Iciness Emojis & Symbols

⣿⣿⠇
⣿⣿
⣿⣿
⣿⡿
⣿⡇
⣿⣇
⡿⠋⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣿⣿⣿⣿⣷
⠇⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⣤⣿⣿⣿⣿⣟⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣶⡄⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣯⣿⡓⠂⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣇⠘⣿⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠴⣿⠙⠿⢿⣿⣿⣿⢠⢿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢻⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣸⣿⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣭⣥⣤⣾⣧⠀⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⣿⣶⠿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢀⣤⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠛⠻⠿⠟⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⠙⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠲⠤⣀⣈⠭⠭⠒⠒⠋⠉⠁⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⣸⡇⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣇⣀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠉⠛⠻⠿⡆⠀⠀⠈⢻⠈⠈⠉⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⡉⠀⠀⠀⠀⠁⠀⠀⠀⠀⡈⠀⠀⠀⠰⡰⠀⠀⠀⣼⠀⠀⣼⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢨⠗⠀⠀⠀⢿⠀⠀⣾⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣿
⠀⠀⠀⣿⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠗⠀⠀⠀⢀⠀⠀⠀⠀⠀⣐⠄⢀⡀⢸⢀⡠⠜⠂⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⣿
⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣠⠤⢠⡄⠰⠠⢤⣤⣤⣤⡄⢠⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠅⠀⠀⠘⠀⠀⠀⠀⠀⠈⠓⠂⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠀⠀⠂⠀⠀⠀⠀⠈⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠉⠀⠀⠸⠃⠃⠂⠀⠘⠓⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠌⠃⠄⠁⠂⠐⠁⠃⠀⠀⠂⠒⠀⠐⠐⠐⠢⠂⠜⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰⠠⠰⠀⠀⠔⠠⠂⠀⠐⠂⠐⠀⠐⠃⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣠⡰⡤⠠⠄⠐⡤⠀⠰⠢⠄⠐⠔⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⢟⣧⣄⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢈⠭⠒⠀⠊⢽⣧⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠛⠀⢀⣿⣿⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠻⣿⣧⣷⣦⣶⣶⣿⣿⡟⠃⢀⣀⣄⠈⠙⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠁⢦⠀⠀⢠⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠖⣩⣾⣻⣏⡻⣿⢿⡀⠤⠀⠀⠀⣠⣦⡙⡄⣡⣤⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢠⣾⣟⣿⠋⠀⡀⠀⠀⠀⠀⠀⠶⠐⡂⠀⢧⣙⣟⣵⣇⣿⣮⣾⡙⠂⠿⠈⡧⣘⢛⣱⣇⣛⠛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⣿⣻⣿⢏⠀⠀⠁⠐⢐⢺⠃⠖⠆⠀⠙⠙⢉⣻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢛⣿⣷⣿⣿⣿⣿⣂⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠒⣦⣶⣴⣾⣿⣿⣿⣧⣤⣤⣤⣤⣾⣿⣷⣮⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢡⠨⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣼⣿⣿⣿⣿⣿⣏⣹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⣾⣿⣿⣿⣿⡟⠋⠉⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⢿⣿⣶⡄⠀⡀⠀⣰⣶⡄⠀⠘⢉⠐⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠤⠤⣤⣀⣀⣀⣠⣀⣀⡰⣿⣿⣿⠿⣶⣿⣿⣿⡇⠐⣾⣿⣿⣤⠒⠈⣾⣿⣿⣿⣿⣯⠀⠀⢀⡀⠀⠀⠁⢸⣿⣿⣿⣿⡆⠀⣒⡂
⠀⠀⠀⠀⣀⣤⣤⣀⣤⡀⣀⢁⠠⠁⢹⣿⣿⣄⣛⣉⣿⡿⢿⣿⣿⠟⣁⢁⡀⢻⣿⣿⣿⠿⠿⢻⠤⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⡇⠀⡀⣀⡀
⠀⠀⠀⠚⠛⠻⣿⡿⠿⠟⠛⠿⠟⠛⠁⠻⠿⣿⣿⣿⣿⣇⣠⣸⣿⠿⠟⠻⠷⢾⣿⣯⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣧⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠛⠋⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠛⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⢀⡉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡇⠀⠀⠀⣿⡏⢉⡙⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢸⣿⣿⡿⠀⠀⠀⠀⢿⣁⣀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣾⣿⡿⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⢿⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⡿⠇⠀⠀⢠⣤⡟⠙⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠁⠀⢸⡇⠀⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣰⣶⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠷⠿⠿⠿⠿⠆⠠⠄⣀⣀⣀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⢀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣿⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⣀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣷⣦⡀⠀⠀⠀⠀⠀⢰⡏⣿⣿⠟⢿⣿⠻⢿⣿⣿⣿⡀⠀⣠⣶⡀⣠⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡏⠀⠉⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣦⣀⣻⣆⣀⠿⣿⠟⣿⣯⣨⣿⣽⡟⣹⣿⡿⢿⣏⡀⣀⣽⢳⣽⡿⠁⠀⠀⠀⠀⣼⣆
⠕⠀⢰⡀⠀⠀⠀⠀⠀⠈⢁⣈⣭⣿⣿⣿⣳⡿⠷⣯⣞⣧⣅⠉⣻⣿⣾⣿⡿⠟⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⣟⢶⣅⣄⣀⣻⣾⣿⣷⣿⣿⣿⣭⣰⣶⡿⠏⣥⣤⢿⣶⠰⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣴⣭⣿⠿⠿⣻⣿⣿⣭⣔⡻⠻⢿⣾⣷⣚⣺⣙⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣾⣿⡇⢠⡄⠀⠀⠀⠾⣷⣿⠷⠛⢫⢽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣷⣾⣶⠄
⢸⣿⡟⢰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠻⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛⠀⠀⠀⠀⠀⠀⡀
⣾⣿⣷⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣮⣻⣶⣿⣿⣿⣿⡿⠋⠀⠀⣠⣤⣤⣤⡼⣿⣿⡋⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢨⣿⢿⣻⣿⣿⣿⡿⠿⣿⣶⡶⣾⠟⡒⣿⢋⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⡀⢘⣿⣤⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠛⠿⠿⠀⠘⡇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢰⣆⢰⡆⠲⡶⠂⣶⣆⢰⡆⠲⣶⠶⠂⣶⠶⠆⣴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣾⠁⣠⣿⡀⣿⠙⣿⡇⠀⣿⠀⢀⣿⣉⡁⢿⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈

⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⣤⡤⣤⣤⡤⣤⡄
⠀⠀⠀⠀⠀⢽⣽⣿⣿⣿⣯⣶⠀⠀⠀⠰⣤⡠⢫⠄⣴⠄⠀⠀⠘⢸⡇⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡀⣰⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⠀⠀⠀⢀⣴⣐⢒⣰⣄⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⣰⢟⣷⢴⡿⣟⠿⠀⠀⠰⡿⣿⢷⣷⠀⠀⡯
⠀⠀⠀⠀⠀⣹⣿⣿⣻⣷⣿⣿⠀⠀⠀⠉⠁⠀⡷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣶⠛⣇⠀⠀⠈⣷⣿⣾⣙⣶⣾⡋

⠀⠀⠀⠀⠀⠀⠀⣤⢴⠄⣀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⢠⣾⣖⢾⣞⣿⡄⠀⠀⠀⣤⣿⣿⣯⣶⣤⣶⠀⠀⠀⠀⠀⣮⡧⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣦⡀⠀⠀⠀⣸⡟⠟⠸⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢫⠏⠈⠛⠀⠀⠀⡻⢿⣷⣟⣿⣞⡷⠀⠀⠀⠀⢺⣿⡽⡖⠀⠀⠀⠀⠈⠉⠛⠻⣿⠿⠷⠀⠀⠈⢻⣯⣬⢪⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⠀⠿⠿⠿⠷⠿⠯⠷⠀⠀⠀⠀⠋⢻⠗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠉

⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠠⠀⠀⣲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣶⡦⠀⢤⡶⠆
⠀⠀⠀⠀⠀⣺⡷⣽⠟⣧⢿⣷⠀⠀⠀⠠⣒⣿⣿⣷⣂⠀⠀⠀⠀⠀⢠⣶⣤⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⢽⣯⣿⣻⣿⣿⣽⠆⠀⠀⣞⣿⣛⣛⣻⣽⣇⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⣁⠀⠤
⠀⠀⠀⠀⠀⠿⠿⠻⠻⠿⠟⠻⠁⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠸⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢉⠐⣦⣤⣵⠂⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⢰⡏⡹⢿⠿⣉⣷⠀⠀⠀⠀⠀⣛⣛⡃⠀⠀⠀⠀⠀⠀⣻⣿⣿⣇⣤⠄⠀⠀⠤⣾⣛⣺⣟⣷⠤⠀⠀⢀⠜⣧⠀⢴⠟⢊⡁
⠀⠀⠀⠀⠀⠠⠾⠍⢿⢿⠉⠗⠀⠀⠀⠀⠀⠿⡍⡇⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⡟⠀⠀⠀⠰⢈⡿⠭⢿⡁⠰⠀⠀⢰⣎⡷⣶⣄⣤⣶⡦
⠀⠀⠀⠀⠀⠘⠋⠛⠈⠈⠛⠛⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠘⠋⠙⠛⠋⠁⠀⠀⠀⠀⠂⠈⠐⠂⠀⠀⠃⠀⠀⠘⠉⠛⠋⠛⠛⠙⠃

⠀⠀⢠⠄⢀⣀⣀⡄⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⡀⠂⠀⢤⡤⢸⠆⠂⣠⠀⡇⢠⡜⠉⢸⠀⠠⣤⠄⡗⠀⣆⢄⡄⢠⢀⠄⢠⡴⣡⠀⢸⢠⢸⢤⣤⡤⠀⠈⠀⡀
⠀⠀⠀⠀⠠⠀⠀⠈⠈⠀⠘⠀⠈⠛⠀⠁⠈⠀⠀⠸⠀⠀⠉⠀⠃⠀⠀⠈⠑⠀⠉⠀⢀⣄⠑⠤⠘⠀⠈⡈⠁⠁⠀⠀⠀⠀⡀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⣠⠞⠀⠀⠀⠀⠀⢀⣀⡴⠊⠉⢱
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡃⢥⠎
⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⡄⠉⠞⣼⣿⡀
⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣥⣼⣿⣯⣴⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⣀⣴⣿⣿
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣢⣾⣾⣿⣷⠋⣻⢿⣋⣩⠷⠋⣉⣉⣙⣬⣭⡴⣶⣾⡉⠸⣿⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣿⣿⣏⠙⡿⣿⣿⣿⣾⣷⣶⣾⣿⣾⣿⠄⠤⠛⠉⢉⠍⠉⠃⠀⠚⣻⠻⠃
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠘⡷⠀⠈⠁⠀⠻⣿⣼⣦⣽⣿⣿⠉⠉⠉⣉⠉⡉⢉⣩⣉⡛⠉⠛⠉⠉⠉⠉⠛⠋⠛⡶
⠀⠇⠃⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣌⡁⢁⠀⠀⠀⠀⠀⠀⠀⢉⢉⣹⡟⢻⡿⠀⣀⣸⠿⢼⠇⡿⢭⠙⡇⠀⡀
⠀⡀⠀⠀⠀⠀⠀⣀⠀⣘⣋⣉⣉⡉⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⡇⠠⠀⠟⠳⡿⣸⣷⡟⠃⣇⢰⠄⠀⣀⣼⡆
⠀⣙⣄⣀⠀⠀⠀⠻⣿⣿⣿⠿⢿⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⣼⣿⣾⠀⢉⣏⠛⠀⣇⡾⠀⢠⣿⠿⠿⠶⠆
⠀⡿⣡⢼⠂⠀⠀⠀⠙⠻⠛⢶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⢺⣿⢿⣿⣼⣿⠛⠁⠀⣿⣿⣦⢾⠻⠂⠄⠀⡴⣽⡆
⠐⣧⣿⠀⢁⡀⠤⡤⠄⠄⠀⠄⠈⠀⠠⣶⣶⣬⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠈⠉⠉⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹
⠠⣾⣿⣧⡸⠿⢓⣸⠏⠋⠀⡀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢷⣦⣤⣶⣶⣶⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠉⠉⠉⠛⠂⠐⠈⠀⠒⠂⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠳⠶⠒⠶⠲⠶⠶⠾⠿⠿⠟⠒⠚⠿⠿⠟⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢷⣦⡀⠀⠀⠀⣴⡿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠙⣷⡄⠀⣼⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠘⢿⣾⡟⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣼⣿⡆⠈⠋⠀⢼⣿⣦⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠉⠉⠉⠉⣉⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠛⠛⠛⣿⠟⠀⣤⡀⠘⣿⡟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣼⠿⣷⡄⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣼⠏⠀⠘⢿⣄⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠟⠀⠀⠀⠈⠻⠷⠟⠁⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠷⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠉⠙⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡘⣿⣄⣾⠏⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣘⣷⡜⠿⢋⣼⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣉⣉⣉⣁⠀⠀⣉⣉⣉⣩⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠈⠉⠉⢩⣿⢃⣶⣆⠻⣯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⣿⢃⣾⠏⠻⣧⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⣶⣤⣄⡀
⠀⠀⢀⣴⠟⢉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠙⣿⡄⠀⠈⠉⠻⣦
⠀⣴⡿⠁⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠀⠀⢀⣿⠇⠀⠀⠀⠀⢸
⣼⡟⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣄⣀⣀⣠⣤⣤⣤⣤⣴⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠉⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠟⠋⠁⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⢀⣼⠟
⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠛⠛⠋⠁⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠋⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠈⠙⠻⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⡶⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⢻⡟⠙⠛⠛⠛⠋⠉⠉⠉⠉⢵⣶⣦⣤⣤⣤⣤⣶⣶⣶⠶⠾⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠿⣿⡋⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠟⠛⠉⠀⣠⣿⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⠶⠿⠛⠋⠉⠁⠀⠀⣀⣠⣴⡾⠛⠁⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⣛⣛⠛⠋⠉⠉⣉⣀⣀⣀⣀⣠⣤⣤⣶⠾⠿⠛⠋⠁⠀⠀⠀⠀⢀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⡾⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠉⠉⠙⠛⠛⠛⢻⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⣉⣼⡟⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣷⣤⣀⡀⠀⠀⠀⠙⠛⠻⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠛⠁⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⢙⣿⡿⢶⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠙⠿⣶⣤⣈⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⢻⣿⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⣀⠉⠛⠻⠷⣶⣦⣤⣄⣀⣀⣀⣀⣠⣤⡿⠋⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠉⠛⠻⢶⣶⣤⣤⣀⣉⡉⠉⠉⠉⠉⠉⠁⠀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⣛⠿⠿⠷⠶⠿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠢⣄⢀⡤⠖⠚⠋⠉⠙⠓⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠾⠄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⡤⢾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣆⡀⠀⠀⣀⠼⣄⣀⠀⠀⠀⠀⢀⣼⡏⣹⡅⠈⢹⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠚⠉⠁⠀⠀⠉⠉⣭⡟⢦⣬⣽⠝⢯⡿⢯⣿⠛⣾⡭⠶⠤⠞⠵⠯⠴⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⠞⣹⢟⡴⠋⢳⣞⢟⣴⡻⣽⡾⠉⢧⢯⣉⠙⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡾⢧⣀⣨⢗⠼⠒⠷⡼⣅⣀⣼⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⢻⢧⡼⣄⣀⡰⣣⣔⣖⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠫⡟⠧⠼⢻⡤⠗⢘⡎⢳⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢻⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠔⣪⠿⠋⠀⠀⠀⠀⠀⠀⣠⠄⠂⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣉⡼⢋
⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠠⠚⠁⠈⡙⠀⠀⠀⢀⡤⠔⠊⠡⠉⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢰⡆⠀⠀⠀⢼⡇⢨⣡⣶⣮⠈⠒
⢠⣾⠴⣻⠇⣸⠀⠀⠀⠀⠚⣍⡄⢦⠀⠀⠀⠄⣦⠐⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣧⠀⠀⣠⣿⣿⣈⣋⡼⠟⢶⠶⣶⢀⣆
⣿⡿⣊⢃⣲⣼⣇⣤⡶⠚⢈⠉⢰⢌⣁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢸⡆⠀⠀⣫⣜⠅⠀⡜⢛⡎⢉⣻⣀⣤⠈⢃⡀⠙⢿⣀
⣿⠞⣹⣈⡽⢌⣿⣿⡷⠂⠀⠈⡃⠀⠀⢣⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡷⠂⠘⣁⡙⢶⡀⠟⠁⡴⣄⡘⣿⡏⠳⡌⠙⠷⣾⣿
⠿⠓⣅⡟⢘⣦⣹⡿⠗⠚⠶⠖⠉⠛⠧⣌⠳⣦⣦⣴⣀⣴⣠⡠⢼⡿⢄⣀⣰⣄⣦⣦⣾⣷⣶⣏⢜⡁⢸⠞⢉⡅⢸⡡⠒⠉⠻⡀⠻⣌⣗⣦⣤⣀⠈⠻⣿
⣰⡎⠀⣿⢺⣏⣠⡤⢾⣀⣤⠾⢶⢸⡆⠘⠷⣿⣿⣿⣿⣿⣿⡗⡹⡟⢺⣿⣿⣿⡟⢹⣿⣿⣿⡥⢟⠙⠓⠛⣩⢸⢛⣀⠀⠂⣧⠘⣤⣼⣿⣇⠀⠙⠷⢴⣿
⠴⠳⣀⣿⣶⠟⠉⣀⢀⣉⣇⠀⢨⡽⡟⢦⣀⠸⣿⡟⡟⡿⡿⣉⣠⠉⢈⢻⣿⣿⡴⢊⣻⣿⠋⡠⠴⠗⠶⣦⣽⣇⣼⠡⠤⠖⠛⢿⡀⠘⢯⠉⠁⣄⠀⠀⢹
⢀⣶⡟⣹⣷⡞⠋⢀⣬⠋⠀⡖⠈⠀⢀⡀⠙⠳⣾⣿⡏⣿⠯⠎⣀⢧⡼⠨⢿⡵⡁⠊⢉⡟⢋⠀⣠⢤⠦⣀⢹⣿⣅⠀⣠⡀⠀⢹⣉⠉⠺⣆⡀⠈⠂⢤⣀
⣾⣁⣼⣿⡯⠀⠚⢻⣁⣠⡞⠀⢠⡀⠘⢳⡄⣀⠈⡿⢿⡅⠀⠈⡇⢸⠀⠀⠠⡾⠁⠲⢎⠁⣣⣤⡇⢀⡷⣄⣉⣿⣿⠜⠛⣧⠀⢠⡏⠶⣄⡘⢧⣠⠂⠀⢻
⠀⠀⡽⠃⠀⠀⣀⡤⠞⠉⠀⠀⠀⠛⣆⢨⡗⠛⠓⠇⠘⠓⠐⠋⠙⠛⠒⠀⠀⠈⠀⠀⠀⠁⠀⠀⠑⠁⠀⠘⠛⣁⠆⠀⢈⠉⠓⠃⠀⠀⠀⠙⠻⣯⠁⢀⢈
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠲⠀⠀⠀⠙⠻⠇⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⠠⠾⠴⣄⡀⠀⢠⣀⣣⡀⠈⣻⠿⠿




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢀⡠⡆⠀⢀⠛⠃⠀⠀⠀⠐⡀⠂⢄⠈⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠉⠀⣠⣤⣤⡄⠀⠀⠀⠡⠄⠤⡔⠀⠀⠀⣀⠹⢼⣦⡔⣤⡌⠳⣌⡇⠈⠁⠒⢼⣆⡿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣆⢰⣾⣿⣿⣿⣷⣄⡀⢀⠀⠠⠀⠀⠀⠀⠀⠙⡀⠶⠦⠿⣾⣿⠆⠈⠻⡄⠀⠛⠿⣿⡇⠈⢣⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠒⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠲⢞⣫⠉⠃⠤⣄⠀⢰⣿⠟⠁⠈⢳⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣤⣤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⡀⢈⠙⣿⣿⡄⢣⡀⠀⣿⡇⡀⠀⢅
⠀⠀⠀⠀⠀⠀⣀⣴⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⠉⠓⠀⢀⠀⠀⢅⠠⠦⢀⡭⠙⠒⠲⢼⣿⣇⠀⣿⡀⣘⣧⡅⢠⡏
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠶⢄⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡷⠿⣧⠀⢿⡆⣸⣇⡠
⠀⠀⠀⠠⣼⣿⣿⣿⡿⠛⡻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠚⠶⠒⠲⢦⣄⣀⣀⡀⣠⣴⢶⡞⢻⣿⣿⠄⠈⣷⣾⣿⣿⡟⣀
⠀⠀⠀⠀⣻⣿⠟⠋⠀⠀⠉⠙⢻⣷⡆⠈⠙⣿⣿⢿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⡶⣆⢀⣠⠜⠉⣹⡿⠛⠛⠻⠿⠷⣾⣿⣿⡀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣾⠃⠀⣀⡀⠀⠀⠀⣧⣿⣿⣦⠀⣷⣿⠿⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⣔⠒⣚⡙⢀⠀⢀⣄⠀⠀⠀⣿⢿⣷⠈⢸⣿⡿⠁
⠀⠀⠀⠘⠷⠶⠛⣷⣯⣴⣿⣿⣿⣿⡿⠟⠠⠛⢟⡄⠁⢹⣻⣿⠛⢿⡿⠿⢿⠿⠟⠛⠛⠻⠊⠒⠾⠓⠐⠂⠒⢿⣋⠘⢷⣿⡾⢿⠀⡷⠈⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣦⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠓⠚⠛⠛⠛⠛⠛⠛⠛⠃⠒⠂⠀⠀⠀⣸⣽⣷⣿⣟⡇⠀⢿⣧⠄
⠀⠀⠀⠀⠀⠀⠀⡀⢙⡹⠟⠏⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢰⣴⣶⣶⣶⣾⣿⣿⡿⠋⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⠿⢿⡷⠶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣦⣤⣤⣤⣶⣬⣾⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⠟⠉⣉⡥⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⠀⠀⡉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡀⢀⡼⣿⣬⣀⠀⣤⣈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠘⣷⡟⠸⠋⢨⠉⠿⠈⠉⠙⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢻⣤⣾⢋⡀⢡⡆⠁⠀⢀⠈⢀⡔⣰⠃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠊⠂⣬⠟⡇⢠⢊⠉⠀⡀⠀⢡⣭⡎⢳⣟⠀⠀⢷⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣤⠞⢿⣏⠀⢹⣠⣖⡀⡢⢸⡼⢏⣿⡇⠾⣧⢤⣤⣼⠷⣧
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡶⣾⢹⡆⣸⣇⣀⣸⡇⢻⣷⢃⣼⠁⣾⣿⣷⡶⠟⠻⠉⠛⢶⣏⣷⣰⡆
⠀⠀⠀⠀⠀⡰⠿⢸⢏⣤⠿⠿⠛⠿⠾⢷⣿⣷⡿⠙⣦⢿⣶⡿⠋⠁⠀⠠⠖⠃⠀⢀⠹⣮⣟⢳⡄
⠀⠀⢀⣠⣼⣅⣠⡾⠛⠰⠋⠀⠠⠄⠈⠑⠂⢄⠙⠻⣿⣯⣉⣀⠁⠘⠀⠀⠤⣄⡀⠀⠁⠬⠻⢦⣷⣄⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠒⠀⠁⠀⠀⠀⠂⠔⠀⠀⠀⠀⠀⠀⠙⠉⠀⠈⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠉⠀⠀⠀⠈⠉⠉⠙⠒⢤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠢⠤⣀⡀
⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣀⡤⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⡏⢀⡔⠓⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣄⠀⠀⠀⠀⠀⠀⣼⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⢀⡇⠸⣇⣈⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠄⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⡞⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⠃⠀⠀⠀⠈⢆⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠈⠑⢆⠀⠀⠘⠒⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼
⠸⡆⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢀⡾⠶⠃
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⣠⡄⠀⢠⣿⠶⠶⠶⠶⢤⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣷⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣀⡤⠖⠉
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⢀⣀⠔⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠑⠦⣄⣀⣀⣀⣀⡤⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠙⡆⣴⠟⣁⣀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣤⡄⠀⠀⠈⢧⡈⠛⠷⠸⠟⢉⡿⠀⠀⠀⢀⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠹⡄⠀⠀⠀⠉⢳⡄⣠⠞⠉⠀⠀⠀⢠⡞⢠⡞⠁
⢀⣠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠘⢧⠀⠹⣄⠀⣾⠳⢼⡇⣾⡴⠒⣦⠀⢠⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤
⣿⠉⠉⠛⣶⠀⣿⠳⣄⠀⠀⠀⠈⢧⠀⠙⣆⠙⠳⣄⠀⠉⣠⠴⠃⢠⠏⢠⠏⠀⠀⠀⢠⡾⢧⡀⣴⠋⠁⢈⣿
⠈⠳⣤⣤⣬⣛⠻⠀⢷⠀⣶⠓⢤⠈⢧⠀⠘⣆⠀⠈⡇⢸⠁⠀⢠⡏⣠⠏⢰⠞⢳⡄⢸⠀⠸⠟⣩⠴⠶⠛⠁
⠀⠀⠀⣴⠚⠋⢁⣠⣘⡳⠾⠀⢸⡄⠈⠳⢤⣷⡀⠀⣷⢸⠀⢀⣼⡴⠋⠀⣾⠀⢼⠶⣋⣤⣀⠛⠳⣦
⠀⠀⠀⠉⠑⠚⠉⢁⡬⠿⠂⠀⣀⠳⣤⡀⠀⢳⡳⡄⣿⢸⢀⣞⡽⠁⣀⡴⠏⠀⠀⠾⢭⡄⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠿⢤⡴⠖⠛⠉⠙⠶⣍⡳⢦⣷⡹⣿⢸⣾⣿⠴⣛⡥⠖⠋⠙⠓⠲⠤⠗
⠀⣴⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢤⣤⣤⣭⡷⠬⠙⠋⠈⠉⠴⣾⣥⣴⣶⣶⠖⠒⠚⠒⠛⠛⠛⠛⠛⠛⠛⣳
⠀⠈⠛⠒⠒⠒⠒⠒⠚⠓⠒⠒⠛⠉⠉⠉⣉⡽⣛⣥⠀⢀⣀⡛⢯⣍⡉⠉⠉⠙⢛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣟⠛⠳⢦⣀⣀⣤⢶⣫⠵⠊⢡⢫⣿⢸⣞⣏⠓⢮⣝⠓⠶⠖⠋⠁⣀⣿⠀⢀⡀
⠀⠀⠀⢸⡛⠳⢦⣌⣙⣦⠀⠉⣩⠖⠋⠀⠀⣰⣳⠋⣿⢸⠘⣎⢧⠀⠈⢳⡀⢀⣲⣯⣥⡴⠞⠋⢉⡿
⠀⠀⠀⠀⠉⣳⡄⠈⢩⡴⣶⠀⡟⠀⠀⢀⡖⢳⠃⠀⣿⢸⠀⠘⣮⢧⡄⠈⣇⠘⡏⢻⡄⢀⣰⣾⣋⣀
⢀⡶⠛⠛⢋⡥⣦⠀⣿⠀⠻⣄⡿⠀⢠⡞⢀⡞⢀⣠⠟⠸⣄⠀⠻⡄⠹⡄⠻⣄⡵⠀⣧⠈⣿⠻⣯⠉⠙⢶⡄
⣼⣇⣀⣠⡿⠀⢿⣀⡿⠀⠀⠈⠀⢠⠏⢠⢏⡴⠋⢁⡀⢀⡈⠓⢦⡹⣄⠹⣆⠈⠀⠀⠹⢤⡟⠀⠈⠳⢦⣴⠿
⠀⠈⠉⠁⠀⠀⠀⠙⠁⠀⠀⠀⣠⠏⣠⠏⠾⣤⡴⢋⡿⢸⡙⢦⣬⣧⠙⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣰⠏⠀⠀⣀⡴⠋⠀⠀⠙⢦⡀⠀⠀⠘⣆⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣸⣇⣀⡴⣧⢻⠳⣄⣙⣧⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⠋⠘⣦⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣿
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣀⣀⣀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⠟⠛⠛⣛⣿⣿⣿⡉⣽⣿⣿⡿⠶⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⡀⠀⢰⣿⣿⣿⣿⣷⣿⣿⣿⡇⢀⠀⠈⠙⠻⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡇⠀⠀⠀⠀⢀⣿⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡄⣴⡀⢀⣶⡀⠉⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣀⡰⠁⠀⣠⣾⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⡄⠀⠀⠀⠈⠙⢻⣶⣤
⠀⠀⠀⠀⠀⠀⢀⣴⢾⡿⡆⢸⠋⠁⢀⣴⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠈⠁⣾⡇⠙⠋⠀⣰⠟⠉⠀⠀⠀⠀⠀⠀⣈⡽⠟⠋⠉⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣤⠾⠋⠀⠀⢀⣼⣧⣄⣀⠀⠀⠀⢀⣰⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⢀⡿⠁⠀⠀⠉⠻⣄⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⣿⡀⠀⠀⠈⣧
⠀⠀⠀⠉⠁⢼⡇⢰⡆⣰⠏⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⡇⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣼⠃⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠰⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⣶⡀⠀⢸⡇
⠀⠀⠀⠀⢠⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⢀⣤⠾⠳⢦⣀⣤⣴⠶⠶⠶⣤⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠈⣷
⠀⠀⠀⠀⣼⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠀⠀⠀⠀⣾⢡⠞⣩⡾⠋⠀⠀⠀⠀⠀⠀⢙⣷⠶⠓⠿⣿⣿⣿⣿⣿⣿⣠⠄⣿
⠀⠀⠀⢀⡟⠀⠀⢸⡷⢶⣤⣄⡀⠀⠀⣰⣿⡾⠇⠀⠀⠀⠀⢿⣄⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠉⢳⣸⣿⣿⣿⣿⣿⠋⠀⢹⣷⡄
⠀⠀⠀⣼⠇⠀⠀⣼⠇⠀⠀⠈⠛⢷⣟⣿⠟⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⣺⣾⣿⣿⣿⣿⠃⠀⠀⢸⣿⠁
⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢈⡿⠁⠀⠀⠀⠀⢴⠶⠶⠿⣶⣿⠰⣾⠃⠀⠀⢤⣠⠀⠀⠀⠈⠙⣻⡇⠀⠈⢻⡟⠁⠀⠀⠀⣼⠇
⠀⠀⢸⡇⠀⠀⢸⡿⠶⢴⣤⣄⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⣸⡇⠀⠀⠀⣰⣟⡀
⠀⠀⣾⣤⡶⠶⠛⠿⠟⠛⠛⠻⢿⣯⣙⣷⣤⣤⠖⠛⠳⢶⣄⠀⢸⣿⣴⣤⣤⠀⡀⠀⠀⠀⣀⣠⡶⠟⠀⠀⠀⢀⣿⠷⠶⠶⠛⠉⠉⠙⣷
⠀⢰⡟⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣄⠀⠀⠀⠀⠈⠻⣤⣿⡿⣿⡥⠞⣥⡶⢾⡟⣋⠁⡀⠀⠀⣠⠔⠋⠀⠀⠀⢀⣀⠀⠀⠀⢸
⠀⢨⡟⠉⢷⣀⣰⠶⣄⠀⠰⣦⣄⠀⣤⡀⢀⡈⣷⣀⡀⠀⢀⠀⠀⠙⠷⣦⠶⣿⠛⣿⣸⣿⠃⣼⣣⠾⠛⠉⠀⢀⡴⢦⠴⠛⠱⠞⠓⠶⣷
⠀⣿⣃⣀⣀⣭⣥⣀⣈⡓⠾⠃⠘⠷⠿⠻⢾⡟⠋⠉⠙⠓⠾⠿⣤⡀⠀⣘⣧⣿⣤⡿⠋⠉⠛⢿⣃⣤⣠⡟⣠⠞⢁⣀⣠⡤⠖⠚⠓⠛⠛
⠀⠉⠉⠉⠀⠀⠀⠉⠉⠙⣻⣦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣙⣓⣚⠉⣹⣶⣤⣤⣤⣤⣞⣩⣭⣭⣍⣥⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⠋⠉⠉⠉⠉⠛⠉⠀⢀⡴⠾⠛⠉⠁⠀⠾⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠠⠀⠤⠀⠂⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⣿⠆⠀⠀⠀⣠⣴⣾⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡏⣇⠀⣸⣶⣝⣠⢴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣀⢠⠖⠈⠁⠀⠀⠲⣻⡶⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⡰⢧⠀⢠⡀⠀⣄
⠀⠀⠀⡀⠀⠀⠀⣦⡀⣀⠀⢞⠛⠋⡼⢡⠿⣞⣏⠌⢉⡅⠀⠀⠀⢀⣤⠆⠉⠁⠂⠀⢸⡧⠀⠀⣿⢉⣦⡄⠀⠀⠰⢿⠆⠀⠀⠀⣝⡄⠶⣷⡀⡶⣷⢴⣿
⢠⣦⣸⣷⠀⣶⣜⣍⣁⣿⣶⣯⠼⣷⢶⢿⡀⢈⠛⠁⠈⠀⠠⠔⠪⢿⠇⠀⠀⠀⠀⠀⣻⡟⠄⠘⣻⣾⢧⣀⠀⠀⠶⢻⣼⢠⡄⢸⣏⣹⢼⡀⢻⢧⣼⣌⣿
⢸⣿⣵⢾⣿⣯⠼⡯⣤⢿⣃⡞⠀⣿⠂⡸⣧⣰⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢤⡇⠿⠠⠶⣿⣌⡟⠀⠰⡶⣿⣄⠚⠄⠚⣿⣥⡾⠷⠾⣧⣏⢸⣹
⢸⣿⢿⡤⣿⣁⡠⢆⣦⣤⣿⣧⣾⣿⡿⢀⣾⣷⡀⢦⣠⣀⡆⠀⡀⡀⠀⠀⠀⠀⠐⣸⠟⣿⢼⣤⠚⢻⠉⠉⠀⠠⠖⠻⠎⢃⡄⠘⠻⣯⡴⣦⡀⢹⣽⢻⣿
⢸⣷⣿⣿⡀⣠⠀⣈⣧⣀⠙⣿⣿⣿⣽⣿⡏⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⠶⣾⣶⣋⢼⡴⢿⠶⣴⣦⣼⣤⣤⢺⣧⣤⡖⣲⠃⠑⣊⠻⣿⣾⣿⣿⣿⣷⣼⣿
⢸⣿⣿⡿⠉⢉⡶⠏⠈⢻⡟⢻⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⢷⣷⣯⣿⣿⣿⡵⢚⣇⢘⠧⣜⣦⣿⡿⡄⣩⡐⢿⣋⠉⡇⢸⡅⢙⣻⣿⣿⣿⣿⣿⣿⣿
⢸⡿⣿⡿⠑⢺⡀⠈⡧⣀⣷⡖⠟⠘⠁⠹⡇⠁⠈⠋⠛⠁⠀⠀⠀⠉⠙⠛⢻⡡⠒⠻⠋⠀⠴⠗⠀⣿⠁⢯⠡⠅⠐⠵⡎⢁⣏⠙⠦⢭⢹⠟⠛⠉⠀⠙⠻
⠀⠀⡈⢛⠚⠉⡉⢁⣄⠀⠈⠿⠒⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠘⠃⠀⠚⠂⠉⠁⠀⠀⠀⠐⠈⠘⠃⠋⠸⠀⠆⠀⠦⠴
⠀⠀⠉⠉⠀⠈⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣥⣽⠶⢾⠶⠶⢮⣿⣍⣓⣦⡞⠟⠫⣝⡭⢭⡍⢝⢿⣿⠟⣿⢿⣿⠟⣧⠀⡀⠀⠀⣿⡇
⠀⠀⣿⣿⣿⣿⡿⣋⠣⠀⠀⢉⣬⣧⡿⠶⠶⠾⢿⠿⠶⣭⣍⣸⢣⣶⢼⢱⣧⠻⣧⣣⠐⠃⡰⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⣿⠯⢏⠁⠩⣻⣷⠟⢵⡆⠉⠀⠀⠀⠁⠁⠀⠀⢩⣝⣿⣿⣾⣷⠟⠛⢻⡿⠰⣶⡆⠀⠀⢀⡀⣀⣾⠃
⠀⠀⣿⠿⣛⠓⡌⠀⠐⣿⢂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢻⣽⠿⢿⣔⣤⡡⠥⠻⣦⣿⣧⢀⣖⠚⣷⣪⣿
⠀⠀⣿⣽⣓⣂⢤⣖⣤⣿⣚⠄⠠⡠⣤⠀⠀⠀⢢⣀⠀⠀⢱⣷⣖⡻⢷⣾⣧⠃⡎⢼⠘⠱⠄⣸⣗⠷⣌⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡶⢿⡔⢤⠤⣄⠼⣧⠀⡄⢳⡟⢦⢠⣾⣿⣿⣇⣶⣞⡛⣛⢳⡝⡀⠃⠀⢙⣹⢟⣿⣿⣿
⠀⠀⣿⢳⢮⣛⣛⠩⠷⣯⡻⣮⣰⠡⣂⢿⣔⣉⣜⣧⡰⢀⡿⢟⡽⠛⠼⠟⡪⠕⠇⡿⢬⠣⡠⣈⡴⣟⣿⠿⣿
⠀⠀⠷⣿⣯⡿⣆⣙⡛⠿⣿⣺⠽⢷⣵⣾⣟⡽⢯⣯⣽⡛⢷⣟⡁⡄⣠⢾⣎⣃⣀⣀⣠⣤⡾⣏⣑⢻⣧⣹⡟
⠀⠀⠀⠀⠈⠉⠉⠙⠚⠛⠻⠴⠿⠿⠟⠶⣮⣵⣊⣽⣋⣁⣬⣛⣳⣿⣿⣳⣿⣿⣭⣍⡶⠟⠷⠯⠷⠒⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠄⠀⣄⡀⢀⡁⢸⡇⠀⠀⠂⠔⠉⠀⠐⠒⠒⠢⠠⢤⣀⠀⠀⠀⠀⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠
⢡⢊⣹⣿⡛⠄⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⠀⠀⠀⠀⣠⡴⠊
⣩⠘⣛⢟⣛⡳⠦⣦⠔⠀⢀⡀⠀⠀⠀⠀⠀⣀⣦⡭⠴⢒⡠⠂⠀⠀⠀⠈⠀⠩⠄⠀⡠⢄⠋⠉⠀⠀⠀⠀⠐
⠀⠐⢫⣿⣿⣿⠋⡱⠆⠴⠂⠀⠀⠀⣀⠤⢈⡥⣇⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠴⡞⢻⢾⣿⣖⡹⢤⡀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠉⣰⡶⠂⠀⣀⣐⣂⠀⠀⠀⠀⠀⠀⠀⠙⣟⢻⡶⠲⠒⠀⠣
⢬⣭⣟⠛⠋⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠡⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢴⡛⢶⡶⣀⠀⠰⢆
⢰⡿⠛⠋⠀⠀⠀⠀⠀⠐⠲⠖⠀⠀⠁⠀⠘⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢩⣣⢸⣙⣒⡂⠈⠓⠂⠀⢈⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⢠⡄⠀⠀⠀⠀⠀⠉⠄⠍⠩⡼⢷⣄⠀⢈⣁⣠⡤⠲
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠠⢤⣤⡾⠀⡀⠀⠀⠈⠑⡀⠀⢐⢄⠉⠀⠀⠀⠀⠀⠠⡖⣆⠀⠐⠺⢒⡠⡙⠊⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡏⣸⠆⠁⠀⠀⠀⣾⠀⠀⠹⠀⡒⠀⠀⠀⠀⠀⣰⠂⣿⡑⠔⠀⠈⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⣌⠀⠙⡶⣂⣀⡀⠀⢀⡿⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣠⡾⢋⡿⡴⠃⡀⠀⠀⠀⠀⠀⠀⠠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠵⠎⢰⡿⢡⠅⣀⢀⠠⠔⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣐⣚⠃⡞⣠⣿⠇⣠⡖⠀⠀⠀⡠⢆⡐⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠛⠒⠀⠀⠐⣠⣺⠏⠰⢼⠿⣅⠀⠀⢀⠉⠛⠀⠋⠀⠀⠰
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠗⢰⣷⡻⠉⡁⠁⠀⠓⠀⠀⠒⢀⡃⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠁⢀⣜⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠏⣰⣻⠤⠤⠂⠀⠀⠀⠀⠀⠕⡂⠠⡰⡀⠠
⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠼⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠛⠀⢀⠰
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⢀⡟⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠆⠀⣴⣶⠋⠁⠀⠀⠉⠀⠀⠐⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡐⠃⠤⡀⠀⠀⠀⠀⣤⣤⡀⢀⠀⡀

⣰⣷⡟⠆⠀⡼⠛⣧⣠⣿⣿⠆⠀⠈⣸⢃⠛⡄⠛⠃⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡴⠋⠠⠆⠀⠀⠈⠀⠜⠋⠁⢀⣶⣀⣥⣤⡶⢿⣿
⠿⣿⠠⣀⠀⠏⠀⢹⣿⡿⠃⢀⠀⢀⣿⡿⠀⠀⠀⠀⡼⡋⠀⣠⠘⠘⠃⠀⠀⠀⠀⠄⠀⠠⢠⠮⠃⠈⠏⠇⠀⠀⠀⠀⠀⠘⡇⠀⠘⢿⠿⠿⣳⣶⠿
⠀⢿⣿⣿⢷⣦⣤⣾⡟⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⡸⠁⠉⠃⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⠀⠀⠈⠓⡀⠀⠀⠀⢁⣠⣤⡀⠀⢀⣾⣿⡦⢰
⣀⠈⢿⣿⣷⣤⣭⣿⡇⠀⠀⡀⢴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠐⠀⠀⠀⠀⢀⡄⠘⠂⠀⠀⢀⠀⠀⠈⢠⣗⣄⣰⡴⢾⣿⣿⣧⠀⠘⠟⢿⣷⣿
⣿⣿⣥⣿⡿⡿⣿⣿⠧⣤⡾⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠈⠀⠤⠄⠀⠀⠠⣿⠿⠿⠿⠿⣿⣇⠀⠘⢦⡙⣝
⣯⣿⣿⣿⣿⣿⣾⣄⡀⠻⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀⣦⠀⠀⠀⠉⠀⠀⠀⠙⢮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⠧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⢿⢿⣿⡀
⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢏⣅⠀⠈⠻⢎⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠟⡉⡞⠹⣿⣯⡛⠛⣿⠃⠀⠀⠁⠀⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐
⢈⠛⢀⣶⣬⣿⡟⢦⣍⠣⣔⠆⠀⠀⠾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⠁⠀⠀⠀⠀⠀⠀⢠⡆
⢸⡟⣾⣿⣿⣿⣿⣾⣝⣆⠈⣓⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣴⡇⠀⠀⢀⡠⠋⠁⠀⠀⠙⠦
⣻⣸⣿⣿⣿⡿⠛⠛⠻⠿⢻⣿⡃⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⣄⠀⠀⠀⠀⠀⡀⢀⣄
⣿⣿⠛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⣿⡟⠑⡷⣬⡀⣿⣿⣿⣿⢿⡈⢤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⢰⠀⠀⠀⣀⣬⡿⠀⠀⢀⣠⠐⢀⠀⡀⠈⠉
⢸⣤⣠⣻⣾⣿⣹⡿⢿⣛⠛⠉⣁⠾⠉⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⠀⢀⠆⡀⡉⠉⠻⣿⠃⠀⢀⡜⡧⢡⡈⢇⠀⣤⣄
⠹⣷⣿⣿⠻⣿⣟⠧⡄⠹⠷⣷⢿⣦⣤⡀⣀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⢀⣿⡯⠀⡘⢠⣸⣇⠀⠀⡟⠀⢀⣴⣿⡇⢻⣷⡈⢻⡄⣛
⡟⣿⣿⣿⢢⡄⢻⡄⣌⠐⠿⣿⣿⣭⣉⡉⣉⠀⠀⡀⠀⢦⡄⠁⠀⠀⠈⠁⠀⠙⡈⠀⠡⠃⠠⣦⣶⣿⠋⠈⠹⣿⣿⠁⢀⣰⡈⠛⢜⢨⣿⡇⣺⣿⠏
⣿⡀⠻⢿⣿⣿⡾⣧⣈⣵⡾⠿⣿⣿⣏⣯⡍⠙⠓⠀⠀⢨⠀⠀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⢀⣹⣿⠏⢀⠀⠀⢹⣿⡠⢠⣎⢻⣿⣮⡉⢿⣿⠏⢘⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠄⢐⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠠⠠⠸⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⣀⠠⠀⠀⠀⠀⠀⡠⠂⠐
⠀⠀⠀⠀⠀⠁⢀⡐⠀⠀⢄⢤⡀⠀⡆⡌⠄⠐⠈⠠⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠀⢈⠊⠀⠀⢄⠀⠐⠀⠂⠈⠄⣀⠠⢀⠌⠁⠂
⠀⠀⠀⠀⢀⢀⠀⠁⡀⠀⢈⡓⠈⠈⠁⢂⡀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⢐⠀⠀⠀⢀⠆⠂⢆⠀⠈⠄⠀⠀⠐⠀⡂⠈
⠀⠀⠀⠀⠀⠀⠆⢀⡂⠀⠂⠄⠀⠀⠈⡀⠎⠁⠂⠑⠈⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢈⠔⠁⠀⠠⠀⠀⠰⠀⠀⠀⠠⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⡥⠖⠆⠍⠢⠀⠀⠁⠄⡀⠠⡀⠀⠀⠀⠒⠁⢈⠄⠀⠀⡀⠀⠀⠁⠈⠀⠀⠂⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠂⢀⠉⡄⠀⠀⠄⠀⠀⠀⠄⠂⠃⠀⠈⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠠⠈⠀⠄⢀⠀⠑⡠⠂⡄⠤⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠂⠢⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⢀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠠⢀⠈⠀⠰⠐⠴⠈⠆⠎⡄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⢀⡠⠀⡀⠀⠈⢀⠘⠁⠀⠀⠀⠀⠘⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠀⠂⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠾⠂⠀⠀⠀⠀⠸⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⠀⡈⠀⠃⠀⠀⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⢠⠸⡳⠁⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠠⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠁⠀⠀⠰⠄⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠆⠀⠀⡤
⠀⢀⡄⠀⢀⣄⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⡠⠀⠠⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠉⣄⠑⠀⠁⢀⠀⠀⠀⠀⢀⣿⠀⠐⠀⠀⠀⠺⠀⠀⠐⠀⠀⢢⠀⣰⡄⠊⠀⠠⠀⠈
⠀⠀⠀⠈⢀⢃⠈⠀⣠⣤⣤⣵⠀⠀⠖⠢⠂⠒⠆⠀⡌⣂⠀⣐⠩⠁⢀⢠⣆⠰⢃⠱⡀⠤⣼⡇
⠠⣾⡀⠀⠐⠐⠰⠛⠛⠛⠃⠌⠶⠒⠀⠓⠐⠃⠘⠘⡖⠿⠀⠿⠀⠗⠀⣤⠈⠻⠫⠛⢋⠈⢀⠃⣠⣤⡀
⠈⣾⡅⣠⠨⠺⠀⠰⠂⠗⠀⡂⡄⠚⢀⠄⠄⠄⠘⠃⡇⠀⣏⡅⠀⠀⣶⠀⣶⠀⠿⠿⠀⢠⡄⢘⢁⣤⠉
⠐⠛⠂⢸⠐⠾⠀⠐⠂⠂⢸⠽⠃⠀⠀⠂⡀⠂⠀⠰⡇⠰⠃⢧⠈⠘⠛⠀⠛⠂⠿⠽⡄⠘⠃⢸⠀⠅⢠

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢘⣿⣻⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡃⠀⡄⠀⢠⣯⠄⠀⠀⠀⠀⣸⠀⠀⢀⠀⠀⠀⠀⣨⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠠⣿⣿⠿⣿⣄⡀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢢⢠⣇⠀⣰⣿⡇⢰⠀⠀⣴⣿⡷⠀⢀⣆⢰⣿⣇⠀⣾⠀⠀⡀⠀⣼⡆⢀⠀⠀⢀⣼⣧
⠀⠢⢼⣿⣿⣶⣉⡶⢿⣤⠀⠀⣼⣿⣇⠀⢰⠀⠠⣿⠀⠨⠀⢠⣿⣾⣿⣤⣼⣿⣿⣿⠀⢴⣾⣿⡟⠂⢼⣿⣿⣿⣿⣿⣿⣦⣠⡆⠀⣼⣧⣾⡆⠀⢠⣿⣿⠄⢰
⢠⣾⣾⣿⡿⢿⠯⢹⣿⣿⣷⣾⣿⣿⣿⣶⣿⣶⣼⣿⣦⣾⣄⣸⣿⣿⣿⣾⣿⣿⣿⣿⣀⣿⣿⣏⣼⣷⣿⣿⡿⠟⢟⡛⢿⣿⢿⣿⢈⣿⣿⣿⡇⠀⣼⣿⣿⣇⣾
⠘⢿⣿⣿⡿⣌⣴⣿⠿⠉⣿⡿⠿⠿⠟⠛⠙⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⢿⠟⠓⠚⠛⣵⡎⢿⣾⣿⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠛⠻⠿⣤⣿⣿⢡⠤⡤⠠⠀⡦⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠉⠀⠂⠀⠀⠀⠀⠀⠉⠋⠉⠉⠙⠛⠛⠿
⠀⢺⠙⠇⠉⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣤⣤⣀⣀⣠⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡄⠤⠀⠀⠦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣶⣶⣶⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣀⣤⣤⣤⣴⣶⣶⣶⡶⢶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠉⠉⠉⢠⣾⣿⣿⣿⣇⣼⣿⣿⣿⠉⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢠⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⠀⠀⠈⠙⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⣿⠀⠀⠀⡀⠀⣸⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⡀⢠⣿⡄⠀⠉⠙⠻⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢡⣄⣰⠃⠀⣠⣾⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠉⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡄⢸⠋⠁⢀⣴⣿⣿⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠈⢁⣿⠀⠛⠋⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠐⣠⡿⠟⠛⠉⠈⠀⠀⠀⠀⠀⠈⠹⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣾⣏⣀⣀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣠⣾⣿⠁⠀⠀⠀⢠⣾⠋⠉⠉⠛⠻⣧⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢸⣄⠀⠀⠀⢿⡆
⠀⠀⠘⠟⠁⣿⠀⣤⡄⣠⡟⠁⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣾⣿⠀⠀⠀⢸⣇
⠀⠀⠀⠀⢀⣿⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢰⡆⠀⠀⣿
⠀⠀⠀⠀⣸⠇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⢀⣹⣧⣀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣼⣷⠀⠀⢹⡄
⠀⠀⠀⢀⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⣴⠟⡥⠦⣽⣿⠟⠋⠉⠉⠉⠙⠻⢷⣄⣤⣤⣼⣿⣿⣿⣿⣿⣿⡆⢀⢸⡇
⠀⠀⠀⣸⡇⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⠀⣴⣿⣼⠃⠀⠀⠀⠰⣿⠸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟⡡⠶⣌⢻⣿⣿⣿⣿⣿⣷⠟⠈⣿
⠀⠀⠀⣿⠀⠀⠀⣿⠉⠙⠛⠷⣦⣄⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠙⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣿⣿⣿⡿⠋⠀⠀⣿⣿
⠀⠀⢸⡏⠀⠀⢠⡿⠀⠀⠀⠀⠈⢹⣿⡾⠋⠀⠀⠀⠀⠀⢀⣀⣴⢿⣗⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⡵⠛⠿⣿⣿⡿⠁⠀⠀⠀⣸⡏
⠀⠀⣿⠃⠀⠀⢸⡟⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠿⠛⠛⠛⠿⣿⣝⡿⠁⠀⠀⠘⠶⠂⠀⠀⠀⠀⠠⣽⡇⠀⠀⢹⣿⠁⠀⠀⠀⢠⡟
⠀⢰⡟⠀⠀⠀⣿⣿⣿⣿⣶⣦⣄⣘⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠟⠀⠀⠀⢠⣿⠀⠀⢀⣀⣾⣥⣀
⠀⣼⣧⡶⠟⠛⠛⠟⠋⠉⠙⠛⠻⣿⣿⣿⣶⡶⠞⠛⠛⠛⠷⣤⡀⠸⣿⣶⣶⣶⠀⣠⠀⠀⢀⣀⣠⣴⠿⠋⠀⠀⠀⢀⣼⠿⠛⠒⠛⠉⠁⠀⠘
⢠⡟⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⠀⠀⠀⠀⠈⠻⣤⣿⡿⣿⠥⠞⣡⣶⠟⣿⠋⡍⢀⡀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⡄
⢀⣿⣿⣿⣆⣀⣼⣶⡀⠀⢰⣶⣄⠀⢠⡀⠀⣀⠸⣇⣀⡀⠀⣀⠀⠀⠉⠳⣶⡶⢾⠛⢻⣇⣿⣿⢁⡾⣡⠟⠛⠉⠀⠀⣠⣶⣤⣾⣿⣷⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣼⣿⣦⣿⣿⣿⣿⣿⣶⣾⣷⣤⡀⠀⣈⢷⣼⣧⣼⣿⣿⣿⣿⣿⣃⣤⣠⡞⣠⣾⣿⣿⣿⣿⠿⠿⠿⠛⠿
⣿⡏⠉⠉⠉⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠛⠛⠿⣿⣟⠛⠛⠋⠛⠛⠛⠛⠉⠉⢀⣤⡿⠟⠛⠉⠉⣴⠟⠁
⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠑⠛⣿⠿⢿⣶⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⣿⣷⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠴⡆⠀⠘⢷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠀⠀⠀⠀⣿⣿⡗⠀⠴⣄⠤⣄⡀
⠀⠀⠀⠀⠀⢴⡇⡠⠁⢀⡀⠈⠂⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⢹⣽⡄⢀⠖⣼⣹⣿⣟⠂⠀⠀⢿⡀⢀⢀
⠀⠀⠀⠀⢠⣿⣭⣽⣧⡄⣾⣷⡀⠀⣠⣤⣿⣧⠀⡀⠀⣗⣠⣿⣿⣿⣿⣿⣿⣿⡿⠿⢶⣀⠀⠀⠀⠀⡯⢷⡄
⠀⠀⠀⠀⢰⣿⡃⣨⣩⣟⣻⠿⠭⣹⠎⠉⠛⠿⢧⣦⣤⣄⢲⢿⡏⠙⢻⣿⣿⡿⠀⠀⠀⢹⡇⠠⠀⠀⠀⠊⢿⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠻⢿⣿⣷⣌⡓⠀⢸⣿⡙⠁⠀⠃⣠⣿⡷⠩⠀⠀⠀⠨⢿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⠟⣁⠉⠉⠉⠀⠙⠲⢶⠶⢿⣿⣿⣿⣿⣿⣿⡀⣹⣿⣇⣀⡀⠀⠈⣿⣿⠀⠀⠀⠀⠀⢾⡁
⠀⠀⠀⠀⣈⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⡇⠀⠀⠀⢾⣧⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⡿⢿⣿⡇⠀⠀⣀⡠⠄⠀⢳⣾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡉⠻⡈⠀⠙⠁⠲⢃⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠘⠽⠢⠀⠈⠻⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⣀⣀⠄⢀⠀⠀⠐⢆⠀⠰⣤⣠⣐⣶⣿⣾⣿⣶⣿⡟⣿⠃
⠀⠀⠀⢄⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣁⠀⠹⠿⣍⣵⣿⣶⣦⣤⣯⣴⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠁⠀⡱⠀⣤⣄⡄⠈⠁⠀⠀⠀⠀⠀⠀⠐⠊⢙⣉⣉⢛⢻⠿⣿⠿⠿⠛⠿⢿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠱⢹⣿⣿⣷⣖⣸⣏⡤⠄⠀⠂⠁⢀⣀⣉⣭⣤⣤⣤⣠⣤⣴⣦⣴⣤⣶⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠑⠿⠻⣿⣿⣿⣾⣿⣾⡷⠗⠺⠏⠽⠟⠙⠿⠿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢀⣄⡰⠏⠀⠀⠀⠀⠀⠀⠈⢛⣶⡇⢰⠢⣽⠤⠖⣰⡤⠗⠀⠀⠀⠘⢦⣄⡀⣐⣟⣂⠀⣀⡠⠆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣒⢩⣬⡉⡆⣬⣤⣤⠤⠀⠀⠀⠀⢠⡔⠛⡖⣽⠲⠟⠭⡁⠀⠀⠀⠀⠀⠈⠙⡻⢳⣭⡼⢟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠬⣉⢴⡓⠈⠀⠀⠀⠀⠀⠀⠠⢤⡩⠾⠓⣽⠚⠶⣉⡠⠀⠀⠀⠀⠀⢀⣪⣗⣜⣛⣳⣮⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠄⠀⠠⢳⣄⠀⠀⠀⠀⠀⠀⠶⠉⠁⠘⣉⣭⡑⠃⠈⠙⠶⠀⠀⠀⠴⠊⠉⠁⠩⣧⡏⠁⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⣠⠀⡠⢒⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠄⡄⡄⠀⠈⠛⠁⠀⢰⢠⠰⠀⠀⠀⠀⠀⣀⡘⢄⠃⠿⠘⡠⢃⡀⠀⠀⠀⠀⠀⠀⢐⣻⡌⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⠤⠛⠀⠲⠈⠂⠀⠀⠀⠀⢀⡠⠬⠝⣃⠟⠉⠙⣌⠩⠐⢒⡠⠀⠀⠀⡀⢄⠀⠄⣨⡨⠄⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠲⠒⠤⠒⠤⢀⡠⠀⠀⠀⠈⠃⠒⠒⣒⡭⣦⣀⣠⡓⠭⣍⠁⠀⠀⠀⠙⠙⠝⠁⠂⢛⠇⠀⠙⠍⠁
⠀⠀⠀⠀⠀⠀⠊⠁⠃⠀⠀⣃⠀⠀⠈⠘⠲⠀⠀⠀⠀⠀⠈⢉⠊⠸⢰⡌⢄⠑⡄⠀⠀⠀⠀⠀⠀⠀⣤⠟⠈⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠃⠈⠁⠈⠑⠖⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⠈⠒⣿⠚⠀⡆⣀⡤⠀⠀⠀⠀⠀⠀⢳⡄⢰⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠡⠓⣤⢀⣹⣀⣤⠶⣛⠀⠀⠀⠀⠀⠀⡹⠿⢤⡀⢿⢠⡴⠿⢉⠀⠀⠀⠀⠀⠀⠲⢄⢡⣜⡴⣁⠤⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠼⣿⠿⣤⢁⡠⠄⠀⠀⠀⠀⠀⢀⡀⣠⠄⢻⢣⣄⢀⣀⠀⠀⠀⠀⠒⠓⠓⢐⠲⣿⡷⡂⠰⠶⡷
⠀⠀⠀⠀⠀⠀⠰⠎⡏⠈⠀⡒⠄⠀⠍⠰⠢⠀⠀⠀⠀⡴⠞⢻⠀⠀⣿⠀⠈⡟⠶⡄⠀⠀⠀⠀⠀⠋⢁⡜⢰⠙⡀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠊⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠸⠀⠝⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠴⣀⠀⡗⢀⡤⠆⠀⠀⠀⠠⠀⢀⠀⢀⠀⠀⠀⠀⢠⣶⡞⣟⢳⣶⡄⠀⠀⠀⠾⣷⣿⣿⣶⡦
⠀⠀⠀⠀⠀⣀⠑⡷⢀⡀⠀⠀⠀⠐⠀⠀⠻⠢⠀⠀⠀⠀⠀⢠⣭⡜⠿⢧⣽⡄⠀⠀⠀⣴⡿⣿⣿⣿⣦
⠀⠀⠀⠀⠛⠁⠀⡧⠀⠑⠂⠀⠀⠀⠈⠀⠠⠀⡀⠁⠀⠀⠀⠈⠙⠱⣿⠎⠙⠁⠀⠀⠀⠀⠀⠻⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠀⠀⣅⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠉⠀⣤⡄⠀⠀⠀⢠⠄⠀⡅⠀⢤
⠀⠀⠀⠀⠀⢘⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢀⣀⠀⠗⠀⣀⡀⠀⠀⠀⢀⡀⠐⠇
⠀⠀⠀⠀⠐⠈⠉⠛⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣦⠀⠉⠁⠀⠀⠀⠈⠁⠀⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⣰⡀⠙⠏⢰⡄⠀⠀⠀⠀⢠⣤⣿⣤⡄⠀⠀⠀⠀⠰⣶⢘⡛⣴⣶
⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⣉⡀⠜⠓⢤⣼⠀⠀⠀⠀⠠⠿⣿⡿⠇⡀⠀⠀⠀⢠⣷⡘⡟⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢤⡦⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠸⡿⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠻⠦⡄⢘⡃⣤⠞⠇⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⢀⢀⡄⠳⠜⣤⣀⡀⠀⠀⠀⠀⠀⠣⠼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠚⠊⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⢰⡷⠂⠀⡀⠀⠀⠀⠀⢦⠀⠀⡰⠁⠀⠀⠀⢀⠀⠀⢻⡇⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠰⢫⢤⠖⠛⢦⡞⠹⠂⠀⠀⠀⠀⣱⢤⠁⠀⠀⠀⠀⠛⠳⢦⠹⢣⡴⠟⠃⠀⠀⠑⠂⣤⣦⡀⠰⠂
⠀⠀⠀⠀⣀⣸⣄⢛⣸⢇⢤⡀⠈⠉⠉⠉⡳⠺⡁⠉⠉⠁⠀⣀⣤⠶⢠⡐⠶⣤⡀⠀⠀⣀⠀⠛⡿⠓⢀⡀
⠀⠀⠀⠈⠓⠁⢈⣽⡀⠀⠋⠀⠀⠀⠀⡜⠀⠀⠱⡄⠀⠀⠀⠈⠁⠀⣼⡅⠀⠈⠁⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⣪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⢀⡤⠖⢒⣋⣉⣤⣒⣒⣂⠠⢀⠀⣚⣷⣂⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣯⣥⠞⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡀⢾⡥⠾⣗⡀
⠀⠀⠀⠀⠀⠀⣀⣷⠄⢀⣾⢽⡷⢁⣾⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⢿⣿⣿⣿⣆⢣⣘⣯⡴
⠀⠀⠀⠀⠀⠀⠤⣟⣉⠤⣿⡟⢠⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠹⣿⣿⣆⢫⣹⡦⠄
⠀⠀⠀⠀⠀⠐⢚⣯⣵⣚⣿⠁⣾⣿⡟⠁⠀⠀⠀⠀⠠⣀⡜⠀⠀⠀⠀⠀⢸⣿⣿⡌⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠉⡯⣭⣭⡏⢸⣿⣿⠁⠀⠀⠀⠀⠒⠄⠈⡇⠀⠀⠀⠀⠀⠈⣿⣿⡇⢧⢹
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡇⢸⣿⠟⣇⢰⡂⠀⠀⠀⠀⣰⣁⣀⠀⠀⠀⢀⡼⠙⠙⡧⠼⢸⣄⣀⣀⡀
⠀⠀⠚⠋⠉⠉⠉⠉⠉⠉⠀⠘⢦⣀⠘⠢⣀⠀⠀⢤⠼⠃⠀⠀⠈⠉⠉⢉⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⣭⣥⣂⣤⣥⣴⡤⠴⠖⠛⠉⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⢐⠀⠐⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠓
⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠀⠀⠁⠀⠀⠁


⣿⡿⠿⡿⠿⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠁⡄
⠀⠀⠀⠀⠀⡀⠀⠘⠄⠰⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⢃⠐
⠀⠀⠀⠀⠀⠉⠐⠂⣰⣦⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠽⣻⠮⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠂⠉⠠⠀⠄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡄⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠌⠁⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠉⠀⠀⠀⠀⠀⠀⠰⣶⠀⡀⠀⠀⠀⡄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠓⠁⠀⠰⠆⠀⠀⠀⠀⠐⠢⢿⡁⢠⣦⠀⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠿⢠⡾⠋⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⠤⠽⡏⠈⡿⠥⢤⡄
⠀⠀⠀⠀⠀⢠⢴⠶⢆⡻⡱⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⣄⣷⣤⣬⣧⣤⣽⣾⣥⣤⣯⣤⣴⣭⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⣴⣃⣠⡞⠙⣦⣀⣳⡄⠈⠃⠀⠀⠀⠀⠀⠐⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⢳⣴⠉⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⣿⣿⣿⠃⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣩⡟⡇⠀⠀⠀⠾⢻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⣦⣽⣿⣧⢶⣰⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣧⣼⢿⡷⣾⣿⣏⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⢾⣙⣿⣽⣿⣿⣿⣷⣾⣧⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⣿⣟⣿⣽⣏⣻⡙⢿⣿⣾⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⡀⢁⢠⠃⢀⡀⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠛⣻⣿⣿⣩⢿⣿⣭⡁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠟⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢀⠃⠈⡀⠀⠉⠪⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣬⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⢶

⣿⣿⣿⣿⣿⣿⣿⡇
⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢤⡄⢀⠈⣤⡈⡑⠃⣨⢐⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡤⢢⡤⠬⣿⣿⣿⣚⣉⡼⢙⣣⢖⣇⡒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠠⣄⡓⣎⡳⣷⣬⢻⣿⣽⣿⣿⢾⠟⢻⣆⡹⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢸⠤⢧⢵⣿⢿⣳⣾⣿⣿⣿⣛⣿⣶⠾⢟⣼⣗⠶⢷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠱⢴⢶⣼⣼⣿⠿⣿⣿⣯⣬⣿⣝⣿⣿⡿⣧⣭⢽⡄⣿⡥⠑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠞⣭⣿⢷⣿⣿⣿⣻⣿⣿⣽⣟⣿⣿⣿⣿⣿⣾⣷⣶⠏⢀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠛⣿⠻⣿⣏⣿⣯⣿⣿⣻⣯⣿⣽⣿⣟⣟⣷⡿⣿⣏⣩⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡘⣀⡏⣹⣿⣌⣼⣯⣽⢷⡾⣯⣻⣽⣿⣿⣯⢿⣷⢩⣻⡿⢪⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠑⠙⣿⣾⣿⢭⣭⣻⣿⢿⣿⣧⢿⡿⣿⣽⣻⣾⣎⡱⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⠀⡛⢢⡟⢻⣽⣉⣿⡗⣷⣫⢷⣟⣏⡻⠎⣙⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⠒⢻⡦⣻⣯⣿⡝⣿⢋⡈⠽⠁⢹⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⡀⠈⢘⣺⢓⢣⠈⡳⠘⠉⠟⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⢀⠀⣘⡅⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣆⢼⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡆
⠀⢾⣞⢻⡇⠱⣿⣶⣖⣶⣞⣃⣴⣤⡌⣗⣆⣄⢘⠏⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⢠⣿⢯⢿⠓⠂⣦⣠⣤⡜⢂⣤⣼⣰⣿⣰⡆
⠀⣻⣥⠚⡍⢛⠿⡟⢙⡄⠁⡭⢨⣗⢩⡍⢹⡟⢋⣩⣬⠇⣀⢀⡀⢀⣤⠀⠀⣀⣠⣀⠾⢠⠯⣳⠈⣼⠪⣯⣳⡍⢿⣿⠯⡁⠛⡚⢧⠤⢳⠾⣧
⠀⡯⠘⢶⣸⢛⣶⢹⣥⣷⠚⡳⢘⣵⠈⣗⡤⠶⣤⠒⣶⡃⢿⣿⢻⡏⠛⢿⣿⣯⣿⡿⣺⣛⢈⢫⠀⣶⡀⢾⢧⠑⠶⣿⣖⠩⢢⡈⢻⠒⡼⢷⡞
⠀⠈⣠⣯⡜⢸⣦⡸⠿⣬⠋⣥⡬⡀⢟⡿⢂⡱⢉⣾⠉⡍⠺⣿⡴⠋⠡⠈⢿⣣⡹⡋⡩⠎⢹⡯⣹⠀⢯⡐⢆⠱⠦⣬⡁⠰⡆⢓⠘⣥⡯⡜⠳
⠀⠀⠀⡙⠐⠺⠤⡘⢀⡀⠀⠉⠘⠉⠛⢡⣄⢱⣏⠀⢳⣸⡛⠂⠁⠒⠒⠀⠈⠀⠁⠉⠁⠉⢚⡙⢉⠑⠟⢉⠒⢯⣠⡃⠛⠠⠆⠨⠢⣬⠔⢠⣍
⠀⠀⠐⠇⠐⠁⠄⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡇⢈⠧⡀⡘⡟⠢⠩⠉⠁

⠀⠀⠀⠀⠀⠀⣾⣿⣶⣷⣶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣤⣀⣀⣀⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⠿⣿⠋⢻⡿⠑⠿⣿⡏⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣟⠁⠀⡇⠀⠛⠀⠐⠇⠀⠈⣿⠀⠀⠘⣿⠉⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⠀⠻⡏⠀⢻⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠃⠀⠁⠂⠈⠿⠋
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠘⣶⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⡿⠄⠐⢛⣻⣔⠲⢼⣶⣦⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠻⣿⣳⠶⠦⣴⡖
⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠓⠊⠁⠀⠀⢀⣤⣶⣾⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⣀⣠⣄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣤⡀⠀⠀⠈⠉⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡷⣤⣉⣀
⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢻⡿⣟⠽⢟⣣⡾⠛⠓⠎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠾⠯⠷⠶⠍⠐⠋⠉⠉⠈⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠉⠀⠀⠀⢐⡜⠡⠶
⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⡀⢠⣤⡄⠀⣀⡀⣴⠓⠂⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣄⡁⠀⠂⠤⣈⠙⠉⠉⠀⠺⠂⠀⠀⠠⣴⠶⣤⣾⣤⣤⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠈⢀⡶⠄⠒⠂⠉⠉⠀⠊⠉⠥⠴⠒⠂⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠋⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠸⢦⠥⡴⠁⢠⡆⢀
⠀⠀⠀⡀⠀⠀⠀⠠⠾⣖⣠⣐⡾⠆⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣡⠚⠤⣄⠌⡎⢅⡀⠜⢢⣁⣠
⠀⠀⠈⠂⠲⢢⣖⡐⢗⣁⣽⣄⣱⢗⣐⣤⠶⠀⠊⠀⠀⠀⣄⡈⠀⢥⠱⠄⢆⣓⠆⡴⢫⢅⠀⢀⡀
⠀⠀⠀⠀⠀⠈⢡⡧⢴⣟⠩⢙⣷⢤⡧⠁⠀⠀⠀⠀⠀⠠⠌⡗⡪⠥⢬⢱⠡⣷⢹⠸⡤⡭⡒⡏⠤⠄
⠀⠀⠀⡀⢀⡨⣗⢓⣼⠿⢶⠿⢯⣔⢶⡧⣀⠀⡀⠀⠀⠀⠔⠋⠁⣱⢈⡥⡁⡆⡋⣬⡐⡹⠈⠑⠤
⠀⠀⠐⠐⠁⠀⠈⠠⣍⣖⠲⢒⣎⡅⠈⠐⠀⠑⠈⠀⠀⠀⠰⠶⠲⣁⠯⣖⡄⡇⣔⡨⢅⣱⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠉⠀⠈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣸⠀⢀⡼⠬⢆⠀⢸⡆⠑
⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣤⣀⠀⣦⠀⢹⠁⣠⡆⢀⣠⠄⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠄⠀⡆⠀⢄⠀⢀⣤
⠀⠀⠀⠀⠀⠘⠱⣦⢰⠓⣈⠀⢳⢠⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⢠⡸⠿⣸⢈⡰⠎
⠀⠀⠀⠀⠈⠻⢴⡒⡵⣯⠻⢻⠷⡔⡲⠜⠋⠀⠀⠀⠀⠀⠀⠐⠉⠠⣭⠔⡡⠨⡉⢨⡥⠄⠕
⠀⠀⠀⠂⠗⠒⢊⠘⡟⣂⠪⢂⡺⡧⡠⠒⠒⠗⠂⠀⠀⠐⠂⠒⠒⠿⣀⠨⡀⠒⡨⢠⡘⠟⠐⠂⠒
⠀⠀⠀⠀⠠⠾⠙⣒⢝⠧⣾⡮⢟⢕⡚⠱⠦⠀⠀⠀⠀⠀⠀⠐⠅⠊⣥⢐⡮⠈⣦⢠⣭⠃⠕
⠀⠀⠀⠀⠀⣰⣞⠋⣘⠎⢲⠈⢞⡈⢻⣶⡀⠀⠀⠀⠀⠀⠀⠀⡄⠟⢀⠊⠘⡟⠸⢠⠘⢳⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⢼⠄⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⡃⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣾⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛
⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠚⢿⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣿⡿⠖⠂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠘⠃⢰⡆⠀⠀⢀
⠀⠀⠀⠀⠀⣷⣤⣤⡤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠹⠁⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⠀⠻⠁
⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠁⠠⣾⡄⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢴⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣤⣤⡴⠀⠛⠃⠀⠀⠀⠀⣠⣶⣄⠀⠀⣰⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⠀⡹⢿
⠀⠀⠀⠀⣀⣠⣾⣷⣤⣀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⢾⣿⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠛⠿⠄
⠀⠀⠀⠀⠉⠛⢿⣿⠟⠉⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠰⠆
⠀⠀⠀⠀⠐⠆⠈⠁⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠗⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣴⠃
⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢤⣤
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⣡⡄⠀⠀⠚⠛
⠀⠀⠀⠀⠀⣤⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠛⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⠶
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁


⣿⣷⣶⣾⣶⡷⢾⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣷⡶⢷⠾⠿⠿⠿⣷⣶⠿⡶⠶⠶⠾⢶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣹⣿⣫⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⢟⣽⣿⢿⣿⣿⣻⣿⣛⣿⣿⣿⣾⣿⣿⣿⣿⣿
⡋⠿⣍⡻⡭⣟⢻⣾⣯⣿⣿⣫⡼⢟⡻⣿⢤⢸⣉⣛⠿⡿⣟⣋⢿⡵⢿⡘⣿⢿⡃⣽⡟⢻⠻⣟⠟⠯⢻⣿⣿⣤⣽⡍⡙
⠙⣟⠿⢙⠖⠸⢭⡷⠛⠃⢛⠟⡷⠛⣧⠽⢲⣏⣧⣿⣇⠻⣭⠻⠚⠷⠧⠓⢃⡾⡻⣿⠌⠧⡇⡹⡛⠄⣜⣹⣷⣶⣿⣧⠛
⠀⠉⠂⠁⠄⠀⠘⠀⠀⠚⠉⠀⠀⠀⠡⠆⠀⠋⠀⠃⠀⠡⠎⠃⠉⢀⠀⠆⠀⠀⠒⠁⠀⡀⠁⠂⠋⠉⡀⠁⠀⠀⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣤
⠀⢀⠠⠀⡖⠀⠀⠄⠀⢠⢀⣠⠄⣰⡄⠀⡀⢀⠀⠀⢰⠈⡂⠀⠀⠀⠀⣀⢰⣄⠄⠀⢀⡅⡀⢄⡁⢀⠘⠀⠀⡀⠀⠀⡠
⢲⣼⣅⣤⡧⡤⠴⡷⣶⠌⢿⣣⡤⢥⣬⣡⡽⣍⡖⠻⣏⡷⣇⣶⠢⣄⡛⡃⠈⣶⣤⣇⢺⠟⡋⠋⣭⠔⢪⣊⢦⣶⣙⠓⢖
⡁⣒⣻⣷⣷⣾⣰⣿⣿⣿⣟⢿⣱⣺⣟⢿⣌⣍⡳⣮⡘⢿⣿⣛⠿⠟⢿⣈⣹⢈⣿⣥⣿⡌⡟⣿⣆⢶⣶⣧⣯⣼⣿⣴⡿
⣿⣼⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣳⣾⣿⣿⣯⣿⣿⣿⣿⣴⣿⣿⣯⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠴⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠂⠀⠀⡀⠀⠂⠀⠀⢄⡴⣤⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⣿⣓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠦⠤⢄⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠠⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠐⠀⠐⠵⠶⢄⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠈⢀⡀⠛⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢔⡠⠆⡠⣀⢄⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠞⢁⡄⠏⢠⢄⢤⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⣠⢠⡀⣉⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⢰⠇⠀⠠⠸⠟⠽⣈⡀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣱⢀⡁⢍⣬⣙⢢
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠽⠡⠠⣤⡀⡀⠀⢀⢀⠀⠀⠑⡴⠊⠐⠔⠂⠀⣷⣭⡥⠄⡛⠚⠿⠻⠤⠐⠂⠀⠂⠐⠂
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⣀⣒⠓⠧⠗⠀⠾⠿⡇⠀⡧⣿⣏⣷⠁⠈⠃⠀⠿⠓⠚⣇⢀⠠⠀⠦⠔⠐⠒⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠸⠒⠀⠀⠐⠒⠸⠔⠒⠢⣼⠀⠐⡆⡠⠴⠊⠋⠉⠉⠐⠀⠀⠀⠓⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠺⣄⠤⢄⣀⣀⠀⠀⣀⣀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⢠⠀⠠⠀⠀⠀⠀⠐⢤⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢋⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣈⣰⢧⡀⠀⠀⠀⠀⠙⡃⠀⠀⠀⡆⢀⡼⢔⣈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⠦⣀⠤⠚⠁⢄⡀⠴⠛⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠛⠢⣄⡠⠔⠓⠤⣤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⡖⠋⢹⠀⠀⠀⢠⡀⠀⠀⠀⠃⠉⢲⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⡸⠁⠀⠁⠀⠀⠀⠀⠀⠉⡟⠢⡀⠀⠀⠀⠈⠆⠀⠋⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠔⠁
⠈⠻⡀⠢⡀⠰⡀⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠀⠀⠀⡄⠀⡐⢂⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⢲⠀⠀⠀⠀⠀⠀⠐⢄⣸⣀⠔⠀⠀⠀⠀⢠⠀⢀⠖⣻⠟
⠀⠀⠀⠀⢉⣲⣧⠀⠠⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⣸⣷⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣸⣧⡀⠁⠀⠀⠀⠙⠁⠀⠀⠀⡆⣀⣼⣄⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠢⣄⡠⠄⠁⠤⣀⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠾⠄⠀⠀⠘⠂⢄⡀⠘⠿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠚⠢⢄⣠⠴⠛⠦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⣤⠄⠚⠢⣄⡠⠖⠃⢤⣤⠒⠂
⠀⠀⠀⠀⢐⣲⡶⠀⠠⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⢲⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠋⡹⠀⠀⠀⢈⡀⠀⠀⠀⡎⠙⢶⠂⠈
⠀⣠⠂⠡⠋⠠⠁⠀⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠀⠀⠃⠉⢋⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡹⠀⠘⠀⠀⠁⠀⢀⠔⢹⠛⠦⠀⠀⠀⠀⠘⠀⠐⣍⣙⣄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃
⣶⣶⣶⠶⡶⢶⢶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠟⠛⠋⠉⠉⠉⠙⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠛⠉⠛⠛⢲⣾⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠀⠀⠈⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⠤⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⢠⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣧
⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣿
⠀⠀⣿⣇⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⣾⠏
⠀⠀⠘⢿⣦⠂⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠄⡀⠂⡀⢂⣥⡾⠋
⠀⠀⠀⠀⠙⢷⣦⣥⣈⣀⠄⠀⢀⣰⣤⡶⠏⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠾⣤⣥⣀⣤⣥⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠙⠲⣥⣬⣈⣠⣂⡄⣐⣀⢀⣅⣈⣤⡬⠿⢷⣬⣄⢄⠀⠄⠤⢀⢠⠠⣠⣴⠟⠋⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠙⠛⠳⠿⠶⠶⠛⠛⠉⠀⠀⠀⡀⢀⠀⠀⢄⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠤⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣣⠆⠀⠪⠃⠊⠠⡆
⠀⠀⠀⠀⠀⠀⢈⣐⡸⠀⠙⠋⠈⢀⢩⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠁⢬⠳⠀⢀⠠⠐⠕⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⢂⡐⠀⠤⡀⣱⠩⡈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⢌⠂⠐⡀⠭⠌⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠮⠂⠄⠌⠔⠀⠙⠈⠃⠀⠀⠀⠀⠀⠀⢀⢐⠔⡎⠄⠒⠠⢑⢄⡀⢀⠁
⠀⠀⠀⠀⠀⠀⠡⢰⠢⠀⠂⠖⠕⢀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠂⠄⡬⠆⡠⡆⢌⠀⠀⠀⠀⠀⠀⠀⠀⠃⢁⠀⡤⠀⠀⡞⡕⢂
⠀⠀⠀⠀⠀⠀⠈⠤⠁⠠⣦⠦⠀⢁⠅⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡨⢲⠁⢠⣤⠀⠰⡰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠂⠂⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡏⠑⠂⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠁⠀⠊⠰⠐⠩⠒⠂⠀⠀⠀⠀⠀⡉⠠⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⡆⠐⠭⠊⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢄⠑⠨⠃⠀⠀⢼⠡⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠚⢀⢠⠀⡀⢄⢒⠏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠲⣁⠄⠄⠒⡕⠀⢁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣒⡄⠀⣡⢀⡒⠀⢀⣁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⣀⠘⠠⠰⠂⠠⠩⡎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢂⠜⢀⣀⣄⠀⠐⣑⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣒⡆⠀⠤⡔⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢚⠢⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⢈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⡇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣹⣿⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣿⠀⠀⠀⣷⠀⠀⣦⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⣶⠀⠀⢀⣿⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣨⣿⣿⡀⠀⢠⣿⠀⠀⠈⠳⡄⠀⡇⠀⢀⣰⠟⠀⠀⣿⡇⠀⠀⣿⠀⢀⣼⠿⠷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠻⣄⢸⡇⠀⠀⠀⠀⠙⣦⣧⡴⠋⠀⠀⠀⠀⢻⡇⠀⠀⣿⣴⣟⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠶⠾⢿⣇⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⣾⠃⣀⡴⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣾⣯⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⡇⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠉⠉⢙⣧
⠀⠀⠀⠀⠀⠲⣦⡀⠀⠳⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⣠⣴⠖⠀⠀⠀⣠⡴⠆
⠀⠀⢀⣤⣠⣤⣼⣿⣦⣤⣼⣷⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣶⣏⣥⣤⣄⣀⣀⣠⣤⣾⣟⣁⣀⣠⣴⣿⣁⣀⣀⣠⣞⣉⣀⣀⣀⣀⡀
⠀⠀⠈⠉⠉⢉⣼⠟⠁⠀⣠⡾⠃⠀⣠⡿⠋⠀⠈⠉⠉⠉⠉⠉⢉⣥⢿⡟⢧⡀⠀⠀⠀⠀⠈⠉⠙⠻⣍⠉⠀⠙⠿⣍⠉⠉⠉⠻⣯⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠠⡾⠋⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢸⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠻⣦⡀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⡀⠀⣀⣀⣀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⠿⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠙⣶⡶⠶⠶⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⣶⣾⠋⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡏⠀⢀⡇⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣷⡒⠲⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢿⣿⡿⠁⠀⢸⠇⠀⠘⠗⠀⠀⣠⡾⠛⢹⡇⠙⠶⣄⡀⠀⠀⢻⠀⠀⢀⡏⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡇⠀⠀⢸⠀⠀⠀⠀⠀⠸⠏⠀⢀⣼⣧⡀⠀⠀⠙⠃⠀⠀⠀⠀⢸⡇⠀⠘⣿⣟⠛⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣏⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢰⡀⠀⢸⠀⠀⣴⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢠⠠⢀
⠀⠀⠀⠀⠀⠢⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠃⠀⢈⠀⠀⠁⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠
⠀⠀⠀⠀⠈⠡⢠⠨⠁⠀⠀⠀⠀⠘⠀⢤⣄⠀⠀⢠⡀⠀⢿⠀⢀⣤⠀⠀⣀⣤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠘⠠⠞⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠙⠛⠉⡀⢀⢀⡉⠛⠛⠁⠈⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠖⠀⠀⢰⠟⠁⣼⠀⠙⢦⠀⠀⠒⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠙⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢰⠃⠀⢸⠀⠀⢷⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢈⠀⠀⠀⠂
⠀⠀⠀⠀⢄⠈⠂⠘⠀⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠢⠀⠰⢄⠸⢀⡴⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡘⠇⠸⠁⣀⡄
⠀⠀⠀⠒⠀⠒⢂⠀⢀⠒⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠭⠀⠀⣍⡁
⠀⠀⠀⠊⢀⠐⠃⠸⠀⠓⢀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠃⠳⠀⠁⠁
⠀⠀⠀⠀⠁⠠⠂⢰⠀⠢⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣆⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢤⣒⣐⣐⣴⣶⣛⣀⣁⡘⠄⠄
⠀⠀⠀⠀⠀⢸⣏⠙⡯⣉⠩⣍⠏⠉⢉⠙⠉⠉⠉⠋⠛⠈⠋⠇⠑⠿⡍⢙⠑⡿⠩⠹⠃⢿⣇
⠀⠀⠀⠀⠈⢼⡞⠛⠓⠀⢙⠙⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⢈⠈⣡⠀⠀⡀⠀⠀⠀⣄⣸⢇⠁
⠀⠀⠀⠀⠐⢸⡏⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⢠⠈⠀⠁⠈⠀⠤⠤⣼⡿⠂⠁
⠀⠀⠀⠀⠐⢺⡏⠨⢥⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠼⠆⡢⣜⠀⠤⡆⠀⠀⠤⠀⢸⡇⠘
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠐⠈⠀⠂⢘⡂⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⣟⡜⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠃⠀⠈⠓⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⠀⢸⡇⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠒⠀⠐⠨⠀⠀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠠⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠠⢜⡀⠀⠀⠂⠸⠇
⠀⠀⠀⢀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡀⠀⠈⠙⢹⡇
⠀⠀⠀⠀⠐⠸⡇⠢⡄⠁⠀⠀⠀⠀⠠⠀⠀⠀⠄⡀⠀⠀⠲⢂⠀⢀⢀⡠⠀⠀⠂⠀⠈⣸⡿
⠀⠀⠀⢠⣤⢰⡃⠀⠀⣤⠀⡦⠂⠈⠀⠒⠀⠐⠐⠃⣄⠀⢀⠀⠀⠀⠀⡀⠀⠤⠠⢧⠂⣸⡇
⠀⠀⠀⠀⠀⠼⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⣈⠤⠄⠀⠀⠀⠀⠁⠀⠀⢔⡨⣆⣻⡆
⠀⠀⠀⠀⠂⣸⣧⣤⣤⡠⡊⠐⠸⠎⠃⠀⠚⠂⠤⠨⢇⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢍⢹⡇
⠀⠀⠀⠀⠀⢸⣇⣁⣡⣅⣀⣠⢄⢀⢤⣀⣲⠂⣈⣄⣀⣁⣰⢂⣀⣀⡀⣀⢀⣉⢹⣼⣩⣽⡆
⠀⠀⠀⠀⠰⠤⣁⠙⠉⠩⠉⠁⠈⠉⠉⠉⠉⠈⠉⠉⠙⠉⠙⠙⠋⠉⠓⠉⠋⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠟⠛⠿⣿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠠⣾⣾⣿⣶⣄⠀⠀⠀⠀⠀⠘⢷⣌⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⢀⠸⢿⢙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣧⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢤⡟⢸⣃⣬⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢠⡶⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡄⠀⠀⣉⣦⡆⣿⣾⠓⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣴⣶⣫⣅⣀⠀⢾⡇⣽⢾⣦⣻⢿⣞⣿⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⢛⣼⣋⢠⡀⢰⣛⣸⡇⣉⢋⣹⣻⣿⣍⣭⣦⡀
⠀⠀⠀⠀⠀⣄⠀⡀⠘⠖⣿⢠⡀⠐⠂⣀⡀⠀⠀⣀⡄⣂⡾⣻⢷⢋⣿⣿⣻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠄
⠀⠀⠀⠀⠀⢬⡻⢤⠤⢼⠿⣏⡀⣤⡄⠀⠀⠐⠂⠉⢙⣋⡶⣉⡄⠙⣿⣿⡟⠿⢟⣫⡿⢟⡿⣿⣿⣿⣿⣋⣥⢼⣇⣶⣄
⠀⠀⠀⠀⠀⠀⠠⠈⣤⣤⡤⣿⣧⡄⠳⢄⣤⣤⣀⠲⣾⣿⣴⠏⢠⠟⠹⣿⣤⣦⣟⣉⣷⢟⣿⡟⣿⣷⣾⣿⢻⣿⡿⠿⡝⣄
⠀⠀⠀⠀⠀⠀⠀⢾⣄⠐⠂⠞⢻⣧⣀⢀⣍⠛⢋⣴⣿⣛⣥⡆⠀⣠⣾⠛⢻⣟⣿⣿⣷⢬⣿⣼⣿⣿⣿⢿⡼⣿⡇⣶⣷⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⢄⣠⠼⢿⣿⡿⢃⣥⣿⣁⡿⢧⣿⣀⡾⢻⣇⣵⠟⢉⣽⣿⢿⡿⣿⣿⣿⣾⢛⣼⣇⣻⣿⣿⣧⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣮⣳⣶⣊⣿⠿⣿⣾⣯⣿⣟⣷⢿⣯⢥⣿⡟⣻⣆⢸⣯⣴⣎⣾⣯⣿⣻⡿⠿⣿⡛⣿⣣⣼⣽⣷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣿⠟⣽⣾⡟⣻⡿⠿⢿⣣⡾⣻⡾⢻⣿⡿⣿⣼⣯⡿⢿⣿⠏⣹⡿⣷⠿⣿⡿⢿⣿⣿⡿⠻⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣾⣋⣷⣿⣍⣛⠻⣻⣿⣿⢛⣿⣿⣧⣴⣋⣿⣏⣴⢦⢶⣾⣻⣶⣏⣤⣾⣵⣶⣿⣶⣶⣾⣿⣿⣿⣯⡛⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣟⣻⢶⣿⣿⣹⣷⣾⣏⢛⣿⣿⣩⣿⣿⣻⣿⣽⣯⣶⣿⠛⡿⡟⣿⣿⡿⢿⣿⢿⣏⢉⣿⣽⣿⣿⣿⣿⣽⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣯⡽⣿⣿⣯⠵⣿⣿⣽⣿⣿⣏⣴⣿⣿⣿⣿⣏⣴⣤⣧⡆⢩⣼⣀⠀⣼⢛⢿⠻⢿⡛⠛⣍⢿⣿⣷⡿⣯⠛⠩⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠱⠶⢻⣷⡺⣿⡋⢷⣅⣭⣿⣿⣿⣿⣿⣿⣿⠛⢿⡛⠿⣿⡟⣿⣿⡾⢿⣿⣴⣿⣤⣿⣿⣿⣼⣿⣿⣷⣄⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣿⣾⣿⣮⣿⣽⣿⣿⠿⣟⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣻⣿⣎⣻⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⠿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣯⣟⣹⣷⣿⣷⣶⣛⣿⡼⢿⣵⣿⣿⣿⣿⣿⣿⣿⣟⣭⣿⣯⣷⣿⡿⣿⣿⣿⣿⣿⣿⣯⡢⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣡⣯⣍⣬⣯⣙⣿⣿⣋⣶⠾⢿⣿⠟⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣭⣿⣟⣿⣾⣷⣤⠶⠶⢿⡾⢫⡜⢻⣿⣿⣯⡀⠙⠻⢿⡿⠿⣿⣿⣷⣿⡿⡏⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⡿⠋⠙⢿⣯⣷⣶⠞⣻⡅⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⢇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢀⣾⣿⡟⠀⠀⠈⢀⣀⣀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⢻⡏⠙⠃⠀⠀⠀⣼⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣻⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢺⡛⠉⠉⠉⠉⠉⠈⠉⠁⠀⠀⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢲⣟⠛⠙⠋⠛⠛⠉⠉⠀⢀⠀⠁⠐⡇⠀⠀⠀⢠⣤⢠⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⡴⠖⠛⠉⠉⠉⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⢀⣶⡀⠀⠀⢀⡇⠀⠀⠀⢸⣿⡜⠃⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢰⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡜⢀⡀⠀⣶⠀⢠⣇⠀⠀⣸⠹⣧⠀⠀⣸⣷⠀⠀⠀⡞⣿⣧⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⣠⡄⠀⣸⣇⠀⢠⢿⣷⢠⡇⢸⣇⠀⣿⣆⢸⣿⡄⠀⡅⠀⣿⡇⢀⠅⣿⠀⠀⠀⡇⣿⣿⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣧⡀⡿⣿⡀⣼⠈⣿⣼⣷⣼⣿⢸⢻⣿⣾⣿⣇⠀⡇⠀⡿⣿⢸⠀⣿⡇⠀⢰⠃⢻⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⣿⠀⡇⢻⣷⡏⠀⢻⣿⡿⠛⣿⡿⠀⢻⠁⣿⣿⢀⠇⠀⡇⠹⠟⠀⢹⡇⠀⢸⠀⠀⠀⣇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣿⣿⡇⠘⢷⡇⠀⠀⠿⡇⠀⠙⡇⠀⢸⡆⣿⠹⣾⠀⠀⡇⠀⠀⠀⣼⡇⠀⣼⠀⠀⢀⡿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡏⣿⠋⣷⠀⠀⠁⠀⣰⠀⡇⠀⠀⡇⠀⢸⠇⠻⠰⢹⠀⠀⠁⠀⠀⢰⣿⡇⠀⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠸⡀⣸⡆⠀⠀⠀⣿⠀⠟⠀⡆⢹⠀⢸⠀⠀⠀⣼⡇⠀⠀⠀⢀⣿⢻⡇⠀⣿⠀⠀⡌⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⣿⣿⠀⠀⠈⣿⡆⠀⠀⠀⣿⡆⢸⠀⠀⠀⣿⣧⠀⠀⠀⣼⢹⢸⣿⢀⢿⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣧⠀⣿⢹⡇⠀⠀⣿⡇⠀⠀⡀⣿⣇⣸⡄⠀⠀⣻⣿⠀⠀⠀⡇⢸⠸⡏⢸⠘⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⡘⣿⠀⠘⡟⣿⡀⠀⠀⡏⢹⣿⡇⠀⠀⡏⣿⠀⠀⢰⠃⢸⢰⣷⡜⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡏⣿⢿⠀⢰⡷⣿⠀⠀⢠⡇⣼⢹⡇⠀⠀⡇⣿⠀⠀⢸⠀⢸⣸⠻⠇⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⢸⡆⢸⣟⢻⠀⠀⢸⣇⣿⠸⡇⠀⢸⠁⣿⠀⠀⡏⠀⢸⣿⠀⠀⠀⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⢸⣾⠄⠀⢸⢿⠟⡀⡧⠀⢸⠀⣿⡄⢠⠇⠀⠈⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⢿⡇⠀⡾⠈⠀⠃⣟⠀⢸⠀⣿⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢸⣿⠀⢸⡄⡇⢯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇⠀⠀⠀⢹⠀⣿⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠘⣦⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡎⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡀⢀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣦⠠⢠⣤⠀⣀⡀⠀⣠⠴⠀⠀⡉⠻⣀⠯⠤⠶
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠃⠀⠘⠤⠧⠽⠀⠀⡁⠣⡀⠀⡁⠜⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠃⠀⠀⠀⢰⡀⠀⠀⠀⠖⠒⠒⡀⠀⢀⡐⠀⠈⠑⢂⠂⠁⣸⠷⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠠⠄⡀⠢⠅⠀⠀⠀⢀⠤⠀⠘⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠚⠁⠀⠑⠬⢀⡀⠀⠀⢠⠃⠀⣀⣤⣒⡉⠥⠀⠐⠸⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠋⠙⡗⠛⠥⣌⠀⠄⣸⠃⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⠠⠀⠀⠑⠢⡉⠢⣄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⠴⠟⠂⠀⠈⠑⠠⠈⣈⠁⠉⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⡀⠄⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁
⠀⠀⠀⠀⠀⠀⢦⡄⠠⡀⠸⢠⢁⠴⠁⣠⠀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠬⣄⢀⡄⠀⢻⡈⡼⠂⢀⡄⢀⡮⠄
⠀⠀⠀⠀⠀⠀⢄⠡⣐⡄⣀⡌⡋⣤⡀⢴⣠⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣄⠣⣔⣤⢣⣣⣆⡴⢃⣬⡄
⠀⠀⠀⠀⠀⠠⡄⠀⣠⣄⢮⣥⣧⡭⠖⣤⡀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢨⣯⠳⣁⢽⢌⡵⣫⡥⠀⢀⡄
⠀⠀⠀⠰⠰⠆⢈⡳⠀⠶⢺⡱⡷⣹⡱⠆⠰⢏⠀⠶⠰⠆⠀⠀⠀⠰⠦⠂⣉⡱⣹⢞⡇⢾⠆⡏⢾⡱⣉⡁⠴⠶⠐
⠀⠀⠀⠀⠀⠐⠃⠀⠘⠃⢖⡛⡟⢛⠦⠛⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢘⣛⣴⡉⢺⢊⡳⡙⡓⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠊⡐⠩⢇⠉⢃⣅⠛⠃⠪⠙⣈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠁⡔⠩⠛⡜⡝⠏⠳⡌⣛⠃
⠀⠀⠀⠀⠀⠀⠞⠃⠐⠁⢰⠘⡈⠲⡀⠙⠀⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠃⠀⣼⠁⢳⠄⠈⠃⠈⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠐⣽⠔⠀⣰⠆
⠀⠀⠀⠀⠀⠐⠦⡀⠀⢙⡄⠠⡧⠀⣼⠃⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡀⠭⣥⢠⢹⢂⢡⡯⠄⣠⡼
⠀⠀⠀⠀⠀⢀⠀⠉⢶⡀⢵⣀⣧⣰⠅⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣤⢀⠠⠹⠣⣅⡚⠇⠾⡆⠟⣀⡥⡛⡁⢀⣠⡀
⠀⠀⠀⠀⠀⠙⠑⠦⣦⡽⢿⣤⢿⣬⠾⣥⡦⠶⠚⠃⠀⠀⠀⠀⠀⠀⠊⠕⢃⡦⢙⡉⣽⡴⣼⡍⣛⠰⣔⠓⠍
⠀⠀⠀⠶⠆⠶⠰⠶⠶⡳⣷⠶⣹⢾⡷⣟⠶⠶⠰⠆⠰⠆⠀⠀⠰⢾⠶⣌⠶⠶⢎⣿⡇⢎⢎⣿⣉⢶⠶⢎⠶⢾⠶
⠀⠀⠀⠀⠀⣠⡠⠖⠟⣳⣾⠙⣾⢛⣖⡟⠗⢦⢄⡄⠀⠀⠀⠀⠀⠀⢄⡢⡌⠗⣨⣁⣻⠳⢻⣃⣩⠰⠣⡤⣂⠄
⠀⠀⠀⠀⠀⠈⠀⣠⠾⠁⡺⠉⡇⠹⡂⠙⢖⡀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠐⣠⡑⡋⢥⡇⢶⠇⡦⠉⡓⣡⡁⠈⠙⠃
⠀⠀⠀⠀⠀⠠⠖⠁⠀⣬⠃⠐⡗⠀⢻⡄⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⢒⡛⠘⣸⡌⡘⣗⠂⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠁⠠⣻⠃⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢀⠀⡄⠁⢈⢦⠀⢳⠄⠀⠀⠀⡈⠄⠘⠁⠀⠐⣇
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠲⡆⡑⢈⡦⠓⢆⡨⠸⠃⠘⠃⠀⢄⢀⠁⠀⡇⠀⠂⠀⣈⢠⠄⠐
⠀⠀⠀⠀⠀⢰⠸⠃⠀⠀⢀⣀⢙⡜⡏⢀⡆⠀⡇⠘⡄⠞⠀⠀⠀⠈⡀⠀⠙⠲⣄⠀⢸⣅⣀⡀⠀⣀
⠀⠀⠀⠀⠘⠠⡇⠀⠀⢀⠈⡘⠋⢹⡇⠀⠹⣴⠃⠀⠙⡇⠐⠉⠱⣸⠃⠀⠀⠀⠈⣷⠋⠀⠀⠉⠈
⠀⠀⠀⠀⠒⠂⢧⠀⠀⠀⠘⡀⢹⠞⢧⣄⠀⢸⠀⢀⢀⡗⠀⠀⠀⢹⡀⠀⠀⠀⢠⡤⣶⡄
⠀⠀⠈⢀⡀⠀⠀⢓⡴⢦⣄⡁⣿⠀⠀⠈⠉⠛⠣⣌⢨⡇⠀⠀⠀⠈⢳⣄⣴⠞⠋⢉⠉⠁⠀⠂
⠀⠠⠀⢠⠐⠉⠉⠁⠀⠀⠈⠳⣜⣦⠀⠀⠀⠀⠀⠈⣿⠀⢠⡨⠀⠀⣸⡟⠁⠀⠀⠰⣠⠄⢒⡠⠀⢀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⠶⣶⣶⠀⠀⣿⡤⠔⠁⠀⢀⣿⠀⠀⠀⢰⠞⠉⠐⢉⠅⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠉⠢⠤⡆⠀⠀⠀⠀⠈⢿⣆⠀⣿⡄⠀⠀⣠⣾⠏⠀⠀⢀⡿⠀⠀⢠⠌⢀⠀⢀⠠
⠀⠀⠀⠈⠶⠲⢦⣀⣀⡀⠀⠘⣄⠀⣴⡿⠀⠈⢿⣆⣿⡇⣰⣿⣟⣁⣀⣀⣶⣋⣠⠴⠛⠛⠒⠡⠴⡁
⠀⠀⠀⠄⢠⠚⠉⠉⠉⠉⠙⠓⠚⠲⠿⠷⣤⣤⣈⣿⣿⣿⣿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠠⣴⣶⣶⡾⢷⣶⣶⣶⣶⣶⣶⠖⣀⡌⢉⣉⢙⠉⡉⠉⢁⣀⠲⠶⠶⢶⣶⡶⠶⠶⢶⣶⣶⣶⣒⡂
⠀⣀⣀⣴⣿⣿⣿⣿⢿⠿⠏⣉⢁⣴⣶⣾⣿⡇⢸⣿⣮⡇⢹⣦⣬⠹⣷⡻⣿⣶⣦⣜⣻⣷⣿⣿⣿⣿⠿⠧
⠀⠠⣽⣿⣿⣿⣿⣿⢟⣴⡿⣣⣿⣿⣿⣿⠟⣠⠘⣿⣿⣧⠰⣬⠻⣦⡙⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣞⡀
⠀⢛⣿⣿⣿⣿⡿⣵⣿⣟⣶⣿⣿⣿⣿⡟⡄⢻⣆⣛⡛⢿⣿⣜⣷⣶⣽⡆⢙⡻⢟⠻⢟⣭⣿⣿⣿⣿⠋⠃
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣷⣘⠿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣶⣮⣭⣭⣿⣟⠛⠋
⠀⠈⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣽⣿⣿⣿⣿⣶⣮⣝⢻⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣯⠭⠅
⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠄
⠀⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⡄⢣⢠⠁⠀⠀⠀⠀⠀⠠⢬⡄⣰⣾⠁⠀⠀⠀⠀⠀⠀⡄⠀⡨
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠋⠀⠠⠀⠀⠀⠀⡂⢤⡄⢄⡦⢄⠀⠀⠀⠀⠈⠀⠘⣔⣅⠤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⠬⠭⠕⢘⢛⢻⠅⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢃⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠂⠴⢶⡋⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⡠⠌⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠔⢏⠀⠀⠈⡼⠑⡜⠀⢀⡠⠊⠁⠀⠀⠀⠀⠁⠀⠱⠚⠒⠎⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠢⠀⠀⠐⠀⠀⠠⢀⡡⠀⠈⡇⠀⠉⠐⠉⠀⣴⠊⠁⠀⠁⠀⢄⣀⢀⢀⡂⠐⠶⠚⠲
⠀⠀⠀⠀⠀⢴⣤⣨⡦⠐⠶⠜⠶⣖⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣈⣉⢁⣉⡑⠶⠶⠴⣴⡄
⠀⠀⠀⠀⠠⣖⢤⠤⣴⠲⠶⠻⠔⠴⠄⠀⠐⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠈⢉⠉⠉⣶⣄⢠⣤⣄⠴
⠀⠀⠀⠀⢐⣠⣀⣤⣬⢖⢰⣠⢤⠠⣄⠐⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠐⡋⠉⠉⠉⠙⠮⣌⠠⡀⢈⠁⠀⠀⠄
⠀⠀⠀⠀⢄⣠⡠⣄⣬⢅⡀⢀⠀⡀⣀⡠⠀⠀⠈⠂⢄⠈⠁⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠛⠓⠓⠘⠓⠓⠦⣿⡆
⠀⠀⠀⠄⠄⢀⣀⢀⠍⡉⠛⠙⠛⠉⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⡆⠀⠀⠀⡾⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠠⣇⠀⠈⠠⠁⢺⡆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠠⠀⠀⡁⠀⠀⠀⠀⡌⠉
⠀⠀⠀⠀⠀⠠⣁⠀⠀⠀⠤⠆⡗⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠬⠀⠀⠀⠀⠉⠤
⠀⠀⠀⠀⠀⠀⠉⠓⠶⠀⠐⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠁⠛⠀⠀⠀⠐⠀⠠⠀⠀⠈⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠠⡄⢠⠀⠀⠀⢀⡤⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠝⠁⠀⠀⠀⢸⠀⠀⠀⠂⠔⠁⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠠⠘⠀⠀⠀⠁⠀⠂⠀⠄⡸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⠀⣀⣀⣀⣀⠠⠄⠒⠈⠀⠀⠀⠀⠀⠀⠤⠤⠦⠤⠤⠤⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠀⢄⠀⠀⡀⠀⠀⠀⢀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⡡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠀⠀⢀⡔⠂⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠀⠠⢀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⢀⠠⠄⠀⠈⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠇
⠀⠀⢀⠂⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠸
⠀⠀⡌⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠐⠊⠉⠀⠁⠀⠉⠀⠂⢄⠀⠀⠀⠀⡒⠀⠄⡀
⠀⢠⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⡀⠀⠐⡄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠠⠄⣡⠀⠀⢡
⠀⠀⠢⠃⠄⠀⠀⠀⠀⠀⠀⠀⣘⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡻⡀⠀⠘
⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢦⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠠⣊⣀⣀⡀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠃⠀⢠
⠀⠀⢀⡀⠀⠡⡀⠀⠀⠀⢌⠇⠀⠀⠀⠀⡬⠈⠉⠁⢀⡜⢄⢃⠀⠀⠀⠀⡇⠉⠓⣄⣩⣹⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡄⠀⡆
⠀⠌⠀⠈⠉⢡⠈⠑⠀⡜⡌⠀⠀⠀⠀⠊⠁⠀⠀⢠⡟⠀⠀⠙⢦⣄⠀⠀⢡⠀⢼⠏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠒⠒⠴⠀⣃⠀⠄⠠⡁⠀⠀⠐⣤⢢⢣⠀⠈⢳⡀⣹⢡⠊⡉⠢⡀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⢡⢳⣀⢀⣠⡏⠆⡼⠧⠖⠊⠉⠁⠘⢾⢁⠖⠈⠀⠠⠤⠤⠎⠤⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠔⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⢀⠀⠀⠈⠱⠀⠄⠴⠐⢤⠄⠀⠤⠀⠠⠀⠀⠀⠙⠄⠀⠀⠀⡠⡔⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠃
⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠉⠑⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡠⢀⣑⡠⠎⠀⡀⡠⠺⡠⠃⠀⡰⠁⠦⠔⠒⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⣀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠐⠂⠈⠁⠀⠀⠀⠀⠈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠒⠒⠒⠂⠤⢀⠀⠉⠐⠒⠒⠈⠉⠁
⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠤⠄⠠⠀⠂⠀⠉⠀⠉⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠊⠀⠀⠀⠀⠀⠰⣉⢀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠶⠖⠒⢤⠄⠐⠒⠒⠒⠂⠀⠀⠐⠒⣠⣄⢀⡤⠖⠒⠒⠒⠒⠒⠒⠒⢦⣤⡀
⠀⠀⠀⠀⠀⠻⠤⡀⣀⡀⣐⠤⠖⠚⠛⠋⠀⠀⠠⣀⡀⢀⡀⠀⠀⠀⠈⠉⠉⠉⠩⠽⢯⣄⣀⣀⣀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢃⡏⢙⡧⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⣻⣦⠶⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠘⠦⢤⠀⣠⣄⠀⢀⠀⠀⠀⠑⠦⢤⣄⢠⣶⠶⣸⢟⠀⠀⢲⢸⣿⡞⡏⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣶⢏⠘⡇⡟⠀⠀⠀⠀⠀⠀⠹⢸⡇⠀⣏⣌⠀⢠⡿⣼⣿⡇⣁⣸⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⣷⡆⢠⠖⠀⠀⠀⠀⣾⡁⠀⣼⣿⠀⢸⣇⢻⢸⠀⢻⡜⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⡏⣿⡇⢸⡆⠀⢰⡄⠀⣿⡇⠀⡿⢹⠀⣿⣿⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣷⢸⣿⠀⣼⡇⢠⡇⡇⢰⡇⢸⢘⣿⣿⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣲⢿⢸⢸⣿⠀⣿⠇⢸⡇⡇⣸⡇⣷⢸⣿⣿⡀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⢸⣿⡇⣿⢰⢸⣧⡇⠏⡇⣇⢸⣿⣿⡇⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⢸⡇⡇⣿⢸⠸⣷⡷⡆⡃⡟⢸⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⣇⢹⣼⠀⣿⣿⡄⠀⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⡇⣿⣾⣿⡆⣿⣿⡇⠀⡿⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⡇⣿⢻⢿⣧⣿⣿⡇⠰⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢃⡟⣼⣿⠷⠿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠛⢻⠀⠀⣿⠇⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⡆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⣀⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀
⠀⠀⠀⠀⣶⣾⣤⢼⣿⣿⢄⣸⣷⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⡀⠀⠐⣷⣿⡁⠀⠀⠀⠀⠀⠀⠠⣼⡆⣀⣿⣿⣁⢰⣇⡄
⠀⠀⠀⣀⠉⡿⠿⣦⣻⣡⡾⢿⣏⣉⡀⠀⠀⠀⠀⠀⢀⠀⠾⢿⡇⢸⣷⣯⡍⠀⠀⠀⠀⠀⠀⣈⠉⣻⠿⣥⣼⣧⣨⠿⡟⠛⡀
⠀⠀⠰⣿⣿⡷⠶⣾⣿⣿⡟⠻⡿⢿⡟⠀⠀⠀⢠⣿⣾⣷⣤⣤⣿⣾⣧⣴⣿⣴⣿⠤⠀⠀⠀⢾⡿⡿⠶⣿⣏⣿⣿⠤⣿⣾⠥
⠀⠀⠀⠉⣤⣿⣿⣋⣼⣏⢻⣾⣧⣄⠀⠀⠀⠀⠀⠋⠘⠋⠶⣶⡏⢹⣷⣦⠝⠀⠛⠀⠀⠀⠀⢉⣀⣹⣶⠛⢻⠟⢳⣴⣃⣈⠃
⠀⠀⠀⠀⠛⠻⠉⢉⣽⣯⡉⠹⠟⠃⠀⠀⠀⠀⠀⠀⠠⢶⣾⡋⠃⠘⢫⣿⡶⠆⠀⠀⠀⠀⠀⠀⠚⣻⠉⢙⣿⣟⠋⢹⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠙⠃

⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠙⠻⡄⢠⡄⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⠁⣀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣃⠀⠀⣸⡿⠇
⠀⠀⠀⠀⠀⢰⣦⣹⣾⣧⣏⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠋⣷⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⠟
⠀⠀⢿⡿⠶⠶⣶⣿⣿⣿⣿⡶⠶⠶⣾⣷⠀⠀⢠⣶⣿⣦⣼⣧⣼⣿⡧⢴⣧⢤⣾⣵⡆⠀⠀⣾⡷⢶⡶⠶⣿⣿⠶⢶⡦⢾⣷
⠀⠀⠀⠀⠀⠘⠋⣱⢿⡟⣯⠹⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠾⢥⣼⠉⣷⣤⠿⠆⠈⠁⠀⠀⠀⠀⠀⠀⢀⣼⠋⢻⣦
⠀⠀⠀⠀⠀⢀⣴⠃⠘⠋⠈⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡙⠿⠋⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠀⠀⢹⣦⡄
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣄⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⡄⠀⢀
⠀⠀⠀⢀⣤⣧⣈⣿⡷⢾⢯⣄⣿⣆⠀⠀⠀⠀⠀⠀⠀⣻⣦⡿⠀⠀⠀⢻⣶⣟⡀⠀⠀⠀⠀⠀⢠⣤⡼⣻⣭⣽⣏⣳⢿⡃
⠀⠀⠀⣺⣉⡿⢷⣾⣿⣿⣶⣟⣳⣴⣧⠀⠀⠀⠀⢠⡌⠉⠛⢷⡄⣴⣠⡾⠋⠉⢉⠀⠀⠀⠀⣀⣨⢿⡿⣭⣷⣿⣾⣛⣧⣽⡿⠂
⠀⠀⠠⣟⢻⡟⣿⣾⣏⣹⣿⣿⣩⣏⣽⠅⠀⠀⠠⣤⣿⣦⣤⣿⡿⠛⣿⣿⣥⣴⣿⣥⡀⠀⠀⠙⢿⢿⣛⣳⣿⣹⣿⣿⣽⣇⣧⡄
⠀⠀⠀⢿⡟⢯⣹⢾⣽⣻⡽⢯⣼⣛⡿⠁⠀⠀⠀⠠⠟⠁⠀⢻⡿⣶⢿⣿⠃⠈⠻⠌⠀⠀⠀⢰⡾⣟⢏⣵⢿⡿⣟⢳⣾⣱⠋⠁
⠀⠀⠀⠈⢺⣿⠟⢶⣿⠼⣷⡛⢻⠿⠁⠀⠀⠀⠀⠀⠰⢶⣶⡟⠀⠉⠀⣹⣿⡷⠆⠀⠀⠀⠀⠀⠀⣼⡿⣝⣻⣗⣻⣥⠞⠻⠇
⠀⠀⠀⠀⠀⠈⠐⠻⠻⠼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠷⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠈⠛

⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠙⣛⣸⣦⡀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣀⢼⡧⣀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣴⣇⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢄⡱⡄⠀⠀⠀⠀⢸⢳⠀⠀⠘⢿⡿⠃⠀⠀⡜⡇⠀⠀⠀⠀⢠⢎⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢖⡦⣀⣀⣀⣇⢣⣀⠀⢸⡇⠀⣀⡜⣸⣀⣀⣀⢴⡲⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⢻⡲⣤⠔⠛⡌⢯⡑⢼⡧⣊⡽⢡⠛⠢⣤⢖⡟⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀⠀⢸⢀⠟⢺⣶⡒⠙⡜⡌⢻⡟⢡⢣⠋⢒⣶⡗⠻⡀⡇⠀⣀⣀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⣙⡛⠤⣜⠀⠑⣤⡘⣿⢾⡷⣿⢃⣤⠊⠁⣣⠤⢛⣋⠭⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠘⢎⠳⡒⠭⣶⣬⣿⡻⣏⣹⢟⣿⣥⣶⠭⢒⠞⡱⠃⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠶⡷⣿⡷⠶⠶⠶⡷⣿⠶⢾⡷⣏⣹⣏⣹⣏⣹⢺⡷⠶⣿⢾⠶⠶⠶⢾⣿⢾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⢠⣞⡴⠥⣒⠿⢛⣽⣵⡯⣹⣮⣿⡛⠿⣒⠬⢧⣱⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣒⣩⣵⠒⢫⠀⡠⠛⢡⣿⢾⡷⣿⣌⠛⢄⡀⡝⠒⣬⣍⣒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠀⢸⠈⣦⢼⠿⠥⣠⢣⢃⣼⣧⡘⡜⣄⠬⠿⡧⣴⠁⡇⠀⠉⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣼⠵⠛⠢⣤⢃⢞⡡⢺⡗⢭⡳⡘⣤⠔⠛⠮⣧⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠮⠗⠉⠉⠉⡏⡜⠉⠀⢸⡇⠀⠉⢣⢹⠉⠉⠉⠺⠵⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⡱⠃⠀⠀⠀⠀⢸⡼⠀⠀⢠⣾⣷⡄⠀⠀⢧⡇⠀⠀⠀⠀⠘⢎⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣭⢹⠟⠁⠀⠀⠀⠀⢠⣾⠀⠀⠀⠉⢺⡗⠉⠀⠀⠀⣿⡄⠀⠀⠀⠀⠈⠻⡏⣭⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠒⠚⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠂⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠒⠤⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⣀⠤⠤⠒⠒⠋⠉⠉⠑⠒⠒⠢⢄⣀⠈⠐⠤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⢦⡀⠀⠉⠀⠂⠁⠀⠀⡆
⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⣀⢤⠀⠈⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⣌⠔⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠄⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢠⠉⠉⠀⠾⠟⠀⠀⢀⡌⠀⠀⠀⠠⠀⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠀⡀⠀⠀⠚⠀⠀⠀⠠⠇⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⡰⠾⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢬⢺⣁⠀⠀⣰⠀⠀⠀⣂⢠⣭⢀⣶⣠
⣤⣤⢧⢰⣆⡋⣼⣶⠦⢶⡶⢧⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠺⣾⢅⡀⠀⢺⡦⢀⢐⣏⡷⡎⢻⢼⣞
⣿⣿⠛⡿⠊⡓⠚⣧⡇⣼⣡⠚⣶⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣣⣇⡃⢺⡿⠬⠁⠘⣻⡧⠑⢈⣿⠞⡓⠛⡿⣴
⣿⣥⣷⠓⠋⢸⡏⠙⣿⣿⣧⣾⣿⣦⣿⣷⣷⣴⣶⣦⢤⣤⠒⣧⠯⢝⣄⡀⣀⢠⣌⡠⢥⠘⢄⢴⣯⣿⣦⣿⣈
⢸⣿⣟⠉⡱⢋⠙⣟⢻⡿⡿⣿⢻⢿⣿⣿⠿⠿⢶⣿⣿⡯⠔⣣⠘⢦⠷⣿⢇⡨⡚⣧⢉⠄⣍⢸⣿⣿⣿⠿⢿
⠘⠹⢏⡨⠦⠈⠓⠛⣍⡁⠀⠸⠀⠀⠈⠀⠀⠀⠀⠀⠩⠃⠁⠭⠀⠉⠠⠓⠐⠀⠀⠠⡇⠘⠀⠓⢊⣃
⠀⠐⠒⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠂⠂⠠⠤⠤⠤⠤⠀⠄⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣩⣶⣤⠠⠄
⠀⠀⠀⠀⠀⣀⣰⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠈⠡⠔⠂⠀⡴⠆⢞⠿⡿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠤⠤⠤⠤⠷⠾⠳⠲⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠠⠴⠶⠛⠡⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿