⠛⠿⢿⣿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣿⣷⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠸⣷⣿⣾⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣻⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠿⠟⢹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⡿
⠀⠀⠀⠀⠀⠀⣸⡇⠐⢛⡓⠲⠀⠀⠀⠴⢒⣛⠒⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠈⣉⡓⠦⠀⠀⠀⠔⢊⡉⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠫⠛⠁⠀⠀⠀⠀⠻⠙⠃⠀⣃⠀⠀⢀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⡀⠘⠫⠛⠀⠀⠀⠀⠀⠻⠝⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⡄⠀⠀⠀⣀⠀⣀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣥⡀⠀⠛⢕⣒⣪⠟⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⠀⠄⠀⠀⠀⠠⠔⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡤⢞⡟⢿⠳⣄⡀⠀⠀⠀⠀⢀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡜⠀⠈⢇⠈⠙⣦⡀⠀⠀⠈⢳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠼⢇⡀⠀⡞⢉⡭⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⠁⠀⠀⠙⢺⠟⠁⠀⢸⣇⣠⠴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⡆⠀⠀⠀⢸⡄⠀⣠⡞⠋⠀⠀⡏⢳⡀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡇⠀⣿⠈⠢⣀⡰⠋⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢳⡀⠀⠀⣇⠀⡏⠀⠀⢸⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡾⢫⣹⢷⠀⠀⢹⠀⡇⠀⠀⣼⠀⠀⣰⠃⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⣧⢤⡇⠘⣧⣀⣸⣸⡇⢀⣠⢿⣀⣴⡧⣤⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡙⣄⡿⢹⡉⠻⣷⢻⡀⢸⣙⣯⠔⢁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣿⡏⠉⢱⠋⣿⠀⡷⠋⣰⠿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣄⣿⠀⡼⣰⡇⢰⢃⣴⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠳⠷⠛⠳⠾⠞⠛⠋

⠀⠀⠀⠴⠶⣶⠀⠀⠠⢤⣄⡀⠀⠀⣀⠀⠀⠀⣀⣀⣄⣠⣤⣤⣶⣤⣤⣤⣤⣤⣤⠖
⠀⠀⠀⠀⠀⠑⠲⢦⢀⣀⠈⠙⠳⠦⡿⣿⣶⣶⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀⢀⡀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣬⠤⣜⡛⠛⡷⣈⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣷⣾⣴⣿⣷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣬⣿⠿⣿⣿⣿⣿⣿⡟⠋⣩⢗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣉⣻⣿⣯⣿⣹⣯⣄⣸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⢿⣯⣭⣽⠟⣿⣿⣿⣿⣿⣿⣿⡟⠰⣾⣿⣿⣿⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠻⣿⣿⣿⣿⣿⣿⣽⡾⣋⣀⣌⣻⡟⢻⢿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠻⣿⣿⣎⢿⣿⣏⠙⠀⠻⠇⠛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠗⠀⠀⢈⣷⡿⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠹⢟⢿⡏⣧⡀⠀⢺⡅⠈⠁⢀⣨⣦⣿⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠸⡿⠇⠈⢂⡈⠈⣤⣶⣂⠀⡙⠿⢿⣿⣷⣴⣬⣿⣦⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣅⠀⠀⠉⣟⣻⣿⣿⣿⣿⢻⣇⠀⠀⣿⣿⣯⣽⣦⡴⢶⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⣶⣶⣦⣷⣼⡆⠀⢌⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⢹⣿⣿⢿⣵⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⠄⠉⣠⣆⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⣿⣍⣯⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢤⣤⣴⠟⣛⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣥⣽⣷⣾⣯⣉⣄⠽⣿⡿⢿⡿⠶⣋⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⠖⢻⣷⣾⣿⠟⣻⣭⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⡴⠞⠿