Garbage can Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢰⣶⡄⠀⠀⢠⣶⡆⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠒⠒⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣖⠉⠉⠉⠉⠁⠀⠀⠈⠉⢉⠽⠄⠠⡃⠠⠦⡌⠙⣧⠂
⠀⠀⠀⠀⠀⠀⡄⣾⢿⡩⡐⠂⠤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠓⠒⠻⢬⠁⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⢉⠦⠅⡀⠬⢀⠀⠀⠀⠉⠒⠒⠠⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⡏⠒⠒⠒⠒⠒⢊⠡⠒⠀⠠⠀⣀⠀⠀⠀⠈⠉⠉⠒⠒⠂⠤⠄⠀⠀⠀⠀⣠⣤⠇
⠀⠀⠀⠀⠀⠀⡇⠀⢀⢀⠤⠾⠭⣍⡓⣄⠈⠁⠀⠀⠡⠤⢐⣒⣀⠀⠀⠀⠀⣀⣀⡈⠉⠛⠛⣿⠆
⠀⠀⠀⠀⠀⠀⡇⡔⡕⠸⠿⡿⢷⣯⡑⣾⠀⠀⢠⠖⠉⢀⣀⠀⣏⡈⠉⠑⡖⠒⠶⡀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⡷⡄⢄⣀⢀⡁⢀⡠⢃⣿⠀⠀⠶⠀⠘⠁⠀⣷⠇⢹⠀⢰⠃⠀⠀⢸⡆⠂
⠀⠀⠀⠀⠀⢸⡇⠙⠒⠮⢭⠭⠵⠒⠁⡇⠀⠀⡄⠀⠀⠀⠀⡇⠀⠈⢹⣸⠀⠀⢀⡞⡸
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢀⡇⠀⢀⠏⠁⠀⢠⡞⢀⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡞⠀⠀⠀⢠⡇⠀⢰⠇⠀⠀⢸⢸⠀⠀⡼⠀⠀⠀⣿⠀⣸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡜⢸⠀⠀⡇⠀⠀⡜⡟⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡀⢸⠀⠀⢸⠀⠀⠀⡇⡟⠀⣼⠁⠀⢰⢠⡇⢸⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠀⢠⠃⡞⠀⠀⡌⠀⠀⢰⠁⡇⠃⡇⠀⢠⠇⣸⠀⡞
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⡞⢠⡇⠀⠀⡇⠀⠀⡞⢸⠁⢰⠇⢀⠞⢀⡇⢠⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⢰⠁⢸⠀⠀⢀⡇⠀⡼⢁⡇⠀⢸⠖⠋⠀⣼⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢺⣠⠇⠀⡿⠠⠎⠀⡷⠊⠀⡸⠀⠀⠈⢧⣀⡴⠃⠀⢸
⠀⠀⠀⠀⠀⢸⠠⢄⡀⠀⠓⠒⠚⠁⠀⠀⠀⠙⠲⠖⠁⠀⠀⠀⠀⠀⠀⢀⡠⡟
⠀⠀⠀⠀⠀⠈⠒⠢⠤⢭⣑⡒⠒⠒⠂⠀⠤⠤⠤⠤⠐⠒⢒⣒⣂⣉⠭⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠄⠠⠄⠉⠍⠉⠃⠧⠠⠤⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣀⠁⠀⠀⠐⠀⠠⠊⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⢁⡐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠐⠀⡀⠀⠀⠨⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠀⠀⠀⠀⠀⢰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠠⠤⠤⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠠⠤⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⣀⠀⠀⢘⠀⠀⠊⠁⡆⠀⠰⠀⠀⠀⠀⠂⠉⡆⠀⠈⠀⢀⢀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠇⢃⠑⢨⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠐⢁⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢸⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠘⠀⢸⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⢸⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡂⠄⢀⠀⠐⠠⠂⠀⠀⠀⠠⠀⠀⠀⠔⠀⣀⠠⠐⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢁⠂⠀⠀⢀⣀⠒⠒⠀⠐⠒⢂⡀⠀⠡⠐⢂⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠀⠤⠤⠠⠠⠄⠀⠐⠂⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣿⢛⣉⣉⣡⣤⡍⢻⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠞⠛⠛⠋⠉⣽⠟⣁⡼⠉⠉⠉⠙⠧⣿⢹⣯⠉⠉⠙⠛⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠒⠒⠒⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣿⢻⡀⠉⠛⠻⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠴⠶⠾⠛⠋⠁⢀⡠⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣦⣍⣓⠲⠤⣄⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⡠⠀⢀⣀⣭⡴⠿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣏⠀⠛⠻⠿⠶⠒⠶⣯⣭⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠩⠉⠉⠿⠆⠀⠐⠛⠙⢿⡉⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⠶⠤⠶⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⣦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢰⡀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠆⠀⠀⡏⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⡇⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣇⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣼⠀⠀⢠⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⣿⠀⠀⣷⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⣧⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡄⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⠇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⠀⢰⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⢿⡆⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⣷⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⢸⡇⠀⢰⣿⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣼⡇⠀⢸⡏⠀⢀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⢸⡏⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣿⡇⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣿⠇⠀⢸⡇⠀⢸⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣷⣤⣄⣸⣇⣀⣀⣸⣿⣀⣀⣿⣤⣤⣼⣷⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣉⣉⣉⣉⣉⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠧⠼⠥⠤⠤⠤⠤⠿⠤⠧⠤⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣉⠤⠒⠀⣀⡤⠂⠀⢀⡴⠂⠀⠀⠀⠀⠢⡀⠀⠐⠦⣀⠀⠐⠢⢉⡑⠂⠄⡀
⠀⠀⠀⠀⠀⣀⣤⠖⠋⠡⠔⠂⠉⠀⠀⠴⠊⠁⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⠢⡄⠀⠀⠁⠒⠈⠉⠒⢦⣄⡀
⠀⠀⠀⠀⣶⣋⣉⡉⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠛⠛⠛⠉⠉⢉⣉⣈⣳⠆
⠀⠀⠀⠀⠀⢀⣯⣈⣉⣉⣉⣉⣉⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⣉⣉⣉⣉⣉⣁⣨⡇
⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⡀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⣍⠀⣠⠭⠭⣉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⡉⠉⠉⠉⠉⢉⡩⠭⢤⡀⢨⠁
⢀⡤⢤⣀⡀⠀⢸⠀⡇⠀⠀⠈⠆⠀⠀⢰⠉⠈⠉⢳⠀⠀⠀⢰⠊⠉⠙⢦⠀⠀⠀⢰⠉⠁⠈⡇⠀⠀⠀⠏⠀⠀⢨⡇⢸⠀⠀⣀⡠⠤⣄
⡇⢀⡤⢤⡈⠓⣾⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⡇⢸⠖⠋⣠⠤⣄
⢧⠈⣇⠀⠈⠳⣿⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠸⠇⢸⡶⠋⠀⢠⠏⢠
⠈⢦⠈⠣⡀⠀⠸⠀⣿⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠸⠀⠀⡠⠋⢠⠎
⠀⠈⠳⣄⠈⠢⣴⠀⣟⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⢰⡤⠊⢀⡴⠃
⠀⠀⠀⠈⠑⠦⣀⡳⢡⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⢰⣃⡠⠖⠁
⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠻⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⣼⠀⢙
⠀⠀⠀⠀⠀⠀⠘⡀⢸⠀⠀⠠⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⣰⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢹⠀⡎
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢰⠁⠀⠀⠀⡇⠀⠀⡇⠀⣇
⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠇⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⡄⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⢡⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢽⠀⢇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⡾⢤⣈⠓⠚⠁⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠑⠒⢃⣠⠾⡆
⠀⠀⠀⠀⠀⠀⠀⢣⢄⡈⠙⠒⠤⣀⡀⠀⠈⠒⠒⠊⠀⠀⠀⠸⣇⠀⢀⡇⠀⠀⠀⠘⠒⠒⠋⠀⢀⣀⠤⠔⠊⠁⣀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡈⠑⠲⢤⣄⣈⠉⠓⠒⠶⠦⠤⢤⣤⣤⣬⣭⣥⣤⣤⣤⠤⠤⠶⠒⠒⠉⢉⣀⡤⠶⠚⠉⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠉⠉⠓⠒⠢⠤⠤⠤⢄⣀⣀⣀⣀⣀⡤⠤⠤⠤⠔⠒⠚⠉⠉⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠐⠒⠊⠉⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠈⠉⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠁⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣀⠤⠀⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠀⠀⠄⣀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠪⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠕⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠈⠁⠐⠒⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠐⠒⠂⠈⠁⠀⠀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠉⢓⠂⠀⠀⡤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢤⠄⠀⠐⠚⠉⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⢠⠀⠀⠀⠃⠀⠈⠈⡏⠉⠉⠉⠉⠁⠀⢸⠀⠀⠀⡀⠀⠀⠀⡃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣈⠑⠂⠀⠠⠄⢀⣀⣨⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣄⣀⡀⠠⠄⠀⠐⠈⣁⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢉⠁⠂⠀⠄⠠⠤⢀⣈⣉⣉⣉⣉⣉⣉⣉⣉⠁⣀⠠⠄⠠⠄⠒⠀⠉⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠃⠀⠀⢠⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣉⠑⠂⠠⠸⠄⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⠠⠤⠀⠒⠊⣉⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠙⠀⠒⠠⠄⠤⠄⣀⢉⣉⣉⣉⣉⣉⣉⡉⢀⠠⠄⠠⠄⠐⠀⠏⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠠⢄⡀⠀⠁⠀⠀⠇⠀⠀⠠⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⢀⡠⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⠙⠀⠀⠂⠠⠤⠼⠤⠄⠤⠤⠄⠼⠀⠀⠛⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠒⠒⠒⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⠁⠽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⢛⣒⣒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣥⣤⣴⣶⣾⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡿⠛⠛⢋⣤⣿⡟⢉⠀⠀⠙⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡿⣿⡿⠛⡻⠟⠉⠀⠀⠁⣹⣯⣿⡿⠿⢦⣤⠀⣠⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡶⠾⠷⠈⠀⠀⠀⠀⠠⢞⡋⠉⠁⠀⠀⠀⠀⠛⢛⣋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣴⡶⠚⢻⣆⠈⠀⠀⠀⢀⡼⢤⣒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⠿⣿⡶⠖⠶⠖⠒⠒⢿⣦⠀⢀⣾⡿⠛⠬⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣟⣻⢻⣿⣿⣿⡷⠀⠀⠀⢀⠀⠈⣿⣷⣼⣇⠀⣤⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⢿⣷⠛⢷⡄⠻⣧⠘⠹⣷⠋⣿⡆⣽⡟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣽⣿⣿⣿⣿⡟⣿⡀⢸⡇⠀⣿⠀⠀⣿⠀⣿⠃⣽⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⣿⠀⠀⣿⠀⣿⠂⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⣿⠀⢀⡏⠀⣿⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⢸⡇⠀⣿⠀⢸⡇⢰⣿⢸⣯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢈⣿⠀⣿⡀⢸⡇⢸⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⢷⣼⣿⣿⣿⣿⣿⣯⣿⡍⣿⠀⢸⡇⢸⣧⢸⣿⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⢸⡇⢀⣿⢸⣯⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⢫⡿⣻⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡆⠈⡇⠈⣿⢸⡗⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠊⣴⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⡇⠀⠁⠀⠟⢸⡧⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣿⣿⣿⣿⣿⣿⣛⣻⡿⠿⠸⠃⢠⡄⣀⣙⣨⡥⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣽⣿⣿⣿⡟⣿⣿⣿⣿⠿⠀⠀⠀⢰⣧⠈⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣟⣿⣿⣿⣿⣿⣆⡀⠀⠀⣸⣿⣤⣼⡷⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣤⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⠶⠶⠦⢤⣤⣤⠶⠛⠛⠙⠉⠛⠳⠶⣤⣤⣀⣀⣴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠘⣧⠀⠀⠸⠋⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⠀⠀⢹⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣃⠀⠳⢦⣄⠈⢀⣀⠀⣠⣠⣠⣬⣧⠀⠀⠀⠀⠀⠀⢀⠀⢀⣼⠃⠀⠀⣼⡿⢻⡄⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠸⣦⣈⠙⠂⠀⠙⣶⠟⣩⡿⠋⠉⠉⣧⠉⠙⠻⣶⣤⣤⣤⣄⣰⣟⣁⡀⢀⠦⠟⠀⠈⢻⣦⣤⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣠⡿⠋⠛⠳⢦⣿⠀⠻⣆⠈⠳⣄⠈⢳⠀⢰⡏⠈⠓⠦⣌⠻⢭⣍⠙⢿⡤⡄⠀⢀⡾⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠲⡄⠀⡾⠋⠀⠀⠀⠀⠀⣘⣷⡞⠋⠛⠳⠦⣤⣤⣤⣾⣧⣤⣄⣤⣤⣤⣤⣿⣤⣬⣿⠶⠶⠾⡇⠀⠀⠃⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⣴⠆⠀⠀⠀⢀⡾⠋⠀⠻⠆⣤⠀⠀⠀⠀⠀⠀⣼⠃⠉⠛⠛⠛⠲⡄⠀⠀⠀⠀⣀⡀⢻⡄⠀⠀⠀⠀⣀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡶⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠙⢧⡀⠀⠠⠀⡄⠀⠀⠀⠀⢹⡆⠀⠐⠡⠂⣠⠀⠀⠀⠀⠀⠄⠀⠘⣧⠀⠀⢀⡀⠀⠀⠀⠰⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⢸⡇⠀⠀⣁⣀⣬⣷⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⠾⣧⠀⠀⣀⣤⣤⣤⣀⣿⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢿⡷⠞⠋⠉⠀⠀⠻⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⡴⠞⠁⠀⠘⠓⠛⠉⠀⠀⠀⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠓⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢠⣟⠀⠀⠛⠛⠳⠶⣄⠀⠀⠀⠀⢻⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡇
⠀⠀⠀⣿⠣⠁⠀⠀⠀⠃⠀⢹⡆⠀⠀⠀⠘⢿⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠁
⠀⠀⠀⠸⢦⣄⡀⠲⠄⠀⠀⣾⠇⠀⠀⠀⠀⠈⠛⢮⣝⠶⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢛⣩⠾⠋⠀⢀⣤⠶⢶⠖⠚⠛⣶
⠀⠀⠀⠀⠀⠈⠙⢦⣤⣤⠾⠋⠀⠀⣀⣤⡀⠀⠀⠀⠈⠛⠲⢦⣭⣍⣉⣙⣛⠛⠛⠛⣛⣛⣩⣥⠴⠞⠋⠁⠀⠀⢰⡏⢹⡀⠘⠀⠠⠄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠀⢻⣤⣤⣤⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢡⣆⣤⠶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⡀⠐⣄⠻⡀⠀⠟⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠻⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡛⢦⣄⣀⣀⠀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣬⣭⣭⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠯⢭⣉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⡏⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠤⢄⣀⡼⠁⡭⢦⠀⠀⠀⠀⣘⡟⠢⠏⢱⠀⡘⠀⣼⠇⡞⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠸⡀⠀⣠⣾⠉⠷⡄⠀⢸⣀⡃⣀⣿⡜⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠚⣄⠀⠀⢸⣀⣠⣤⣧⠖⠳⣜⠦⠀⠉⣵⠾⡉⠁⠹⣿⣴⣄⡉⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠒⠄⠈⠷⢤⣾⠿⠗⠚⢹⠀⠀⠀⠀⢀⡜⠁⠀⢧⢀⣘⡑⠁⢀⡬⢷⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⡤⠤⣄⣀⠄⠀⢘⣆⣀⡀⣀⣧⣀⣀⠀⠹⡃⠀⠀⠈⠉⠀⢉⣉⡿⠤⡏⠀⠓⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠿⠀⠠⠋⡁⠀⣠⣤⣾⣾⣋⣉⣉⣋⣉⣉⣩⠭⠭⠤⠒⠒⠋⠙⢳⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⣀⠀⠀⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄⢴⣲⠶⢸⢳⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣄⡀⠀⠈⠉⠒⠁⠀⠀⢰⣶⣶⠶⢸⣷⢛⣫⢹⠀⡎⣦⣼⠚⣎⣻⣯⡻⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⣄⡈⠙⠟⣟⣷⣒⠀⠀⠀⠰⣿⠀⠸⡿⠛⠓⠮⠖⠛⠁⠀⠙⠋⠉⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠙⠒⠋⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠈⢻⠐⠀⠈⠉⠉⢲⠀⠀⠀⠀⠈⠉⠉⠑⡆⠀⠀⠈⠉⠉⢩⠀⡃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⢱⠄⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠃⠀⡞⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠓⢦⢸⠤⢄⢸⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠁⠀⠳⠲⡜⢾⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⠈⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠤⠦⡀⠀⢀⠀⡇⠀⠉⠢⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⢸⠀⠘⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⣠⠚⠉⠙⠢⠄⠉⠛⠛⠛⠆⠈⠀⢰⡀⠀⠀⢀⣙⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⡟⠉⠉⠉⠉⠉⢹⠳⢖⠛⠛⠒
⠀⠀⠀⠀⠺⣀⣀⣾⣭⡑⠲⠤⠤⠖⠒⠦⣀⢸⣹⢹⠋⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡷⢤⡴⢧⣤⠤⠰⠲⠒⠧⣀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⡜⠙⠂⠀⠀⠀⠀⣄⠀⠀⠀⠈⠹⣿⣸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⢿⡇⢬⣀⡀⠀⠉⣹⠶⠲⣞⢙⠗⠒⠤⢭⣀
⠀⢀⠤⠴⠚⢠⠦⢄⡚⠄⠀⠀⠉⠦⡀⠐⠋⠠⠃⢹⠀⠠⠤⠤⠞⠀⠀⠀⢀⣀⣀⣀⣸⠸⠀⠀⡠⠤⠖⠃⣸⡗⠒⠤⢌⣉⠙⠁⠀⠘⠉⠙⠓⠢⣄⡀
⣏⣁⣀⣜⠉⠁⠀⣈⠷⠚⢆⠀⠀⣀⣤⣀⡀⠀⠀⠾⢿⠟⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⠈⠉⠙⠚⠋⠉⠉⠓⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⣴⣯⣭⡭⣿⣭⣽⣯⣭⣽⣦⡄⠀⢾⣿⣿⣿⣿⣯⣭⣭⣭⣭⣭⣭⣽⣧
⠀⠀⠀⠀⠀⠀⠀⢳⡖⠒⣶⠒⠒⠒⢶⠖⠒⡾⠃⠀⠈⢳⣷⡶⠒⢲⡖⠒⠒⠲⡶⠒⢲⡞
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠿⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⢹⡇⠀⠸⠇⠀⠀⠀⠇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣄⣀⠀⠀⢠⡇⠀⠀⠀⠀⠘⣗⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⡝⠁⢛⣥⠀⢸⡇⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠹⣶⠄⣶⠟⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢸⡏⣿⡀⠀⠀⠀⠀⠀⠀⣿⡏⡇⠀⠀⠀⢠⣞⡽⢯⢳⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣇⡿⣿⣄⣧⣸⣄⣧⣸⠿⣇⡇⠀⠀⠀⠈⢧⣓⣫⣾⣄⣱⣀⣧⣸⡟




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢄⡀⣀⣀⣠⣤⣤⣴⣶⣶⢿⣿⣾⣿⣶⣷⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢫⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⠟⣆⣨⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⡟⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣼⣯⡿⣿⣿⠟⣽⣿⣿⢟⣿⣿⣿⣟⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣛⣻⣽⢿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣴⣿⣷⡆⣾⣯⣯⣍⣸⣿⣿⣻⣙⣿⣏⣫⣩⢻⣿⣭⣭⡬⣿⣶⣾⣿⡿⢿⡿⢁⣩⣿⡇
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⢿⣿⣿⣿⣼⣿⣿⣿⣷⠾⠿⠾⠿⠶⢛⣟⣻⣭⣥⡟⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡂⠐⠀⢀⣘⣿⣿⣿⣿⡿⢿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⢹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⣽⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠹⣷⠀⢠⠐⢶⡄⠀⠀⣿⡇⠀⢀⣿⡌⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠀⣿⠀⠘⠀⢸⠀⠀⠀⣿⡇⠀⢸⣿⠃⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⣿⣿⢸⣿⣿⡇⣿⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⠈⣿⢘⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⡄⣿⣿⡇⣿⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠀⣿⡇⠀⢸⣿⢸⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⣿⣿⡇⣿⣿⣇⢻⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⢀⣿⡇⠀⢸⣏⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢻⣿⡇⣿⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢼⠀⠀⢸⣿⡇⠀⢸⡏⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⡇⣿⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⢸⡇⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢸⣿⣧⢻⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⣸⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⣿⣿⢸⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⠸⣿⠀⠀⣿⡇⣻⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⢸⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢸⠀⠀⢰⣿⠀⠀⣿⠃⣸⣇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣿⢸⣿⣿⢸⣿⣿⣿⠀⣿⠀⠀⠀⢿⠀⠀⢸⣿⠀⠀⣿⠠⢻⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣿⣿⣼⣿⣿⠸⣿⣿⣿⠀⣿⠀⠀⠀⢻⠀⠀⢸⡿⠀⠀⣿⢠⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⣿⡏⣿⣿⡄⣿⣿⣿⠀⣿⠀⠀⠀⣾⠀⠀⣸⡇⠀⢰⣿⠸⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⡇⣿⣿⡇⣿⣿⣿⡀⣿⠀⠀⠀⡇⠀⠀⢿⡇⠀⢸⡇⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⢻⡇⠀⢸⡇⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⡇⣿⣿⡇⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⢸⡇⠀⢸⡇⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿⣿⢿⣿⡇⣿⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⢹⡇⠀⣸⠇⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⣻⣾⣿⣧⣻⣿⣿⡇⣿⠀⠀⠀⡇⠀⠀⣸⣃⣀⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣟⣃⡘⡛⠓⠀⡟⢚⣉⣻⣭⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣧⣀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⢀⣀⡤⠤⠶⢖⣚⣿⡿⠿⣿⠷⠶⠲⢺⠒⡳⢖⠿⣿⡿⠛⠓⠶⠶⠤⣄⣀
⠀⠀⢀⣼⠭⠒⠀⠐⠉⠐⠈⠀⠂⠀⠀⠀⠔⠀⠸⠀⠘⣆⠁⠢⡈⠓⠬⣐⠢⢌⣐⠂⠍⢙⣶⡀
⠀⣴⠘⡟⠛⠷⢦⣤⣄⣀⣀⡀⠈⠀⠠⠂⠀⠀⢰⠀⠀⠈⢆⠀⠈⠢⣄⠀⣑⣢⣠⣥⡶⠾⣿⠇⣧
⠀⢿⠙⠒⠦⢤⣄⣀⡈⠉⠉⠛⠛⠛⠻⠶⠶⠶⠾⠶⠶⠶⠾⠷⠖⠛⠛⠛⠉⠉⣁⣀⣤⡽⠶⠞⣛⣦
⠀⠈⠛⣶⣤⣤⣀⡈⠉⠉⠓⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠶⠒⠚⠛⠋⠉⣁⣠⣤⡴⠟⠟⠃
⠀⠀⠀⢹⠀⠀⠁⠉⠙⠛⠒⣾⣭⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠒⠛⠋⠋⢿⢿⡇
⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾
⠀⠀⠀⠀⡏⢸⠃⣠⠤⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠤⡔⢸⡏⣿
⠀⠀⠀⠀⡇⢸⠀⣿⠀⢹⡇⠈⢰⡏⠁⣀⡞⠋⣄⡰⠋⢡⣴⠋⠹⣼⠃⢸⡏⢸⡇⢸⢰⡇
⠀⠀⠀⠀⢓⢸⡇⢸⠀⢸⡇⠀⢿⠇⠀⣿⠀⠀⣻⡇⠀⠈⣿⠀⠀⣿⠀⢸⡇⢠⡇⢸⢨⠇
⠀⠀⠀⠀⢸⠘⡇⢸⡇⢸⣇⠀⣾⡆⠀⡿⠀⠀⢹⡇⠀⢠⣿⠀⠀⣿⠀⢸⡇⢸⠀⣿⢸
⠀⠀⠀⠀⠸⠀⡇⢸⡇⢸⡏⠀⣸⠇⠀⣿⡄⠀⢸⡇⠀⢸⣿⠀⠀⡟⠀⣾⠃⢸⠀⡏⠈
⠀⠀⠀⠀⠀⡇⣧⢸⡇⠸⡇⠀⢹⡆⠀⣿⡇⠀⢺⣇⠀⢰⣿⠀⢰⠃⠀⣼⠀⣿⠀⡇⡴
⠀⠀⠀⠀⠀⡇⢻⠈⣧⢠⡇⠀⢸⡇⠀⢹⡇⠀⣸⡇⠀⠸⣿⠀⢸⡇⠀⣿⠀⣿⢀⢷⡇
⠀⠀⠀⠀⠀⠁⢸⠀⡇⠈⣿⠀⠸⡅⠀⣸⠁⠀⣸⡇⠀⢀⡏⠀⢸⡇⠀⡿⠀⡟⢸⢸⡇
⠀⠀⠀⠀⠀⢸⢸⡇⣿⠀⣿⠀⢸⡇⠀⣹⡄⠀⣸⡇⠀⣼⡇⠀⢸⡃⢰⡇⢠⡇⢸⢸⠁
⠀⠀⠀⠀⠀⢸⡘⡇⣿⠀⣿⠀⢠⡇⠀⢿⡇⠀⢨⡇⠀⢿⡇⠀⣾⡁⢸⡇⢸⡇⡿⣸
⠀⠀⠀⠀⠀⢰⡆⡇⢹⠀⣿⠄⢠⡇⠀⢸⡇⠀⢼⡇⠀⣾⡇⠀⣿⠁⢸⡇⢸⠁⡇⡟
⠀⠀⠀⠀⠀⠈⡇⡷⢸⡀⣿⡄⢸⣧⠀⢸⡇⠀⢰⣷⠀⣿⡇⠀⣿⠀⢸⠃⢾⢠⡇⡇
⠀⠀⠀⠀⠀⠀⡇⣿⢸⡅⢹⡇⠸⣧⠀⢸⡇⠀⢹⠇⠀⢹⡇⠀⣿⠀⣿⠀⣼⢸⢷⡇
⠀⠀⠀⠀⠀⠀⡇⢹⢸⡇⢸⡇⠠⣿⠀⢸⡇⠀⢻⡇⠀⣿⡇⢰⡟⠀⣿⠀⡿⢸⢸⡇
⠀⠀⠀⠀⠀⠀⣿⢸⡀⡇⢸⡇⠀⣿⠀⢸⡇⠀⢻⡇⠀⣿⠇⢸⣧⠀⣿⠀⡇⣼⣼⠁
⠀⠀⠀⠀⠀⠀⠘⣾⡇⡇⢸⡇⠀⣿⠀⢸⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⡟⠐⣇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣉⠘⠧⠀⣿⠀⢸⡇⠀⢺⡇⠀⣿⡀⢸⡧⠸⠟⣈⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠀⠀⢈⣁⠀⠉⠁⢀⡉⠀⠠⠄⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⠤⠤⠤⣤⣤⣀⣀⣀⣀⡤⠤⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣿⣶⣤⣄⣀⠀⠀⠀⠉⠩⠿⣤⣿⠟⠛⢿⣏⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⠿⠍⡀⠈⠂⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠐⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⢤⡴⠒⠻⠷⠶⢮⣥⣴⣄⣠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⢤⣠⣉⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠻⠿⣿⡿⢷⣶⠿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣴⣦⣤⣤⣬⣤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠿⣷⣿⣷⣦⣤⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣤⣼⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠋⠻⠯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠽⠃⠚⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⢰⠀⡄⢲⣦⡀⠀⢂⠄⠠⣄⠰⠀⠠⠀⠤⡄⢀⠆⠠⠐⢦⡑⠀⠀⠛⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠓⠿⠿⣀⣀⣏⣨⠿⠓⣒⣏⠀⠀⢸⡆⢑⡇⠀⠀⢹⠂⢸⡶⠀⠈⡇⠀⠀⠀⣿⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣄⣀⣀⣐⣼⡖⠉⣾⠀⠀⢸⡇⠈⡇⠀⠀⢸⠀⠀⠒⠀⠀⡇⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠸⡏⠀⣿⡇⠀⣿⠀⠀⢸⡇⠀⡅⠀⠀⢸⠀⢀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⡇⠀⠿⡇⠀⢸⠀⠀⢸⡇⠀⡂⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⡇⠀⡇⠀⠀⣸⠀⠘⠀⠀⢀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⡇⠀⡇⠀⠀⡇⠀⢸⠀⠀⢸⡇⠀⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧⢠⡇⠀⠀⡇⠀⢸⠀⠀⢸⡇⠀⠁⠀⠀⢿⠀⢀⠀⠀⢸⠃⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸⡇⠀⠀⢶⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⢻⠀⢸⠀⠀⢸⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠇⠀⠀⢸⠀⠸⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⢈⠀⠀⢸⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠮⠀⠀⢸⠀⠠⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠘⠀⠀⢸⠀⢈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⣆⠀⢰⠿⠀⠀⠂⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠬⠀⠈⢸⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⠀⡀⠀⠀⢸⠀⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡄⠀⠐⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⣷⠀⠀⣼⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠆⢣⡟⠠⠀⡄⠀⢸⡏⠀⠀⠀⠀⡿⠀⠹⠀⡀⠇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣒⣢⠤⠤⣈⣀⡀⠈⠀⠈⠀⠀⠀⠀⠀⠁⣁⣀⣀⣀⡤⠤⣖⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢹⣿⣿⡷⢶⠶⠿⠬⠭⠭⢭⣭⣽⣯⣭⣭⠭⠷⠶⡾⢿⣿⣿⡅⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣇⣻⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣃⣼⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠲⠶⠶⠶⠶⠖⠒⠚⠛⠋⠉⠁


⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠷⣶⣦⣤⣄⣀⡀⠀⠀⠀⣀⣴⣶⠾⠷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⣀⠀⠉⠉⠛⠻⠿⢶⣾⣿⣥⣀⡀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠈⠉⠛⠛⠿⠷⣶⣦⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠷⣶⣦⣤⣄⣀⠀⠉⠙⠛⠻⠿⢶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠈⠉⠙⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣷⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣿⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⣿⠇⠀⢠⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⣷⠀⠀⣿⡇⠀⠀⣿⡇⠀⢠⣿⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⣿⠀⠀⢸⡟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⢸⣿⠀⠀⣾⡇⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⡄⠀⢸⣿⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡿⠀⠀⣿⠃⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢻⡇⠀⢸⣿⠀⠀⣿⡇⠀⢸⡇⠀⢰⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣷⠀⢸⣿⠀⠀⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠘⣿⠀⠀⣿⡇⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠈⡿⠀⠀⢿⠀⠀⢿⠇⠀⢿⠇⠀⢿⠇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡏

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⢀
⠀⠀⠀⠀⠀⡠⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠦⢄⠀⠀⣀⣀⣀⣖⣢⠴⠤⢤⠲⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠸⣄⣀⢀⡀⣀⣀⡀⡀⣀⣀⠀⠀⠀⣀⡀⡀⣀⣀⡀⣀⢀⣀⣸⠀⢸⠉⠉⠉⠉⠉⠀⠄⠠⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡄⠀⢡⠀⠺⠂⢀⠺⠃⠀⠄⠀⠀⠀⠀⢰⠁⢀⡠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠡⡀⠀⠑⠠⠐⠁⠀⠀⠈⠀⠔⠀⠀⠀⢸⣊⠥⠚⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⡐⠠⢄⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡠⠔⣻⠀⠀⠀⠀⠉⠄⢀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⡠⠒⡡⠖⠉⡘⠁⠒⠓⠀⠐⠒⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠤⠭⢁⣈⣁⡁⠀⠀⠀⣰⠀⠀⠈⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣦⠤⠴⠃⠀⠀⣠⡛⠉⢫⡄⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠰⠉⢹⠀⠀⠀⠀⠀⠹⣦⡤⣬⠏⠀⠀⠀⠀⠀⡏⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡀⢀⠍⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢁⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⢻⡄⠀⠘⣿⣷⠶⠶⠶⠶⠾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡁⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⢻⡄⢀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⢿⡜⠂⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣷⡀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣈⣷⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠶⠶⠿⢿⣷
⠀⠀⠀⠀⠐⣿⣧⣤⣤⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⢙⣿⠉⠉⠉⢉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠟
⠀⠀⠀⠀⠀⠈⣿⡟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢈⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠙⣦⣰⡆⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠶⠾⠿⠃⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢈⣿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣾⡁⠀⠀⠀⠀⠀⠀⣠⣾⣀⣠⣤⡾⠃⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠀⠙⢿⡍⠉⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠻⠆⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣀⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣼⣧⣤⣤⣤⣶⣶⣶⡿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠁
⠀⠠
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣿⠿⠳⠶⣿⠁⠆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠯⠉⠀⠀⠀⠉⠀⠀⠀⠀⠛⠛⠃⠀⠈⠉⠉⠿⣫⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠶⠤⠴⠴⠶⠤⠄⠀⠀⠀⠀⠰⠚⠛⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣿⡛⠙⢉⣉⡉⢉⠉⠉⠉⠉⠛⠛⠛⠳⢶⠤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠉⠛⠛⠛⠻⠷⠷⢮⣤⣧⣤⣤⣤⣴⣤⣴⣴⡶⠶⣶⠶⠶⠛⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠙⠛⠲⠦⢄⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣤⣭⣤⡷⣶⠞⣫⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡔⣶⣿⢀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢉⠉⢨⣿⠀⣼⠃⣻⠀⣿⡿⣫⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣦⣍⠉⢋⣩⣤⣴⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢸⠀⢸⡿⠀⣿⠄⡼⠀⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⢀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⢰⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⠃⢠⠀⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣤⠀⠅⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡆⢸⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠬⠀⠀⢠⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⢸⡇⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⡇⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡧⠈⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⢡⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣌⡀⠛⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣀⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠒⠒⠛⠛⠉⠉


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

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠢⡀⠀⠀⠀⠀⠈⠉⠳⢄⠀⠀⠀⠠⠀⡀
⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠈⠏⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⢸⢰⢦⡦⠐⠂⣶⢰⣶⣴⠂⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢸⠀⠈⠸⠞⠳⠰⠆⠛⠸⠻⠹⠆⠇⠈
⠀⠀⠈⡀⠀⠁⠈⠁⢀⣀⣀⠀⠀⠁⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆
⠀⠀⣀⣅⡀⠀⠀⢰⡹⠀⠘⢏⠂⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡇⠀⢸⠀⠀⢺⡀⢀⣀⣰⠇⠀⢸⠀⠀⡇⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠄⢒⠋
⠀⠀⡇⠀⣸⠤⢀⢀⣉⣙⣚⡁⡀⠤⢾⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⣀⣸⢁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣠⡨⣆⡀
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⡴⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢦⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠴⢦
⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠏⠀⠀⠀⠀⢿⡀⢸⠀⡴⠃⡠⠊
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠐⢋⠉⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡝⠀⠉⠀⠘⠓⠉⠉⣱
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠈⢦⠔⠁⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⢀⣘⠛⠯⡍
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⡇⠀⢀⣲⡀⢸⢀⣦⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣠⠴⣊⡤⠚⠉⠉⠉⠈⠓⠤⠋
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡤⠀⠀⢡⡀⠈⠛⠁⡸⡈⠛⠀⢀⠜⠀⠀⠀⠀⠀⠀⢸⡥⠴⣚⡭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠱⡀⠀⠀⠙⠂⠀⠚⠁⠈⠐⠂⠁⠀⠀⡰⠁⠀⠀⠀⣸⠈⠉
⠀⠀⢀⡠⢖⡩⢿⠀⠀⠀⠀⠘⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⡏
⠀⢴⠁⢶⡉⠀⢸⡄⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠑⠦⢌⡑⠺⡇⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠄⠓⡤⣄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⢠⠖⠒⢼⠁⣧⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢈⡵⠒⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠘⠦⡤⠒⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠳⠖⣫⣬⡇⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠐⢾⡆⠀⠀⠀⠀⠀⠀⢸⣧⣄
⠀⠀⠀⠀⠀⢸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⣶⡾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⢸⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⢿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠣⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⠶⠶⠶⠒⠒⠒⠶⠦⠤⠤⡼⠀⠀⡇⠈⢙⠒⠲⠤⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢝⣒⣒⣣⠉⠙⢙⠇⠀⢹⡾⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠺⡗⠪⠔⡨⢉⠓⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠶⠈⠉⠓⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢑⡦⢁⡀⠬⣁⠊⠀⠀⠀⠈⠁⠐⠒⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠳⠤⠤⠤⠥⠤⢬⢝⣒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠒⠶⢬⣍⠀⠒⠩⠍⡐⠂⠠⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠴⠾⣯⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⢒⣏⣉⣉⣙⣳⣦⡈⡇⠀⠀⠀⠀⢀⣩⠉⠒⠂⠤⡤⠄⣀⣀⣒⣒⠒⢒⠒⢒⠒⢀⣉⠭⠞
⠀⠀⠀⠀⠀⠀⠀⣾⢰⢋⠎⠁⠛⢿⠿⠿⠿⢦⢹⡇⠀⠀⠀⡞⠁⢘⢀⡤⢄⠘⣇⣀⠀⠀⢸⡁⠅⠙⠤⡀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⣅⢠⠀⣄⡀⠀⢸⠀⠀⣠⠞⣸⡇⠀⠀⢸⠀⠀⠘⠁⠀⢨⣴⠀⢹⠀⠀⣸⠀⠀⠀⠀⣿⢀⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⠦⣭⣍⣉⣋⣩⠵⠚⢩⡇⠀⠀⢨⠀⠀⠀⠀⡇⢸⡇⠀⠈⢻⡆⡯⠀⠀⠀⢠⠏⡜
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⠀⠇⢸⠀⠀⠀⡼⠳⠃⠀⢀⢠⠏⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⡆⡞⠀⠀⢠⡇⠀⠀⠀⣼⡏⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠀⢸⢰⡇⠀⠀⡾⠀⠀⠀⢰⢿⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⢸⢸⠀⠀⠀⡇⠀⠀⢀⠏⡟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⡿⠀⠀⢸⠃⠀⠀⠀⡏⢸⠀⠀⣼⠁⠀⠀⡜⢠⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢀⡇⢰⡇⠀⠀⢸⠀⠀⠀⢠⠇⣾⢰⠁⡇⠀⠀⣰⠃⣸⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⠀⠀⢸⠁⣸⠀⠀⠀⡟⠀⠀⠀⣼⠀⡟⠀⢸⡇⠀⢠⡏⠀⡏⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⢀⡏⠀⡟⠀⠀⠀⡇⠀⠀⢠⠇⣸⠁⠀⣼⠀⣠⠟⠀⣸⠁⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⣸⠀⢰⡇⠀⠀⢀⡇⠀⢠⠏⢀⡏⠀⠀⣿⠚⠁⠀⢠⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡁⣰⠃⠀⣾⣀⡠⠊⠀⣧⠔⠋⠀⡼⠀⠀⠀⠸⣆⠀⣠⠞⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠐⠂⠻⢥⣤⡤⠏⠀⠀⠀⠀⠹⣤⣀⡴⠃⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⢇⡈⠑⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠴⢒⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⣤⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⡥⠤⠤⠴⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣀⣈⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣤⣠⣤⣠⣤⣠⣤⣠⣤⣠⣤⣠⣤⣠⣤⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠤⣄⠀⢀⡤⢤⠀⠀⣠⠤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢿⠀⢸⡇⢸⠁⠀⡇⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⢸⠀⢸⡃⢸⠁⠀⡇⢸⡇⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⡁⢸⡇⢸⠁⢸⡇⢸⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⡇⢸⡇⢸⠁⢸⠁⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⡇⢸⡇⢸⠁⢸⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣷⠀⡇⢸⡇⢸⡁⣾⠀⡟⠀⢸⠁
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣤⠗⠘⢧⡼⠁⠿⣤⠇⠀⢸
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠋
⣿⣿⣿⣿⣷⣄
⣿⣏⢹⣉⣭⢙⣷⣄
⣿⣿⡟⠟⡛⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣼⣥⣤⣤⣼⣥⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⢶⡆
⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⣸⡇⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠁⠀⣹⣿⡇⠀⢸⣇⣤⡶⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⢻⡇⠀⢸⣿⡇⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣼⡟⠁⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣼⣧⠀⢸⣿⣧⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣧⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠘⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣼⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⠀⢀⣿⣿⣧⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣉⡙⠛⠻⠿⠿⠿⠦⠴⠿⠿⠿⠟⠛⢋⣁⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣶⣶⣶⣶⣶⠶⠾⠿⠛⠋⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⠤⠀⢀⣀⣀⣭⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⠿⠿⣛⣿⠟⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣿⠛⠹⠋⠁⠀⣸⣿⡿⠛⠦⢄⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣥⣄⠀⢠⣬⢥⡀⠀⠀⠀⠈⣙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⡿⢿⠿⠭⠽⠶⢿⡆⠀⣴⠟⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣽⣿⣦⡀⣀⢀⣄⢠⣿⡺⣇⢰⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣍⣻⣿⣿⡾⣇⢸⡆⢹⠀⢸⡆⣿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⢸⡇⢸⠀⢸⠁⣿⢸⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⣿⢸⡇⢸⡄⢸⠀⣿⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏⡇⢸⡇⢸⢨⡟⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣻⣷⣿⣿⣿⣿⣻⡇⣇⢸⡇⢸⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⢾⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⠀⠇⢸⢸⣿⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢪⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠁⠘⢨⠆⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⢿⣿⣿⣿⣿⣽⣝⠀⠀⢀⡄⢶⡂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣾⣿⣿⣇⠀⠀⢸⣇⣨⡵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡻⣿⣷⣦⣄⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⠀⠉⠻⢿⣿⣶⣬⡙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣶⣶⢶⣮⣝⠻⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣦⣌⢻⣿⠿⢛⣱⡶⣹⣿⣷⡄⠉⠻⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠌⠋⠾⠿⠿⠀⠿⠿⠿⠿⠄⠶⠶⠌⢩⣭⡝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⢛⣭⣬⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇⣾⡏⠶⢹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠃⠾⠿⠿⠿⠿⠿⠿⠿⠈⠻⠿⠟⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠮⠰⠉⠉⠈⠩⠄⠥⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⣒⠭⠐⠂⡠⠔⠀⢀⠔⠀⠀⠀⠀⠢⡀⠐⠢⢄⠐⠂⠥⣒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠤⠄⠡⠤⠤⠤⠉⠀⠀⠐⣁⣀⣀⣀⣀⣀⣀⣈⠀⠀⠀⠉⠤⠤⠄⠉⠠⠤⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣇⢀⡒⣒⣒⡒⠒⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠐⢒⣒⣒⠒⢀⣸⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣀⣀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣀⣀⣀⣀⣀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠂⠐⠆⠀⠀⡠⠀⠤⡀⠀⠈⢉⠬⠭⡉⠀⠀⢠⠤⠠⡄⠀⠀⡐⠂⠐⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⡉⡑⠢⡇⢐⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡄⠀⠀⡇⠀⠀⠃⢸⠔⢊⢉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢄⠈⠑⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡄⠸⠊⠁⡠⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠢⡀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⢀⠔⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⠙⣜⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⢡⠋⡡⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠤⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⠀⠡⠤⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣉⠒⠤⢄⡀⠀⠃⠤⠃⠀⠀⠀⡀⢀⠇⠀⠀⠑⠤⠊⠀⣀⠠⠤⠒⣉⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡉⠒⠤⠀⢉⡁⠒⠂⠀⠤⠤⠤⠤⠤⠤⠄⠐⠒⢈⡉⡠⠤⠒⢉⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀⣀⠉⠉⠀⠒⠒⠒⠒⠒⠂⠈⠉⡉⣀⠠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⣀⠀⠀⠀⠀⢶⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣧⣶⠶⣾⣿⠿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⣿⠿⠋⠉⢰⣿⣿⣤⡀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡴⠿⠈⠁⠀⠀⠴⡛⠛⠉⠀⠈⠱⠛⠫⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣾⣟⣙⣆⠀⠀⢀⣴⢶⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡿⣿⣿⣿⠽⠉⠉⠉⠉⠹⣧⣠⠟⢋⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⡐⣦⠸⣧⠘⢿⠛⣷⢸⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿⣿⣿⣿⡇⢸⠀⣿⠀⢸⠁⣿⢸⣇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⢸⡀⣿⠀⢸⠀⣿⣸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⡆⢹⠀⣿⢰⣯⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⣿⣿⣿⣿⣿⢸⡇⢸⠀⣿⢸⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣚⣭⣿⣿⣿⣿⣿⣿⣿⣸⡇⢸⡄⣿⢸⣇⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠡⢲⠿⣿⣻⣿⣿⣿⣿⣿⣿⡧⣧⠈⡃⢹⠸⡿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢘⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠀⠀⠙⡰⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣿⣿⣿⣿⣷⣿⣿⡷⠀⠀⣤⡄⢲⡍⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣇⡀⣀⣸⣇⣼⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⣿⠿⠿⠿⠿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠆⠀⠀⠀⠈⠉⠀⠒⠀⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠝⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢚⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡑⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠂⡔⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠂⠄⣈⠁⠀⠀⠒⠀⠤⠤⠀⣇⣀⡠⠞⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠀⠠⠄⠀⣀⣀⡀⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⡀⠀⠀⠈⠉⠀⠒⠀⠒⠂⠰⠆⠀⠀⠀⠀⢀⡠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠄⠀⠀⣀⡀⠀⡇⣀⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠛⠻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠿⠿⠿⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢓⠈⣷
⠀⠀⠀⠀⠀⠀⣸⡇⢀⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⢠⡿⠀⠐⡂⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣼⣧
⠀⠀⠀⠀⢸⣟⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣠⣤⣽⡇
⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣼⠇
⠀⠀⠀⠀⠀⠙⠛⠛⢻⡟⠛⠛⣿⠛⠋⣿⠋⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⣿⠉⠉⠉⠉⠉⠉⢹⡏⠀⢨⡏⠀⠉⠈⠈⣿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣦⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⡟⠀⠀⠀⠀⠀⠀⠀⠿⠦⠾⠃⠀⠏⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⠀⠀⠀⠰⣿⡗⠒⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⢦⣄
⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⢆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢸⣿⡇⠀⣿
⠀⢀⠀⠀⠀⠀⠀⠀⠹⢦⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⢿⣧⡾⠋
⠀⠈
⠀⠈
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣋⣉⣉⣿⣉⣉⣿⣏⣉⣉⣷⣄⠀⠀⢼⣿⣻⣿⣿⣿⣟⣋⣉⣉⣉⣉⣉⣉⣉⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⠀⠀⠈⢷⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠻⣿⠂⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠙⠀⠀⠀⠀⠘⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠃⠀⠀⠀⠀⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⣶⢦⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣮⠁⠈⢫⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠹⣷⡆⢰⣶⡟⠁⠀⡇⠀⠀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⢤⡀⠀⠀⠀⠀⠀⣿⠦⢤⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣄⠀⡀⢀⡀⢀⠀⢀⣼⣷⢸⡇⠀⠀⠀⠀⣾⢱⡟⢳⣼⡆⢀⠀⢀⡀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⠿⣿⣤⣽⣤⣧⣬⣧⣬⡿⢿⣸⠇⠀⠀⠀⠀⠘⢮⣙⣫⣾⣧⣤⣧⣤⣷⣤⡿⠃





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠖⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠲⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠉⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠈⠙⠳⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠞⠋⠉⢻⡄⠀⠀⠀⠀⡟⠀⠈⢹⡟⢻⠶⢶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣶⠻⣯⣿⠇⣸⠆⠀⠀⠀⢿⡀⠀⠀⢸⡇⠀⠀⠸⣇⠘⠷⠾⠋⣸⠏⠉⠙⠛⠳⠶⣆⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⠘⠷⣤⣤⡴⠏⠀⠀⠀⠀⢸⡇⠀⠀⠈⣧⠀⠀⠀⠙⢦⣤⣤⡾⠋⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠛⠛⠛⠛⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⣶⠶⠶⣤⣀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠙⣧⠀⠀⠙⢧⡀⢀⣀⣠⡾⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠈⠛⠛⠶⠶⠶⠶⠶⠶⠿⣦⠀⠀⠀⠘⣧⠀⠀⠈⢿⣋⣩⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⡀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⢧⣄⡀⠀⠙⠷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠶⠶⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠈⠉⠛⠳⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⢀⣤⡶⠶⠛⠛⠋⠉⠉⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠉⠉⠙⠛⠳⠶⢦⣤⣀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⢿⣁⠀⢀⣀⣠⣤⣤⢴⣾⣟⣉⠉⠉⠉⠉⠉⠉⠉⠛⣷⣄⣀⣀⣀⡀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢠⡾⢻⡏⠻⢦⣀⠀⠀⠀⠉⠛⠿⣭⣄⣀⠀⢸⡇⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠹⡅⠀⠉⠉⠉⠛⣳⣦⡶⠟⠁⠀⠀⠀⣠⠿⡇
⠀⠀⠀⠀⠀⢀⡿⣧⠈⠻⣄⠀⠉⠛⠶⣤⣀⠀⠀⠀⠈⠉⠛⠛⠳⠶⠶⠶⢤⣤⣤⣤⣤⠴⠶⠶⠷⠶⠶⠛⠛⠋⠉⠀⠀⠀⠀⣀⣴⠞⠉⢠⡟⢷
⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⡈⠻⢦⣄⡀⠀⠉⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠛⠉⠀⣠⡴⠋⢀⣾⡇
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠙⠶⣤⣈⠙⠳⢶⣤⣀⡀⠈⠉⠙⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠉⠉⠀⠀⣀⣠⠶⠛⠁⢀⣴⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠶⣄⡀⠀⠉⠛⠶⣤⣀⡉⠙⠛⠶⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠞⠛⠉⢁⣠⡴⠞⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠙⠳⣦⣀⠀⠀⠉⠙⠛⠶⢦⣤⣄⣀⣈⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣀⣀⣠⣤⡴⠶⠛⠋⠁⣀⣠⠴⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⣀⡀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⢀⣀⣠⣤⠶⠛⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠶⢤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣤⣤⠴⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣈⠛⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⢋⣡⠞⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣍⣙⠛⠶⠶⢤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠚⠛⠉⣁⣤⠶⠋⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠤⢤⣤⣤⣤⡤⠴⠶⠚⠋⠉
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⡉⠉⠛⠛⠷⢶⣦⣴⣟⣉⠁⠈⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣦⣤⣀⣈⠉⠙⠛⠻⠶⣶⣽⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⢶⣤⣤⣀⡉⠉⠛⠛⠷⠶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⢶⣦⣤⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡀⠀⠀⣀⠀⠀⣀⡀⠀⢀⡀⠀⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⣿⠀⠀⣿⡇⠀⢸⡇⠀⢸⡟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⠀⠀⣿⠀⠀⣿⡇⠀⣸⡇⠀⢸⡇⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⠀⣿⡀⠀⣿⡇⠀⣿⡇⠀⣼⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⣿⡇⠀⣿⡇⠀⣿⠃⠀⣿⠁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢸⡇⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣇⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⣭⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⢸⡗⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⠀⢸⡇⠀⣿⡇⢀⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠿⠀⠸⠗⠀⠿⠇⠸⠿⠀⠾⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⣀⡀⠁⠒⠀⠐⣒⣒⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣥⣶⣾⣿⣿⣿⣶⡶⢾⣿⡿⠿⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠟⠉⠉⣴⣿⣯⣄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣏⣹⣏⠐⠉⠀⠀⢀⡴⠟⠛⠉⠉⠉⢣⠾⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣶⣶⣆⣀⣰⣖⡺⣦⡀⠀⠀⠀⣠⠤⢕⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣷⠶⠒⠒⠒⠻⣷⡀⢠⡾⠯⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣿⣿⣿⣿⢀⣀⢀⣤⠀⣿⣿⣾⡄⣴⣆⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⣙⣿⣿⣿⣯⣿⡇⢹⡆⢹⡇⠀⣿⠀⣿⢸⡏⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⣿⣧⢸⡇⢸⡇⠀⣿⢀⣿⢸⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣛⣿⢸⡇⢸⡇⠀⡟⢸⣯⢸⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⣿⣸⡇⠀⡇⠀⡇⢸⣯⡼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣿⣿⣿⣿⣿⣿⡶⡇⠀⣇⠀⡇⢸⡧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣫⣽⣿⣿⣿⣿⣿⣿⣿⡇⣷⠀⣿⠀⣷⢸⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠔⣿⢿⢿⣿⣿⣿⣿⣿⣿⣽⣧⣿⠀⢛⠀⣿⢼⣿⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⢡⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⠀⠗⣸⠎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠍⠀⠄⣀⢨⣼⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣏⠀⠀⠘⣿⠀⣻⣐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⣶⣶⣶⡿⠾⠛⠉⠁

⠀⣠⠖⠋⠉⠉⠓⠦⡀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠓⢤⡀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⠒⢄⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠙⠲⣄
⡼⠁⢀⣀⠀⢀⣀⡀⠙⡄⠀⠀⠀⡎⠀⢀⡀⠀⢀⡀⠀⢱⠀⠀⠀⢀⠏⠀⣀⡀⠀⢀⡀⠀⢳⠀⠀⠀⢠⠃⠀⣤⡀⠀⣠⡄⠈
⡇⠀⠁⠈⠁⠈⠀⠁⠀⡇⠀⠀⠸⡀⠀⠉⠁⠀⠈⠁⠀⢀⡇⠀⠀⢸⠀⠀⠉⢁⣀⠈⠁⠀⢸⠀⠀⠀⢸⠀⠀⣉⣀⣀⣈⡀
⠹⡄⠈⠑⠒⠒⠋⠀⡰⠃⠀⠀⠀⢣⡀⠈⠓⠒⠚⠁⢀⡜⠀⠀⠀⠈⢧⡀⠘⠉⠉⠉⠂⢀⠞⠀⠀⠀⠘⢆⠀⠳⣄⣀⠴⠁⢠
⠀⠈⠓⠤⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠤⠚⠁

⠀⠀⣠⠤⠴⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠦⠤⣄
⢠⠋⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⡴⠁⠠⡀⠀⢠⠄⠙⣆⠀⠀⠀⢀⡜⢁⠀⠀⠀⠀⠀⠑
⡏⠀⠰⠗⠀⠐⠿⠀⠀⡇⠀⠀⢰⠃⠀⠦⠖⠀⠲⠴⠂⠈⡆⠀⠀⢸⠁⣀⣉⣁⣀⣉⣁⡀⢸⡀⠀⠀⢸⠀⢈⠽⠂⠀⠺⠅
⢧⠀⠐⠒⠒⠒⠒⠀⢀⠇⠀⠀⠈⣆⠀⢠⠖⠒⠢⡄⠀⣰⠁⠀⠀⠘⡄⠳⡀⠀⠀⠀⣠⠇⡸⠀⠀⠀⠸⡀⠀⡠⠖⠒⠦⡀
⠈⠳⢄⡀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠢⣄⡀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠘⠦⣈⠓⠒⢋⣡⠜⠁⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⡠⠞
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⢀⡴⠊⣡⠀⢠⣉⠳⣄⠀⠀⠀⠀⢀⠔⠋⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠈⠙⢢⡀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⠑⢦
⡞⠀⢠⣦⠀⠠⣦⠀⠈⡆⠀⠀⢀⠏⠀⢢⣄⠀⣠⡔⠀⠹⡀⠀⠀⢠⠃⠐⣦⡖⠀⢢⡔⠀⢱⠀⠀⠀⢰⠁⠀⢦⡄⠀⢠⡄
⣇⠀⠀⣀⣠⣀⡃⠀⠀⡇⠀⠀⠸⡄⠀⢉⠀⠀⠀⡉⠀⢀⠇⠀⠀⢸⡀⠈⠁⠉⠀⠁⡈⠀⢸⠁⠀⠀⢸⠀⠀⣉⠀⠀⢀⡁
⠘⢄⠈⠁⠀⠀⠉⢀⡜⠁⠀⠀⠀⠳⣄⠀⠉⠉⠉⠀⣠⠞⠀⠀⠀⠀⠳⡀⠉⠉⠉⠉⠁⣠⠏⠀⠀⠀⠈⢣⡀⠈⠉⠋⠉⠀⡠
⠀⠀⠙⠒⠲⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠓⠒⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠖⠒⠋

⠀⢀⡤⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠢⣄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠒⢤⡀
⣰⠃⠀⠖⠀⠐⠦⠀⠱⡄⠀⠀⠀⡞⠁⠐⢒⣀⡒⠂⠈⢳⠀⠀⠀⠀⡞⠁⠰⠤⠀⠴⠂⠈⢦⠀⠀⠀⢠⠎⠀⢠⡄⠀⣤⠀⠘
⡇⠀⠳⠔⠀⠘⠴⠃⠀⡇⠀⠀⢸⠀⠀⣰⠉⠀⠉⣆⠀⠀⡇⠀⠀⢸⠀⠀⠺⠆⠀⠸⠇⠀⢸⠀⠀⠀⢸⠀⠀⠛⠀⠀⠛⠃
⢳⡀⠈⠲⠤⠤⠊⠀⣠⠃⠀⠀⠀⢧⠀⠹⣞⣉⡳⠏⠀⡼⠀⠀⠀⠈⢆⠀⠰⠊⠉⠓⠄⠀⡼⠀⠀⠀⠘⣄⠀⠉⠉⠉⠉⠁⢀
⠀⠙⠦⣄⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠑⠦⣄⣀⣤⠴⠊⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣠⠤⠊⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠋⠉⠀⢰⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⠁⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣴⣿⣿⣿
⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦
⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀
⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇
⠀⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⣠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⠀⣀⣴⣿⣿⣿⠏
⠀⣾⣿⣿⡟⠁⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣸⣿⣿⡟⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣷⣦⡀
⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷
⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡌⠈⢢⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⡌⠀⠀⠠⣷⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢩⠛⠃⠀⠀⠀⠀⠡⡄⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠃⠀⠀⠀⠀⣀⠀⠀⠙⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠂⠐⠛⢿⠒⠒⠒⠋⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠈⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠋⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⡶⠐⠻⡑⡀⠀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠁⠀⣀⠀⢥⠀⠀⠐⡔⠀⠈⠀⡠⠚⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢤⣴⠴⣖⠶⠾⣆⣻⣁⣸⠋⢄⠶⢥⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣟⡻⠭⠥⣼⣄⣈⣈⣠⡴⢉⡕⣩⠷⠴⢮⣀⡎⢠⣟⣈⡻⠿⠟⡢
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠉⠒⠒⠲⠦⠤⠤⢇⣸⠍⠉⠩⠭⠭⠭⠥⠀⠀⠈⠐⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⣿⣶⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢒⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢉⣙⠒⠢⠭⠭⣍⣛⣛⣓⣒⣒⣛⣋⡩⠭⢕⣒⠋⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡏⣿⡇⠀⡔⣿⡆⢀⡴⣦⡀⠀⡔⣶⡄⠀⡏⣿⡇⡇⡇⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⡇⣿⡇⠀⡇⣿⡇⢸⠁⣿⡇⠀⡇⣿⡇⠀⡇⣿⣧⢟⡿⠋⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⡇⣿⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⠇⣸⠁⠀⡼⠀⠀⢀⠤⠄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⠀⣿⠀⠀⡇⠀⠀⢰⢢⡡⡆⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⠀⣿⠀⠀⣧⠀⠀⠸⡆⡇⢁⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⠀⢹⡄⠀⢹⡀⠀⠀⠧⢻⢨⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⡀⠈⣧⠀⠀⢧⠀⠀⠀⡇⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⣿⣧⠀⠘⣇⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢧⣿⡇⠀⡇⣿⡇⢸⠀⣿⡇⠀⡇⣿⡇⠀⢿⣿⣧⡀⠘⣧⠀⠀⠙⠤⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⡤⠢⢀⠀⠀⢻⣧⣀⠀⠀⣇⣿⡇⢸⡀⣿⡇⠀⣇⣿⠇⠀⣈⣿⣿⣷⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠘⢷⡀⠀⠱⡀⠀⠈⠻⢿⣶⣬⣍⣀⣀⣙⣋⣁⣀⡤⠤⢖⡫⠕⠛⠉⠉⠛⠦⣄⠈⠓⠦⣤⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠀⡀⠀⢄⠀⠀⠀⠉⠙⠓⠐⠛⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠼⡳
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⢀⠠⠀⣠⢀⡀
⠀⠀⠅⠀⠀⠀⠀⠀⠀⠈⠀⠉⠇
⠀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠑⠤⠤⠤⠤⡤⢤⠤⠤⠤⠤⠊⠀⡶⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⡇⠀⡖⢢
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡅⠡⡀⣎⠹⢍⣆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠋⠉⠀⠀⠈⠉⠀⠀⠀⠀⠈⡃⠀⠀⠙⢄⠒⠁⡘
⠀⠀⠀⠀⢀⠤⠞⠘⠠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⢀⠀⠃⡀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡸⡱
⠀⠀⠀⠀⠀⢇⢣⡄⢀⡀⠄⢀⠀⠀⠀⢇⠀⢀⡀⠀⠀⠈⠀⠂⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⢞⠕⠁
⠀⠀⠀⠀⠀⠘⠦⠎⠁⠀⠉⠐⠀⠈⠄⢺⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣸⠀⠨⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡴⢶⠄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡔⢺⠀⠀⠀⠀⢺⣀⢀⡻⠀⠀⠀⠀⠸⠢
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢆⣀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⢄⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⣿⣷⣶⣬⡙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⣸⣿⣿⠿⠿⢿⣿⣿⣿⣿⠿⠿⣿⣿⣷⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣧⣶⣿⣦⣿⣿⠿⣧⡶⢷⣼⣿⣿⡄⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠂⢸⢰⣿⣶⣿⣿⡇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⣿⢛⣼⣿⣿⣟⣯⡞⣰⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣌⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣭⣍⣉⣛⣛⣛⣭⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣦⣤⣤⣤⣤⣾⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⡇⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢻⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢸⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⢰⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠈⣿⠇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠈⠙⠻⢦⣄⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠀⠀⠀⠈⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢷⡄⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠘⣿⣧
⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠙⠛⠚⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⣇
⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠻⣍⠛⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⡿⠟⠛⢿⣦⡀⠀⠀⢠⣿⡟
⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⣁⠴⠖⠒⠛⠛⠛⠂⢠⣿⡟
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠗⠋⣡⠞⠁⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠁⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉