Wake up Emojis & Symbols

⠀⠀⠀⠀⢠⡶⠛⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⡄
⠀⠀⠀⠀⢸⣧⡀⢀⣸⠂⠀⠀⠀⡀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀⣀⡟
⠀⠀⠀⠀⠀⠙⢿⡿⠟⠁⠀⠀⡀⢀⠀⠀⢀⢰⣿⣿⢋⠀⠀⠀⠀⢈⡻⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⠛⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⢳⡄⢀⠱⠁⠀⠀⠁⠂⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢀⡀⢸⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⠀⢢⣤⣤⣶⣤⡀⢹⣿⡇⠀⠠⣄⣀⣠⠀⠀⢸⣿⣿⣿⡷⠆⠀⢀⣀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣿⣿⣿⣿⣿⣞⣻⡿⣄⠀⠙⠛⠋⠀⢀⣾⢿⡟⠉⢀⣠⣾⣿⡿⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠻⠟⠛⠉⠁⠀⠁⠐⠛⠑⠂⠀⠀⠀⠻⠿⠄⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣾⣷⣾⣶⣄⣀⣀⣀
⣾⡟⠀⠀⠈⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠀⠀⢹⣿⣿⣿⣿⣿⣿
⢻⣿⣦⣤⣾⡇⠀⠀⠀⠀⣸⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣷⣤⣤⡿⢿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⠋⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡿⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣧⠀⠀⠎⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⢰⡿⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣇⠀⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⣾⠁⠀⣸⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⡆⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡏⠀⢸⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⠇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⢸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⣀⠤⠀⠠⢠⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⠀⢄⡇⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⣸⠁⠈⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⠋⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠳⣄⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠆⠀⡦⠛⠉⠓⠂⢀⠀⣙⣿⣿⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠈⠛⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⢲⠀⠀⣀⠀⠀⠄⢀⡤⠋⠀⠀⠀⠑⢦⠦⠆⠼⠀⢀⣀⢐⠂⠒⠀⡅⠀⠆⠀⠀⠀⠀⠈⠈⢹⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⠀⡀⣀⠀⠀⠸⠁⡀⠀⠀⠀⠄⠨⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠸⠤⠆⠀⠀⠀⠋⠀⠀⠀⠀⠈⠂⠀⠀⠀⡰⠠⡇⠀⠀⠀⠤⠃⠀⠦⠤⠤⡤⠮⠤⡼⢁⠓⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠐⠀⠢⣄⠀⢆⠀⢦⢨⠄⢀⠄⠀⢤⠔⢀⠀⡇⠀⠀⠀⠄⠀⠀⠀⠀⢌⣡⢾⡿⠿⢾⣦⣈⠆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠢⢈⠐⠂⠀⠢⠹⠂⠀⠐⠀⣠⠐⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⠁⠐⡄⠀⠙⣯⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡀⠤⠠⠄⠰⠀⠈⡆⠀⠀⠀⠀⠀⠈⠁⠠⠄⠤⠄⠇⣀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡈⠉⠁⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⣀⠀⠠⠄⠀⠇⠀⠀⠀⠀⠀⠤⠀⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⡟⣶⣶⣞⣷⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⠥⡐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⡠⢤⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠒⠀⠀⢸⠀⡇⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠠⠠⠤⠠⠀⠄⠤⠠⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠠⠤⠬⠥⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⢘⠀⢇⡀⢀⡀⠀⠀⠀⠀⠀⢀⡀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣴⣶⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠆⡑⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣠⠔⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠁⠀⠆⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠟⠻⣿⠿⢿⣿⣿⡄⠀⠀⠀⠀⢀⡂⠀⠓⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠑⢤⡀⠀⠈⢁⠀⠀⠈⢄⠀⠀⠀⠀⢸⣿⣿⠛⡁⠀⠀⠀⠀⣀⠀⠹⣿⣇⠀⠀⠀⢀⠎⠀⠠⠈⠀⠈⠀⠀⢠⠔⠁⠀⡠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠀⠀⠀⠀⢂⡠⠔⠈⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣏⠑⠠⡠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠢⠀⠀⠀⠀⡄⠂⠘⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠋⠀⠄⠀⠀⠀⠀⠂⠂⠀⠀⠠⠁⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠊⠠⡀⠀⠈⢢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠊⠀⠀⡠⠉⠀⠒⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⢀⠂⠀⠀⠀⡀⠀⠀⡌⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠲⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⡀⡠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣴⣦⡀
⡠⠊⠀⠀⠁⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠁⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀
⠘⠤⣀⡀⠀⠈⠄⠀⠀⠀⢀⠼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⠀⠸⠀⠈⠀⠀⣀⡀⠔⠁
⠀⠀⠐⠄⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠄⠀⠀⠀⣤⣀⣤⣀⣀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠄⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⢀⡆⠀⠀⠀⠀⠀⠔⠂⠁⡀⠀⠀⡠⠀⢀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣀⡀⠟⠞⠁⠀⠀⠀⠀⠀⢀⠀⠰⠃⠀⠄⡀⠀⠉⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⠄⠈⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠧⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠄⠀⠈⠁⠀⠀⠇⠀⠠⠀⠀⠆⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⡀⠀⡀⠀⠄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢾⢷⣷⢬⠁⠢⠀⠀⠀⠀⠠⠠⠊⠁⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠂⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⠈⡏⡃⠐⠀⠒⠀⠀⠀⠀⠀⡀⠁⠂⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣀⢈⢀⣸⠟⠁⠁⡠⠆⠐⠒⠀⠀⠦⠅⠀⢀⣘⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠉⣁⠀⠀⠀⠉⠁⠉⠀⡀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⡀⠀⠀⠋⠀⠀⠀⠀⠁⠀⢀⠂⠁⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠠⠄⠈⠁⢲⠶⠒⠀⠀⠀⢀⢈⠀⠀⠆⠀⠇⢀⠀⢀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡅⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡌⠀⠀⠑⠊⠀⠸⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁
⠐⡁⠀⠊⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠄⠀⠤⠂⠁

⠀⠀⠀⢀⡶⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀
⠀⠀⠀⠘⢷⣄⣤⣎⠀⠀⠀⠄⠀⠀⠀⣰⣿⡿⠟⠉⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣿⣤⣤⡞
⠀⠀⠀⠀⠀⠹⣏⠀⢠⠀⠂⠐⢀⠀⢰⣿⡿⠐⠀⠀⠀⠐⠉⢹⣿⣿⠀⠀⠀⠀⢠⡾⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠹⡆⠄⠁⢀⣀⣄⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠀⠂⠈⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣿⣿⣿⣿⣾⣻⡧⡀⠘⠿⠟⠀⢀⣿⣿⠛⠁⣠⣴⣿⠃⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠻⠛⠋⠉⠁⠉⠘⠋⠐⠀⠀⠀⠻⠧⠀⠀⠈⠛⠛⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⣠⡖⠋⠂⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡶⠛⠛⣿⣿⣷⣶⣶⣶
⢿⣧⣀⣠⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣠⣿⣿⣿⣿⣿⣿
⠈⠙⣿⡟⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⣿⣿⣶⣿⣿⣿⣿⣿
⠀⠀⠈⢷⡀⠀⠂⠀⠀⣀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⡀⠀⠀⣸⠇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣷⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⡏⠀⣰⣿⣿⣿⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡏⠀⣼⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⢸
⠀⠀⠀⠀⠀⠀⣟⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠤⣽⠗⠲⣄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠿⢹⢷⠤⡀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡀⠀⠀⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⢅⡀⠈⠑⠤⡀⠀⠀⣧⠴⠓⠃⠑⠻⣄⠀⢸⠀⠀⠀⢀⡠⠤⡰⡖⢭⣿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⠙⠢⣛⡖⣧⡘⡉⠀⠈⠽⡞⡠⠔⠊⠁⢀⣀⠧⠗⠢⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⡀⠀⢈⣇⠳⠞⠁⣠⣆⡜⠋⠀⠀⡠⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠚⣼⠲⡖⢋⠏⡼⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢃⣴⡫⠔⠋⣴⡞⠀⠨⣓⢦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⢦⡀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢸⠃⠀⠀⠈⠑⢮⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠈⠚⠛⠀⠀⠖⠀⠀⠀⢀⡾⠀⠀⠀⢀⣴⡛⢻⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠠⡠⠆⠀⠀⠀⠚⡟⠢⣀⢠⣿⠊⣠⠏⠀⠀⣨⢦⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠛⠉⠉⠁⠀⠞⠁⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣉⠒⠠⢄⣰⡇⠀⠈⠉⠓⠚⠁⣠⠴⠋⠁⠀⡇
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠬⢍⡃⠀⠈⠉⠛⠢⡀⢠⠔⠋⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢸⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣄⢸
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡠⠖⠋⠁⠘⠋
⠀⠀⠀⠀⠀⢣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠙⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠹⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡜⢦⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣼⠋⠀⠀⣠⣤
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡞⠁⠀⡠⠞⠋
⠀⠀⠀⠀⠈⠙⠛⠓⠲⠤⢀⠄⠀⢀⡤⠀⠀⠠⠀⠀⠀⠀⠀⠂⢤⡀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡎⠀⠀⠁⠀⣠⡀⠄⠀⠒⠀⠤⢀⡄⡀⠈⠀⠈⡆⡤⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠃⠀⠀⣀⠔⠁⠀⡀⠀⣄⠀⠀⠀⠈⠳⡀⠀⠰⠁⠃⠠⣊⡥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡴⠁⠀⣀⡈⠉⠀⠀⠀⠀⠁⢀⠀⠘⡓⠢⠤⠤⠤⠄⠤
⠀⠀⠀⠀⡈⠀⠁⡀⢦⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢰⠀⠀⢀⠔⠀⠀⠐⡀
⠀⠀⠀⠀⠉⠐⠁⠀⣸⠃⠀⠀⡂⠀⠈⠁⠀⠀⢠⠃⠀⠀⠀⠀⠁⠀⠸⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⠀⠡⠀⠀⠘⠀⠀⠋⠀⠀⠀⠀⠘⠀⢀⠆⠀⠀⠀⢀⡠⠀⢂⣀⡀
⠀⠀⠀⠀⠀⣀⣠⠤⡀⢀⡇⠀⠀⠑⢄⠀⠀⠁⠀⠒⠀⠈⠀⠀⡠⠂⠀⠀⠀⢰⡃⠀⠭⣭⣍
⠀⠀⠀⠀⠀⢉⣠⠞⠡⠊⠀⠤⡀⠀⠀⠁⠂⠤⠀⠀⠀⠤⠒⠉⠀⠀⠀⣀⠀⠀⠑⠌⠳⣤⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⠸⠀⠀⠲⢄⠀⠀⡀⡤⠔⠂⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⣤⠀⠀⣾⠀⠀⣿⠀⡖⡀⢀⠀⢁⡼⡇⠘⠛⠁⢀⠀⠀⡈⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠀⠘⣧⠀⢻⢠⡀⠹⣸⢡⣇⠈⠀⠚⢰⡇⠘⠋⠀⢸⠀⠀⡇⢸⠃⢰⠄⢻
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢷⡀⣷⠆⠸⢶⡆⣷⡈⢛⠛⠛⠁⢸⣄⠀⢃⣼⠀⠶⠖⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠗⠚⠈⠉⠁⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠛⠊⠀⠘⠖
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠧⠀⡁⠀⡅⠀⠀⠀⠀⠀⠀⠀⢠⡶⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠁⠂⠣⡇⠀⡅⠀⠀⠀⠀⠀⠀⠀⡏⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⡀⣀⡠⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠃⠈⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣈⠐⠦⠴⠤⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⠀⣘⢀⡧⠀⠀⠀⠀⠀⠀⠔⠋⠁⢠⠄⠀⠀⡠⠀⠀⣘⣃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣳⠤⠤⣀⣸⠿⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠾⠁⢀⡔⠀⠀⠘⠁⠘⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡠⠝⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⠁⠀⠀⠈⠢⣸⡄⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠒⠒⠢⡆⠀⢀⠀⠀⢀⡀⠀⣐⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠁⠙⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢠⡆⡰⠶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠤⠄⠐⠠⠄⣀⠃⠀⠒⠒⢂⠠⠤⠤⠤⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⡾⠟⢻⠻⢿⡳⡂⠈⠂⠄⠀⠀⡀⠤⢂⠜⠁⠠⡀⠀⠀⠀⠐⠀⠁⠀⠀⢈⡀⠠⠄⠀⠄⠀⠀⠀⠉⠁⠈⠁⠛⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠀⠈⣧⢉⠁⠀⠒⠒⠁⠀⠄⠀⠀⠀⡀⠁⠑⠠⠀⠀⠀⠀⠠⠂⠁⠀⠀⡀⠤⠀⠀⠤⢀⠀⠀⠠⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣆⡀⠘⢀⣐⡷⠃⠈⠁⣠⡖⠀⠀⠆⠀⠀⣎⡇⠀⠀⡀⠃⠀⠀⡐⠁⠀⡠⠊⠁⠀⠀⠀⠀⠐⠀⠁⠀⠀⢘⠄⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⣉⠉⠛⠋⢙⡠⠀⠂⣉⡤⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠏⠃⠀⢀⠀⠀⠼⠢⠭⠀⣈⡁⠂⠀⠤⠠⠔⠃⠈⣠⠔⠊
⠀⠀⠀⠀⠀⠀⡁⠉⠀⡒⠤⢀⣀⣀⣀⠄⠂⠁⠀⠀⢸⠀⠀⢀⠀⢸⡀⠀⠀⠀⠀⠠⠈⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠒⠊
⠀⠀⠀⠀⠀⠀⡅⠀⡁⠔⠊⠀⠑⠀⠀⠀⠈⠀⠀⠣⠜⠂⠤⠜⠀⢀⣁⡰⠀⠀⡇⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⣂⠀⠂⣈⠄⠂⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠈⢀⣈⠀⠀⠌⠁⠀⠐⠂⠠⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉
⢈⡥⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠀⠀⠠⠖⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⢁⡇⣧⢊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡠⠴⠀⢀⠀⠀⠀⠀⠘⢆⠛⠀⠀⠁⢎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠒⠉⠁⠀⠀⠀⠀⠘⢀⠆⠀⠀⠀⡜⠉⠁⠐⢤⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⣀⣀⣤⢌⡆⠀⠀⢠⠃⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡨⠋⠀⠀⠀⠀⡠⠐⡘⠂⠉⠀⠙⣄⣀⠜⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⡁⠖⠈⠀⠀⠀⠀⠁⠈⣆⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢄⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⡀⡈⢄⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠟⠓⢠⠄⣀⠀⠀⠀⠀⠂⠀⡔⠀⢩⠉⠒⠒⠢⠤⠒⠒⠒⠂⠠⠤⠤⠐⠲⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡆⠀⣠⠇⠀⠈⠲⠄⠤⠤⠰⠊⢆⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣉⠉⠒⢦⠀⠳⡈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢢⡔⠀⠀⠀⠀⢀⠀⣀⡴⠚⢁⠴⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⣀⠤⠤⣔⣒⣒⣚⠀⠀⠀⠀⢏⣢⡀⠀⠮⡀⠀⠀⠀⠀⠀⡈⠢⣠⠔⠚⠒⠒⠒⠢⣖⠉⡨⠥⠐⠊⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⡴⠊⠀⠀⠀⠀⠀⡠⠊⢁⡀⢀⡠⠞⠶⢼⡋⠀⢱⠀⠀⠀⠀⠀⣀⣴⡁⠀⠒⠀⠐⠢⠀⠈⡏⠀⢀⣠⡖⠉⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢮⠤⠊⢡⢠⠃⠀⠀⠀⠀⠽⡎⢣⠔⠹⠃⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⡇⢠⡥⠚⠉⢰⠀⡸
⠀⢀⣀⡤⠒⠊⠓⠤⠐⠒⠒⠒⠒⠂⠤⢕⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⢀⣇⣀⡠⣄⠀⠀⠀⠸⠁⡌⠀⠀⠀⠈⠉⠁
⠀⡏⠉⠉⠉⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠤⠵⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠖⠁⠀⠀⠀⠆⠀⠀⠀⡇⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠒⢳⠊⠁⠀⠀⠀⣀⠤⡞⠀⠀⠀⠀⡇⢀⡇
⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡠⠖⠊⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⣀⠔⠊⠁⠀⣇⠀⠀⠀⣸⠉⠹⡀
⠀⠀⠈⡏⠉⢹⠋⠉⠉⠉⠒⠒⠒⠒⠒⠒⠂⠺⡄⠀⠀⠀⣠⠮⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⡧⠔⠉⠀⠀⠀⠀⢰⠁⠉⠉⠙⡝⡀⠀⠠⡇
⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⠔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⠀⠸⣙⡒⠋
⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣠⡬
⠀⠀⠀⠧⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠲⠘⠐⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⠁⠀⠘⢠⠂⠀⠀⠓⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠀⠀⢤⢰⠰⠄⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠐⡠⠀⠁⠀⠀⠐⠆⠁⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢈⠂⠀⠀⠀⠀⠀⡈⠄⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⢡⠂⠄⡀⠀⠀⡠⠂⠀⠀⠉⠁⠂⠉⠈⠀⠒⠀⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠂⠠⡄⠠⡐⠁⠀⢀⠀⠀⠀⠀⠀⠐⠂⢄⠀⠀⠀⠀⠀⣠⠔⢊⠔⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⢠⠤⠀⠄⠀⠈⡀⠀⠀⢏⠦⣀⢦⠀⠀⠀⠀⠀⠠⠐⠘⠂⠒⠲⣀⠜⠂⢈⣠⠔⠁
⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⡐⠁⠀⠀⠀⡄⡠⠔⠠⠂⠉⠙⢣⠠⣁⢤⠄⠀⢐⠇⠀⠀⠀⠑⠀⣇⡠⠒⡋⡘
⠀⣀⡀⠀⠚⠤⠄⠀⠀⠠⠀⢣⡀⠀⠀⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⢀⣆⡀⣀⠀⠀⠐⢠⠁⠀⠀⠓⠁
⠀⠁⠀⠀⠉⠉⠉⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠐⠁⠀⢀⠆⠀⠀⡄⢈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡠⠄⠒⠒⠒⠉⠀⠁⠀⢀⠠⠒⢹⠀⠀⢀⠆⠎
⠀⠉⡏⠁⡖⠒⠒⠒⠒⠒⠒⠀⠸⡄⠀⠀⡰⠯⠤⠤⠤⣄⠀⢀⠠⠄⠊⠁⠀⠀⡎⠁⠒⢊⡀⢈⡆
⠀⠀⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠊⠀⠀⠀⠀⠀⢸⠀⢘⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠈
⠀⠀⢇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⢠⡴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡏⣇⠀⠀⠀⠀⠀⠀⢰⡎⠉⠐⠋⠉⠳⠖⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢥⡟⠉⠒⢄⡀⠀⠀⣟⣀⡤⠲⢤⡀⠀⢫⠀⠀⠀⠀⣀⢀⡤⢲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠈⠒⠄⡿⡤⡆⠔⠂⠘⣲⠞⣀⠤⠊⠁⢀⣦⠦⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⣇⠯⠊⢀⣔⡼⠋⠀⢀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⣾⠲⠊⡝⢴⠁⢀⠔⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠞⠒⠉⢾⡏⠀⠺⢕⢦⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠉⠉⠓⢄⣤⠀⢀⡁⠀⠀⠀⢸⠀⠀⠀⠀⡽⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⢀⡀⠀⠀⠰⡯⣄⠀⣠⡮⠃⡼⠀⠈⣦⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠤⠔⠒⠒⠉⠩⠟⠁⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠑⠤⣀⣁⠐⠤⢀⢀⡇⠀⠑⠻⠤⠚⢁⡤⠚⠁⢷
⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⣙⠀⠉⠑⠒⢆⠀⡤⠚⠁⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡠⠶⣸⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠴⠚⠁
⠀⠀⠀⠀⠈⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠹⣄⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⡟⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠘⠆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣰⠋⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠋⠰⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢠⠁⠀⠠⠞⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠢⡀⠀⢢⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⢐⠦⠒⠂⠉⠉⠉⠐⠂⢵⣠⠀⠀⠀⢸⠆⡇⠀⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠂⢠⠔⠁⠀⢀⡀⠀⢤⠀⠁⡀⠀⠈⠣⡀⠀⠎⠐⠁⠐⡫⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣸⠃⠀⢡⣄⠈⠁⠀⠀⠀⠀⠁⠀⡀⠀⠹⡓⠒⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠉⠁⢅⠐⢆⠀⠀⠉⡍⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢁⠀⠀⡇⠀⠀⢀⡔⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠑⠄⠀⠀⣸⠂⠀⠀⠇⠀⠀⠙⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⠀⠀⡆⠀⠀⣏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠸⡀⠀⠀⠆⠀⠀⠊⠀⠀⠀⠀⠰⠂⠄⢀⠁⠀⠀⠈⠁⢀⡀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡆⠀⠀⠑⡀⠀⠀⠀⠀⠀⣤⠀⠀⠆⠀⠂⡠⠃⠀⠀⠀⢠⠞⠁⢐⡒⠛⠛
⠀⠀⠀⠀⠀⠐⠟⢋⡵⠂⡴⠁⠀⠀⠀⠈⠲⠄⡀⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠀⠀⠀⠈⠧⠐⢬⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠶⠟⠀⠈⠀⠀⠈⢳⡀⠁⠀⠀⠀⠈⠉⠉⠉⠉⡀⠀⠈⠈⠀⣰⠂⠁⠀⠀⠁⠀⠙⠷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⢰⠈⢁⡀⠈⠉⠢⡀⢠⠄⢚⣉⡄⠈⠀⠀⠀⢃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⣇⠀⠀⣿⠀⠀⢾⠀⡿⢠⠀⡖⠐⣱⢛⠂⢈⣀⠀⠀⡆⠀⢠⡎⢀⡄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠻⠰⡄⠈⢰⠃⢾⡄⠀⠀⠁⢺⡀⠈⠁⡀⠀⡇⠀⢸⡇⣿⠀⢺⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢻⣄⣛⠆⠀⠛⣖⣀⣷⣈⣋⠉⠉⠁⠀⣧⣀⣘⣡⡏⠀⠒⢊⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠉⠀⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠈⠛⠋⠀⠘⠓

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⠥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡀⣀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡸⠣⠴⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠛⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⣛⠩⠀⠀⣀⣀⣄⣀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠅⠐⠒⠂⠉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠙⡆⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⣴⠟⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠟⠛⢉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠳⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⣠⠤⣔⠊⠉
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠙⢦⡙⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠂⢄⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢴⠖⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢳
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠬⠭⠭⠭⠭⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⣀⣈⠁⠒⠂⠠⠤⠄⠀⠤⠠⠤⠀⠠⠤⠀⠐⠒⠈⢁⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⣾⣟⡯⠍⠓⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣽⣿⣧
⠀⣿⠈⠉⠻⠓⠒⢶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣶⣶⣶⡶⠟⠛⠉⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠋⣉⣉⣉⣙⠻⣷⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠋⠉⠉⠛⣷⡌⢿⣆
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠃⠀⠀⠀⠀⠀⠘⣿⠸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⡟⢠⡿⠃
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣾⠋⣰⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⡾⠋⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠛⠋⣁⣴⡿⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣴⡾⠛⠁
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⡭⠵⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣍⣓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⢀⣀⣠⣤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠉⠛⢦⡙⢦
⠀⠀⠀⠀⠀⢠⡏⡏⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠉⠙⠲⣄⠀⣿⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢣⡞⠉⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠋⠀⡤⠤⡄⢹⡀⠀⠀⠀⠀⠀⢀⡿⣡⢾⡇⣀⣤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⢸⡈⠳⣌⡳⢤⣀⡀⠀⠀⠸⡄⠀⠀⢰⠖⠒⠚⠁⠀⢹⢸⡇⠀⢀⣠⡴⢞⣡⠞⣡⠞⠋⠁⠀⣀⣀⣀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠓⠮⣍⣛⠒⠶⠿⠦⢤⣬⣷⣤⣤⣤⠤⠿⠾⠒⢋⣩⡤⠖⠉⠀⠀⣧⣀⡤⠖⠋⠁⠀⠉⠙⣦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢧⣄⣀⣀⣀⣀⡤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠈⠉⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⣍⠛⠋⠉⠉⠁
⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⣌⡙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⣋⡥⠞⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠪⣝⡲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣚⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠺⠭⣍⣓⣒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⣖⣒⣻⠭⠷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⠁⠀⡾⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠇⠀⣸⠃⠀⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡟⠀⢰⠇⠀⢠⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⣾⠀⢸⠃⠀⡿⠀⢠⡟⠀⢀⡏⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠴⠒⠀⠀⡏⠀⣿⠀⢸⡇⠀⢸⠁⠀⣼⠀⠀⠠⣌⣙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢾⣿⣶⣞⣋⣥⣤⣿⣤⣿⢠⣼⡇⣤⣼⢠⣤⣿⣀⡀⠒⠦⣭⣛⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠈⢉⣠⠟⢑⣶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⠓⠂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⡴⠾⣛⣵⡆⣚⣛⠧⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢋⣉⣉⣭⣴⡶⠿⣛⣭⠀⠉⠉⠙⣾⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠃⢸⣟⡳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣥⣴⡶⠿⣛⡅⠈⠑⣂⡴⣻⡣⢠⡏
⠀⠀⠀⠀⠀⢀⣤⠞⣋⡥⢒⡠⠄⠀⠀⢻⣟⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣉⣉⣩⣭⣴⠶⢟⡋⢡⣞⣛⣽⣾⢟⣵⠟⢶⣄
⠀⠀⠀⠀⣰⠟⣡⡞⢡⡞⢉⡴⠊⡀⠀⠈⢿⣟⠒⠄⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣭⣭⣴⡶⢿⡛⢡⡿⢿⣛⣭⡶⠛⠁⣀⢢⡈⢷⡄
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡀⢾⡀⠀⠀⠀⠻⣯⡒⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣭⣥⣤⠴⠶⣞⡛⣱⣿⣿⣿⣿⣿⢿⡌⢳⡈⣆⢳⠈⡇
⠀⠀⠀⠀⠻⣆⠹⣧⣌⠳⢮⣛⠶⣬⣁⠀⠀⠀⠈⠻⣥⣄⣀⠀⠀⠀⠀⠀⠤⠤⠶⢶⣶⣾⣿⣿⣿⣿⣿⢸⣿⡜⣿⢎⡇⢸⠇⡏⢀⡼⠃
⠀⠀⠀⠀⠀⠈⣳⣮⣙⠷⣦⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠻⢯⣿⣛⣛⣛⣛⣛⣯⣽⡿⠿⢛⣫⣵⡿⢋⣾⠟⣰⠟⠘⠁⢋⣠⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⠶⢮⣭⣙⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠷⠶⠶⠶⣚⣛⣋⣭⡵⠾⠛⢁⣈⣡⣤⣶⣾⣿⣿⠿⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣹⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⠛⠛⠛⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣡⠶⠋⡹⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣠⠞⠂⠀⣼⠁⢠⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠛⠀⠀⣴⢃⣠⡦⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠂⠀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡤⠚⠀⣠⣦⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠌⠃⠀⠁⠈⠉⢒⡆⠀⠙⣿⠀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⣤⢀⡉⠻⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡿⠀⠀⢠⠗⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣤⠦⠈⠢⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⣰⡿⠚⠁⠰⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠉⠻⠆⠐⠶⠚⠾⠃⠀⠀⠶⠀⠀⠒⠛⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠠⡟⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣦⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠈⠁⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣧⠀⠀⠶⣦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠲⠚⠀⠀⠀⠀⠀⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣶⣶⣶⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘






⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⡟⢿⡿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢁⠈⠀⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢺⡀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣹⠀⠀⣏⠉⢵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠡⠐⢧⠀⠱⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⡈⡗⢤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢀⢊⠐⠁⠀⠀⠀⠑⢤⡈⠑⠂⠷⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠴⠊⠉⠀⠀⠀⢀⠻⠲⡐⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⠂⠠⠀⢤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⠁⠀⠀⠀⠀⠀⣠⠞⠀⠃⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣁⠤⠖⣒⠼⠶⠶⠦⠤⠶⠚⠁⠀⠀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣠⠴⠶⠒⢉⣡⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡁⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠒⢈⠠⢐⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠶⠾⠛⠛⠓⠊⠉⠉⠠⠀⠂⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠐⠒⠒⠒⠒⠒⠒⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡴⠀⠀⠰⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡎⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠀⡘⢡⡷⢤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⢖⠀⣠⣴⣶⣶⣿⡿⢷⣼⣿⣿⣿⣿⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⢂⢹⣧⣤⣬⠍⠉⠉⠁⠉⠉⠉⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠠⠐⠞⠻⣦⡀⠀⠀⠀⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠷⣤⣍⣓⣶⣶⡤⠴⡋⠁⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣌⠻⣿⣿⣿⣿⣦⣌⣉⣉⣉⣁⡀⠔⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⣀⣀⣤⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠉⠁⠀⠈⠁


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⠶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡑⢄⣀⣀⡀⠈⠉⠙⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢈⢀⣀⣈⠉⠑⠒⠦⢤⣀⠀⠈⠙⠛⠶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠖⠛⠛⠓⢊⠔⠉⠀⠀⠀⠢⢄⡀⠀⠉⠑⠢⢄⡀⠘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣟⠋⠀⠀⠈⠑⠒⠴⡃⡀⠀⠀⠀⠀⢀⠀⢀⠉⠡⢄⠀⠀⠀⠀⠁⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠉⠑⠒⠤⢀⠀⠀⠈⠑⠲⠤⣀⣀⡁⠐⠁⢀⣀⠀⡀⠦⢄⡀⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⢉⣁⠀⠀⠀⠈⠑⡀⣿
⠀⠀⠀⣠⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⣀⠀⠀⠈⠑⠤⠐⠃⠀⡇⣿
⠀⠀⢸⡏⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠝⣦⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⢸⡟⡉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⣰⠁⣿
⠀⠀⢸⡇⢸⠑⠢⠄⡈⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠊⠁⡸⠀⣿
⠀⠀⢸⡇⢠⣍⠀⠀⠀⠁⠂⠄⣀⠉⠒⠤⣄⡤⢔⠂⢀⡄⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⠀⢰⡟
⠀⠀⠈⣧⠐⢤⡙⠢⢄⡈⠐⠠⠀⠉⠒⠤⣀⠃⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣤⠶⠟⠀⠈⠛⠛⠁
⠀⠀⠀⢻⣤⣾⠙⠳⢦⣌⡑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣈⠉⠒⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡇⠀⡄⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠹⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡄⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠃⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⠏⣸⠇⠀⢰⢿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⡞⢈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣾⠁⠀⡼⠁⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣰⠏⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠖⠚⢻⡀⠈⠁⣿⠀⠈⠀⠀⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣋⣥⣤⠴⠶⠶⠒⠈⠻⠦⡘⠙⢧⡘⠛⠳⠶⠶⠤⢤⣀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣀⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡁
⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠶⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⢸⣿⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⠀⠀⠀⠀⠀⣹
⠀⠈⢿⣦⡀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⠿⣶⣄⣈⠙⠿⢷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣬⣉⣉⡙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉⠁⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⣦⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠛⠾⣭⣟⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣭⡛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠳⢦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⣠⣾⠟⡋⠹⠙⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠙⠳⣬⡻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⡛⠙⠳⣤⣀⠀⠀⠀⣿⣥⠂⠀⠀⠀⠀⠀⠀⠈⠙⡻⣷⣦⡀⠀⠀⠀⠀⠈⢻⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠉⠲⢄⡀⠉⠳⢦⣀⠈⠛⢷⣦⣄⡀⠀⠀⢀⠐⣨⠷⢚⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠉⠛⢦⣄⡈⠙⠻⣶⣴⣠⣟⣥⣶⠟⠋⠉⠛⢦⣄⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠈⠙⠶⣄⡀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠶⣼⡇⣿⡇
⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⡇⣿⡇
⠀⠀⠀⢸⡿⣥⡀⠀⠀⠀⠀⣴⡟⠙⢀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠈⠛⢦⣄⡀⠀⣠⡴⠛⠉⠀⠀⢀⡿⢹⡇
⠀⠀⠀⢸⡇⠈⠙⢦⣄⠀⠀⢿⡻⣷⢄⡉⠰⣀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣨⣿⡟⠁⠀⠀⢀⣠⠶⠛⠁⢸⡇
⠀⠀⠀⢸⣧⠀⠀⠀⠉⠻⢦⣀⠙⢶⣕⣭⡲⣄⠘⢠⠀⠀⣀⣤⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢻⠁⢸⠇⣀⣤⠾⠋⠁⠀⠀⣀⣼⡇
⠀⠀⠀⢈⣿⣦⣀⠀⠀⠀⠀⠉⠳⣦⡈⠛⢿⣮⣷⣤⣚⡯⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⠀⢸⣠⡼⠟⠋⠀⠀⠀⣠⣴⡿⠛⠉
⠀⠀⠀⠀⣿⠀⠉⠳⢦⣀⠀⠀⠀⠀⠙⠳⣤⡙⠻⠿⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⢀⣠⡴⠛⠁⠀⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⢀⣤⠾⠋⠁⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠈⠳⣦⡀⢀⣠⠶⠋⠁⠀⠀⣠⡴⠞⠋⠀⠀⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠈⢻⠋⠁⠀⠀⣠⡴⠛⠉⠀⠀⠀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠈⠛⢦⣄⠀⢸⠀⣠⡴⠛⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠈⠛⢿⠟⠁⠀⠀⠀⣀⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⢸⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣼⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠿⠛⠻⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠁⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢸⡇
⠀⢀⣀⣀⣀⡀⠀⢀⣠⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⢠⣿⠋⠉⠙⣷⠀⠀⠀⢸⣿
⣼⣿⣿⡿⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⠇⠀⠀⢸⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣼⠟⠀⠀⠀⢸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠻⢶⣤⣸⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡶⠟⠋⠉⢀⣀⡀⠀⠈⠙⠻⢶⣄
⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠿⢾⣿⣥⣀⠀⠀⠀⠈⠁⠀⣀⣠⣤⣶⣾⣿⣀⡀
⣿⣿⣿⡇⢀⣠⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣶⣤⣶⠾⠟⠛⠉⠁⠀⠀⠈⠉⣛⣷⣦⣀⡀
⣿⣿⣿⡗⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠋⠉⠈⠉⠛⠿⢶⣤⣄⡀
⣿⣿⣿⣿⡿⠟⠻⠷⣶⣤⣤⣴⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⣴⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣄⣀
⣿⣿⣿⣅⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣦⣄⣀
⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⣀⣤⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⢻
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠟⠛⠉⠀⠀⠀⠀⢸
⠀⢸⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢸⣿⣿⡇⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠛⠉⠁⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠶⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠚⠉⣁⣀⡤⢤⢴⠒⠒⠲⣄⢸⡆
⠀⠀⠀⠀⠀⡴⠊⢁⡠⢴⢺⠉⠁⠀⠀⢼⢸⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⣸⠀⣰⠋⠀⢸⢸⠀⠀⠀⠀⢸⢸⠀⠀⠀⣸⣸⡇
⠀⠀⠀⠀⡏⠀⡏⠀⠀⢸⢸⠀⠀⢀⣀⣼⠼⠖⠛⠛⠛⢮⡑⠤⡀
⠀⠀⠀⠀⡇⠀⡇⢀⣀⣼⣼⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⡆⠈⠓⢤⡀
⠀⠀⠀⠀⡇⢰⣏⠉⠀⠈⢿⡿⡲⣄⠀⠀⠀⠀⠀⣀⡤⢖⣚⡥⠴⠒⠋⠙⠳⢤⡀
⠀⠀⠀⠀⡇⢸⠀⠑⠦⡀⠀⠉⠪⢿⡦⠤⠒⣊⠭⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠸⣄⠀⠀⠈⠳⢄⡀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⡇⠀⡇⠑⢦⡀⠀⠀⠙⠺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠷⠒⠋⠉⠉⢲⡀
⠀⠀⠀⠀⢧⣤⠇⠀⠀⠈⠳⢄⡀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⢉⣀⣤⠴⣞⣿⠷⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⢀⡔⠋⢁⣠⡴⣖⣋⣭⡶⢿⡀⡏⣁⣠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠙⠷⣄⡀⠀⡞⠀⣸⡥⠾⡇⣟⢉⣀⡤⢼⡇⡏⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠈⠙⠿⡇⠀⣯⠠⠴⡇⣿⠉⠀⠀⣘⣇⡧⠔⣚⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⡇⠀⡇⠀⢀⣇⡿⠔⢚⣉⠥⠖⠚⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢴⡇⠀⣟⣉⠥⠼⠒⠉⠁⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠆⠉⠈⡈⠉⣁⠉⠀⠀⠀⠀⣼⣿⣿⠿⣽⣶⣶⣶⣮⣉⠙⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠴⠀⠀⠀⠀⢀⠀⢲⣂⣀⣤⣤⣶⠂⠀⡀⠀⠁⠘⠛⣩⠉⠿⣿⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⣸⠃⠀⠀⠀⠀⠀⢈⡀⠁⣙⡂⠐⠛⢿⢷⣄⡀⠈⠃⣬⣿⡿⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢌⣙⠀⠤⣄⣀⠀⠈⠉⠀⠩⠁⣠⡀⠀⢐⠛⢛⣛⡻⠞⠋⣤⡞⢾⣏⣀⣄⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣶⠄⠀⠀⠀⡀⠐⠓⠛⠓⠂⣙⡋⠩⣷⣴⡀⢠⡿⣧⣿⡟⠁⠀⠙⣯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠀⠉⠄⠈⢸⠏⣿⠇⠀⠀⣠⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠶⠶⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠷⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡴⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀⣶⣿⡿⢟⣳⡄⠈⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢘⣿⣉⣻⣷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⠀⣛⡾⣿⣟⣩⣿⣥⡀⠀⠱⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢁⣯⣽⡟⠉⣻⠏⣿⣾⣧⣤⣀⣀⠀⣀⢀⠀⣀⣁⣠⣶⣿⣫⢊⡽⣒⣿⣿⣷⠞⠀⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣥⡀⣌⠉⢙⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣟⢍⣯⣱⣝⠋⠁⠀⠀⠀⢀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠰⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠉⢁⠀⢀⡮⢶⡋⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠤⠦⠤⠤⠤⣄⣢⣤⣄⣤⡐⠿⠯⠁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢛⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡉⠉⠉⠓⠒⠦⠤⣄⡀⠀⠈⠉⠛⠷⢦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠧⣄⠗⡢⠒⠒⠒⠠⢀⠀⠈⠉⠒⠢⢄⡀⠀⠈⢹⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⠛⠛⠥⢀⡀⣰⠀⠊⠀⠀⠀⠀⠀⠀⠉⠲⠦⠀⠀⠀⠈⠉⠒⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⠋⠙⠣⠤⢄⡀⠀⠀⠀⠈⠑⠼⣀⡀⠀⠀⠀⡔⢁⠄⠂⠈⠙⠂⢀⠀⠀⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⡀⠀⠀⠉⠑⠒⠦⠧⣨⣤⣤⣤⠤⠤⠈⠉⠒⠤⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⢄⠀⠀⠀⡀⠀⠀⢸⡇
⠀⠀⠀⣠⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣀⠀⠀⠀⠑⠆⠈⠀⠀⡁⢸⠃
⠀⠀⠐⡏⣉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⢹⡄⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⣿⢉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⠁⣸
⠀⠀⠀⣿⠈⡍⠓⠢⢄⠉⠐⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠊⠁⣸⠀⣿
⠀⠀⠀⣿⠀⣍⠐⠀⠀⠈⠐⠠⢄⡈⠉⠒⠤⣄⣀⡤⣒⠀⢀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣷⢶⣟⠁⢀⣿
⠀⠀⠀⣿⠐⢬⡙⠲⢄⡀⠑⠢⢄⠈⠑⠢⢄⡀⠙⠀⢸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⡴⠏⠀⠙⠿⠟⠃
⠀⠀⠀⢸⣇⢰⡟⠷⣦⣈⠑⠢⢄⡀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠉⠋⠁⠀⠀⠉⠛⠶⣤⣈⠙⠲⠤⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢸⠀⠀⠀⣀⣠⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣷⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠋

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠰⠶⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⣊⣉⠭⡤⠤⢤⠤⠬⢭⣙⡒⠦⣀⠀⠻⠷⣀⣀
⠀⠀⠀⠀⠀⡰⣡⣶⣋⣭⣥⣴⣶⣶⣶⣶⣧⣔⠀⠈⠑⠪⡻⣄⠀⠀⠈⠑⣄⣀⣠⠄⠀⠤⠄⠠⢄
⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⠗⠀⠀⠀⡹⣏⣹⠦⠤⠚⡁⠀⣀⡴⠂⠈⠀⠠⠊
⡴⢊⡭⠭⣙⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⣠⠤⣚⣹⡟⠋⢀⠄⣸⣷⣚⡉⠉⠀⠀⣠⣆
⣇⢸⡀⢀⡼⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⣍⣴⣿⣿⣿⢧⣤⡷⢞⣉⠁⠀⠀⠀⣴⣉⣠⣄⣙⡢⢄
⠘⢦⡙⠯⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠀⣌⢧⡀⠭⠀⢠⢶⡉⠻⠀⠉⠈⠉⠂⢘
⠀⣼⠙⡷⠦⣽⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⣌⠙⣿⣻⣿⣿⠇⢀⡿⣧⢿⣯⣭⣓⢦⣉⣀⣠⠤⠤⠶⠋⠉
⠀⢿⠠⠂⠀⠀⠙⢦⡀⣠⣄⣀⣄⣠⣀⣦⣿⣼⣿⣿⣿⣿⣶⣄⣠⡿⣻⣧⣩⣿⠟⠁
⠀⠘⢆⠠⠀⠀⠀⠀⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠤⠆⣱⣿⣍⣧⣽⣀⡀
⠀⠀⠈⠓⢤⡀⠀⢀⡀⠀⠀⠈⠙⠛⠿⠟⠿⠿⠟⠛⠉⠉⢀⣠⣾⣿⠛⢽⣿⣭⣿⢿⡆
⠀⠀⠀⠀⠀⠈⠓⠲⠤⣍⣁⣀⣀⣀⢀⣀⣀⣀⣠⣤⣶⣞⣩⣿⣿⣿⢀⡘⠿⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠉⠉⠈⠿⣯⠭⠶⣿⢿⣝⢧⣀⣾⣯⣽⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣼⠏⠳⠬⡅⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⣦⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣟⡿⠋⡁⠄⠀⣠⡀⠈⠁⠒⠬⢝⡺⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠕⣿⡷⠉⢂⠕⠊⠀⠀⠈⣃⠐⠀⠀⠀⠐⢍⠲⣝⢷⣌⠷⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⡴⣫⠞⠁⣾⠏⡄⡔⠁⠠⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠈⠎⢿⣦⣤⠖⢘
⠀⠀⠀⠀⠀⢀⡞⡴⠁⠀⢸⣼⠘⠨⠀⠀⠀⠁⡀⠀⠀⣴⠄⡀⢁⠀⠀⠀⠀⠀⠀⠘⣼⡇⣠⢾⣧⡀
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⢿⢀⠀⠐⡀⡀⠀⠘⠦⠄⣀⣄⠀⠈⠀⠀⠸⠀⠀⠀⠀⡇⣿⣥⣀⡀⠀⠈⠀⠒⠄
⠀⠀⠀⠀⢰⠃⠁⠀⠀⠀⢻⠸⡈⠌⢆⢳⣕⢄⡀⠀⠀⢈⠃⡴⣋⢔⠵⠁⠀⠀⡸⢸⢹⣿⠟⠻⠉⢗⡶⠦⠤⠃
⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠈⣧⠱⡀⠀⠀⠙⠻⢟⣓⠶⣤⡁⣴⡿⠃⠁⠀⢀⠜⡱⢣⣿⠛⠃⠀⠀⠈⣧
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⣷⣙⢦⡈⠲⢄⡀⠀⠉⠢⢱⠇⠀⠀⠀⠔⣡⢞⣵⣿⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢍⡲⠤⣌⣁⣀⣀⣀⣀⣠⠤⢖⣫⠴⣻⠞⠁⠀⠀⠀⠂⠀⠀⡟
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢂⠈⠻⡷⣍⣙⡒⠲⠾⠭⠶⠶⠒⢛⣉⡴⠞⠁⠀⡀⠠⠀⠌⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠠⡣⡈⠮⡛⠻⠷⠶⠶⠶⠖⠛⠋⠉⠀⠀⠠⠊⠀⢀⠌⠄⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠓⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⡪⢀⠕⡡⠊⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠈⠂⢅⡀⠀⢀⠀⠈⠀⠀⠀⠂⠉⢀⠁⠊⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣗⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣖⣫⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠯⠭⣿⣿⠿⠭⠭⠷⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠈⣇⢀⠈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⡉⠁⢀⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢹⠀⠀⠰⠀⠂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠀⡄⠀⠀⠸⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⠀⠐⡆⢸⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⡆⢠⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⡇⠀⣰⠀⠀⠀⠃⡆⠀⠀⠀⠀⡇⢠⠀⠀⠀⡆⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⠀⣇⠀⢸⠀⠀⢀⡀⣇⠀⠀⠀⢀⡇⢘⠀⠀⠀⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠛⠛⠋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣈⣉⣈⣉⣉⣉⡉⠉⠉⠙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡰⠁⣀⡠⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠂⠠⠤⠤⢄⡀⠱⡀
⠀⠀⠀⠀⠀⠀⣡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣀⢀⣀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⡀⢀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⢸⣿⡀⢸⣦⡀⣿⡏⠀⣾⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠹⣶⣦⣿⣷⣤⣿⣿⣿⣷⣼⣿⣧⣾⡟⠀⣤⠀⠀⠀⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣼⣿⡿⠟⠛⠋⠉⠉⠙⠛⠿⣿⣿⣧⣾⣷⣀⣴⣾⠟⠁
⠀⠀⠀⠒⠶⢶⣤⣤⣀⠀⠙⠾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣶⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣾⡿⠀⢀⣀⣀⣀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣩⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⠤
⠀⠀⠒⠛⠛⠛⠛⠛⠛⢛⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡛⠛⠛⠻⠿⠷⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⠓⠂
⠀⠀⠀⠀⠀⣠⣶⠿⠟⠋⠉⢸⣿⠟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠻⢿⣦⣄
⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⠋⢁⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠿⢦⠀⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⢻⡟⠀⣿⡿⣿⣿⠻⣿⡿⣿⣧⠈⢻⣷⡀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠀⣸⣿⠁⠉⡏⠀⣿⣇⠀⠘⠂⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠐⠀⠀⠀⠀⠀⣀⡀⠘⢃⣀⣉⠀⠰⠇⠀⠀⠀⠀⠀⠀⣄⠹⣇⠹⠀⠀⡜⢀⡀
⠀⠀⠀⠀⠀⡀⣄⣴⠟⢯⡓⣄⠀⠀⠀⠀⠀⠀⠙⠁⡄⠀⡀⠀⡀⠀⠀⠶⠂⠀⠀⠀⠲⠀⠁⢈⣤⣤⣄⠐⣡⡴⡆
⠀⠀⠀⠀⠀⢀⠸⡧⣸⣅⣼⣇⠀⠀⠀⠀⠀⠛⠃⠰⠀⠢⣀⣀⡡⠄⠁⠠⡤⠀⠀⠨⠭⠄⠀⣿⣿⣿⣿⡇⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠛⠏⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠶⠒⣡⠌⠛⠛⠋⠀⢌⡙⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣤⠀⠲⠄⠀⠀⠀⠀⠀⠀⠺⠃⠀⡆⢰⠀⠘⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠲⠄⠸⡄⠀⢠⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢃⣀⠃⢠⠆
⠀⠀⠀⠐⠶⣄⠢⠄⠐⠈⡔⢀⣤⡄⠀⠀⠀⠀⠀⢠⠿⣟⣛⡛⠿⣷⡀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣦⡀⠤
⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠠⠄⠀⢤⠄⠀⠀⠀⠀⢿⣜⢾⣜⣟⡶⣿⠁⠀⠀⠀⠀⠀⠐⠂⣿⣿⣿⣿⣿⣿⡇⠤⠄
⠀⠀⠀⠙⠋⠁⠔⡀⠄⣀⠢⠘⠲⠄⠀⠀⠀⠀⠀⠈⠮⣯⣿⣿⡵⠃⠀⠀⠀⠁⠀⠀⠐⠂⡘⠿⣿⣿⣯⠟⠡⢄
⠀⠀⠀⠀⠚⠁⡸⠁⠀⠘⡄⠐⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⢀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⡀⠀⢠⡄⠀⣠⠆
⠀⠀⠀⠀⢠⣀⢻⠢⡸⠣⠞⣏⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣤⣀⣹⠟⠀⠀⠀⠀⠑⠧⢤⣤⣤⠀⠀⠀⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠍⠫⣝⢦
⠀⠀⠀⠀⠈⣲⠄⠀⠀⠀⠀⠀⠺⣍⣀⠀⠀⠀⠀⠀⢰⠡⠄⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢆⢞⣻⣾⣿
⠀⠀⠀⠒⠛⣡⣟⣀⠀⠀⠀⠀⣏⠈⠁⠀⠀⠀⠀⠀⠈⠢⣈⣋⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠧⣂⠥⣕⣵⠏
⠀⠀⠀⠀⠘⠉⠀⡶⠉⣦⠲⡏⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣠⠄⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⣼⡏⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢻⣧⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠻⣷⡀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢹⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⡼⠃⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠀⠒⠒⠂⠒⠒⠒⠒⠐⠒⠒⠒⠒⠐⠒⠀⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡖⢉⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡍⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⣇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡰⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⠤⠊⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣀⣀⠤⠐⠁
⠀⠀⠀⠀⡠⠄⠒⠒⢈⣉⣭⣤⣬⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⣤⣤⣤⣉⡁⠒⠒⠠⢄
⠀⠀⠀⠀⠢⢄⣀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⢤⡀⠭⠭⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠭⠭⢀⡤⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠂⠀⠤⠤⠤⠤⠤⠤⠀⠐⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠓⠒⠲⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡾⠉⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⣿
⠀⠀⠀⠀⣶⣶⣿⣿⠷⠄⠀⠀⠀⠀⣧⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢿⠓⠦⣤⣀⡀⠀⠀⣀⣠⣴⡾⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⢤⣀⠈⠉⠉⢉⣩⡵⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


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

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⣰⡁⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⢿⣿⣟⣛⣛⣛⠛⠻⣛⡿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⡉
⠀⠀⠀⠀⣦⠻⣿⣿⣿⠿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣷⣬⣉⣙⢻⣿⣷⣆⣴⢁⡼⢀⣠⡔⠂⠉⠀⠲⣄
⠀⠀⠀⠀⢻⡷⢈⣛⡷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣥⣾⣿⣿⣣⠴⠀⠀⠈⠙⣿⡄
⠀⠀⠀⠀⢈⠁⠀⠀⠁⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⡛⠛⢋⢡⣴⣾⡯⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠈⠼⣿⣿⡯⢸⣿⡿⠟⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣻⣿⣧⣾⠇⠀⠀⠀⠀⠀⠀⠊⡀⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⡏⠀⠀⠀⣀⠤⠚⣡⠜
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⡴⠒⢊⣁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡞⣿⣿⡿⣛⣉⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠙⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠀⠀⠒⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠁⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠖⠒⠒⢲⣍⠤⠦⠤⠄⠀⠴⣆⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⡇⢐⣰⠀⢀⠕⠀⡀⠄⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠊⡇
⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⣀⣈⣑⣐⣈⡡⠂⠁⢀⠤⠂⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡡⠋⢀⠎
⠀⠀⠀⠀⡏⡉⠭⠭⠭⠄⠀⠒⠒⠒⠒⡆⣀⠔⣊⠥⠤⠄⠀⠉⠁⠒⠢⡉⠑⠄⠀⠋⢀⡐⠒⢒⠞⠁⠀⡴⡇
⠀⠀⠀⠀⢧⢃⠀⠀⠀⣎⣑⠀⢀⡠⢐⡉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠊⠙⠁
⠀⠀⠀⠀⢸⠸⠤⠤⠤⣤⣴⠾⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠃⢀⠔⠁
⠀⠀⠀⠀⠘⣆⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⡀⣠⢎⠌⠀⡠⠋
⠀⠀⢀⡠⠒⠉⢸⠀⠀⠀⠈⠉⠩⠀⠈⠩⠭⠥⠄⠒⠒⠀⠀⠐⠒⠒⣒⣒⠒⠚⠁⡘⢀⠞
⢠⠞⠥⠤⠀⠀⠀⠛⠒⠒⠒⠒⠒⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠦⠔⡱⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊
⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠤⢤⠤⠞⠁
⠀⠀⠈⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼
⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠤⣉⡑⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠓⠒⠲⠤⢌⡉⠒⠢⢬⣉⡒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢴⡯⣄⡀⠀⠀⠀⠀⢀⣨⡷⠤⠤⠤⣉⡉⠒⠤⢍⣙⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠈⠙⠺⠷⣦⣤⣠⣿⠋⠀⠀⠀⠀⠀⠈⢓⣤⣀⠀⠙⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠭⣖⣤⣄⣀⣴⣊⠥⢖⣫⠽⠲⡇⢸
⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⣥⡔⠊⠁⠀⢀⣠⠇⢸
⠀⠀⠀⢰⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣇⡠⠔⠚⠉⠀⠀⢸
⠀⠀⠀⠈⡦⢄⡀⠀⠉⠑⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡅⠀⠈⠑⠢⢄⡀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠈⠉⠒⠶⠚⠉⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⣀⣸⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⡀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣄⠀⠀⢳⡄⠸⠿⠇⢀⣾⠀⠀⣀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠻⣿⣿⡏⢻⣿⣀⣘⣿⠋⣿⣿⡿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⡿⢂⣠⣶⣶⣿⣶⣶⣤⡐⢿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⢀⣽⠟⠋⠉⠉⠉⠉⠛⢿⣅⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠶⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢰⡶⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣍⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢋⣽⣿⣿⣿⣿
⠀⠀⠀⣀⣠⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣄⣀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠻⠿⣿⣿⣿
⠀⠀⠀⠈⠉⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣶⣦⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠞⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠘⠳⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⢬⠷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣬⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⠆⢙⠛⠿⠿⠿⠟⠋⠠⣾⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡞⠀⢹⡷⠦⢀⣀⣠⣤⣴⣿⣋⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠉⠀⠀⠼⠃⠰⣶⡆⠈⠿⠀⠀⠉⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣏⣼⣿⠉⢹⣿⣄⣿⣿⣷⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⣠⣿⠀⢹⣇⣀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢺⣏⠉⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⢉⣿⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⠛⠛⠶⠶⠶⣤⣤⡟⠀⠀⢀⣿⠃⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⢻⡇⠀⠀⠀⢿⣤⣤⠶⠶⠶⠛⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⠾⠇⠀⠀⣾⠋⠀⠀⠀⠈⢻⡄⠀⠀⠿⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢿⣤⣄⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣤⣿⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠙⢷⣄⣀⣠⣴⠟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠧⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠾⣧⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⠟⠳⢶⣤⠀⢠⡴⠾⠛⠷⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢳⣄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⣶⠏⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠹⣶⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⣿⣤⡀⠀⠀⠀⠀⢀⣠⣼⡇⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⢿⣤⣤⣤⠿⠈⠙⠳⣦⣤⠶⠛⠉⠸⣧⣤⣤⣼⠇⠈⠛⠶⣤⣴⠞⠋⠁⠿⣤⣤⣤⠿⠀⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⢀
⣿⡟⡋⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⡎⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⢁⣠⡤⠞⢋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣶⠟⠁⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠁⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠻⣦⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣸⡷⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣴⠟⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡾⠃⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⡭⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⣈⡙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣡⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣭⣽⣟⣷⣦⣄⣙⣦⢸⡷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢸⣇⣀⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⢀⣠⣾⠉⠉⠻⡆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⡏⠀⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡿⠀⢀⣴⠏⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⢀⣾⣡⡴⠛⠁⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⣹⡷⢛⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠶⠶⢶⣟⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣴⠋⢀⡾⢁⣿⡿⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢰⡏⢀⡾⣿⣯⡥⠶⠶⠚⣛⣿⣧⣀⣤⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠈⢷⣾⣡⣽⣟⠒⠒⠛⠛⢉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢮⣭⣉⣉⡓⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⠶⠖⠒⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⡀⠈⣷⣄⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⠀⣼⣿⣷⠀⣿⣿⣿⠃⠀⠀⣶⠀⠀⠀⠀⣀⣴⣶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣶⣦⣌⢿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡏⢀⣠⣾⣿⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⢠⣄⣀⠀⢀⣀⣀⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣇⣤⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣀⡈⢻⣿⣿⢟⣯⣶⣿⣿⣿⣿⣿⣷⣾⣝⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣿⡟⠉⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣽⣿⡿⣼⣿⣿⣶⣶⣦⣝⣿⣿⠿⢛⣛⠻⢿⣿⣎⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠿⣿⣿⣿⣧⣿⣿⣿⣯⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢸⣿⣿⣋⣉⣀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣟⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠛⠉⣩⣵⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠉⠁⠀⠀⣼⣿⣿⠿⠿⣻⣿⣮⣝⡻⢿⣿⣿⣿⣿⡿⢟⣫⣾⣿⣿⣿⡿⠿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡏⠙⢿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⣿⣿⣿⡏⣿⣿⣿⡟⣿⣿⣇⠀⠈⠻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⣿⣿⠏⠀⣿⣿⣿⡇⠈⠻⣿⣄⡀⠀⠈⠛⠛⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠘⣿⠀⠀⢿⣿⣿⣧⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠉⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠉⠛⢻⣿⣷⣿⢿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⡿⣛⣵⣴⣦⣀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣿⣿⠿⠟⣷⣿⣿⣿⣿⣦⣀⡀⠀⠀⢽⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣿⣿⠅⠒⠄⣶⣍⡻⢿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⣿⣿⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⢼⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣧⠀⠀⠐⡟⢡⡿⣻⣿⣿⣿⣿⣿⠶⣄⣀⡲⢿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠆⠀⢘⢆⡾⣱⣿⣿⣿⠻⣿⢿⠑⠈⠹⣙⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣏⡿⠃⡭⡸⣿⣿⡿⠋⠙⣿⡝⠧⡄⣰⡀⣻⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⣧⡞⣹⡇⢠⡶⠐⠻⣿⣿⣧⣶⢹⣼⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣹⣿⣿⣿⠟⠁⢹⣿⠜⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⡟⠉⠀⠘⣸⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠸⠯⠀⠀⠀⠀⠿⠼⠻⠿⠿⠿⡿⠿⠿⠿⡿⡿⠿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉