Pork Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⡾⠀⠀⠀⣀⢀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⣠⣽⣿⣄⠀⠀⠀⢿⣦⣠⢈⣽⠻⣿⣿⣿⣿⡄⠀⠀⠀⣐⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠛⠛⠻⠿⢿⣿⡿⠿⠿⠀⠀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠾⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣃⠉⣉⡁⣠⡄⡄⡄⠀⢠⣤⣀⣤⡈⣉⡙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡭⠘⣿⡃⡷⠀⣑⡆⡗⣇⠀⢸⡞⢻⣃⡇⣿⡟⣸⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⡆⠀⠀⠀⠃⠀⠁⠁⠉⠁⠈⠀⠁⠀⠀⠈⠀⠀⠉⠀⠁⠁⠃⠛⠀⠀⠀⡆⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢶⣶⠦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠹⣷⣶⣭⡻⣿⣶⡤⠖⠚⠋⠉⠛⠻⣿⡷⡶⠾⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠠⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠒⠒⠒⠒⠒⠢⠤⠤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣧⠀⣀⣶⣿⣿⣿⡿⠋⠀⠀⠈⠙⠲⣤⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣀⢔⣪⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⢛⣶⣦⣼⣷⣽⠉⠛⢿⣿⠟⠲⣾⣏⣿⣷⣄⠈⠃⠀⠀⠀⣠⡘
⠀⠀⠀⠀⠀⢀⢞⣵⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠏⣿⣿⣿⣿⣦⣤⣼⣿⣤⠀⠠⠛⠛⢿⣿⣷⣄⠀⠀⠀⠉⠁⡀
⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣸⣿⣿⢃⢂⢀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣶⡛⣿⣿⣦⡇⢾⠀⠀⠀⠘
⠀⠀⠀⢀⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣾⣰⡀⡆⢀⠀⠀⠀⠀⠀⠀⠀⣤⣷⢸⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣷⣤⣀⣤⡦⠊
⠀⠀⢀⡾⠃⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣼⣆⣆⣇⣧⢀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣛⣹⠟⠋
⠀⢀⠞⠁⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⢿⣿⣿⣿⣿⣿⣷⡮⠭⠍⠉⠉⠉
⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡌⠈⠀⠀⢸⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⣼⣿⣿⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢿⣿⡃⠀⠀⢠⣿⣿⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣼⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢹⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣧⣀⡆⠀⠀⠘⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡀⠀⠀⠙⢻⣿⣿⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡰⢻⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢸⠳⡀
⠀⠀⠀⠀⢰⠁⠘⡄⠀⠀⠈⠙⠒⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠒⠉⠀⠀⠀⡜⠀⢳
⠀⠀⠀⠀⣸⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⢀⣀⠤⠄⠒⠒⠒⠒⠤⢄⣀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢹⠀⠀⠀⠀⠐⠆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠆⠀⠀⠀⠀⢸⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡸⠀⠀⠀⢰⣿⣆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣾⣷⠀⠀⠀⠸⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⠀⠀⠀⠌⠙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠋⠄⠀⠀⠀⢱⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠁⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⢉⣉⣉⡁⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢁⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢸⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢸⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡂⠈⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡈⠀⡺⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⢠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢦⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠴⠶⠄⠀⠀⠴⡶⠄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠎⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠣⣳⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢠⡡⠋⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠠⠤⠤⢀⣀⡠⠔⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠤⢄⡀⠀⠀⢀⡀⠤⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⡿⢟⣟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠈⣿⣿⣿⣿⣿⣿⣿⢋⡾⣿⣿⣿⠀⣻⣿⣿⣿⣿⣿⣿⡏⡄⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣿⣿⣿⣿⣿⣿⡇⣾⡇⣼⣿⠟⣠⡿⡿⢿⡿⠿⠿⣿⠀⢡⠿⣿⣿⣿⣿⣿⣿⣿⠿⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠑⣿⣿⣿⣿⣿⣿⠀⣿⡅⣨⣷⣾⡟⢠⢰⡄⢿⢰⠆⣿⠀⣴⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢻⣿⣿⣿⣿⣿⣆⢿⠇⣿⣿⣿⣷⡘⠷⢀⣴⣿⠐⣫⠀⣤⡙⢟⣼⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⣭⠙⠛⠛⠻⠟⠛⠛⠛⠛⠛⠋⠉⠉⣶⣍⢿⣿⣿⡟⠛⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⢹⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠛⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠛⠉⢋⠛⠛⠲⠶⠶⠟⠛⠋⠉⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢢⡖⠉⠀⠀⠀⠀⠠⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡜⠀⠀⠀⠀⠀⢠⠃⢸⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢇⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠁⢠⠃⠉⡆⠘⠉⠄⢸⠇⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠸⣆⠀⠀⠀⠀⠘⠀⣸⠀⠀⠀⠘⢄⠐⠏⠀⢸⡀⢺⠛⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣤⣿⠿⠿⠷⢦⣤⡤⠤⠶⠶⠾⠛⠛⢻⣿⣦⠀⠀⠐⠟⠗⠒⠒⠒⠂⠐⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢳⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠙⣄⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠈⠻⠿

⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⡹⢁⡾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠡⡃⠐⠁⣀⣐⠄⠀⠀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠀⠐⠀⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠱⣔⠸⠆⢼⣦⡀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠑⠀⠐⢊⡀⣀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠁⠈⠋⠉⠀⠀⠀⠀⠀⠘⠀⠢⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡐⠁⡐⠀⠀⠀⠀⠀⠀⢰⠟⠁⢀⠀⠀⠀⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⣊⡄⠀⠀⠀⠀⠀⠀⢀⣆⠀⡘⢠⠀⢀⠀⠀⠄⠀⠀⠀⣿⠆⠀⠀⠄⠀⠂⢈⠀⢐⢴⠀⠠⠤⠤⢤⣅⡐⠢⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢸⠋⡄⠀⠀⠀⠀⠀⠀⡆⢻⠎⣠⢬⠼⣦⣰⡄⣀⡀⠀⢠⡇⠀⠂⡀⠄⠁⠀⢸⡄⢀⡿⠀⠀⠀⠀⠀⠀⠋⠻⣇⠀⠳⣄⡄
⠀⠀⠀⠀⠀⠀⢸⣾⡧⡀⠀⠀⠀⣄⢄⣤⣸⣯⡔⠁⠂⠈⠋⠺⡿⢸⣤⣾⣇⠀⣞⠄⠈⠀⠀⠠⣷⣼⣿⠀⠀⠀⠀⠀⠀⠀⡄⠈⠂⠀⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠑⠿⣧⠀⠀⠀⡿⠐⣼⢿⡗⡹⠃⠴⠡⠠⠀⠀⡄⢹⣯⡻⣶⣿⣇⠸⡆⠀⠀⢸⣿⣯⡘⠄⠄⠀⠀⠀⡐⠳⣤⣭⣳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠃⠀⠄⣀⣴⡁⣁⠋⠘⠓⡁⠀⣴⣮⣾⠕⢅⣠⡷⠁⠁⢁⠂⠀⠑⣴⠟⠁⠉⠀⠁⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣄⣼⠟⡟⠉⠀⠈⠉⠈⠉⠉⠉⠁⠀⠀⠀⠰⣆⠀⠢⣾⡿⡇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⣵⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣀⠀⡀⠋⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠻⡟⠆⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠃⠑⠀⢰⣤⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⣄⡘⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠶⣤⠎⠍⣩⣥⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⣀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣦⣬⣷⣦⡝⠿⢳⣀⣠⡤⠖⠲⢶⣦⣤⣀⣰⠟⣟⣵⣶⣯⣭⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠛⠿⣿⣿⣿⣶⠀⠋⠁⠀⠀⠀⢀⡄⠈⠛⠋⢀⣿⣿⣿⡿⢛⣿⣿⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⠛⢿⣿⣿⠏⣀⡀⠒⡀⠀⠀⠈⡴⠀⢀⣀⡈⢿⣿⣿⣿⡟⠹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⣿⣿⠟⢼⣿⣆⠀⠀⠀⠀⠀⠀⠁⡛⣼⣿⡞⠻⣿⣿⡅⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢉⣤⣾⢘⡛⢻⡄⠀⠀⣀⣉⠓⠀⢰⡛⢛⡺⣷⣶⣉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠰⠋⢀⢀⡯⠩⠭⣅⣀⡀⠳⢌⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠆⠀⢀⣵⢋⣴⡀⣠⣌⠻⣦⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⡀⣇⠚⠛⠁⠙⠛⠃⣿⢠⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣝⠿⣷⣦⣤⣤⣶⣿⢟⣁⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⣷⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡒⠞⠉⠉⠿⠽⠄⠄⠠⠀⠌⠍⠑⠒⠲⠤⢄⣀⠀⠀⠀⠀⢠⣌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⠕⠈⢀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠉⠲⢄⡀⠀⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠁⡀⠂⠈⠀⢂⠀⠀⠠⠀⠢⠸⠀⠅⠘⠲⠀⠀⠈⠇⠀⢦⠀⢰⢀⠉⢻⡛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠆⡄⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⣧
⠀⠀⠀⠀⢀⣤⡴⠁⠀⠀⠀⠐⠡⡆⠀⠀⠀⠀⠀⠀⢀⢀⣀⢤⠀⠖⠶⠒⠀⠀⠀⡆⢰⠀⠰⡀⠆⠔⠀⣸
⠀⠀⠀⣰⠟⠩⢣⣶⠂⠠⠿⠀⠀⡄⡀⣀⢀⣀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠌⠛⢻⡟⢠⠗⠀⠀⠚⣇⢀⢤⠰⡰⢴⢢⠄⢠⡀⢠⢀⠀⡄⡤⢄⠈⢳⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⢀⣂⡠⢅⣀⢞⡨⠟⠢⡀⠀⠀⠀⣾⣧⣌⣀⣀⣀⣀⣀⣀⡀⣤⣾⣧⠁⠀⢄⡴⠞⠁
⠀⠀⠀⠀⠀⠛⠶⠾⠷⠶⠚⠁⠀⠀⠀⠙⢆⠀⠀⠙⢻⠟⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡷⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⣆⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠞⢁⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⣿⡟⠛⠛⠿⠿⠿⢿⣮⡻⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠁⠀⠻⠃⠀⠀⠀⠀⠀⠚⠟⠁⠈⠻⠋






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠤⠄⠠⠄⠀⠀⠤⠤⠤⠤⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⣔⠇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⡤⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠐⠈⠷⣤⠾⠀⠣⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠻⢦⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⢠⡀⡀⠀⠀⡠⠤⠄⢀⠀⣀⠀⠀⠀⢀⠀⡄⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠠⠛⡂⠀⠀⠀⠀⠈⠉⠉⠈⠁⠂⠠⡀⠄⠸⠀⠀⠀⠀⢠⠀⠐⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢀⠈⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡶⢄⠀⠀⠀⠀⢈⠱⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡰⠁⣄⢃⠤⡜⢡⡈⡄⣌⠢⡜⠑⡄⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢠⠒⠀⢴⣿⣭⣠⡄⠏⠀⠀⣨⣷⣠⡇⠧⠁⣆⢔⣹⠀⡠⡰⡀⠠⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢿⣎⠿⠉⠘⡁⠀⠀⢰⡿⢿⣟⠁⠘⠾⣵⠟⠸⠴⢰⡄⢢⡠⡁⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡒⢀⠈⡲⠋⠀⠀⢀⡡⢦⡷⣙⠸⡌⡃⠾⢂⢄⡀⠕⡁⠀⠈⢋⠮⣸⢇⣋⠇⠀⠀⢀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⢰⠽⠋⠁⠌⣄⢰⠸⣴⠜⣵⡸⠇⣣⡤⠀⠈⢫⡆⡼⢺⠋⣛⣈⢁⢉⣌⡬⠬⣧⣀⡠⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢘⠶⠤⠀⠂⢁⢉⣀⣄⣠⠴⣅⠦⠀⠒⠂⣠⡸⠷⢸⣮⠄⠀⠁⠀⠀⠀⢀⡀⠉⠉⠇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠉⠁⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⡇⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠃⠑⡄
⠀⠀⠀⠀⠀⢠⠃⠀⠢⣌⠙⠢⣀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⠀⠈⠆
⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠑⡄⠈⠳⠲⠶⠶⠒⠊⠀⠰⡅⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠘⡗⠢⢄
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠇⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⢀⣄⢀⠀⠀⢷⠋⠁⠀⠀⠀⠀⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⠀⠈⠁⠸⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡤⠖⠒⠈⠁⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⡶⢄⠀⢀⠀⠀⠈⠢⠤⠤⣤⣄⣀⣠⠞⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡠⢲
⠀⠀⠀⠀⢤⠂⠁⠀⢹⠃⠄⠐⠂⠠⠄⢀⣀⡀⠙⣄⢀⢀⣀⣀⡀⠠⠄⠒⠃⠠⠐⡏⠀⠈⠐⡤
⠀⠀⠀⠀⠀⠂⢄⠀⡧⢄⠀⠀⠆⠀⡀⢀⠀⠈⠉⠀⡀⠀⢀⠀⠀⠀⠠⠄⠀⠀⡠⢼⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠟⠒⠠⠄⢀⣈⠀⠉⠀⠀⠃⠐⠈⠀⢀⡠⠤⠄⠒⠻⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣾⣿⣷⣶⡄⠀⠀⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠛⠛⠃⠀⠹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣤⣦⣄⠀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣠⣶⣶⣦⣴⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠈⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⡟⢻⠟⢿⠿⢛⡿⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣧⣼⠇⠀⠀⠀⢀⡴⠋⠉⠙⢷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢛⡿⣿⡿⣿⡀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣿⢇⣿⢿⠀⠀⠀⠀⣸⠃⣼⠛⢦⣀⣉⣉⡙⢷
⠀⠀⠀⠀⠀⢀⡶⢋⡵⠒⢉⣡⢾⣿⣧⠘⣷⠀⠀⠀⡰⠊⠀⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⡾⡼⣸⡿⢸⡤⠀⠀⣰⠟⡴⠃⠀⠀⠉⠀⠈⡷⢸⡇
⠀⠀⠀⠀⠀⣿⠁⡼⠀⡔⢉⠔⣿⡏⡏⣇⠸⡇⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠤⠴⣧⠀⠀⠀⢰⠇⡇⠹⠃⢿⡇⠀⢰⢣⡞⠀⠀⠀⠀⠀⢀⡼⢃⡞
⠀⠀⠀⠀⠀⣿⠀⢿⠘⡇⣿⢰⣳⢃⡇⡿⢀⡇⠀⢸⡀⠀⠐⠤⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⣼⢸⡀⠀⠀⣸⠁⠀⢸⡌⠳⠤⠶⣄⠀⠀⣸⢣⡏
⠀⠀⠀⠀⠀⠹⣧⡈⢧⢱⣿⣾⣫⢞⡴⢃⣼⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢈⡽⠃⠀⠀⠀⡏⠸⠇⠀⢠⠇⠀⠀⠀⠙⠛⠲⡆⠈⠓⠚⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⣟⣛⣉⣤⠞⠁⠀⠀⠀⠀⠈⠳⡄⣰⠖⠚⠛⠉⠀⠀⠀⠀⠀⣧⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⡀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⢰⠃⠀⣤⠀⠀⡼⠀⠀⠀⠀⢀⡴⡖⠉⠉⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⡴⠋⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⣧⣀⠀⡀⠀⢀⠇⠀⠀⢀⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠁⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢉⣩⣤⡞⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⢹⣄⡴⠃
⠀⠀⠀⠀⠀⡾⠀⠀⢀⠀⢠⣄⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢰⢟⡆⠀⠀⠀⠀⢠⡷⢤⣀⠀⠀⡜⠀⠀⠀⠈⣇⠀⠀⠆⠀⣄⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⢷⠀⠀⣾⠆⠘⠿⠀⠀⠀⣿⣿⠃⠀⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⣼⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⠙⢦⣀⡀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⡿⢿⢸⠀⠀⠀⠀⢠⡇⠀⠠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣄⡀⣀⣤⣤⣴⣾⡿⠟⠀⠀⠀⠀⠀⣿⢸⡏⠀⠀⠀⠀⢸⠋⠂⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣩⡤⡤⣄⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣀⠀⠀⢸⡀⣠⠏⠀⠀⠀⢀⣤⠶⠒⠶⣄⠀⠀⠀⣼⣳⠏⡁⢸⡵⣀⡹⣆⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡇⠀⠈⢣⡉⢧⡀⠈⠛⠁⠀⠀⠀⡴⢋⡴⠛⠛⢦⢹⡆⠀⠀⣿⣿⢺⡽⣠⣄⠳⠆⣿⢸⡇
⠀⠀⠀⠀⢠⡞⠉⢠⡇⠀⠀⢹⡿⢦⡀⠀⠀⢠⡏⠀⠸⠁⠀⠀⠀⠃⠈⡇⠀⠀⠀⠀⣀⡼⢡⡿⠀⠀⠀⣸⠀⣧⠀⠀⢻⡜⢦⡀⠳⠞⢀⣴⢃⡼⠁
⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⠀⠈⢻⡀⠀⢼⠀⢠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⠋⡴⠋⠀⢀⡀⠀⠙⣦⠘⡆⠀⠀⠙⠶⣭⣙⣛⣩⡵⠞⠁
⠀⠀⠀⠀⠈⢻⣶⠀⢀⡴⠀⠀⢀⠀⣼⠁⠀⠘⣧⠘⣆⠀⠀⢸⣀⣠⡟⠁⠀⠀⢸⡃⠸⣇⣀⡴⠛⢷⡀⠀⣸⠀⡿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢧⣤⡤⠾⠞⠁⠀⠀⠀⠈⠳⠿⣦⣄⣼⣿⠉⠀⠀⠀⠀⠘⠷⣤⣬⣥⠴⠶⣌⠓⠚⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣶⠀⠉⠀⠲⠖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡅⣠⣤⣤⣥⡀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⡟⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡧⠸⣤⣧⣌⣩⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡛⣿⡿⢉⣀⣀⣀⡄⣀⠉⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡐⠈⠀⠉⠉⢟⡟⠉⠻⠟⢷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣀⠀⠂⠀⣉⣝⣓⣚⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡻⠿⢹⡟⣿⣆⠀⠀⠛⢒⣀⠾⢲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠦⢄⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡃⠀⠸⣧⠙⣿⣿⣦⣀⠉⠉⢁⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣾⣿⡛⠙⠅⠉⠢⡀
⠀⠀⠀⠀⠀⣀⠤⠒⠢⠞⠻⠿⢿⣦⣀⢻⣧⣈⢻⣿⣏⠉⠛⢻⣯⡲⡀⠀⢀⡠⠖⣊⣉⣉⣛⡿⠿⢟⠫⢑⠉⡻⣿⣶⣕⠀⢀⠈⢢
⠀⠀⠀⢠⢎⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣏⠀⠀⠀⠈⠙⠢⣼⡛⠛⢺⢖⣭⣾⣿⣿⣿⣿⣿⣿⣷⣦⣌⠢⠑⢌⠨⠻⣿⣦⡀⠀⠀⢣
⠀⠀⢠⠋⣾⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⣧⣤⠤⠄⠀⠀⠰⢿⣷⢺⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⠁⡐⠘⢿⣷⡀⠀⠀⢣
⠀⠀⠀⡀⢻⣷⠀⡀⠀⠀⣦⠀⠀⠀⡇⢸⣯⡔⠀⠀⠀⠀⠀⠚⣿⣏⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣦⠁⡀⠀⠘⣿⣧⠀⠀⠸
⠀⠀⢀⢳⡈⢻⣷⣜⢦⣀⢸⣆⢀⣴⣇⡿⠿⣿⣶⠶⠶⠶⠶⢿⣿⣿⣿⣿⣿⣟⣴⣿⣿⣿⣦⡄⠙⣿⣿⣿⣿⣿⣇⠀⠠⠀⢹⣿⠀⠀⢀⡇
⠀⠀⠈⢦⡻⣶⣝⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣷⣶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⡄⠀⠀⠘⣿⣇⣶⣿⠁
⠀⠀⠀⠀⢹⢾⣿⣿⠿⠿⢿⣿⣿⠛⠻⢦⣄⢠⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⡆⢹⣿⣿⣿⣿⡇⠀⣀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠘⡈⣿⣧⠀⠀⠀⣿⣿⠀⠀⠀⠹⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⣿⡇⣼⣿⣿⣿⣿⣇⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⢡⡈⢻⣷⡄⠰⡘⣿⣷⣄⠀⠀⠉⠉⠹⠟⠛⠛⠻⠛⠉⠙⣿⣿⣿⣿⣮⣿⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡙⢿⣦⡙⢮⡛⣿⠃⢀⠀⠀⠀⢀⠄⠀⠀⢀⣤⡾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⢿⣄⠈⣿⣦⣿⣀⣤⣾⣯⣤⣲⣾⣾⣿⠟⢋⣴⢟⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣆⠻⣌⠻⣿⣿⠿⣿⡟⣿⣿⣋⣁⡾⢟⡥⠊⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢿⣦⣬⣹⣿⣿⣿⣿⣿⣿⣿⣯⣵⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢍⣙⣛⣩⠭⠗⠂⠐⠒⠚⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠉⠉⠙⠻⣶⣜⢿⣿⣿⣿⣟⡵⠋⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⣫⣾⠟⠋⠉⠉⠛⠻⢷⣦⣄⣀
⠀⠀⠀⢀⣠⣴⡾⣿⠿⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠙⣷⣽⣿⣿⣼⠁⠀⠀⠀⠀⠀⠀⠈⣏⣿⣿⣯⣾⠋⠀⠀⠀⠀⢀⣀⡀⠀⠈⠙⢿⡿⢷⣦⣄⡀
⠀⢀⣴⠿⠋⡡⠞⠁⠀⠀⣠⣾⢟⢹⣧⠀⡄⢠⢀⣤⣿⣸⣿⣿⣿⠀⢤⣤⡀⢀⣠⡤⠀⡟⣿⣿⣏⣿⣷⡀⡄⢠⢀⣼⣏⡻⣷⣄⠀⠀⠈⠢⡈⠙⠿⣦⡀
⢠⣿⠃⠀⠀⠀⠀⠀⡴⠋⠉⣿⢹⣷⡹⠷⣷⣾⠿⣟⣵⣿⣿⡇⣭⠃⠉⠉⠁⠀⠉⠉⠘⣷⢸⣿⣿⣮⣻⡿⣷⣾⠾⣯⣾⡇⣿⠉⠑⢦⠀⠀⠈⠂⠀⠙⣿
⣾⡇⠀⠀⠀⠀⠀⠈⠀⣀⣴⡿⠷⠷⣮⣟⠷⢾⣿⠿⣿⣿⣿⣷⣹⡷⠀⢀⣐⣒⡀⠀⣾⢯⣾⣿⣿⣿⠿⣿⡷⠾⣻⣵⠶⠾⢿⣦⣀⠀⠁⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⢤⡈⣿⠟⠛⠛⠛⠷⣮⡻⣿⣏⣧⡀⠈⠉⠉⠀⣠⣟⣼⣿⣿⣵⠾⠛⠛⠛⠿⣿⢁⡤⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⢘
⠙⢿⣦⣀⣀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠤⢌⣿⣎⣵⠟⠙⢶⡤⢤⡾⠋⠻⣮⣵⣿⡡⠤⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⢈⣷⣤⣀⣀⣀⣴⡿
⠀⠀⠉⣿⡟⠛⠛⠛⢷⣤⣄⣀⣠⣤⣴⣿⢀⠄⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⠀⠀⣠⣴⠞⠋⠉⠀⠀⠀⠀⠀⠠⡀⣿⣦⣤⣄⣀⣠⣤⡾⠛⠛⠛⢻⣿⠉
⠀⠀⠀⠘⢿⣄⠀⠠⢀⣉⡿⠿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣷⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠿⠿⢟⣉⠀⠄⠀⣠⡿⠃
⠀⠀⠀⠀⢠⣝⡿⣶⣤⣤⣤⣤⣾⢻⡄⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⢻⡟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢸⠟⣷⣤⣤⣤⣤⣶⢿⣫⣦
⠀⠀⠀⠀⢸⣿⣿⣷⣾⣯⣽⣧⢿⡇⠇⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⡸⢸⡿⣼⣯⣽⣷⣾⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡞⣷⡈⠀⠙⣿⣿⣷⠦⢤⣤⣤⣤⣀⣠⣼⣿⣿⣧⣄⣀⣤⣤⣤⣤⠴⣾⣿⡿⠋⠀⢁⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡜⣷⡀⠀⠈⠻⣏⠳⡄⠀⢀⡤⠖⠂⠉⠙⠏⠁⠐⠲⢤⡀⠀⢠⠞⣹⠟⠁⠀⢠⣾⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣦⡀⠀⣯⠱⠍⠀⡟⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢻⠀⠠⠎⣽⠀⢀⣴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣶⣿⡙⠄⠀⣷⣤⡤⠄⢠⣾⣿⡄⠠⣤⣤⡾⠀⠠⢋⣿⣶⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣷⠀⢠⡿⠋⠀⠀⠀⢹⡟⠀⠀⠀⠙⢿⡀⠀⣾⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡄⠘⣧⡀⠀⠀⠀⣼⣧⡀⠀⠀⢀⣼⠁⢠⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣧⡀⣾⠟⠛⠉⠉⢿⡿⠋⠉⠛⠻⣧⢀⣼⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⡻⣿⡀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡿⢟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣦⣀⠀⠈⠁⠀⣀⡴⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣛⣛⣛⣛⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠿⠿⠳⣦⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣀⡀⠀⣀⣉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠰⠀⠀⠙⠛⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠠⠀⠀⠠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠐⠒⠉⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡝⠳⠶⠒⠁⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⠃⠀⠀⠀⠀⠄⠈⠉⠀⠀⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠘⠋⠉⠀⠀⠀⠀⠠⣤⠖⠀⠀⠒⠒⠆⠀⢤⣀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢹⣷⢾⣆⣀⣀⣠⡾⠃⠲⠤⣤⣀⣠⣤⣿⡟⠉⣧⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⠿⡆⠈⠉⢉⣀⡀⠀⠠⣤⣤⠴⠀⠀⠀⠁⣼⢿⣆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢀⡿⠀⣿⠄⢀⣀⠉⠀⡆⠀⠀⠀⢀⠀⠀⢀⡼⠃⠀⠙⠷⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⠀⠀⡾⠁⠀⣿⡄⠀⠈⠁⢀⡀⠒⠒⠚⠋⠀⠀⢸⡇⠀⠀⠀⠀⣤⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⠀⠀⠀⠁⠀⠀⠀⢰⡆⠀⢸⠇⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠇⣰⠁⠀⢀⣇⠀⢸⡇⠀⠀⣇⠀⠀⢀⡾⠀⣀⣿⡀⠀⠀⠀⠀⠈⢷⡄⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣴⠃⠀⢠⡾⢍⡛⠿⠷⢶⣶⣿⠶⠶⠾⠟⠛⢛⣩⣿⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠃⠀⠀⠘⢁⣠⡴⠂⠀⠐⢺⣿⠚⠛⠀⠸⣦⣤⠤⢽⡆⠀⠀⠀⠀⠀⠈⣧⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠭⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⠹⣆⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢠⢂⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠚⠁
⠀⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣻⣝⣿⣧⣩⡀⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠿⠛⠛⠛⠛⠿⣖⠚⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠄⣶⡾⢦⡉⠀⠘⡏⠉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠸⠋⠉⠁⠀⠀⣠⠀⣔⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠋⠀⠀⠀⢰⡿⠏⢰⠬⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⢀⡄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣠⣤⣴⠖⠋⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠉⠈⠙⣿⣧⡀⠀⠀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⣀⢀⠀⠀⠀⠈⢿⡃⠀⠸⠀⠇⠹⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡴⠶⢢⡿⢛⣉⠕⠲⣴⣾⠷⠀⠀⠀⠀⢸⡆⢻⣤⠆⡘⠀⠀⠈⡙⠳⣄⡀
⠀⠀⠀⠀⣠⡾⠋⠀⢰⠏⠴⠋⠁⠀⠀⠈⢳⠀⠀⠲⠆⠀⠉⠙⠺⣿⣰⡏⠒⠀⠀⠳⣤⣌⣷⣦⣄⣀
⠀⠀⠀⢰⣿⠃⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠙⢧⡀⠈⠙⢿⣶⣄
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢧⣄⠀⠀⠀⠀⠀⠙⢆⠀⠀⠹⡟⢷⡀
⠀⠀⣠⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⣾⣿⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠉⠂⠀⠀⠀⠀⠀⠀⢣⣄⠀⠘⡈⢷
⠀⣰⣿⡟⠻⣿⡄⠀⠀⢀⣴⣿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠁⢸
⢀⣿⣿⠁⠀⠀⠀⠀⢼⠀⠁⠀⢀⣾⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣀⡀⠀⠀⠀⠀⣠⠄⣰⣿⣥⡄⣠⡿
⢸⣿⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡇⠈⠙⠿⣿⣿⣿⣷⣶⣶⠶⠶⠟⠋⠉⡄⠉⠛⠿⢶⣶⣶⣷⣾⠋⠉⠛⣦⣿⣷⡀
⢸⡟⠀⢀⡄⠀⠀⠀⣿⠀⠀⠀⣿⠃⠀⠀⠀⠈⠉⠓⠠⠤⠤⠴⠶⠀⠀⠒⣯⠀⠀⠠⠴⠤⠿⣿⣧⠀⠀⠀⠹⣯⢻⣧
⣾⣇⢀⡌⠘⠀⠀⢠⠇⠀⠀⢰⡿⢤⠀⠀⠀⠑⣄⠢⣀⠀⢤⣀⠀⠀⠀⢀⣾⠀⠀⢀⡄⣠⠀⣿⣿⠀⠀⠀⠀⡇⠇⣿⡄
⣿⣿⡌⠁⠀⠠⣀⣌⣀⣀⣴⠿⣿⣦⠑⢄⡀⠠⣀⠀⠈⢦⣀⡉⠛⠛⠛⠻⣿⠛⠻⢿⡔⠃⣰⢿⣿⡄⠀⠀⠀⡇⡘⠻⣇
⣿⣿⡇⠀⠀⠀⠘⣿⣿⠟⠁⠀⠈⠻⣷⣦⡻⣆⠈⠳⡀⠀⡏⠀⠀⠀⠀⢀⣿⠀⠀⠈⣷⡼⡃⠘⢿⣿⣦⣀⢀⣷⣣⠀⠹⣦
⣿⡝⢿⡘⣄⠀⠀⠘⣷⡄⠀⠀⠀⠀⠈⢿⣷⠘⠷⣄⡀⠀⠘⣦⠀⠀⠀⠈⣇⠀⠀⣠⡇⢰⡟⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠸⣇
⢻⣿⡌⢇⠘⣦⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠙⢶⣄⠘⣿⠋⠉⠉⣟⠀⠙⢻⣧⡿⢣⡀⠀⠀⣷⣌⣉⡛⠈⠀⠀⠀⣿
⠀⢿⣧⠸⡄⠈⢷⡀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠙⢳⣿⠀⠀⠈⠐⠀⠀⠀⣿⠀⠘⣧⠀⢀⡏⢹⣿⡀⠀⠀⠀⣰⣿
⠀⠘⣿⡄⠙⢦⡀⢻⣄⣻⡇⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⢣⠀⠀⢹⡆⠀⠀⢤⠄⠀⠀⢸⠀⢠⡟⠀⠘⣧⠈⢿⣇⠀⢃⣰⢏⣿
⠀⠀⢹⣷⡀⠈⠻⣆⠹⣿⠃⠀⠀⠀⠀⠀⢸⣿⢿⡟⠶⣼⣄⣀⢀⡇⠀⠀⠀⠀⠀⠀⣈⣠⠾⡇⠀⠀⠹⣷⡄⠙⣦⢈⠏⠸⣿
⠀⠀⠀⠻⣷⡄⠀⠈⠳⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣦⣼⣄⣉⡉⠛⠲⠶⢦⣤⣴⠞⢉⣥⣶⣿⠀⠀⠀⠙⢷⣤⠙⣿⡀⠰⣿
⠀⠀⠀⠀⠙⣿⣄⠀⠀⠘⢇⠀⠀⠀⠀⣼⣿⣿⡉⠻⣿⡷⣌⠉⠉⠛⠓⠲⠶⣼⣿⡟⠉⢁⣿⣿⢷⡀⠀⠀⠀⠻⣇⣿⠙⣄⢻
⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⣄⠀⠀⢸⣿⣿⣿⠁⣄⠈⠻⣿⣷⡀⠀⠀⠀⠀⣿⣿⡇⠀⣸⣿⣿⠈⣷⠀⠀⠀⠀⠘⣿⡀⠈⢿
⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⠈⠛⠲⠟⢿⣿⣿⠀⠘⢦⠀⠹⣿⢿⡄⠀⠀⠀⢹⣿⡟⢰⣿⣿⠇⢀⠻⣆⠀⠀⠀⠀⣹⡿⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠘⢄⠀⠀⢠⡆⢹⡏⠀⠀⠈⡇⢄⠙⣿⢿⡄⠰⣄⣸⣿⣷⣿⣿⠉⠀⡘⠀⢻⡄⠀⡔⠊⡉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠃⠀⠀⢿⣄⢹⡄⠀⠀⠁⠈⣄⠘⢎⢻⣶⣿⣿⣿⣿⡿⢡⠄⠀⠇⠀⠈⣇⡀⢀⠞⣡⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡀⢠⡈⠻⣏⠹⠂⠀⡆⠀⠸⣆⠘⣄⣿⣿⣿⡿⠋⣰⠏⠀⠐⠀⠀⠀⢿⡅⠉⣳⠏⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣶⣌⣦⣈⣶⠏⠀⠀⠀⠀⠀⠀⢻⠀⢿⣿⣿⣿⠃⢰⠏⠀⠀⠀⠀⠀⠀⢸⣗⣒⣠⣶⣡⡞⠁
⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣷
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡏⠀⠈⠻⣿⣿⠁⢀⣀⣀⣀⡛⠀⠀⠀⠀⠀⠀⣀⣼⡆
⠀⢰⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡟⠃⠘⠿⠏⠈⠿⡿⠀⣸⣆⣠⣴⣴⣿⣿⠂
⠀⢸⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣾⣷⣿⣿⣿⢧⠆⠀⠀⠀⠐⠀⠸⠿⣿⣿⠿⠿⠟⠛⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡿⠟⠛⠁⠶⢇⡸⣷⣶⠴⠐⣶⣦⣤⣴⠞⠁
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠈⠻⠁⣀⠴⠿⠋⠀⠀⠀⠻⣷⠖⠀⠀⠘⠋⠙⠧⠀⠀⠀⠀⠀⠠⡇⠛
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣆⠀⠀⠀⢀⠀⠀⠀⢰⣿⣿⣿⢰⣦⢿⣷⠐⠂⠀⠀⠀⠐⣾⣿⠀⠀⠀⠀⠀⢀⠀⣦⣤⣤⣤⣤⣾⣤⣄
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣶⣄⣠⣿⣿⣦⣀⣿⣿⣿⡇⠛⠿⣶⣿⣧⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠈⣷⠟⠋⠈⠉⠁⠹⣿⣿⡆⠘⠃
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣤⣶⣿⣿⣿⣃⣀⣀⢠⡴⢿⣾⣦⠀⠀⠀⠀⢤⣿⡐⢄⣀⣀⣠⣤⠀⠉⢀⣀⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠛⠉⠙⠛⣿⡟⢋⣽⣇⣸⣦⠈⠹⠿⣷⣾⣾⣿⣿⣿⡾⢿⡿⠋⠀⠀⠀⢸⣿⣿⣤
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⣿⡄⢀⣿⣤⡀⣰⠬⣿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠚⠋⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠸⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣇⡼⠟⠀⡘⠧⢄⡉⣅⠰⠛⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⢹⣇⠀⢰⠀⠀⠀⠙⢁⣤⣾⢠⡴⠋⠀⠀⡴⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣾⣯⣀⣀⣀⣀⣀⣠⣿⡿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣹⡇⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣿⠉⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣻⣿⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣶⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢻⣿⡀⠀⡀⠀⠀⣀⢀⣿⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠘⣿⣿⣾⠀⠀⠀⢹⡿⠃⠘⣿⠃⠹⣿⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣇⠀⢸⣿⡇⠀⠀⠀⢨⣆⠀⠀⢸⠀⠀⠘⢿⡄⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⢸⣿⣧⠀⠀⢀⣾⡟⠀⠀⠸⣷⡄⠀⠈⢿⣶⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠈⠻⠿⡿⠾⣿⠟⠀⠀⠀⠀⢻⣷⡄⠀⠀⢹⣧⡀⠀⣰⠾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡀⢀⣀⡀⢠⣄⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣿⣿⡿⠿⠋⠀⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠘⣿⣿⣏⠁⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣧⣀⣀⠀⠀⡈⠉⠙⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣾⣿⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠸⢿⣶⡄
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢹⣿⣧⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠘⣿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀⠹⣿⡆
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣎⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠰⠆
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠢⠀⡀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢦⠄⢰⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣻⡔⠀⢻⣽⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⠿⠯⠠⣶⣾⡏⠸⢿⡷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠋⢀⡇⠀⠀⢀⡍⠀⠀⢰⡟⠀⠐⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠒⢃⢤⣿⣿⣷⣤⣠⡇⢀⣾⣿⣿⣤⣀⢠⣴⣦⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⣿⣯⣿⣿⣿⠿⠛⡿⠛⣿⡿⢿⣿⣟⣿⣷⠀⠙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣏⣠⣾⠟⢿⣟⢹⣷⣀⢾⣷⣾⣿⠏⠐⢿⣿⣿⠿⣧⣼⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡅⠀⠀⠉⢹⣿⣿⣶⣾⣿⣿⣇⠀⠙⠋⠁⠀⠈⢻⡄⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⠀⣾⠇⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠄⠀⠀⠀⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠏⠀⠀⠀⢈⣿⣿⣿⣟⣿⣿⣿⣿⣿⣧⢀⡀⠀⠀⠀⠀⣼⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢀⣿⣿⣿⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣟⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢄⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⡀⠊⠀⠀⠀⣄⠀⠀⠀⠀⡄⠀⢸⠀⢻⡇⠀⠀⠸⠿⣿⣿⣿⣧⣬⣛⣿⣿⣿⣿⣿⣿⣿⣦⣼⠃⠀⠀⠀⢀⣀⡄⡀⠀⠀⠀⠀⠀⠈⠂⢀
⠀⠀⠀⠂⣀⣴⣷⣾⣶⣿⠀⠀⣶⡄⡆⠀⣾⣷⣈⣁⡀⠀⡀⠀⠈⠉⣿⣿⣿⣿⣿⠛⠛⠉⠀⣩⡇⠀⠀⠀⠸⠀⠀⢸⣿⣿⡇⣼⣶⣧⣴⣆⣀⡀⢼⡄
⠀⠀⠀⣶⣿⣭⣬⣤⣤⣤⠀⠀⢸⡷⣷⣤⣿⣻⣿⣿⣿⣶⠶⠛⠶⣜⣋⣀⣉⣻⣿⣀⡴⠶⠶⠿⣃⣀⠦⠀⣠⣶⣶⣶⣤⣤⡄⣤⣬⣥⣭⣇⣿⣟⠀⡶
⠀⠀⠀⣟⠻⢿⣿⣿⣿⣿⡆⠀⢸⡇⡇⠀⠙⠿⠿⠿⠁⢠⡄⢀⡄⠀⠀⠀⠀⣿⡏⠈⢀⣀⣠⠟⠛⠿⠿⠇⠈⠀⠀⢸⣿⣿⡇⢿⣿⣿⡿⣿⣟⡛⢶⡇
⠀⠀⠀⠘⢿⣶⣀⣙⠋⠉⠁⠀⢸⣧⠇⠀⠀⠀⠀⠀⠀⢸⣇⣼⠀⠀⠘⣤⣼⠉⣿⠀⠈⢻⣿⠀⢀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠟⢈⢉⡀⣴⣦⠹⡿⠌
⠀⠀⠀⠀⠀⠘⢻⣿⣦⣶⣶⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⢠⣿⠁⠀⢻⣆⢀⣾⠿⣷⠟⠀⠀⠀⠀⠀⠀⠈⣤⣦⣄⢻⣿⣿⡙⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣼⡏⠀⠀⠀⠻⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠉⣿⠀⠀⠀⠀⠀⠘⣿⣦⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⡾⠉⠀⠀⠀⠀⠀⠀⠻⣿⡟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠘⣷
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣧⣻⡆⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⠿⣿⣿⠿⠿⠃
⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡼⠒⠒⠠⢩⣶⠘⠟⠒⠈⠤⠒⠀⠖⠆⡶⠂⠧⠖⠗⠴⠐⠀⠂⠆⠃⢠⣮⠡⠐⠒⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠆⠀⠀⠀⠀⠀⠁⠶⠀⣀⡀⠀⠀⠀⢮⣧⠞⠀⢬⡷⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠠⠀⠠⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠐⣿⠆⠀⠐⢷⠖
⠀⠀⠈⠀⣿⠦⠀⠀⠀⢀⠄⠒⠇⡈⠃⠀⠀⠀⠀⠀⠛⠀⠀⠀⠚⢀⠀⠀⢀⣀⠀⠀⠀⣀⢠⣤⣤⡤
⠀⠀⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⡀⠀⠀⡄⣠⣄⠀⠀⠙⠀⠀⠁⠠
⠀⠀⠀⠀⠰⠀⠀⠀⣀⡀⠀⠀⠀⠤⠉⠰⠄⢂⠀⠈⠀⠀⠀⠸⠀⠂⠀⢰⠇⠋⢸⠀⠀⠀⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠐⠀⠀⠀⠀⠘⠀⠈⠄⠀⠀⠀⠄⠁⠀⢸⠁⠀⠘⠀⠀⠀⠀⠘⠷
⠀⠐⡾⠚⠀⠀⠓⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠈⠂⠠⠤⠄⠀⠈⠀⣰⠓⠀⠀⠀⠀⠀⠀⠚⠶⢷⠚⠃⢐⡄⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⢰⡷⠝⣇
⠀⢠⣄⡀⠀⠀⠀⠐⠟⠛⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⡠⠄⠀⡀⠤⡁⠀⠀⠈⠁
⠀⠀⣠⡷⠻⠃⠀⠀⠀⠠⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⡴⠔⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠰⠈⠃⠀⠀⠀⠂⢠⠀⠠⠀⠀⢀⣀⣴⣴⠀⠀⢰⣿⡀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⣿⣿⣿⠀⠀⠸⣿⠃⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠘⠀⡘
⠀⠀⠀⡡⠂⣢⢬⡳⡄⠀⠀⠸⠟⠀⠀⠀⠉⣷⣿⣿⡤⠀⠀⢻⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠉
⠀⠀⣄⠣⠀⠠⠄⠂⠇⡖⠀⣈⣡⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠛⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠠
⠀⠀⠈⠀⠀⠀⠀⣀⠜⠀⠀⠈⠃⠀⠀⠀⠀⣿⣿⣽⠃⠀⠢⣤⠄⠀⠀⠁⠤⠤⣤⣄⠀⠀⠀⠤⠖
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣂⠈⡉⣱⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⡤⠜⠉⠉⠀⠉⠉⠓⢦⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⢺⣋⡵
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⡾⠁⠀⠀⡴⠋⠉⠉⠁⠂⠀⣴⠏⠉
⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⠀⠸⡏⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⢐⣲⠆⣀⠀⣰⠶⠚⢹⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠴⣦⠴⠦⣬⡑⠚⠋⠉⠒⠮⡙⠍⢂⡀⢸⠀⠀⠀⠀⠀⠀⠈⠟⢌⣀⣀⣠⡾⠁
⠠⠚⣅⡀⠁⠀⠀⠈⢻⡄⠀⠀⠀⠀⠘⢆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣴⠓⢄
⡂⢦⠏⡋⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⢣⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡆⢱⡤⢤⡀
⣀⠚⠉⠃⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⡷⠊⠙⠺⢿⠛⠙⠲
⠘⣇⠀⠀⠒⠤⠄⣠⠴⠦⠽⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⣏⡐⢲⣦⣄⡀⠀⠀⠀⣼⠀⢰⠃⠀⠀⠀⠀⠇
⠀⠈⠳⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠵⢒⣿⣿⠴⠋⠀⠈⠹⣆⠀⠀⣿⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢀⣴⠾⢯⣍⠉⢧⡉⠒⢦⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡇⠸⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⢀⡴⠋⠂⠀⠁⠳⠈⠀⠙⣆⠐⠿⣦⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋
⢠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣇⠀⠀⠙⠢⠤⢄⣠⣤⠴⠞⠁⠀⠀⠀⠙⠲⠤⣤⣀⣠⣇⠴⠃
⢸⠀⠛⡆⠀⠀⠀⠀⠖⢠⡊⠰⠤⣤⣼⠎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⢀
⣿⠀⠀⠳⠦⣀⣰⠧⠬⠀⠀⢀⡎⢀⠇⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠴⠃
⠹⣄⡇⠈⠲⢶⠶⣄⠀⠀⢀⢞⡔⠁⠀⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠉⠀⠴⠛⠁⠚⠋⠉⠉
⠀⠘⢧⠆⠀⠨⣄⠈⠙⢯⣴⣂⠀⢀⡞⢁⣸⠃⠀⠀⣀⡤⠴⠒⠋⠁⠀⠀⠀⢀⠀⢀⣶⠀⢦⡉⠉⠙⠒⠤
⠀⠀⠘⢧⣀⣀⣈⠓⠙⢓⣺⡿⣻⠋⡰⠋⠀⢠⣶⣉⣀⣠⣀⣠⣤⣤⡶⠴⠶⠾⠛⠛⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⢰⣿⠀⠈⣡⣾⡆
⠀⠀⠀⠀⣤⠚⣿⡇⠈⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⡇⠀⢹⣿⡇
⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⢿⠁
⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡄⡀⢰⣇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠃⠘⣆⠀⠀⠀⠀⣾⠏⠹⠟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠘⣆⡀⠀⢸⠁⠲⠄⣀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣁⠀⡄⠉⠙⢦⠈⢀⣤⣤⡀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢿⣇⠀⠀⠈⢿⣦⠈⢈⣥⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡏⠀⠀⠀⠀⠛⣿⣿⣿⣋⠣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣧⠀⠀⠀⠀⢀⡉⠈⠁⠀⠀⠀⠉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⣧⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠙⠉⢛⣶⠋⣴⣄⡀⠀⠀⢐⣶⣆⠀⠘⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⠀⠈⠋⠀⠈⠻⣿⣿⣿⣿⣿⡏⢷⣄⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠒⠏⠙⢷⣦⣤⣬⣿⣿⡟⠀⠀⠙⠻⢶⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢘⣿⣿⣯⠟⠀⠀⠀⠀⠀⠀⠻⢶⣶⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠀⠀⠴⢯⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠖⠊⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣠⣄⣀⣄⣠⡤⢶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢺⣿⣿⣿⣡⡜⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣄⣿⣿⣿⣾⣷⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠻⣿⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⠈⠻⠇⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠛⠛⠛⢶⣴⢿⣿⣿⣿⠟⠉⠁⠉⠛⢿⣿⣿⣿⣷⣴⠞⠛⠛⠛⠷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡶⢟⠿⠋⠁⢀⣤⣄⠀⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠁⠀⠀⢀⣤⣄⠀⠙⠻⡟⠶⣤⣀
⠀⠀⠀⠀⠀⣠⡞⠁⠄⠁⠀⡠⠶⣿⣷⣻⣦⣆⣧⣿⣿⣿⣿⡿⠸⠷⠂⠰⠿⠸⣿⣿⣿⣿⣧⣇⣧⣾⣳⣿⡷⢦⡀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢀⣠⡿⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡰⠂⠀⣼⣿⣿⣿⣿⣷⣿⣿⣿⡿⠾⣧⣀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⣰⠋⠀⠀⠀⢄⣻⠛⠛⠛⠻⣿⣿⣿⣦⡀⠈⠁⣠⣟⣿⣿⡷⠛⠋⠙⢻⣁⠄⠀⠀⠈⢳⡀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠙⠳⣶⢶⣶⣿⣄⠀⠀⠀⣀⣿⠀⠀⠀⠐⠚⠷⢿⣁⠙⠛⠛⣁⣽⠷⠟⠂⠀⠀⠀⢸⣇⠀⠀⠀⢀⣼⣷⡶⢶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⢙⣻⡿⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣾⠋⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⠿⣿⣛⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣤⣤⣴⣞⡇⢿⣧⡀⠀⠀⠀⠀⠀⠠⢌⣻⣋⠄⠀⠀⠀⠀⠀⠀⣠⣿⠇⢟⣶⣤⣤⣴⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⡱⠘⢿⣷⣄⣀⠀⠀⠀⠀⢢⣿⣧⠂⠀⠀⠀⠀⣀⣼⣿⠟⠘⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⣿⢍⠉⢉⣻⠿⠛⢿⠟⠻⢿⡋⠉⢉⢽⡿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣿⡪⠁⣞⠀⠀⠀⢠⡀⠀⠀⠸⡆⠸⣪⡇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡍⠀⣹⡶⠂⠐⣿⡷⠀⠲⣾⡁⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣏⠀⠀⠀⣸⡀⠀⠀⢘⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⠗⠒⠐⢿⠟⠐⠓⢿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡻⣄⠀⠀⠸⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣦⣄⣀⠀⣿⣿⣷⣾⣿⣿⠿⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄
⠀⠀⠀⠀⠀⣾⣿⠋⢀⣿⠉⠛⠻⢿⣿⣿⣿⡿⠛⠁⣀⣤⣤⣄⣈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⢻⣿⣾⣏⡁⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠿⠟⠛⠻⢿⣷⣦⡀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣦⡀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠈⢿⣿⣷⡀
⠀⢀⣾⣿⡿⠉⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠙⢿⣿⣦⡀
⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣄
⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢤⣦⣄⣀⠀⠀⠀⠀⠀⠠⠂⣠⠄⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠘⢿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣾⠁⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠘⠟⠛⠛⠳⠂⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢘⣛⣿⣿⣿⠄⠀⠀⠀⠠⣿⣿⣷⠀⠀⠀⠀⠀⢀⣾⣿⠏⠁⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠐⣾⣾⣿⣽⡇
⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⢠⠿⠋⠁⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⡴⣣⣄⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⠘⠀⠀⣠⠀⠀⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠘⠛⠿⠿⠛⠃⠀⠀⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⢠⣶⠿⢷⣦⠀⠀⠀⠀⡆⣠⣤⣄⡶⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⠀⣠⣮⣄⠀⠀⠀⠀⢀⣀⣴⣋
⠀⠀⠻⣟⣀⣨⣻⠁⠀⠀⠀⡟⣿⣿⡿⡇⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠖⠔⠓⣶⣶⠄⠀⠀⠀⠘⣿⢻⡇
⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠃⠀⠁⠀⠃⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠈⠒⠊⠙⠁⠀⠀⠀⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀
⠀⠀⣠⣻⣿⣶⠴⠄⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠙⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠒⢰⠒⡆⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠈⠉⠁⠁⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⠀⠀⠀⠀⣬⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⢀⡴⠋⠈⠛⠛⠛⠛⠻⠶⣤⣤⠶⠟⠛⠛⠛⠛⠀⠙⢦⡀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠈⠻⣦⣀⣶⠶⠶⣤⣼⠏⠀⠀⠀⢀⣤⠶⠶⣶⣀⣴⠟⠁⠀⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⢀⡀⣿⠀⠀⠀⠀⣿⢀⡀⠀⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡛⠻⢿⣄⠀⠀⣠⡿⠟⢛⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠈⢷⣄⢀⣿⠛⠛⣿⡀⣠⡾⠁⠉⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠙⠟⢻⣦⣴⡟⠻⠋⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⣷⠀⠀⢀⣀⣀⣀⣀⣀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢿⡀⠀⢸⣯⣭⣭⣭⣿⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠃⠀⣠⠀⣀⣀⠀⠀⠘⠀⠀⠨⠀⠊⠉⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠠⣀⢀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⣀⠠⣤⣄⠀⠶⡄
⠀⠀⠀⠈⣇⣠⡉⡾⠛⢧⣦⡄⠀⠀⠀⠀⠀⣠⠀⠠⢀⢄⠀⠈⠛⡘⢷⣄⡀
⠀⠀⠀⠏⠛⠑⠀⠁⠀⠸⡏⢰⣤⣇⠁⢴⣦⢾⣾⠁⠀⠈⢁⣠⣀⡀⢀⠻⠿⡏⠑⠂⠀⠀⠓⠭⠒⠤⢀⡀
⠀⠀⢧⠀⡠⠀⠐⠀⠀⠀⢸⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣮⢶⣄⠈⠙⠢
⠀⠀⠐⢄⡀⣀⣀⣠⢴⣾⣿⣿⣿⣿⣯⣿⣿⠛⠑⢷⠄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡆⠙⢎⠳⣽⠷⡆
⠀⠀⠀⠈⠛⠉⠸⠗⠛⠛⠻⠿⣿⣿⣿⡟⠁⠀⣸⣿⡖⠀⠀⢢⣠⠀⣞⠉⠁⢀⠀⢀⠚⠛⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡏⠀⠀⢀⠀⠀⢀⠀⠚⢻⡄⠙⠃⠴⢛⡅⠝⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠂⠀⠀⠀⣀⠁⠀⣀⠀⠐⠉⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢻⠉⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠏⠀⠲⠆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠁⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠂⢈⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠖⠀⠀⠀⠀⠀⡀⠘⣼⠀⠛⢿⡗⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠉⢠⠀⠘⠈⠲⣄⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⣀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⢳⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠦⠉⠛⢻⣆⠀⢀⠀⠀⠀⠀⣸⢗⡀⠀⠀⢀⣼⠻⡿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡀⠀⠀⠀⠀⣾⠻⢿⡿⡾⠟⠛⠉⠀⠤⠄⢉⣻⣿⣿⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠈⢀⡼⣷⣄⣶⣷⣄⡀⠠⣀⣀⠰⢀⣤⢿⡿⣿⣆⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠈⠿⠋⠀⠈⠻⢿⡗⠈⠻⠄⣄⡀⣀⣀⡅⣹⠁⠈⠹⡿⠏⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⠀⢀⠀⠀⠀⠀⢸⣧⡀⠀⡆⠀⠀⠈⠀⣄⢹⠀⠀⠀⣿⢀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢧⠀⢠⠊⠀⠀⠀⠀⢸⡇⢹⡆⠈⠀⠀⠁⠀⡇⠘⡀⠀⠀⣇⠀⠂⡸⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠡⡌⠰⠀⠀⠀⢀⡾⠀⠀⢌⢤⠀⠀⠀⠈⣨⡄⢥⠀⠀⠘⢶⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠁⠀⠀⠀⠀⢸⣟⠀⠀⣚⠉⣧⠀⠀⠸⠋⠈⢞⡄⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣾⠯⠀⠀⠀⠠⢋⡳⡄⠀⣠⠄⠀⣷⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⣿⠀⠀⠀⠀⠐⠙⢻⡔⠋⣐⠀⠀⢹⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣤⠍⠹⠀⠀⠀⠀⠀⢠⢾⠃⠉⠁⠀⠀⢸⠇⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠉⠉⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠂⠉⠛⠳⠛⠋⠁⠺⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣷⠀⢸⡇⠀⠀⠀⠀⠟⢁⣹⠇⠀⠀⠀⠀⣿⠀⢰⡟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠿⠶⣤⣤⣀⠀⠀⠀⠀⠿⠁⠀⠀⠀⢀⣠⣤⡴⠾⠇⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⣀⡀⠀⠈⠉⠻⢦⣄⠀⠛⠀⢀⣤⠾⠋⠉⠀⠀⣀⡀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣿⠙⠛⠶⣤⡀⠀⠙⢷⣄⣴⠟⠁⠀⣠⡴⠞⠛⢹⣇⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠻⣆⠀⢀⣿⠃⠀⢀⡾⠋⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼⠃⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠠⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠄⠂⣠⣦⡀⠠⠀⠀⢀⠀⠀⠀⠀⠂⢠⣤⢴⠵⡀
⠀⠘⣄⠀⠄⠀⡿⠀⠀⠀⠀⠠⡀⠀⠀⠀⡊⠀⠀⠀⢄⠙⠮⣙⠒⠂⠀⠀⠀⠀⠈⠐⢺⠋⠑⠀⠑⠂⠀⠒⠉⠀⠀⠀⠀⣤⣲⡭⣆⣼⣽⣄
⠀⠀⠈⠓⠺⠀⠘⠆⠀⠀⣀⡴⠃⠀⠀⠀⣧⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠜⡰⢡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⡀
⠀⠀⠀⠘⠠⠟⠄⠐⢂⣠⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠤⠬⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠀⡜⢀⡴⠒⠀⣄⠀⠀⠀⢰⠀⠃⣀⣸⢼⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠈⢠⠀⠐⠄⢠⠈⠀⠀⠀⠈⠦⡴⠒⠁⠈⠣⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢰⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⡄⣀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠉⠓⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠉⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⢀⢭⠘⠶
⠀⠻⠶⠄⠀⠁⠒⠦⢄⣀⠀⠠⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⢀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠉⠓⠒⠂⠀⠀⠰⢄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣤⡤⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠤⢺⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠒⠛⠃⠈⠀⠀⠀⠀⠤⠀⠠⠜⠀⠃

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⡄⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣥⣖⢦⡀⠠⠄⡂⣤⡇⠂⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⡠
⠀⠐⠄⠑⡀⠐⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡿⣹⠃⠀⠀⢀⠴⠋⠀⠠⡔⠀⠀⠀⠈⠁⠠⠂⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠒⡈⠆⠐⡀⠀⠛⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠁⠁⠃⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠴⠁⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠈⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢧⡀⣀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠃⠀⠀⠀⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⠋⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⡾⠥⠽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠞⣳⠀⠀⠀⠀⠀⠀⢀⡾⠂⠳⣄
⠀⢸⡑⠦⣄⣀⣠⠴⠋⠉⢻⠁⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣖⡿⢈⢂⡟⠀⠀⠀⠀⠀⡴⡫⠀⢠⠀⢊⠑⣄
⠀⠀⠙⠦⣀⣀⠀⣀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢹⡔⠙⡇⠋⢣⠁⣴⠟⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⠦⣧⣀⣠⣤⡠⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣀⠀⠀⣀⣰⠞⢛⢶
⠀⠀⠀⠀⠀⣀⣤⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠯⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣮⣷⠶⡒⠦⣄⠀⠀⢰⣉⢊⣠⠌⣳⣴⢣⣊⣰⠒⠊
⠀⠀⠀⢠⠞⡽⢪⡽⢧⠙⣄⠀⠀⠀⠀⠀⠀⢀⣯⣭⡯⣿⣇⠀⠀⠀⠀⠀⢀⡞⢁⠊⠀⠂⠀⢂⠀⠱⡈⣇⠀⠀⠈⠉⠘⠦⠚⢿⡷⠃
⠀⠀⠀⣜⠀⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠿⣯⣿⠛⣿⣇⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠈⠀⠀⡇⣿⠀⠀⠀⠀⠀⣰⢞⠉⠑⢢⡀
⠀⠀⠀⠘⢆⣀⣀⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣇⠸⣟⠂⠀⠀⠀⠘⣆⠰⡀⠸⠀⠀⢀⠀⠰⣠⠇⠀⠀⠀⠀⠀⢣⡀⠀⢀⣸⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡏⠉⠛⠁⠀⠀⠀⠀⠈⠓⠚⠒⠓⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⠒⠋⠙⠲⢤
⠀⠀⠀⠀⠀⢠⠟⠁⠉⣯⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⡻⣗⢤⡀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣼⠀⠢⢠⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢠⠃⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⣼⢛⠹⣻⡻⡛⣗⠝⡄⠀⠀⠀⠀⣾⠀⣀⣀⣀⠀⢤⣤⣄⣹⠀⠀⠀⠸⣇⣑⡄⣀⠀⠂⠠⠴⡤⠃
⠀⠀⠀⠀⣼⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢸⡇⢃⠰⠸⣏⢸⢸⢰⣹⡀⠀⠀⠀⠘⠶⠯⢿⡇⠀⠸⡟⠋⠁⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⣾⠁
⠀⠀⠀⢠⡇⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡐⠵⢬⣿⣃⡯⣂⡿⠁⠀⠀⠀⠀⠀⠀⠐⣧⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠸⣀⡇⢀⣀⢀⡟
⠀⠀⠀⠘⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⣠⠤⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⣋⣩⢤⢤⣽⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠲⠦⣄
⠀⢀⡞⠁⠀⠀⣀⡠⠷⠒⠒⠒⢦⡀⠀⠀⠀⡴⣫⠝⠿⢍⡑⢢⠀⠀⠀⠀⢸⡥⠒⠋⠉⠙⡆⠀⠀⠀⠙⡆⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠳⣀
⠀⡟⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⡀⠀⠀⠀⡄⢸⡇⠀⠀⠀⢺⠀⠀⠀⣀⣾⣳⣤⣤⣄⣀⡇⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⡇⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢻⣠⠀⠀⢠⠁⡸⠀⠀⠀⠀⠈⠓⠒⠺⡻⠃⠁⠈⣼⠀⠉⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⣠⠎
⠀⠙⠢⠤⠼⠦⢄⣄⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠄⠀⣻⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠛⠛⠋⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⣄⡀⢀⣤⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⢀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠸⠠⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⠈⠀⡀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⡌⡠⠤⠤⡀⠀⠀⠀⠀⢀⠔⠀⠀⠄⠠⠄⠀⢀⠀⠀⠀⠀⠈⠂⣀⠀⠤⢄⠀⡀⠔⠊⠀⡄⠀⠀⠀⠈
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠎⠁⠀⢱⣊⠀⠴⠆⠀⢤⣤⣴⡏⣠⠬⠥⢤⢄⣀⠀⠀⠀⠐⠲⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠄⠀⠀⠀⠀⣀⡶⠀⠀⠀⠀⠀⡀⠔⠉⠈⠀⠀⠀⠀⠀⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠉⢀⢀⡀⠀⠀⠀⠀⠁⣠⠀⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⢀⠈⠛⢦⠀⠀⠀⠀⢈
⠀⠀⠀⠂⠀⠠⡀⠀⠀⠀⠈⠴⠶⠎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠁⢈⣰⡶⠶⠄⠀⠀⠀⠈⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠀⠇⠀⢲⡀⠀⠀⠀⠀⠀⠸⠧⢄⣀⠀⠀⠀⠀⠀⢀⠄⠔⠛⠋⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢰⠀⠀⠙⢶⠂⠖⠂⠁⠐⠀⠀⠀⠙⠦⠤⠤⠶⠶⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠠⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠐⠊⠀⠲⣄⠀⠀⠆⠘⠁⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠊⠃⠀⠀⠠⠄⠁⠈⠂⠤⠄⠤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡆⠠⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢠⠄⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⢡⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⢀⠀⠀⢀⡜⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠄⠒
⣿⠿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣤⣄⢀⣤⣶⣾⣿⡿⠛⠻⢿⣿⣿⣶⣦⣄⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠉⠀⠀⠀⠈⠳⣟⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣻⠟⠉⠀⠀⠀⠉⠛⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡁⠊⠀⣠⣾⣻⡆⠀⠀⣤⣿⣿⣿⡇⣠⡀⢀⣤⢨⣿⣿⣿⣧⠀⠀⢰⣟⣷⣄⠀⠑⢌⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠊⢙⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠉⠁⠈⠉⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⡉⠑⠄⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡴⠞⠛⠙⢿⣿⣿⣿⣿⣿⣿⣟⠀⠤⠥⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠛⠳⢦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⣼⠁⠀⠀⠈⢾⠁⠀⠀⣙⣻⣟⡿⢢⣄⣀⡞⢿⣻⣿⣉⠀⠀⠈⡷⠁⠀⠀⠈⣧⡀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⢦⣄⣀⣤⣼⢀⠀⠀⠀⠈⠙⠳⣦⡁⢈⣤⠞⠋⠉⠀⠀⠀⡀⣧⣤⣀⣠⡴⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠠⠿⠛⣻⢿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⡿⣟⠛⠯⠄⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣷⣶⣿⡿⠘⣿⣆⠀⠀⠀⠀⠀⠒⢾⡧⠒⠀⠀⠀⠀⠀⣰⣿⢃⢻⣿⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠁⠹⣿⣧⣄⣀⣀⣀⣉⣿⣿⣉⣀⣀⣀⣠⣼⣿⠏⠈⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠘⣟⢢⠀⣠⠜⠋⠙⠋⠙⠣⣄⠀⡄⣻⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣄⢻⡑⠀⡇⠀⠀⢠⡄⠀⠀⢸⠀⢊⡟⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠀⡿⠛⠀⢻⡟⠀⠛⢿⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡇⠀⠀⣰⣇⠀⠀⢸⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡿⠋⠁⠹⡟⠉⠙⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣉⣛⣙⣛⣛⣛⣛⣛⣛⣛⣛⣋⡛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡏⣠⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳⡄⢻⡀
⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠙⢦⡀⢸⡇⣿⠀⠀⣤⠀⠀⠀⠀⢠⡄⠀⣠⣤⣤⣤⣤⣤⠀⠀⣠⡤⢤⣄⠀⠀⠀⡇⢸⡇⢀⣴⠏
⠀⠀⠀⠀⠀⠉⢸⡇⣿⠀⠀⠈⢳⡄⠀⣰⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠈⠀⠀⠀⡇⢸⡇⠈⠁
⠀⠀⠀⠒⠚⠒⢸⡇⣿⠀⠀⠀⠀⠙⣾⠁⠀⠀⠀⣿⠶⠶⠶⠦⠀⠀⠀⠙⠶⢤⡄⠀⠀⠀⡇⢸⡇⠐⠒⠓
⠀⠀⠀⠀⣀⡤⢸⡇⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇⢸⡇⢠⣄
⠀⠀⠀⠾⠋⠀⢸⡇⣿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠀⠐⢦⣤⡤⠟⠀⠀⠀⡇⢸⡇⠀⠈⠷
⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣧⣼⣇⣰⠞⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠙⢦⡀⠀⣀⣤⣤⣾⠁⠀⠙⢷⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠈⢧⡈⠳⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⢿⣄⠀⠀⠀⠹⣶⡏⠀⠀⠙⢦⡀⠀⠀⠙⢦⡀⠀⠀⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⣄⠀⠀⠀⠙⣦⡀⠀⠀⠙⢦⡀⠀⠀⠙⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠙⣦⡀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠳⣄⠀⠀⠀⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⠲⢮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣟⢳⡄⠀⠀⠀⣟⠀⠀⣠⡴⠛⠛⠛⠶⣄⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠹⣆⠀⠀⡏⠀⢰⠏⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠉⢳⡶⠦⣤⣀⡀⠀⣠⠞⠁⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢧⡀⣷⠀⢸⡄⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠈⠹⣟⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⡏⠀⠀⠻⢦⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠳⠾⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠤⠴⠞⠁


⡖⠒⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠒
⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⢠⠤⢀⠀⡀⠤⠤⠀⣠⠀⢠⠤⢀⢠⠀⠀⠠⠄⠀⢀⠠⠄⠠⡤⠄⡤⢄⡀⡠⠤⡀⢠⠀⡀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⢸⠀⢈⠂⡇⠀⡆⢰⠄⠇⢸⠂⢣⢸⠀⠀⠗⠀⠀⠈⠑⢆⠀⡇⠀⡦⢺⡰⡇⠀⣸⢸⠿⡀⢸⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣶⣷⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠤⢁⡀⠈⠁
⠀⠀⠀⠃⠀⠀⢀⡀⠀⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠠⠆⠉⡵⠀⠆⠒⡲
⣤⡄⠀⠀⠆⠀⠈⠆⠰⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⡏⠁⠀⠐⣆⠠⣞⣤
⠘⡷⠂⠀⠀⠀⢀⡉⠀⠀⢀⠀⢐⡂⡀⢀⡤⠀⠀⠀⠀⠁⠀⠑⡀⠃⠀⠠⠀⠀⠀⠐⡀⠀⢀⢀⠀⠀⠂⠀⠀⠀⠀⡇⢤⠀⠴⠹⠀⠍⠉
⠀⠱⣄⠀⠀⠀⠀⠳⡴⠋⠁⠀⠀⠀⠄⠆⠀⠀⠉⠀⠀⠀⠐⡀⢠⡤⡀⠀⣀⡀⠀⠐⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠐⠠⠕
⠀⠀⠈⠑⠂⢰⠀⠈⠀⣤⣄⠠⠞⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⢠⠈⠰⠶⡀⢤⡇⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣿⠆⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⢀⠀⠀⠀⠰⢃⠈⢩⠀⠀⠀⠭⠿⡀⢉⠀⠙⠋⡄⡎⠙⠀⠀⠀⢄⡁⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡇⠀⠙⠒⠜⠁⠁⠀⠀⠀⠁⢀⠀⠙⠂⣀⠀⠀⡤⠤⠞⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣮⡵⠀⢀⠄⠀⠀⣄⠀⠀⠀⠀⠀⡄⠀⢁⡀⠀⠀⠻⠥⠔⠁⠀⡠⠢⡄⠀⢀⣤⡊
⠀⠀⠀⠀⠀⠀⢀⡖⠀⠐⢖⠊⠀⠈⣲⠖⠁⠂⠀⢖⠁⠀⠀⢀⡴⠋⠉⠁⠲⣄⠁⠘⢄⠀⠂⠄⠀⢉⡀⠄⠊⠀⢼⡁⠀⠁⠀⢱
⠀⠀⠀⠀⠀⣠⣬⣵⡄⢠⣞⣀⡀⣀⣳⣤⠀⠀⢠⣞⣀⡀⢀⣀⣙⣦⠀⢀⣴⣁⣈⠛⠛⠁⠀⠀⠀⣀⣼⡂⠀⢀⣀⣙⣦⠀⢀⣞⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣤⣶⣶⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⣴⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⣿⣿⣿⣿⣿⣟⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⣰⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣶⣿⣷⡀⠠⠊⠁⢠⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠻⣿⣿⣿⣿⣿⣿⣟⢯⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⡛⠛⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠠⠋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢩⣟⡛⣛⣛⣛⢛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠈⠉⠙⠓⢂⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠉⠀⠀⠉⠁⠀⠀⠙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⢤⡀⠀⠀⠤⠄⢘⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠁⠁⠠⠈⠁⠁⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⠒⠚⠀⢀⠄⠰⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀⠔⠉⢹⠦⣄⡠⠞⠉⠀⠀⢀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠉⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣁⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣠⠖⠋⠀⠀⠀⠑⠀⠀⠠⠴⠖⠲⠶⠶⠶⠚⡛⠉⠉⠁⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡸⠁⠀⠤⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⡄⠀⠀⠉⠁⡼⠀⠀⣀⡀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⡇⠀⠀⠀⠉⠉⠂⠀⠀⠀⠉⣻⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠠⣀⠀⠙⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⣄⠊⠗⠒⠦⠤⠤⠤⠄⠤⠤⠶⠚⠉⠀⢹⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡀⠀⠀⠹⢄⣀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠐⠒⠢⢄⠀⠈⠉⠉⠀⠀⠀⢀⠴⠊⣠⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡐⢤⣀⡀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⢊⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣉⠉⠒⠄⠀⠀⠀⠀⠈⠉⠙⠢⡔⠉⠀⠀⠀⣀⠄⠀⠀⡠⠊⣠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⠰⠂⠀⠀⢄⠠⠠⡀⢀⢸⠀⠀⠐⠋⠀⠀⣀⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⣄⣱⠬⠋⠐⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠤⠂⠀⠀⡀⢠⠒⠤⠠⡀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠄⠀⠴⠀⠀⠀⠀⠀⠠⠀⡀⢐⠀⠀⠠⠀⠀⠀⠀⠀⡐⠘⠉⠙⠐⠀⠀⠀⠀⠰⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠁⡄⠀⠀⠂⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠃⢠⠈⠀⣀⠀⠀⠡⠀⠀⠀⠐⠀⢀⠀⣜⠀⣎⠄
⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢀⠈⠂⠀⡐⠐⠀⠰⠈⢠⠠⠄⠁⠀⠀⠈⠣⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠇⠠⠃
⠀⠀⠀⠹⠄⠀⠀⠈⠢⠀⠀⠀⠃⠀⠀⠀⠈⠂⢄⡀⡐⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡷⠋⠂⢄⠀⠠⠀⠀⠀⠂⡠⠾⢟⡃⠀⠀⣸⠂
⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡃⠈⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠀⠀⠈⠇⠀⠀⠁⠐⠛⢂⠤⠐⠂
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⢀⠀⠁⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠄⠀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠄⠀⣠⡾⡇⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠰⠎⠀⠀⠀⠀⠀⠒⠁⠄⠀⠀⠀⠀⠀⠄⠀⠄⡀⠀⠀⠀⠙⠀⣠⠣⢈⡆⠀⠀⠀⠸⣡⢀⢀⠀⠄⠈⠀⠀⢀⣀⢀⣀⡀⠀⠀⣠⠀⠀⠀⢀⠅
⠀⠟⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠭⢙⡚⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣾⡉⣠⣊⢔⠝⡄
⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⠉⡅⠀⠀⣞⢮⣱⠆⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢀⡀⠀⣈⢁⠌⠙⠛⠛⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠟⠀⠀⠀⠀⣠⣞⠗⠁⠀⠀⠒⠀⠀⠘⢓⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⢦⠤⢬⠃⠀⠀⠁
⠀⠀⠀⠐⠀⠤⠈⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠀⠀⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠿⠿⠿⠋⠁⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠁⠀⠀⣠⣾⣿⡷⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠈⣿⣿⣧⡀
⠀⠀⠀⠀⢀⣀⣤⣀⣀⠀⣀⣾⣿⣿⡋⠀⣀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠙⢻⣿⣿⣄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣴⣾⣶⠀⠀⣠⣾⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⡏⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⠿⠛⠉⠀⠀⣿⣿⡟⠁
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣷⣀⣀⣿⣿⣿⣿⣇⣀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⣿⣿⣿⣿⣿⡿⠉⠉⣿⣿⣿⣿⡏⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠉
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠉⠉⠋⠉⠁⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠑⢒⡆⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠙⠲⠄⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠁⠒⠦⡀⠀⠀⠀⠀⠀⠘⢆⠀⠀⣀⠄⠀⠀⠢⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠈⣆⠀⠁
⠀⠀⢠⠀⠄⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡈⢆⠀⠀⠀⡰⢻
⠀⠀⠀⠁⠢⠄⠉⠉⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠚⠉⠁⢉⡷⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠐⠁⢘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⣠⣧⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⢞⠁⠀⠂⠀⠒⢒⠁⢁⠂⠤
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⡠⠞⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠄⠙⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡤⠘⠉
⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣁⣤⣶⠟⠁⠀⠀⠀⠀⠑⠒⠀⠤⡠⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠞⠉⠀⠠⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⠒⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠑⡢⢤⣴⠀⡇⣀⣴⣔⡋⠁
⠀⠀⠀⠀⠀⢀⠀⠦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡒⠡⠄⡀⠈⠉⠉⠀⠀⣀⡤⠝⡆⠀⠀⠀⢀
⠀⠀⠀⠠⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠑⢒⢤⠒⠋⠁⠀⠠⣏⠀⠀⠀⠈⠙⠳⢦⣤⠴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⠀⠠⠤⠤⣌⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⠔⠈⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠀⢘⡀⣀⠤⠖⠉⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⣙⠚⠋⠉⠀⠀⠀⠀⠀⠀⠉⣆⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⢸⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⡞⠉⢉
⠀⠀⢰⡏⣁⣤⠀⠀⠀⢀⠈⠀⢀⠠⠤⠤⠤⠤⠄⠤⠤⠤⠤⠠⠤⠤⠤⠄
⠀⠀⠈⠋⠁⣿⠐⠀⠀⠉
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⡄⠀⡶⠶⠶⠶⠶⠶⠀⠀⣾⣀⣠⠖⢦⠀⠀⠀⠀⠁⠀⢀⠀⢀⡀⢀⡀⢀⢀⠀⢀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠈⠉⠉⠉⠀⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⢀⣞⣉⣠⠦⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿
⠀⠀⠉⠉⢱⠖⠃⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠒⠐⠒⠒⠒⠂⠐⠒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⣀⣀⡘⠛⢦
⠀⠈⢯⡀⠙⠶⠋
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢆⠀⡞⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⢛⡇⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉⠁⠀⠈⠀⠈⠀⠀⠁⠁
⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣈⣉⣉⡁⠀⠀⡀
⠀⠀⢸⠉⢉⣀⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣧⣀⣀⣁⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡿⠀⠼⠗⠒⠦⠀⢀⠀⠀⠀⠰⠰⠖⠲⠴⠂⠒⠶⠴⠶⠐⠲⠴⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣿
⠀⠀⠛⢒⡚⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠘⢯⡉⠳⠴⠟⠀⠀⠀⠄
⠀⠂⠀⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⡖⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠈⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠊⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠂⠂⠀⠀⢄⠼⠂⠀⠀⢄⡀⠀⠂⠀⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠄⣀⠀⢠⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⠀⠑⢄⣀⣀⢀⠄⠊⠉⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢂⢄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠒⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠃⠀⠡⠀⠠⠒⠢⡀⢀⡩⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⣀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠉⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢣⠀⡠⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⡴⠂⠀⠀⠃⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡂⠄⡀
⢠⠊⢄⠀⠰⠀⣀⡀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠤⠀⣀⠄⠈
⠀⠁⠢⣍⠁⠀⠀⠀⠀⠁⠀⠀⠠⠌⢁⣐⠒⠂⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠈⢦⠤⠤⠀⠒⠒⣈⣁⡄⠀⠀⠀⠀⡠⠐⠊
⠀⠀⠀⠀⠑⠒⠒⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⡀⠤⠄⠀⠠⠎⠀⠀⠈⠁⠀⠀⠀⠤⠠⠔⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠨⠄⠤⠤⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡠⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠠⠤⠀⠤⠒⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣷⣶⣴⣧⣴⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣭⣽⣿⣿⣯⣭⣤⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⡀⠉⠉⢀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠚⠋⠉⠁⠀⠀⠈⠉⠉⠓⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢴⣿⣀⣤⠄⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠠⣤⣠⣿⣦⠀⣀⡀
⠀⠀⠀⢀⡴⠶⠶⠋⠀⠀⠀⠈⢻⣧⣤⣤⣤⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣤⣤⣤⣼⡟⠁⠀⠀⠀⠙⠶⠶⢦⣀
⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠉⠉⠉⠉⠻⠧⠄⣀⡀⠀⠀⠀⠀⢀⣀⢠⠾⠿⠉⠉⠉⠉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⣻⣄⠀⠀⠐⡀⠀⠀⢀⡀⠀⡀⠴⠛⠛⢧⣤⠄⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠠⣤⡾⠛⠛⠦⡀⠀⢀⡀⠀⠀⢀⠂⠀⠀⣠⣟
⣸⠿⠛⠓⠤⣀⣴⠆⡠⠛⠛⠂⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⡀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠐⠛⠛⢀⠰⣦⣠⠤⠛⠛⠿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇
⠇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⡀⠀⠀⢀⣠⣷⣤⣀⣀⣠⣤⣾⣿⣿⣿⣿⣷⣤⣄⣀⣀⣤⣿⣄⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠇
⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠿⢿⣿⣿⣿⣿⡿⠻⣿⠿⣿⣿⣿⣿⠿⣿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠋⠀⠀⠀⠀⢸⣿⣿⡅⠀⠀⠀⠀⠙⠟⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣼⠀⢀⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⡀⢀⣧
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠶⠾⠿⢿⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⡿⠿⠷⠶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⢻⣿⣯⣥⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣬⣽⣿⡟⠻⠿⠽⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢹⡿⠻⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⢿⡏⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡄⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣠⣿⡀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⢀⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠙⠲⠶⠛⢩⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡍⠛⠶⠖⠋⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢹⣇⠀⠀⢀⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⠀⠀⠀⣸⡏⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠻⢶⡶⠟⠁⠀⠙⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠋⠀⠈⠻⢶⡶⠟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠀⠀⠀⠀⢠⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡄⠀⠀⠀⠀⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠈⣲
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢆⣀⣠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣄⣀⡰⠚⠁
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣁⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣵⣾⡝⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⡦⣟⠻⠛⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡓⠅⠈⡶⣅⢠⣞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⢑⠄⠀⣣⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡁⠡⡜⠆⠁⡸⢃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⢟⢍⡚⢷⠀⢀⡞⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⢳⣕⠄⡍⠂⠀⠉⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢅⠧⡈⡓⠄⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠫⡂⣕⢕⠕⠂⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠗⢝⠪⡒⠅⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⢋⢴⠠⡓⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡡⢀⠑⠐⡳⡄⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡏⠑⢬⠀⠐⢈⠈⢣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣷⣿⡳⣤⡀⣂⠐⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⢿⣿⢟⣵⣝⠪⠁⠈⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣛⣮⡳⣿⣿⣽⡆⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡾⣿⡤⡽⢳⣙⣇⣩⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⠙⢦⣹⡤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣻⣿⣀⠰⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢏⣥⣶⠈⢻⣿⡿⠁
⠀⠀⠀⠀⠀⢀⣴⡿⣯⣎⣡⡈⠉⠀⢀⡟
⠀⠀⠀⠀⣴⣿⣿⠋⣰⡟⣰⠃⠀⡰⠋
⠀⠀⢠⣾⣿⡝⠁⠀⠙⠛⠁⢀⠞⠁
⠀⣰⣿⣟⠏⠹⣯⠇⠀⠀⡰⠋
⣾⣿⠳⣮⡳⢤⣀⠀⣠⠊
⢹⣿⣷⡄⠙⢻⡿⠋
⣤⣽⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠛⠿⣷⣿⣿⣿⣿⣿⣿⣧⣴⣾⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣤⣀⣀⣀⣀⣤⣶⡿⠟⠋⠉⠀⠀⠉⠙⠻⢿⣶⣤⣀⣀⣀⣀⣤⣶⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⣶⣿⣿⣿⣶⣤⣤⣤⣤⣄⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣿⣿⣿⣷⣼⣿⣿⣿⣿⣤
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣶⣾⣿⣿⡻⢟⣿⣿⣷⣶⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠻⣿⣿⣟⣫⣿⣿⣦⣍⣉⠛⠛⠂⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡟⠐⠛⠛⣉⣩⣴⣿⣿⣝⣻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⣿⣿⣿⣦⡙⠿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⠿⢋⣴⣿⣿⣿⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣶⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢫⣿⣿⡟⢿⣿⣿⡿⢿⣿⣿⡿⢻⣿⣿⡝⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢸⣿⣿⣿⢾⣿⣿⣶⣶⣿⣿⡷⣿⣿⣿⡇⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⣿⣿⣋⣙⣿⣿⣠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡙⢿⣿⡿⢿⣿⡿⢋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⢿⡇⣾⣿⣷⣾⣿⣷⢸⡿⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠛⠿⠿⠿⠿⠛⠛⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣁⣉⡛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠋⠁⠀⠙⡆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣦⡀⢀⣠⡴⠟⠉⠀⠀⠀⢀⣾⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠚⠝⢯⡁⠀⠀⠀⠄⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠟⠛⠓⠉⠲⣄⠈⡳⣄⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠟⠋⠉⠀⢀⣠⡀⢀⣾⣅⡈⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⣠⠖⠋⠀⠈⠂⣻⡏⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⣠⡴⠟⠁
⠀⠸⣾⡛⠋⠉⠁⠀⠀⠀⠀⠀⠤⠒⠉⠁⠀⠀⠀⢀⣠⡶⠟⠉
⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⡠⢀⢀⠀⠀⠀⠈⠂⠠⠀⠒⠀⠒
⠀⠀⠀⠀⠀⠸⢀⠀⠄⠈⠁⢈⠀⠀⠀⠀⠀⠀⠄⠤⠄⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢐⠀⠀⠈⠑⠄⢀⠀⠁⠀⠀⠀⠂⠠
⠀⠀⠀⠱⠀⠀⢠⠀⠄⠀⠀⠁⠀⠀⠈⠁⠀⠐⠚⠀⢀⢀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠅⠀⠀⢠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⢳⡴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠸⠏⢁⠀⠀⠀⠊⠀⠀⣀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠠⠀⠀⠀⠀⠀⢈⣧⣂⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠂⠀⣜⠉⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣀⠀⠂⠡⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠄⠀⠒⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠁⠀⠂⠀⠄⠀⠃⠨⠌⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⢀⡀⠦⠀⠀⠀⡐⠠⠀⠠⠀⠀⠈⠀⢰⠀⠀⠀⠀⢃⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠁⡀⢒⠀⡈⠀⡀⢆⠈⡀⠀⠀⠀⠘⠀⢘⠁⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⢁⠐⠄⡠⠀⡀⠢⠀⡌⠀⠀⠀⠀⠳⠆⢀⠘⢀⠆⡠⠞⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠴⠺⠀⠀⢀
⠀⠀⠁⠄⠀⠀⠈⠡⠠⠀⠀⠀⠀⠀⠀⠲⠆⡴⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⠂
⠀⠀⠇⠁⡄⠀⠸⠈⢠⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢡⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠠⠀⢐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢄⠰⠀⠀⠉⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠴⠀⢈⡴⡀⠛⡤⠀⢄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠠⣁⠆⠀⠀⠀⡀⠀⡀⠀⠁⠀⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠠⡄⠀⠀⠀⠀⠐⠢⢘⠀⠀⠀⠈⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠃⠀⠀⠀⠠⡀⠂⠂⠀⠀⠀⠀⡀
⠀⠀⢸⠄⠀⠰⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠐⣄⠀⠐⣁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠘⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠒⠒⠒⠠⠄⠀⠐⠁⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠻⠃⠀⢰⠀⠀⠀⢀⠀⢠⠖⠛⠓⠂⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⢀⠂⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⡠⢠⠀⠘⠄⣠⠊⡀⠈⠄⡠⠂⠀⠀⠀⠀⠀⠀⠀⣰⠞
⠀⠀⠀⠀⠀⠀⠘⠋⢳⠀⠀⠀⠀⠀⠢⣆⣡⡔⠉⢒⠰⡖⠫⠀⡀⠀⢀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡀⠢⠁⠥⠓⠒⠒⠆⠰⠂⣶⠃⠀⢀⠠⠊⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⠀⠐⡄⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡀⠈⠢⣰⡠⠺⡀⠀⡇⠀⣟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠶⠣⡀⠀⠙⡀⠀⡇⠀⡇⢠⠏⠀⠙⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⡧⠀⡇⢈⠃⡎⣸⠀⢰⠈⡄⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠐⢒⡶⡇⠸⠀⠀⠟⢠⢆⡼⠁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢄⢠⣀⣁⡀⡀⠱⠴⠓⠉⠀⠀⠀⢤⡀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢽⣀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠲⠤⡀⠀⠀⠀⢨⢀⠔⠂⠀⢀⡀⠨⣤⣤⣤⡤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⡘⡆⠀⠀⢀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠀⠀⠀⢢⡀⠉⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠈⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠐⠚⠋⠉

⡿⢿⠿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⣎⠀⢀⡠⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢤⠀⠀⠀⠀⠕⠀⡀⢽⠀⠀⠀⡀⠀⣠⠌⢂⡔
⠀⠀⠊⠳⠘⠈⠀⠀⣀⠴⡆⠠⢄⠀⠐⠀⠀⠀⡀⠗⣤⣄⠂⠀⠀⠀⠀⠀⡞⢅⡻⣦⢰⡾⠇⠀⠈
⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠈⣧⠈⡧⠀⠀⠈⠢⠆⠺⠇⠩⠀⠀⠀⠀⠀⠀⡏⠸⠈⠠⠀⡇⠀⠀⠀⢰⠧
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⢸⢈
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠤⡶⠄⠀⠨⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠲⠴⠂⠀⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⡀⡀⣼⠀⡦⠀⡔⠁⠀⢀⠄⠁⡠⠀⠈⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣀⠤⠂⠴⠆⡀⠀⠈⠻⣤⢿⣬⢡⡞⠁⠂⠀⠈⢆⠀⢗⣻⠂⢠⡀⠀⠀⠀⢀⠀⠀⠁⠀⡀⠊
⠀⠀⠀⢈⡁⠒⢅⢐⠘⡄⠀⠀⠀⠈⠙⣧⡋⠀⠀⠀⠀⠀⢠⢰⢌⠽⠛⠁⠀⠀⠀⠀⠀⢉⠀⠉⡶⠁⠘⡧
⠀⠀⠀⠀⢈⡁⡁⠂⡇⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠰⢿⡟⠉⡆⠘⠀⠀⠀⠀⡠⢠⠄⠀⠁⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠰⠛⠁⠱⡀⢄⠀⢀⡆
⠀⠀⠀⠋⠀⠀⠀⢀⣠⡀⣀⣀⠀⠀⢀⡶⠀⠁⠀⣤⣶⡄⠀⠀⠀⠀⠀⣲⠆⢀⣀⠐⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠉⠉⠁⠒⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠋⠉⣿⠑⢶⣤⣾⠉⠀⠀⢀⡄⠤⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡛⢀⣤⢀⡀⠀⢠⠇⢈⡿⣴⣄⣶⡷⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡁⠀⠉⠛⠁⠠⠆⠀⣿⣿⡿⢿⣃⡇⠀⢀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⠠⠤⠋⣴⠀⠀⠰⠦⠀⠹⠟⠳⣯⡙⢭⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠑⢋⣄⠘⠃⠀⠠⠦⠀⠶⣠⡄⠲⢃⣹⣷⣶⣦⠿⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡜⠃⣤⡜⠉⠶⠀⣤⠀⡤⠀⠶⠀⠀⠀⠈⣽⣿⡼⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⢒⣶⣿⣷⣿⢛⢿⣿⣿⣟⣻⣿⣿⣿⣿⠿⣿⡿⣿⡟⠙⢁⣠⣠⠄⢠⣤⠀⠀⠀⠠⡦⠀⠻⣤⡀⢈⣿⣷⡛⠦
⠀⠀⠀⠀⣰⣾⣿⣿⣭⣿⣿⣿⠗⠋⣻⠿⣯⡍⣿⣽⡃⣿⣥⣾⣿⣿⠿⣏⣿⣇⣫⡷⢸⡶⠒⣈⠁⠱⠆⠀⢁⠀⠙⠃⡈⠐⠶⠀⠉⢀⣼⣤⣿⣿⣦⡀⠀⡀
⠀⠀⠆⠈⠛⠿⣿⣾⡟⢋⣿⣿⠞⣛⢣⣬⣿⡿⣿⣷⠤⣛⡟⢀⡋⢿⣿⣿⠯⣭⣽⣾⣛⣿⣯⣿⣥⣤⣀⣛⢀⡤⢀⣹⣇⠠⠞⢛⣀⣠⣴⣿⣿⡿⠿⠃⠀⠆
⠀⠀⢀⣽⣀⠄⠀⠉⠉⠉⠻⠛⢶⣿⣾⡧⢿⣱⠾⠣⣦⡿⢛⣫⣽⣤⢍⡙⢺⣿⣛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣤⣶⣤⣿⣿⠿⠟⠛⠉⢀⣠⡘⡄
⠀⠀⢸⣿⢿⣷⣶⣴⣯⣤⠶⣆⡀⡀⢉⠁⠈⠐⠁⠚⠛⠓⠺⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠲⠛⠟⠛⠛⠛⠚⠉⠉⠉⠁⠉⠀⢀⣠⣤⣶⡗⢲⣾⣿⢿⣷
⠀⠀⢸⣿⣿⡿⣿⣷⣾⣿⣾⣿⣿⣿⢶⣶⣴⣯⣤⣴⣧⣠⡴⣶⡴⣶⣶⣶⣴⣤⣶⠆⠀⠀⠐⣀⣀⣀⡀⣀⡠⣤⡴⠠⣞⢂⡲⠯⠁⠉⢿⡷⣮⣽⣿⣲⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡉⠙⢿⠟⠻⠿⠾⠛⢯⡿⠿⠿⢿⣷⣾⣿⢿⡿⣯⡝⢋⣹⡌⣾⢋⡙⠴⢏⠱⠻⣿⡓⣿⢿⡇⠶⢫⡴⠊⣿⠶⠛⢡⡿⢡⡟⢻⣿
⠀⡆⢸⣿⣟⠿⣥⣿⣿⡃⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠠⣷⣾⣿⡟⣻⣿⣿⡿⠿⢷⡖⠛⢿⡟⠶⠀⢶⣓⢾⡟⠤⢓⠖⣴⡇⠟⠰⠯⠘⠁⢀⣱⠘⠃⠿⣿
⠀⡇⣸⣿⣻⣿⣿⢻⣟⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣯⣿⠎⣹⣯⣹⣧⣤⣀⡐⢏⣄⢸⡟⣦⢚⡱⢦⣏⣰⡿⠟⠷⠍⠴⠶⠞⢓⠀⠀⠀⣯⣀⣿⢿⣿
⠀⠀⣿⣿⣟⣵⣿⣟⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⡛⢡⣞⢋⣽⣿⣯⣼⣷⣾⠁⣿⢿⣴⣀⣤⢿⣍⢰⣶⢐⡋⣴⡾⠒⣟⠀⠀⠀⣟⢫⡿⠺⣿⡆
⠀⠀⣿⣿⣿⣿⣻⣟⣙⠋⠀⠀⠀⠀⠻⠆⠀⠂⠸⠗⠀⣿⣤⣿⣿⣩⣤⣬⣶⠆⢀⠛⠣⣿⢿⡿⠾⠿⢿⡻⠧⠜⣁⣉⡷⠘⢧⣠⡆⠀⠀⢀⡿⢰⣿⣿⣿⡇
⠀⠀⠉⠻⢿⣿⣿⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣫⠙⠿⣽⣏⣽⣿⢁⡀⠐⢹⣇⣠⠰⣃⡀⢹⡇⢰⡞⢶⣿⡇⢔⣢⣜⣿⠀⠀⠀⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠻⢿⣀⠀⠀⠀⣾⡄⠀⠀⠠⠶⠄⢙⣿⡿⣷⣿⢉⣟⣭⣁⣩⣴⣦⡿⠽⢿⣿⡣⠞⣁⡷⢻⣧⣉⣷⡟⣺⢿⣏⣱⠀⡀⠀⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠀⠀⠀⠀⠀⠀⢰⣟⣧⣿⣿⣿⣿⣿⣿⣧⣸⣿⣷⣿⣩⣷⣾⣘⣿⣄⣫⣦⣯⡿⠷⠚⠚⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠇
⠀⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠏
⠀⠈⠻⣿⣿⡿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠖⡋⠟⣡⠞⠁
⠀⠀⠀⠘⠻⣷⣄⠉⠙⠳⣾⣋⣹⢟⡻⣦⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⠤⢤⡴⠒⡒⠋⠉⠈⠊⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⣀⠀⠉⠀⠲⠈⠀⣄⡉⢀⡉⠉⠉⠛⢉⠞⠚⠋⢻⡟⢻⠛⠛⠓⠂⠛⠀⠁⢠⠉⠁⡀⠦⡀⠀⠀⠀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣤⣤⡀⠈⠉⠀⠙⠁⠘⠂⠁⠐⠂⠀⠌⠡⠴⠁⠐⠂⠀⠀⠀⠀⠀⡀⢀⣀⡤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠾⠶⠶⠶⣶⣦⣤⣤⣤⣤⣠⣤⣠⣤⣀⡶⠶⠶⠖⠛⠛⠋⠈⠁

⠀⠀⠀⠀⠀⠀⣼⢣⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⠀⠹⣄⠀⠀⣀⡴⠚⡝
⠻⣍⠒⠦⢤⣀⣸⠀⠀⠈⢦⠞⠁⠀⡼
⠀⠈⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠶⠤⣤
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠨⡗⢄⡀⠀⢾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢧⣀⣠⣄
⠀⠰⠿⠶⠶⠤⠤⠶⣦⠀⠀⠹⡀⠙⢦⣠⠴⠛⠛⠀⠀⠀⠀⢠⣴⡒⠛⠁⠀⠉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⠴⢷⡀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠛⡆⣠⠤⣬⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡷⠟⠁⠀⠈⢷⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⢼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢄⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠑⢦⡀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠉⠢⣀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠈⠳⣄⠈⠳⣦⡀
⠀⠀⠀⠀⠀⢠⣄⣀⣰⠃⠀⣧⡀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠑⠄⡀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢙⣲⡶⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠉⠢⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⣞⣡⣤⣄⠰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠓⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡠⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠀⣠⠞⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢠⡾⢷⡀⠀⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⡀⠀⣀⡼
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣒⢤⣀⡀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣀⡀⠀⢀⣀⣤⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⣴⠋⠉⠉⠙⠻⣿⣿⣿⣿⠛⠛⠛⢻⣆⠀⠀⠀⣰⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠙⣧
⠀⠀⠀⠀⢻⣦⣄⣤⣴⣾⣿⠟⠛⢿⣿⣶⣤⣾⠏⠀⠀⠀⠻⣤⡤⣴⠖⢿⡿⠟⠛⠉⠁⠑⠢⢄⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⣀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⢀⣶⠿⠿⣿⣿⣶⣦⣤⣴⣶⠿⠛⠛⠛⠑⠲⢵⡀⠀⠀⢀⡂⠀⠀⠈⠙⣳⣦⣶⣿⣿⠏⠁⠀⠚⠛⡆
⠀⠀⠀⠀⢸⣇⣀⣀⣠⣴⣾⡿⠟⠛⠓⠦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠸⣷⣤⠤⡶⠛⡿⢻⠿⠛⠛⠶⢤⣀⣠⣼⠃
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⢶⠾⠋⠀⠀⠀⠀⠓⠚⠓⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀⡀⢀⣦⢄⡀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⢿⡛⣿⡄⠀⢨⡖⠀⢙⣿⣿⣿⣟⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠓⠈⠉⠳⠻⠛⠁⠀⠘⢿⣾⡿⠟⠉⠙⠻⢿⣿⠟
⠀⠀⠀⠀⠀⢀⣾⠿⠛⠿⢿⣿⣷⣾⡟⠃⠀⠙⢶⡀
⠀⠀⠀⠀⠀⢸⣧⡀⠀⣀⡴⠂⠈⠉⠻⢷⣤⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⢀⣀⡤⣐⣾⠿⠷⢶⡄
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣴⣾⡿⠟⣅⣀⣀⣀⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠈⠓⠘⠛⠋
⠀⠀⠀⠀⠀⣰⣦⠴⠲⢿⣆⣄⣀⡀⠀⠀⠀⠐⠒⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠈⠙⢿⣇⠀⠔⠁⠀⠀⠀⠈⢿⡆⠀⠀⠀⣴⡶⣶⣶⣄⣑⣦⣤⣴⣶⣿⡿⠿⠿⣦
⠀⠀⠀⠀⠘⣿⣷⣤⣶⣪⣵⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢻⣄⣀⣤⣼⣿⣿⣿⣿⣿⣤⣀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠋⠁⠀⠉⠙⠻⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠦⠀⡰⠊⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠢⢎⠀⠀⠀⠀⠀⠉⠄⠀⣀⠀⠀⠀⠀⢠⠀⡀⡔⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢠⠚⠉⠁⠈⠉⠑⡴⠛⠉⠉⠁⠒⢤⠀⠀⠀⠀⠀⠉⢢⠀⠀⡀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣁⠈⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠣⣀⡀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠜⠉⡀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠘⠦⡀⠀⠀⠀⡠⠔⠉⠒⠒⠒⠉⠁⠀⠀⠈⠢⠀⣀⠠⠀⠁⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡔⠉⠱⡀⠈⢁⡰⢀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠊⠀⠀⠀⠈⠉⠁⠀⠀⠓⠒⠊⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠦⠤⠊⠑⠤⠠⣄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡸⡂⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠢⠤⠊⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⢀⠔⠒⠒⢒⠃⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⣤⠤⢀⡀
⢀⡤⣊⠀⠀⠰⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⡀⠉⠒⡌⠓
⠘⠄⣉⠒⠤⠈⠒⠊⠑⠒⠒⠉⢉⡒⠒⠤⠄⣀⣀⣀⢀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⣀⡠⠤⠒⠋⠁⠀⠈⠉⠁⠉⣀⠴
⠀⠀⠀⠑⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠤⠤⠄⠈⠉⠩⣤⣄⠀⠀⠀⠀⠀⠀⠀⡋⠉⠉⠡⠤⠤⠤⠔⠒⠉⠀⠀⡀⠀⠐⣅
⠀⠀⠀⠀⠀⠀⠁⠨⡃⠘⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠠⠤⣀⠀⠈⠢⠔⠂⠉⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⢒⣉⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⢀⠀⠈⢉⣒⡂⠀⠀⠀⠀⠀⠸⠴⠖⠒⢛⣉⣉⣛⣉⣒⣒⣋⣁⣀⣀⣀⣀⡀⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠠⠤⠤⠴⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠄⣄⠀⠀⠀⡀⡀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠛⠋⠉⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠊⣙⠳⡆⠸⠿⡭⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢉⣉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠡⠤⠄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠚⣷⠀⠐⠤⢤⣤⠤⠔⠁⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠁⠀⠀⠀⠈⠂⠀⠀⢦⠀⠀⢀⠀⠀⠈⠛⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠏⠐⠀⠀⠐⠒⠒⠒⠓⠲⠶⠤⣬⣷⣤⣯⣤⠶⠶⠒⠒⠒⠤⠷⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠂⠀⠀⠀⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣀⣀⠀⠀⠀⠀⠐⠻⣿⠒⠋⠉⠀⠀⠀⠀⠒⣼⡤⠔⠒⠀⠀⠀⠀⢤⣗⠀⠀⠀⠀⠤⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⠁⠀⠀⠠⠀⠀⠐⢦⡀⢱⡀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠐⢄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣨⣷⣦⣤⣄⣀⡀⠀⣸⣇⣀⣀⡀⢀⣀⣠⣼⠁⠀⠀⠀⠀⠀⠀⢳⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⣙⠻⢧⣀⣢⠤⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⢀⣠⣾⣿⡷⠞⠉⠀⠀⠀⠀⠀⠀⣰⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⣀⣤⠶⠶⠛⢋⣥⡾⠟⢉⠩⠁⠀⠀⠀⠲⠶⠶⣶⣶⠿⠋⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⢤⣤⠖⠁⠀⠀⣈⡁⣀⣠⣴⣫⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⣠⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣤⣶⣷⣿⣿⣿⣿⣿⡿⠿⠷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣭⣵⣶⣾⣿⠿⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡟⠛⢻⣿⣿⠁⠀⠀⢀⣦⣉⠙⠻⢿⣿⣿⣿⣿⡟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⣿⣿⣿⡿⠿⢿⡿⠛⠛⠻⠿⢿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⢹⣿⣿⠀⠀⠀⢹⠀⠀⠀⠀⣼⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⢀⡟⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠑⠄⠀⠻⠧⠀⠀⠀⠀⠀⠀⠘⠁⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿