Jumanji Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢓⠉⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡖⢋⠀⡀
⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢠⣯⡉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠐⠀⠀⣠⠔⠃⡉⠈⠓⠚⠁⠀⠀⠀⢀⡀⠘⠀⠀⡄⢀⡤⠖⢘⠛⡿⠘⠁
⠀⠀⠀⠐⢶⠀⢺⣧⣀⣀⣀⣈⢹⠁⠀⠀⠀⠀⠀⢊⠆⢙⢥⣀⣀⣠⠊⢱⠆⠘⠤⢲⡛⠋⠁⠀⢸⡃⠘⣋⣀⠀⢠⡴⠋⡧⠀⢯⡴⡿⠵⠚
⠀⠀⠀⠀⠀⠲⣾⣿⣟⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⣡⢀⠏⠹⡄⠌⠐⠀⠘⠀⠀⠀⢻⠉⢀⡀⠀⠈⠀⡜⠓⡆⠠⣀⠀⠂⡧⠐⠀⢸⠉⠀⢀
⠀⠀⠀⠀⣸⣿⣿⡟⠃⡿⣷⣿⣧⣀⢂⠀⠀⠀⠀⣗⣾⡄⠀⢠⠀⠁⡀⢀⢀⠀⠀⡞⠉⠀⠀⠀⠀⣸⠃⠺⡟⢀⠜⢀⠀⠁⣀⡰⢸⠒⠋⠉
⠀⠀⣀⠛⠿⠾⠕⠆⡀⠀⠀⠻⠾⠿⠀⠀⠀⠀⠀⠿⠄⠂⠸⠂⠀⠈⠷⠨⠀⠀⠀⠇⠉⠉⠀⠀⠀⠇⠀⡖⡥⠈⠀⠸⢦⣯⠅⠂⣿⣒⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡀
⠀⠀⠤⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⡤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠟⠛⠋⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠁⠄⠀⠀⠀⠀⠀⠠⣎⠁⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠘⡛⡙⠂
⠀⠀⠀⠀⠀⠀⠀⢰⢯⣀⠴⠆⠀⠀⠀⠀⠀⠀⠂⠀⠾⠢⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⣤⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠶
⠀⠀⣠⡀⠐⠻⡇⠀⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣶⠀⠀⠀⣀⢘⠄⠀⠀⠀⠀⢸⠅⠀⠀⠀⢧⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠉⠉⢳⠿⠋⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠻⠶⠇⠵⠀⠉⢠⡀⠂⠀⠀⢼⠀⢠⠀⠀⢠⣶⠀⠀⢳⡄⠸⢀⢠⠴⢶⣤
⠀⠀⠈⠀⠀⠆⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡖⠑⠠⡂⠔⣏⠈⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠁⠀⠀⠈⠁⢠⣤⠂⠀⠘⠋
⠀⠀⠀⠀⢀⠀⠀⣧⣈⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⡈⠀⠈⠃⠈⠛⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈
⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠐⠦⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠆⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠀⢢⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠳⣤⡄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⡇⠀⠘⢆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠂⠀⠸⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣷⡀⠀⡌⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⣹⣟⢈⡿⠄⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀
⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⣠⢾⣇⡀⡀⠀⠀⠀⠀⠀⠀⠀⢇⠁⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⢃
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡟⠉⠉⠒⠖⠈⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠠⠀⠀⠀⠀⠀⠐⣆⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⣤⣸⡣⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⢢⠀⠂⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠿⡆⠀⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡄⠀⠿⡅⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠘
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡄⠀⠀⣇⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣟⠒⠂⠀⠀⠀⠀⠀⢀⣿⠀⠀⡆
⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⣿⣯⡁⠐⣒⠒⠂⢀⡤⠴⠖⢉⡕⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⣻⠚⠓⠂⠀⠀⠓⠒⠉⠹⡆⠀⡇
⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣇⣉⣋⣹⠒⠚⡅⢆⡰⠞⠋⢇⡟⠃⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠠⠀⢠⠀⠀⠀⠀⠀⣷⣰⡇
⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠁⠈⠻⡛⢛⡩⠒⠚⠉⠁⠀⠀⢀⢸⡗⢰⠀⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⡻⠀⠀⠀⠀⢰⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣠⣀⣪⠗⣪⣄⢠⡠⠤⢂⠴⣾⠃⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠈⣻⡆⠀⠀⢰⠀⠀⢰⠡⡈⢯⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣿⡅⠀⠁⠈⠟⠷⠔⠋⠀⢸⣇⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢛⠓⠀⠀⠀⡇⠀⢸⠀⠀⢸
⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⣶⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠀⠀⠀⢇⠀⠈⠀⢠⠊
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠃⡄⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢸⡆⠀⠀⢰
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⠎⠀⠘⣄⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢈⢷⠂⠀⢸⡇
⢭⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⡖⠁⠀⠀⠀⠈⢢⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⢸⠀⠀⠀⢳
⢸⣽⡄⠠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠂⠀⠈⡇⠀⠀⠀⠀⢀⠂⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠸⡌⡄⠀⠀⢨
⢰⡸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡼⠀⠀⠀⠀⢻⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠠⣏⠁⠀⠀⢃
⠀⠳⡹⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡜⠁⠀⠀⠀⠀⠈⣇⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⣠⠋⡇⠀⠀⠈⢦
⠀⠀⠈⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⡀⠂⠀⠀⠀⠀⢀⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⡇⠀⢳⣤⠠⠄
⠀⠀⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⡆⠀⠀⠀⠀⠀⣸⡀⡀⢘⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠳⠀⣸⡀
⠀⠀⠀⠀⠀⠈⠀⠐⠒⠀⠀⠀⠀⠀⠠⠐⠏⠁⠀⠀⠇⠀⠀⠀⠀⠀⠘⠈⢐⣱⠋⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⢀⠰⠊⢉⡁⠠

⠀⠀⠀⠠⡀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⢀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡈⢩⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠠⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠗⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⢽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠙⣿⣟⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⠀⣸⢇⣾⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠐⡌⣯⡆⠀⠀⠀⠀⢄⠀⢀⠀⠙⢽⡄⠀⣼⣿⡇
⠀⠀⠀⣶⡖⣖⢀⠀⠀⠀⢀⣀⠀⠈⣦⠄⠉⠀⠀⠀⠀⠀⠀⢈⣀⢸⠀⠀⠀⠘⢆⢻⣿⠃⠀⠀⠀⣤⠀⠀⠀⣀
⠾⠀⡌⢿⣿⣿⣿⣾⠒⣠⣿⣿⡀⢨⡿⠀⣀⠴⣶⣤⡀⠀⠀⠺⣿⢈⣀⠀⠸⠀⠑⢾⠇⢀⣆⠠⢚⣴⠀⠀⠀⠻⣿⣷⡦
⠄⠄⡀⠘⢻⣾⣿⠛⠄⠺⠿⠯⠽⢿⣧⠴⣯⣴⣷⡏⣹⠀⠀⢉⡿⡉⠈⠀⠀⠀⠀⠈⠁⢸⢉⠓⡆⠐⣦⡀⠀⢀⣟⠿⣷
⠤⠴⠀⠀⡶⣭⣄⠀⠀⠀⣀⠤⠚⠬⠱⢶⣿⣿⣿⣿⣏⠀⠐⢻⡏⣃⣰⡤⠗⠂⠀⠆⠀⠡⡞⣸⣧⢤⠼⣻⢀⣿⠛⠺⣏
⠀⠀⠀⢸⠇⠀⠀⣱⣤⠔⡁⠀⣰⠠⡀⣼⣛⡟⣷⣾⢃⠀⠀⠘⡇⠉⠉⠀⠈⠀⠀⡀⠀⠀⠀⢹⡷⠈⠀⢉⣿⣇⠴⠋⠉
⣃⢀⣄⣸⠀⢀⣴⣻⣏⡀⠲⠿⠛⣂⣡⣿⣿⣿⣶⡽⣯⡧⠀⢸⡟⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⣻⢻⡄⠀⠘⡿⣉⣠⣊⣴
⢫⣶⣿⡏⣠⠟⣕⠻⠶⠶⢶⡪⠛⠣⠼⣤⣿⣿⣿⣬⣾⣷⠀⢀⣿⣇⣐⠒⠲⠶⢦⠷⡤⢐⣾⣿⣹⡷⣄⠀⣻⣿⠋⠩⣻
⣆⠻⣿⢃⠁⠈⠁⠀⠀⠐⣿⡁⠒⠠⢤⠉⠉⠙⠳⣿⣶⣿⡷⠿⢻⡯⣛⠹⣻⢷⡿⠶⣿⢟⣿⠟⣟⡛⠁⠉⠹⣇⣴⠾⢋

⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⠍⠉⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢰⡾⢿⠳⣦⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠸⠀⢀⠀⠏⠀⠀⠀⠀⠀⠀⠀⣸⣇⣤⠰⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⡄⠀⠀⠀⠀⠀⠀⠀⠐⠾⢁⠁⡜⢹⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡄⣤⡄⠀⠀⠘⠀⠀⠀⠀⢁⠰⠀⠘⠀⠀⠀⠀⠀⢀⢀⣴⠀⠈⡇⠀⠀⠀⠀⠀⠀⣄⠀⢸
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣄⡇⠀⣶⠀⣄⠁⢸⡆⢠⣠⡄⠀⠀⠀⠘⡛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⢿⣿⠀⣿⡇⣿⡤⢾⡇⠘⣿⣥⠀⠀⠀⣴⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡐⠀⢰⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⡏⠒⠈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⢀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢃⠀⠰⠀⠀⠂⠀⠞⠀⠀⠀⠀⠀⠀⢰⣄⠸⠃⠀⠀⠀⢀⠀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⡄⠀⠃
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠘⠓⠸⡆
⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠠⡀⠀⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣿⠀⢳⠀⠐⠀⠀⡧
⠀⠰⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠈⠉⠈⠹⠀⠀⠀⠄
⠀⡀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⣿⡆⠠⠀⠀⠀⠀⠀⠀⢀
⠀⣿⠀⣸⠀⢀⡄⠀⢈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣄⣰⠀⢸⠀⠀⠀⠀⠈
⠀⡏⠀⢻⠀⠀⠀⠀⠈⠀⢸⡇⠀⡀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠘⠇⠀⠺⠀⠀⠀⠀⢴⠀⠸⠄⠀⣄
⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠘⡇⠀⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠘⠀⠀⠀⠀⠇⠀⠈⠀⠀⠄⠘⢃⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠂⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡏⠀⠀⠀⠀⡀⠀⠈⢀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠸⠒⠲⠇⠀⠀⠀⢸⡇⠀⠀⠀⠘⠃⠀⡀⠀⢸
⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⢘⡥⣄⣤⠀⢠⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⢠⡅⠁⠀⠀⠰⠀⠀⣧⠀⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠺⠀⠨⡁⢰⡄⠀⠀⡄⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⡿⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢸⢀⠀⠀⠀⠀⠀⠀⠓⡄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⠀⠀⠀⠸⢰⠀⠀⢰⠇⢳⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⡏⠀⡏⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠐⠀⠀⠀⠀⢠⡟⠀⠃⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠰⢀⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢁⡄⢀⡀
⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡇⠈⢿
⠀⠀⠀⠀⠀⠛⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣇⠀⠸
⠀⠀⢠⠂⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⡴⠊⠀⠀⢀⠀⠀⠏
⠀⠀⡘⠀⠀⠟⠀⢸⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣾⣦⠀⠀⢀⡏⠀⠀⠀⠀⡏⠀⠰⠆⠀⢈
⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⠓⠀⢀⣴⠂⠀⠀⢀⡆⠀⢸⠴⠀⡆
⠀⠀⡇⠀⠀⣤⡀⢥⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⣈⠀⢰⠀⠀⠀⠀⠸⠏⠀⠀⠀⠈⡃⠀⠛⠀⢠⡇
⠀⠀⠁⠀⢸⠉⠁⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⢠⠀⠘⢃⠀⠀⡆⠀⢀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⢾⠀⠀⠀⠀⠘
⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣳⡇⠀⠺⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠃⠐⠆⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃

⣀⣄⣀⠀⠀⠀⠀⢰⣀⠀⢠⣼⣇⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⣿⡆
⢿⣁⣠⠀⠀⠀⠀⢻⣿⡝⢿⣿⣽⠃⢠⣄⠀⣾⡇⠀⠀⢂⣸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠞⠿⠃⡤⠀⠀⠀⣘⣿⣧⢼⢿⣼⣾⣿⠛⠀⣼⣴⣶⣾⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⣠⣠
⠀⠰⠎⠁⠀⠀⢈⡽⣿⠷⠈⢠⣿⣿⡏⢱⣦⣟⠉⠛⠈⠘⠇⠉⢈⡇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠱⣿⣿⣿
⠁⠀⠀⢀⣠⢴⡿⣿⣄⠀⠀⠙⢿⢧⡭⢈⣏⣿⡿⢠⡥⣴⣶⠆⢺⠀⡏⠈⠁⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⢸⣿⣿
⣶⠾⠭⠟⠊⠁⠂⠰⠏⠀⢰⡀⣿⣿⣿⣿⣬⡽⠇⣤⠴⢾⡦⣦⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢨⣿⣿
⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠻⣿⠛⣌⣰⣿⠱⣌⣦⠛⠛⠃⣜⣼⣦⡆⠀⡠⢚⣉⣤⢫⣞⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⣯
⠀⠀⠀⠀⠀⠀⠘⡠⠂⠀⠀⡾⠶⣈⣍⡿⢻⣄⠻⣿⡿⣿⣿⣿⣿⣿⠃⠸⣿⢛⣴⡾⠉⠭⣭⡘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠰⠀⣦⣤⣀⣴⣖⣋⣘⣟⠬⢻⣧⠙⣿⡿⠟⣹⡿⡛⠐⡙⣷⡿⠁⠀⠀⠀⠺⢷⣸⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀⣴⣬⣾⣿⣻⣿⢛⣿⣻⣿⣿⣿⣿⣽⣷⣽⣀⣲⣿⣾⢏⡔⢹⣿⣷⣶⣦⢰⣶⣶⣿⣿⣧⡠
⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⠛⣿⣻⣟⣿⣿⣿⣿⣿⡛⣿⣿⣿⡿⢪⣎⣾⡏⠈⠁⣈⠸⡇⠀⢀⡙⣿⡁⠁
⠀⠀⠀⠀⠈⠻⣿⣽⡏⢹⣿⣴⣿⣍⣽⣿⣿⣿⡽⡋⠡⣀⡀⢨⣧⣿⣿⣿⣿⡶⠀⠉⣛⠃⠀⠾⣷⡽⣿⣇
⠀⠀⠀⠀⠀⠀⠘⣿⣶⣟⠙⣿⠿⢹⣾⣿⣿⣏⣠⢴⡖⠒⢶⣾⣿⣯⣻⣿⣿⣧⡞⠻⠿⢿⢄⣾⣿⢢⣿⡏⠇
⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣶⣿⣿⣿⣿⢿⣿⡵⢞⣉⣰⣞⣋⣿⣿⣉⣝⢿⡻⣿⣿⡳⠶⣿⠟⣿⣯⣶⠿⡂⠠⡀
⠀⠀⢠⡔⣚⣖⣽⣿⣷⣾⣿⣿⣿⣿⡵⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠶⣾⣿⣿⣿⣿⡆⢽⡀⠁
⠀⠈⠻⠌⣝⣾⣿⣿⠿⠻⢿⡿⢿⣿⣽⣿⣿⣿⣦⠉⣹⣇⣿⡟⢻⣿⣿⣿⣿⣿⣿⠋⠺⣿⣙⣻⢗⠿⡟⣼⣯⡎⣀
⠀⠀⠀⠀⠘⠛⠛⠟⠛⠄⠤⠽⠿⠿⠿⠛⠛⢻⣿⣿⣽⣛⣻⣿⣿⣿⠿⣿⡿⢿⡿⡀⣀⣈⡛⣿⣷⠆⠁⠛⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡉⠭⢽⣯⣿⣧⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠽⣿⣿⣷⣿⣿⣿⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⢀⠀⣤⣾⣿⣿⣿⣿⣿⡿⠇⠀⡀
⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⢀⠀⠀⢠⣾⣿⠟⠈⡁⣂⠀⣠⠀⠀⠀⠀⡀⢴⣾⣶⣶⣿⣿⣿⣿⣿⣿⠿⠃⠀⡴⣅
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⢉⠓⠀⣠⣮⣤⡄⠀⠈⣣⠘⠋⠀⠀⠀⠀⠀⠞⠛⢿⣿⣿⣿⣿⢿⣿⡅⢀⠄⠊⠀⠀⠀⠀⠀⢀⣀⣴⢆
⠀⠀⠀⠐⡎⠐⠒⣶⣶⣾⣧⡙⢿⣿⣿⣿⣷⣶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠁⠀⡿⠉⠀⠀⠀⣠⣶⠂⠀⢴⣿⣭⣤⡾⠇
⠀⠀⠀⠂⠈⡜⢿⣿⣿⣿⣿⣿⣦⣿⣿⠟⢉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⡀⢀⣠⠗⠀⢈⡀⠀⠈⠉⠁⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⢥⣀⠰⢾⣿⣿⣿⣿⡿⠉⠀⠘⠀⢠⣄⠄⠠⣤⢄⠀⢈⡴⠀⠀⠀⠀⢰⡼⠃⢰⣇⠀⡀⢀⠀⠀⢠⠀⠀⠀⣴⣾⠂
⠀⠀⠀⠀⠀⠀⠁⣤⣈⡛⣿⣿⠏⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣲⡦⡤⣿⠃⠀⠀⠻⣷⣿⠃⠀⠀⡋⢀⣿⣿⣿⡇
⠀⠠⣤⣴⣿⠄⣅⣻⣿⣿⠞⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣄⣠⠞⠁⠀⢠⠁⠸⡤⠜⠀⠉⠀⠀⠀⣄⠱⠞⠋⠛⠛
⠀⠀⠈⠻⠿⢂⣼⠟⠞⠁⠀⠀⠀⠐⠋⠱⠀⢻⠄⠀⠈⠀⠀⢀⣾⡏⠀⠀⠀⣀⢆⣠⣀⣁⠂⡸⠃⠀⠀⠀⡍⠀⠄⠀⠀⠰⣦⣀⣶⣷⣶
⠀⠀⠀⡤⡉⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠂⣀⢠⡁⡄⠈⠁⠀⠘⡏⠀⠀⠀⠀⠁⠀⠁⢉⠀⠀⠉⠀⠀⠀⠀⢃⠀⠐⠠⠠⡀⠀⠛⠛⠋⠁
⠀⠶⢀⣀⡁⠀⡄⠁⠀⡀⢆⠀⠀⡀⠀⠚⠁⠀⠀⠙⠀⠀⠀⠰⠃⣀⠀⣰⡏⠀⠀⠛⠉⠀⠐⠀⠀⠀⠀⠀⠈⠘⠀⢀⣠⣅⠀⣀⣀⣾⡆
⠀⠀⠺⣿⣿⣿⣿⣦⣿⣿⣿⣷⡀⠀⠀⠀⡀⠀⠀⠀⡀⢡⣦⡂⣀⣨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⣿⣿⠿⠻⡿⠟
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⢋⢛⣶⣦⣥⣄⣀⣄⣀⣤⣥⣼⣿⡿⠿⠛⠂⠈⠀⠀⠁⢀⠴⠲⢶⣶⣤⣤⠄⠀⠀⠀⠀⢉⠡⡤
⠀⠀⠀⠀⡘⣭⣋⠉⠉⠀⠀⠀⠀⡽⠋⢹⣿⣿⠿⢻⠙⢋⡾⡛⢵⣆⣠⡀⠀⡶⣤⠔⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠲⡄
⠀⠀⠀⠀⡃⣿⣿⣦⠀⠀⢴⣶⡏⠀⠀⢻⡟⢀⣁⡄⢠⣿⢨⡍⣲⣥⢤⡑⣄⡄⡄⠐⠀⢀⡠⣄⠀⠀⠀⠀⠀⢀⠀⢸⣿⣾⣿⣿⠀⠄
⢀⡀⠀⠀⣧⣹⣿⣿⡆⠀⣿⠟⠀⠀⠀⠈⠿⣦⣴⠞⣻⠏⣾⢿⡥⠄⠐⡽⣞⢷⢇⡀⢶⣿⣶⡿⠂⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠏
⢺⡇⠀⠀⢿⢷⡿⣿⠛⠳⠏⠀⢀⡖⠘⠃⠀⠀⢠⣶⣶⣾⠇⣾⣿⠾⣻⡿⠛⢣⣾⣇⠀⠉⢿⢷⣤⣤⡗⠶⣄⠀⠀⠀⠀⢀⢰⣤⣄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢾⡟⢿⣿⣿⢶⠯⢼⣁⠀⠀⣰⠿⠿⠿⠧⠠⠌⣿⣿⠿⢿⣦⣹⣧⠀⠀⠘⠀⠻⠿⠿⠃
⠀⠀⠀⣠⣀⡀⠀⠀⣠⡄⣀⡀⠀⠀⠀⠀⣀⣼⣇⣸⣿⣿⠿⣁⠀⠈⠙⢿⣿⣦⣴⣶⠒⣢⠚⠿⠁⠀⢀⣿⣿⣿⣄⠀⠐⠂
⠀⠐⠾⣿⣿⣿⣷⣾⢛⣴⣿⣿⣯⡈⠙⠛⢻⡩⠍⠉⢁⠤⠀⠀⠀⠀⠀⠈⠛⠶⣿⣷⠀⠁⠆⣁⣾⣿⢿⣿⣿⣏⠉⠂⠀⣴⣿⡆
⠀⠀⠀⠙⠋⠛⠋⣴⣿⣿⣿⡿⠟⣟⢲⣄⠙⢿⡞⣲⡛⠤⡀⠀⠀⠀⢀⡀⠀⠀⠈⠛⣺⣿⣦⠇⠈⠉⠀⠩⡿⠛⠂⠀⠚⠛⠉⠀⠀⢰⣿
⠀⠀⠀⠀⠘⠆⢰⣿⣿⣿⠏⡴⢀⣴⣾⣿⣟⢳⣿⣿⣷⣦⡰⢀⡠⢤⣄⡀⠀⠀⠀⠀⠘⠙⠁⠀⠀⢸⣧⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⣻⣾⣿⣿⡿⣿⣴⣿⣿⣿⣿⣿⣿⣷⣿⡥⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⢀⣤⡴⠛⢧⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⠿⠛⠉⠁⣾⣿⢋⣿⣷⣮⣝⠿⣿⣿⣿⣿⠀⢹⣿⣿⡶⢆⣲⡀⡆⠀⠀⢀⠀⠨⢁⠀⠀⠈⢠⠀⢆⣀⣲⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣨⣿⣸⣿⣝⡻⣿⣿⣷⣿⣿⠿⠃⢀⣤⣉⢑⠚⢿⡳⠃⣴⣷⣿⣷⡶⢺⣙⡲⠖⣐⢷⣦⡙⢿⣿
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡉⣿⣿⣿⣿⣏⠈⠙⠿⣿⣿⣯⣭⣵⣶⣾⣿⡟⣻⣷⣿⣿⣏⢀⣿⣿⠟⣻⡄⠰⣿⠇⣼⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠘⠷⠀⣤⠀⠀⠀⠙⠻⠿⠿⠻⠀⠀⠀⠀⠀⠀⠙⠋⠀⣿⣿⣿⢧⣹⣿⣿⣿⡃⠀⠉⠛⠙⠛⠺⠀⠓⣀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣽⣽⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⢩⣿⣟⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣠⡄⣀⠠⠀⠀⠀⢦⠈⡉⠉⣡⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⢀⡀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠺⠣⡄⠀⠈⣵⡠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⡧⣰⣦⡄⠀⢸⣿⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢡⠘⢁⠙⡟⠠⡴⡌⠡⢿⣿⢰
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠠⢤⠀⠀⢠⣶⠀⣠⡴⠌⢠⣶⣤⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠈⠛⠈⠃⢀⢠⣀⡀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡄⠀⡀⣤⣴⣿⠏⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠛⠳⠤⠈⠠⠄⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⣠⠴⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠊⠀⠀⠀⢈⠓⠀⣠⡿⠙⠂⠈⠘⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣀⣤⣤⣷⣟⠄⢀⡟⠀⠀⠀⡀⠀⠹⡇⢀⣤⣶⠦⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣬⣿⣷⣤⡀
⠀⠀⣴⡛⢿⣦⡶⠾⢃⢦⡠⡀⠀⣔⣐⣴⣟⢋⡒⠀⠙⡿⣦⡜⡇⠸⠄⠀⡷⠲⡆⠀⠘⣿⢫⠝⠀⠀⠤⣈⠀⠀⡴⠃⠀⠀⠀⠀⣠⡞⠉⠀⠀⣿⡛⣅
⡟⠚⣻⡍⣤⣭⣽⣇⠁⢚⢷⣆⡖⣯⣿⣿⣧⠊⡠⢰⣷⣧⣼⡀⠙⠀⠀⠐⡃⠀⠠⠃⢘⠀⠀⣀⠉⠈⠀⠀⠑⢦⣼⣆⠂⢠⠄⢀⡟⣀⠀⠀⠀⠈⢁⠈⠆
⢶⣶⣶⣶⣤⣤⣿⣶⡶⢿⣿⣿⣷⣿⣿⡟⣹⣇⣠⣤⠽⢻⣿⡇⠀⣄⣤⣤⣌⣤⣤⡤⠽⠷⢬⣭⣕⣀⢀⡠⠐⣃⣿⣿⣷⣄⣾⣿⠁⠀⠀⠀⠘⠃⠀⠀⢸⣶⣶
⠢⢤⡉⠘⠛⠛⠀⠘⠁⠈⠛⠁⠉⠉⠉⠉⠉⢈⣉⣉⣁⣀⣊⠉⠛⠉⠉⠈⠁⠀⠀⠀⠀⠐⠀⠐⠂⠀⠠⠈⠿⠿⠿⠿⡷⠤⠶⠿⠀⠤⣀⡀⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠤⠴⠶⠦⠶⠶⠒⠀⠀⠐⠂⠰⠒⠚⠢⠟⠯⠉⠉⠉⠉⠈⠱⠶⢤⣤⣀⡀⠈⠉⠓⠲⠦⠦⣤⣀⡀⠀⠐⠒⠶⠤⢤⣤⣤⣀⣀⠀⠈⠉⠉⠙⠛⢿⣿⠿⠿
⠀⠀⠄⣀⣀⠀⠀⠀⣀⣤⣀⣀⣀⣀⡀⠈⠀⠀⠈⠉⠉⠈⠛⠛⠛⠷⠶⠶⠾⠿⠄⠀⠀⣤⣄⢀⠒⠛⠛⠛⠛⠛⢛⠛⠛⠓⠒⠈⠉⠙⠛⠷⠶⢶⣶⠒⣶⣀
⠀⢀⣀⣤⣤⣤⣤⣭⣭⣉⣁⣉⣛⣛⠛⠛⠛⠛⠒⠶⢾⣶⣴⣿⣶⣶⣤⡤⣤⣤⣤⣄⣀⣀⣀⣂⣉⣉⣉⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣴⠶⠤⠄
⠀⠛⠗⠒⢶⠶⠶⠷⣾⣿⣿⣿⣭⣍⣉⣉⣿⣿⣯⣬⣤⣿⡿⣿⣿⣿⣿⡷⢿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣛⣛⣧⣶⣀⣀⣀⣀⣀⠒⠲⠦⠤⠤⠖⠦⣆⣤⣈⣁⣒

⠔⠢⠾⠷⠀⠐⠓⠆⠛⠈⢑⣛⡛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠖⠀⡀⣨⡴⢀⣜⣿⣿⢿⡿⢋⡉⣩⣾⣿⠿⢻⣷⣦⡄⠞⠉⠀⡠⠀⠀⠀⠀⠀⡠⠠
⠀⠀⠰⠆⠀⠀⠀⠀⠤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠖⠬⢤⣾⠧⠄⢁⣠⣴⣾⠿⠿⢁⡱⣾⣿⣟⣫⣤⡤⢶⣽⣾⣶⣿⣧⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠈⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⣯⣴⣶⡖⢠⣠⣿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⣀⡀⠠
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠈⠁⢠⠦⠔⢠⣀⡠⣠⣄⠰⠒⠠⠞⠛⠉⠉⠋⠀⠁⠀⠀⠉⠉⠀⠉⠉⠋⠙⠃⠀⠀⠶⣿⣿⣾⣏⣴⣶
⣀⠠⣶⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⣀⣴⣶⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿
⣭⣅⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣿⡷⠉⠀⠀⣀⣀⡀⢠⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣄⣀⣴⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠛
⢟⣛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡠⠶⢂⡍⠋⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⣭⣿⣣⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠊⠀⠀⣀⣾⣿⣿⣿⡿⣿⠿⠿⠟⠘⢻⣆⣴⣾⣿⣧⠉⠁⠙⣿⣿⣿⣿⣿⡿⠽⣿⣿⣿⣿⠆
⠍⠀⡰⣦⣤⠴⣄⠀⠀⠀⠀⠀⠀⣠⡄⠷⠛⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⡏⢁⣾⣿⣿⣿⣿⣿
⡿⢿⣥⡉⠃⠀⠰⠶⠄⢠⡌⣡⡅⠼⠂⣀⠀⠀⢠⣾⣿⣿⠿⠸⣿⡿⡏⢿⣿⣷⣄⠘⠟⠀⣻⠃⠻⠏⠀⠀⣠⣤⣴⠀⠋⢀⣀⣺⡿⠿⣿⣋⣽⣧⣀
⣘⠹⣵⠶⠖⡀⠀⠀⠠⠌⢡⠀⠀⣀⢘⠁⠀⠀⣾⣿⣿⣿⣿⣷⢸⣿⣿⣄⢿⣿⣦⣤⣤⣤⠿⠶⢾⣷⠾⠟⢛⡩⠿⠟⠀⢛⡋⠓⠀⠀⡉⢸⣿⣿⣿⣷⣦
⣿⡆⢈⠛⠂⠀⠁⠲⠆⠁⠀⢤⠘⣿⡟⠀⠀⠀⢹⣿⣿⣯⣭⢛⡄⢩⣬⣭⡤⡿⢛⣧⣄⠐⠻⢦⡘⠟⠚⠛⠃⣀⠄⠀⠈⠀⠀⠁⣂⢰⣦⣈⣛⡟⠿⢿⣿
⣿⣿⡄⣷⣄⠓⣰⡦⠛⠒⠠⠀⠢⠍⡃⠀⠀⠀⢸⣿⣿⣿⣿⢻⠇⠸⠟⠃⠀⠈⠈⠓⠘⠛⡉⠁⣀⡀⠴⠞⠿⠁⠀⠀⠀⣀⠀⡀⡉⠈⢛⡎⠛⠛⢛⣺⣿
⣿⣿⣷⡹⡇⠸⣰⡖⢶⣴⠶⠂⠀⠉⡅⣀⠀⠀⠀⣸⣿⣧⡟⠠⣄⠤⠈⡴⠀⢀⡀⠤⠀⠀⣀⡚⠉⢩⣤⠀⠀⠀⠰⠾⠆⠀⣀⠀⣴⠀⠃⣡⣀⠸⠿⢛⣅
⣿⣿⣿⣇⣼⣿⣿⠣⠘⢻⣠⡁⠀⠚⡖⠃⠀⠀⠀⠙⣿⣿⣿⠾⢋⡀⠀⠀⠐⠈⠁⢐⠂⣤⡌⢁⠚⠶⠤⠂⠌⠀⠀⠀⠀⠀⡹⠛⠁⠀⠀⡁⠠⣠⡀⠻⣿
⠘⣿⣿⣰⣿⣷⣿⡄⠀⠀⠸⣚⡃⡄⢴⠀⠀⠀⠀⠈⣿⣿⣉⣤⣈⡁⠀⠒⠈⠑⠚⠈⡃⠉⡀⢀⡀⠀⣠⣤⡶⢈⡁⠁⠐⠈⠀⠀⠀⠐⠁⣨⣸⣿⣿⣶⡄
⠀⠙⢿⣿⣫⣿⣿⣷⡄⠀⠐⣿⣿⣿⣼⣤⡀⠀⠀⠀⢻⣿⣿⣟⡿⢠⣿⠹⠇⢻⠀⠇⠀⠠⠖⠠⡴⠿⠟⣋⡉⠀⠀⠀⣀⣤⡤⠀⠈⢀⣀⢶⣮⣤⣭⣍
⣦⡀⠈⢻⣷⣿⣿⣿⡆⠀⠀⣿⣿⢿⣿⡿⣿⡀⠀⠀⠸⣿⣿⡿⠣⠘⠉⠀⡁⠀⠀⠀⣠⣤⣤⣤⣲⣿⠟⠃⠀⠀⠀⣿⠛⣍⢀⣶⣶⣶⣿⣶⣿⣶⣞⣲⡃
⣿⣷⡀⠈⢿⣿⣿⣿⣧⠀⠀⢻⣿⣾⣿⣷⣿⣧⠀⠀⠀⢻⣿⣶⣿⣶⣾⣆⠥⠀⣤⣿⣿⣿⠿⣿⣏⣥⣶⣿⣿⣇⢳⣿⣾⣧⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⡿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠀⠈⠃⣿⣿⣍⣻⣿⠇⠀⠀⠀⣿⣿⣯⣽⣿⡿⠀⣄⢻⣷⣿⡇⠀⠈⠉⠛⠻⠿⠛⠿⠿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣷
⠛⠀⠀⠀⠀⠀⠘⢿⣿⣷⠀⠀⠈⢹⣿⣽⣿⠿⡀⠀⠀⠀⢼⣿⣿⣮⡉⢀⡘⣿⢠⣿⣿⠃⣼⣿⣶⣶⣦⣀⣠⣄⣀⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣀⣀⣤⣶⣶⡤⠀⠀⠀⠈⠙⠀⠀⠀⣿⣥⣾⣤⠗⠀⠀⠀⢈⣿⡻⠟⣰⣾⠿⣄⢉⣿⣿⡂⠙⣿⣿⢿⡿⣟⠛⡿⣿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣟⢽⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢼⣿⣿⠷⠏⠀⠀⠀⠸⣿⢏⣴⣯⢋⢼⣿⡛⣿⣿⡇⠀⢻⡇⠀⣁⠀⢮⠁⠉⢀⠀⠽⣿⡅⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠶⣿⣿⣽⡿⠿⠟⠉⠈⠀⠀⠀⢠⠀⠐⣲⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⣷⣿⣳⣿⣿⣿⣿⠁⢰⣿⡇⢠⠏⢸⠃⠀⠐⢀⢾⣧⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠛⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣯⠀⠀⠀⠀⠀⢰⣿⣿⡿⠻⣿⣿⣿⣿⠇⢀⣾⣿⡇⠈⠀⠁⠀⣀⠀⢀⣫⣽⡇⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿
⣀⣀⣤⣤⣴⣶⣜⣻⡃⢥⠂⢊⡀⡀⢹⣛⣽⢣⠀⠀⠀⠀⠀⣼⣿⣯⡗⢸⣿⣿⣿⡟⠀⢨⣿⣿⡅⢠⡅⠀⠀⠀⠰⣿⠿⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⣟⡻⡿⠛⡟⠟⢁⠘⠷⢮⠴⢈⣿⠃⣿⣿⣭⣿⠀⠀⠀⠀⠀⣾⣿⣿⣧⣄⣿⣿⣿⠇⢰⣾⣿⡇⠀⠀⠀⠀⠀⢠⣶⣿⣾⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭
⠙⠛⢷⣶⣳⣾⣳⠀⠠⠉⠀⠘⠀⢨⣵⣿⣿⡯⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⣰⠋⣟⠠⠀⠀⠀⠀⠠⣍⣹⢩⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⡋⢁

⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⢤⡄⠀⠀⠀⠀⠀⠀⣤⣤⡤⣤⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⣴⣿⣿⠿⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡯⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡠⠴⠖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣄⣀⡀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⡏⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⣉⣹⣶⣶⣿⣿⡿⠿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣭⡇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣴⣶⣿⣿⣿⣿⣟⡿⣷⣄⠺⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⡏
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⢿⠛⢡⠎⣩⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⢀⠠⠴⣶⣶⠀⢀⣠⡄⢉⣶⣶⣎⠀⠿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣤⣿⣿⣾⣿⣿⡇⢺⣧⣻⣿⣶⣾⣿⣿⣿⣿⣿⡿⠛⠉⣀⣀⣤⣴⣶⣿⣿⣿⣿⡿⠉⢌⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣄⣰⢾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣿⠿⢟⣛⣍⠉⣡⣤⡿⢳⣵⡇⣠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⣴⣮⣿⣿⣿⣿⣿⡿⣿⣿⠋⢁⣀⣤⣤⣾⡿⠿⢟⣛⣭⣭⣶⣾⣿⠿⠿⠛⠋⣩⠁⢠⠏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢻⠿⣿⣿⣿⣿⣃⣤⣿⣿⣿⣟⣛⣯⣥⣶⣶⣿⠿⠟⠛⠉⣉⣤⣤⣄⣀⣠⡤⣯⣾⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⣠⣤⡶⠿⢟⣛⣩⣭⣾⣿⠿⠿⣿⡟⠉⠉⠀⠀⠀⠀⢰⡿⢛⣻⣿⣿⣿⡏⡸⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠋⠉⠈⣿⠀⠀⢺⡇⠀⠀⠀⠀⠀⣠⣾⣷⣿⣿⣿⣿⣿⡜⠁⣼⣟⣿⠟⡉⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⢠⡏⠀⠀⢸⠇⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠿⡇⣼⡟⢸⡟⢈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠀⠀⠀⠸⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⢠⣷⣿⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣧⡎⢸⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡄⢧⣿⠆⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⡿⣿⣿⣿⣿⣿⣿⣿⡁⣼⡿⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡤⢽⣯⣁⣶⣾⣷⣶⣿⡷⣄⢸⡇⠀⠀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿⣿⠿⣿⣿⠃⢠⡇⡐⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣧⣤⣿⣿⢿⣿⣯⢀⣿⠶⣿⣾⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⡙⢻⣿⣿⣿⣿⣿⣇⣠⣿⢿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣦⣻⠛⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢻⣿⣶⣿⣿⣿⣿⣿⡿⢻⣧⠝⠃⣀⣠⣤⣾⣿⣿⣿⣿⣿⣅⣬⣯⣿⣿⣿⣿⣿⣿⣏⣈⣿⣄⣘⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣏⠍⣿⣿⣿⣿⣿⣧⣼⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉⠉⠉⠁⠀⠈⠀⠈⠁⠈⠉⠉⠉⠉⠁⠈⠀⠁⠈⠉⠉⠁

⣤⣤⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⣿⣿⡿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀
⠾⠿⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡀⠀⠇⠀⠀⠀⠀⠠⠄⠀⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⣻
⣤⣤⣀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠊⢀⡀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻
⣶⣿⣿⣿⠛⠓⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⡀⠀⠆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠿⠿⠿⠿⠛⠛⠂⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠂⠀⠀⠀⠀⠐⡄⠀⠀⠈⠉⠁⠀⠀⠈⢀⠀⠀⠀⠀⠁⣀⣀⣀
⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⣉⣹⣿⣿
⣿⣿⣿⣿⣟⣛⠋⠀⡀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣽⣿⣿
⣿⣿⣿⣿⣟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣉⣙⣿⣿⣿
⣿⣿⣿⣿⣛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢢⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢈⠉⠉⠛⠻
⠟⠛⠛⠛⠋⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠄⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠠⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣩⣽⣿
⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣤⣾⣟⠉⠙⠛
⣿⣿⣿⣛⣉⠁⠀⣦⣀⢀⢀⡀⣠⠀⣄⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⢀⣤⢾⣿⡏⠀⠀⣀⣠⣤
⣿⣿⡛⢉⡉⠀⠀⣿⣿⣸⢺⠻⢻⣼⣽⣾⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⠐⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⡄⢠⡾⢧⣀⠉⠀⠀⠀⠈⢩⣽
⣾⣤⣍⣀⠁⠀⠰⠋⠸⠥⠬⠶⠮⠥⠶⠾⠥⠹⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠙

⠀⣴⡄⠀⠀⠀⠀⠀⡈⣤⣤⠜⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠉⠁⠀⠀⠀⠀⠀⠦⣾⠅⢻⡟⡆⢀⠀⠈⠡⠀⠀⠐⡿⣧⡝⠀⠩⠁⠀⠀⠀⠀⠀⠀⡐⣠⡘⣴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠙⣳⢯⡷⠍⠀⠀⠀⠀⠀⠈⠻⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡅⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢀⡠⠔⠁⢀⡀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠛⠩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠀⠤⢤⣤⣴⢃⣐⣏⠀⢀⡖⠁⠀⠤⣰⠀⢷⣈⠃⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠑⠒⢤⣄⠀⢠⠛⠦⠈⣉⣳⠜⡡⠃⠀⠈⠁⠄⠰⠿⣦⡠⡘⠃⠀⠀⠙
⠀⠀⠀⠠⠀⡚⢀⢺⡧⡶⣾⣷⣗⣂⡆⠻⣿⣏⠉⡆⠀⡏⠡⠀⠀⠀⠀⠄⠀⣧⡀⢶⡀⠰⠆⠀⠚
⠀⡀⠀⠀⠀⠙⠋⣈⢙⣁⡿⣠⠤⠀⢡⡿⠋⠀⠀⠁⡀⠀⠀⢰⡄⠀⣿⠀⠀⠀⠱⠄⠀⠀⠀⠀⠉
⠠⣩⣱⠲⢿⣼⣤⠆⡦⠻⢋⣻⣷⣞⡻⠛⠀⠀⠈⠇⠁⠐⣠⠏⠁⣈⣡⠒⠀⠀⠀⡐⠉⠻⡇
⠤⠸⣧⠀⣀⢹⠏⢠⠧⣴⣿⣿⣻⡏⠁⠀⠀⢀⢀⠀⡻⠀⣡⣜⠳⢶⡭⣤⠀⠀⠀⡿⡆⠀⠇⠀⠲⡄
⠀⠀⢿⣦⠰⢹⣖⣋⡤⠾⠷⣬⠋⠀⠀⠀⢠⣎⡄⢀⡈⢛⡿⠿⣶⠋⢙⣣⣤⠀⠀⠡⠀⠘⠀⡀⠀⠐⢦
⣤⢤⡜⢻⠷⠄⠉⠀⠀⠀⠐⠃⠀⠀⡀⢀⣘⡟⠧⠈⢀⡟⠃⠒⠀⢤⣤⣀⣄⡸⣇⠀⠀⠀⠃⠁⢰⠀⡀
⢈⡉⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⢐⣾⠟⠩⠁⠀⠈⠉⠀⢹⣦⠂⠈⠙⠲⠀⢆⠀⡣⣀⣈⡨⡁⢀⠊⠁
⠛⠀⠀⠀⠀⠀⠀⢠⠖⠠⣾⠇⡰⠛⣋⣵⣻⣤⣤⣤⣤⣤⣼⣿⡀⠀⣀⢀⣀⡈⠉⠀⠠⣀⠀⠀⢀⠒⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡜⠳⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡞⠀⠀⠹⡄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⠎⠀⠀⠀⠀⠘⣆⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢠⠏⠀⣸⠉⠉⡝⠀⠘⢆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣠⠃⠀⠀⡇⠀⣸⠁⠀⠀⠈⢧⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡰⠁⠀⠀⢸⠀⢠⠇⠀⣀⣤⠀⠀⢣⡀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡼⠁⠀⠀⠀⡏⠀⣾⠴⠊⠁⡇⠀⠀⠀⠳⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡜⠁⠀⠀⠀⢸⠁⣀⡤⣶⠀⢸⠁⠀⠀⠀⠀⠱⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠞⠀⠀⠀⠀⠀⠿⠊⠁⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠙⣄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡇⢸⢁⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠹⡄
⠀⠀⠀⠀⠀⢠⠎⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠘⣆
⠀⠀⠀⠀⢠⠋⠀⠰⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠷⠀⠈⢆
⠀⠀⠀⢰⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢸⡀⢀⡇⢸⢠⠞⠉⠁⢸⡂⢀⡇⠀⢰⡀⢰⢃⡞⠉⢳⡄⡇⠀⠉⡟⠁⢰⢷⠀⣰⠊⠉⠀⣾⠉⠁⡇
⠀⠀⠀⢸⠉⠉⡇⢸⠘⣆⣈⣻⢸⡍⠉⡇⠀⠀⢧⡏⠘⣇⣀⣸⠃⣇⣀⠀⡇⢠⡟⠚⣇⢳⣀⣉⡇⣿⣉⡁⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠆
⠀⠀⠀⠀⠀⠰⡄⢀⣀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⢀⠤⠶⠿⣧⡄⣤⠿⠗⠦⢄⠀⠀⠀⠀⠀⢲⣾⣯⣿⠻⣿⣦⡆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢨⣿⡄⣀⣀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣥⣤⣴⠆
⠀⠀⠀⠀⠀⠀⢣⡈⣶⠁⡰⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⢿⠻⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠉⢾⣿⣿⣿⡇⠀⠀⠀⠀⠈⠋⠉⠉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣨⠟⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⠀⠀⠀⢸⣷⡾⠁⠀⠀⠀⠀⠈⠻⣿⠏⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣼⣏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠸⠿⣄⣾⣿⣿⣿⣷⡤⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⡆
⠀⠀⠀⢀⣀⡼⣇⣀⡿⣀⣸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣟
⠀⠀⠀⠘⠟⠀⠀⢿⣷⡿⠁⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡄⠀⠀⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣶⡦⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣿⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢣⡆⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠟⣹⠇⠀⠀⠀⠀⢠⡄⢸⣿⣾⣿⢀
⠀⠀⠀⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠾⣶⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣽⠋⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⡏⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢻⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠉⠀⢛⣿⠟
⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠿⠿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⣤⣶⣤⡙⠄⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⡴⢃⠄⣀
⠀⠀⠀⢀⣄⠀⠘⢲⣿⣗⠃⠀⢀⡄⠀⠀⠀⠀⠀⢠⣾⠋⢀⣿⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠛⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⡈⠀⠴⢊⣡
⠀⠀⠀⠙⠛⠶⣤⣀⠶⢆⣠⠴⠛⠛⠀⠀⠀⠀⢠⡿⠃⠀⢸⣿⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀⢠⣬⣄⠋⡀⠀⢈⡁
⠀⠀⠀⠀⠀⣠⣠⡽⠛⠯⣄⣠⠀⠀⠀⠀⠀⢰⣿⣁⣀⣀⣈⣉⣀⣀⣀⣻⣧⠀⠀⠀⠀⠀⢀⠀⠉⠳⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠛
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠐⠒⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠒⠠⡀⠀⠀⠀⠀⢀⡤⠒⠠⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⡀⠠⠀⠈⢀⠀⠈⠆⠀⠠⠀⡞⠠⠀⠈⠀⠀⢉⡉⣠⣅⢠⡄⠀⠀⡔⢎⠀⢸⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠍⢠⡌⢡⡄⠀⠀⠀⠻⣬⠑⡯⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠅⠀⢠⠀⠀⠡⡈⠀⠘⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⠉⠀⠀⠀⠈⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠚⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢀⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠀⠀⠀⠁⢸⣏⠀⠀⠀⡀⢀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠆⠐⠤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡀⢰⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠐⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⢀⡁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠈⠃⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠱⣀⢀⣀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠂⠉⣩⠉⠑⠠⡀⠀⠀⠀⠰⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⣐⣀⠔⠁⠀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠉⡑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣃⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠃⠂⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⡀⠀⣀⠈⠳⣄⠀⠰⠌⡤⠂⡐⡄⠀⠀⠛⠀⢠⡷⢾⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠢⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠁
⠀⠀⠀⢠⡀⠢⡈⠀⠀⠰⠂⠀⠀⠀⠀⠐⢁⡄⠀⠑⡈⠀⡠⠁⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠈⠒⠴⣦⣿⣔⡾⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⠈⠀⡌⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠐⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⢀⡀
⠀⠀⠀⠀⠀⠀⡀⠔⠒⠁⠀⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⢨⠈⣿⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⢢⠀⣿⠋⠁
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⠀⢤⣸⡄⠀⠀⠀⠀⠘⣄⡿⢸⣼⠀⠈⢻⡇⠀⠙⣽⠇⢀⡀⣿⡔
⠀⠀⠀⠀⠸⠀⠀⠀⢠⡶⠿⠟⠙⣦⠈⡳⣻⢀⣀⠀⠀⠤⠼⢋⢹⡛⡀⢀⡖⢁⡀⡀⠠⠀⣼⢿⣿⣤⡤⢤⣀
⠀⠀⠀⢠⡷⠀⠀⠀⢸⡄⠀⢀⣾⠣⣾⠕⡡⠛⠁⣠⡄⠀⠀⠻⣼⠛⣷⡞⠀⠀⠀⠀⠀⢣⣇⡞⠁⠀⠀⠀⠈⠓⢠
⠀⠀⠀⣼⠁⠀⠀⠀⠈⡇⠀⠀⠉⣡⠥⠎⠀⠀⠈⠛⠛⠻⠂⠀⠹⣧⣻⣇⠀⢀⣀⣀⠠⢊⣿⠋⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⡟⣤⠀⠀⠀⠀⢳⢀⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣦⡀⠀⢀⣴⠛⠁⠀⠀⠀⠀⢀⢠⣶⠄⠈⠋⠑⠠⡀
⠀⠀⢸⡟⠉⢾⡟⠀⠀⠸⡞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⡀⠀⠈⠻⠿⠊⠀⠀⠀⠀⠀⠹⡆
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⢠⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢹⡇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⠀⠀⣡⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣰⣄⠀⠀⠀⠀⠀⠀⣄⠰⣧
⠀⠀⠀⣿⠀⠀⠀⠀⡀⠈⠈⣠⠶⡶⠾⠋⣠⣾⣿⣇⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣿⣿⠳⣷⣖⠀⠀⢰⡿⠀⠸⣆
⠀⠀⠀⢻⡦⠀⢰⠟⣿⡂⠀⠉⠀⣀⡠⠟⠉⢸⠁⢛⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⣿⠘⠳⣤⡀⠀⠀⠺⠃⠀⠀⣿
⠀⠀⠀⠸⣿⣷⣶⣶⣾⣥⣦⠾⠋⠉⠀⠀⠀⣿⣤⠈⠀⠀⠈⠙⠛⠛⠛⠉⠛⠀⠈⠙⠛⠒⠚⠛⠉⣸⣦⡟⣠⠖⠉⢀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣟⣴⠃⠀⠀⠀⠀⠀⠀⢀⡄⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡀⢰⣀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⢂⣠⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠛⢷⣼⠻⠟⠿⠛⢁⣀⡀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠈⠀⠀⠀⠀⢸⣿⣂⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⠀⠀⢀⠔⠚⠲⣬⣉⣈⣉⠁⠉⠛⠋⠀⠀⠀⠀⠀⠀⢀⡠⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿⡄⠘⠓⢭⣄⣀⠉⢳⡄⠀⠀⠀⣀⣠⠰⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣄⠀⠀⠀⢿⣏⠢⣀⠀⠈⠹⡇⠀⣿⣠⡶⠟⡋⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠻⣶⡀⠀⢘⣿⣷⣤⣤⣤⣴⡇⢀⣿⠉⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠈⠉⣿⡶⠛⠅⠥⠉⠉⠛⢛⠤⡈⠻⣦⠀⠀⠀⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣧⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡆⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡤⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡾⠁⠀⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠬⠥⠤⠤⠽⠷⢦⣄⣀⣀⡀⠀⣀⣀⣥⠾⠿⠤⠤⠤⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉

⠀⠀⠀⠀⠀⢀⣤⠖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⣤
⠀⠀⠀⠀⢠⣿⡇⠐⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⢀⢠⡀⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠶⠞⠃
⠀⠀⠀⠀⣾⣿⠓⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⢀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⣤⣶⣶⣦⡀⠀⣴⣶⣶⣦⠀⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣅⢈⣿⣿⡄⠀⠿⣿⣿⡿⠁⠀⢿⣿⣿⡿⠀⢀⣿⣿⣏⢙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡈⠁⠀⠸⠇⠀⠈⢁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⣿⣷⣀⣠⣄⣠⣄⣀⣼⡟⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣤⣿⣿⡟⠁⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⠋⠀⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢤⣶⣶⠤⠀⠀⠀⠀⠀⠠⢴⣶⣦⠤⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣏⠀⠀⠈⠀⢀⣠⣤⣶⣦⣤⣀⠀⠈⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⣤⣀⠀⡀⠀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⣀⣄⡀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢧⢀⠆⠀⢁⣾⣿⣿⣿⣶⣤⣀⣴⠆⠀⢰⣤⣀⣤⣾⣿⣿⣿⣷⡘⢀⢰⠀⡾
⠀⠀⠀⠀⠀⠀⠘⣾⢞⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢀⢤⡘⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⡿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡦⠣⠀⢄⠹⠿⠿⡿⢟⠏⡡⢣⣶⡹⡌⢛⡻⢿⠿⠿⠋⡤⠀⠎⢼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠴⠃⠀⢱⣿⣿⣿⡌⠀⠙⠦⠀⠀⠈⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠶⠶⠂⣀⡀⠤⠀⠀⠀⠭⣿⠍⠀⠀⠀⠄⢠⣀⠐⠶⠶⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⣶⣿⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⣿⣷⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠹⡿⠲⡖⡶⠒⡞⠉⡟⠉⣷⠒⣖⢲⠒⢿⢋⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣷⢸⡦⣧⠤⣧⣀⣧⣀⣷⠤⣷⢼⠇⡟⠘⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢄⡹⠖⢧⣧⠀⡇⠀⣯⠀⣧⠀⣧⠼⠰⢃⠴⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⡄⠀⠀⠉⠈⠒⠉⠂⠁⠋⠀⠀⣰⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢤⣀⣀⣄⣀⣀⠄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠤⠀⠀⠀⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣄⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⣀⠀⣠⡿⠋⠀⠀⠀⠰⣿⣷⣤⡀⠀⠀⠀⠀⠀⢺⣿⣇⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⡿⣷⡟⠁⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠘⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢿⡄
⣽⡟⠀⠀⠀⠀⠁⠀⠀⠀⠈⠋⠻⣿⣷⣄⢀⡤⠖⠋⠉⠁⠀⢠⡉⠉⠓⠢⣄⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⢹⡄
⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢛⠟⠁⠀⠀⢠⠀⠀⠀⣾⠇⠀⠀⠀⠀⠑⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣷
⠁⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⢠⠋⠀⠐⢀⠀⠉⠀⠀⠀⠿⠀⢠⡶⠃⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠐⠀⠸⣾⣷⠀⠀⠀⠀⢠⠃⠀⠀⠔⠀⠀⠠⠊⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠈⠀⠀⠀⠠⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠄⠀⠀⠏⠛⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡇⠀⠀⠀⠀⢸⠇
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢠⠀⠀⣄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠀⢿⠀⠀⠀⠀⠀⢹⣆⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠀⠀⡀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢀⡤
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⡀⠙⢷⣄⡀⠀⠀⠀⠀⢀⣀⠔⠁⠀⠀⢸⠃⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠒⠀⠀⢿⣆⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠚⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠀⠈⣽⡄⠀⠀⠀⠀⠘⠈⢷⣄⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⣧⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⢤⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠋
⠹⣆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣿⣷⣶⣶⣤⣤⣤⣴⣶⣶⣿⣿⠿⠛⠉
⢆⠹⣦⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠙⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢦⡀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⢌⢻⣦⡀⠀⠀⠀⠀⠀⡀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣖⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠃⠀⠀⠙
⠀⠀⠀⠀⠳⣝⣷⣦⡀⠀⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠀⠀⠀⣠⣴
⣀⣀⣀⣀⣀⣈⣙⣛⣛⣦⣄⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣁⣀⣀⣀⣀⣴⣾⣿⣿
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣠⡶⠂⠤⠴⢶⣦⣄⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣭⣴⣶⣾⣿⣷⣶⠾⠁⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣏⣫⡟⣿⣵⢟⠅⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣴⢿⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣼⠟⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣶⠒⠋⠁⠀⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠁⠈⠀⠀⠈⢻⣿⣇
⠀⠀⠀⠀⢀⣠⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⢠⣿⣿⠟⢿⣿⣿⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣼⣿⠃⠀⠀⣿⣿⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢰⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⢀⢀⠆
⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠁⠀⠀⣸⣿⣿⣿⠿⠿⣽⠻⣟⣃⢡⡾⢀⠀⠀⣀⣾⣿⣿
⠀⠀⢸⣿⣿⡀⠀⢸⣿⣿⠀⠀⣰⣿⣿⠋⣡⠀⠀⠀⡆⣿⡋⠃⢁⣾⠀⣰⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⣀⣤
⠀⠀⠘⣿⣿⣇⠀⣾⣿⡏⠀⢀⣿⣿⣷⣦⣷⣼⡇⠀⡇⢻⡟⠛⠏⠹⣆⠈⠻⠏⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣠⣀⣀⡘⠁
⠀⠀⠀⠹⣿⣿⣷⣿⣿⠀⠀⠈⣿⣿⡿⣿⣿⡏⠀⢰⠀⠀⠹⣿⣿⡗⣟⢀⠀⠣⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠹⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⡿⠃⠀⡧⠀⣠⣴⣾⢿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⡀⠀⣠⡏⠘⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⢸⣿⣿⣿⡿⠁⠀⢸⣧⣶⢿⣿⣿⠀⠘⢿⣿⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠞⠉⠉⠁⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⠟⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣋⣁⠀⢀⣴⣟⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣇⠙⠿⢿⣿⣿⣼⡀⠀⠀⠉⣀⠈⣛⠡⢻⣦⣿⢚⣗⣈⠻⣿⣥⣤⢀⣤⣾⠖⢳⣿⣿⡿⠛⠛⠻⢿⣶⣄⣀⣰⣞⣿⠛⣥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⢠⣄⣈⣥⣤⣶⣶⣶⣨⣷⣨⣧⠸⠓⠟⠛⠛⠻⢶⣾⣿⣽⡏⣿⣿⢦⡼⠟⠛⠁⠀⠀⠀⠀⠉⠻⢿⠿⠭⠙⠛⠓⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⠟⠋⠉⠉⠀⠀⠀⠛⠉⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⠏⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠟⠛⠋⠉⠐⠢⠠
⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠈⠛⠿⣷⣶⣶⣶⣴⣶⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠁

⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠿⠿⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣯⣽⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣶⡷⢿⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⡾⠿⠿⠶⡿⠷⣶⡿⠷⢾⠿⠿⠿⢿

⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄
⠀⠻⠿⠿⠁⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⣸⣿⣿⡦⠀⠸⣿⣿⡄⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⣀⠀⠘⠿⠿⠋
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠛⠉⠀⠀⠀⠀⠉⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⣿⣿⣿⠛⠉⠛⣿⣿⣿⡿⠁⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣷
⠀⠀⠀⢻⣿⡇⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⣿⠁⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠻⣿⣦⣤⣶⣿⢻⡿⣿⣷⣤⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠘⣧⣀⣰⡿⣿⢿⣷⣄⣀⣀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣾⣷⣿⣿⣿⡟⠛⢁⣤⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⠿⠛⡀
⠀⣠⣴⣶⣶⠄⠀⠻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⢿⣿⣶⠀⠀⣠⣤⣤⡄⠹⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠘⢿⣶⣦⡄
⠀⠙⠛⣿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠘⠛⠀⠀⠈⠛⢻⣿⠃⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⢠⣤
⠀⠀⠠⣾⣿⣿⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⠀⠀⠀⢠⣶⣀⠀⠀⠀⠀⣀⣴⣶
⠀⠀⠀⠀⢈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠸⠿⠛⠀⠀⠀⠀⠛⠿⢃⣠⣤⣴⣶⣶⣦⣤⣤⣄⡀⠀⣼⣿⣤
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠛⠋
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢻⣿⣿⣿⣿⣿⠋⠀⠈⢻⣿⣿⣿⡿⠿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⡟⠉⠉⠙⣿⣿⣿⡿⠋⠉⠙⢿⣿⡇
⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠸⣿⡇⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄⠀⢀⣸⣿⣿⣿⣀⣀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣿⣿⢙⣛⣿⣶⣶⣾⣿⠏
⠀⠀⠀⠀⠀⣀⣀⡉⠻⣿⣿⣿⣿⣋⣿⣍⣿⣿⣿⢁⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋⠁⢰⣶⣦
⠀⠀⠀⠀⠺⠿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⣿⠟⠋⠀⠀⠀⢿⣿⣧⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡀
⠀⠀⠀⠀⠀⡄⠀⣄⢠⡴⠛⣟⠉⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠰⠞⢿⣷⣄⡀
⠀⠀⠀⠀⠀⣜⣟⣟⣢⡈⢉⡋⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠀⢨⣥⣤⣘⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣄⠉⠀⠀⣤⣤
⠀⠀⠀⠀⢀⣥⣮⣹⠏⣵⣶⠁⠠⠔⠀⠀⠀⠀⠉⢘⣿⣿⣿⣷⣶⣶⣾⣿⣿⢍⣁⣿⣦⡄⠀⠉⠑⠃⠀⢤⡼⣻⣭⡛⢀⣾⡿⡃
⠀⠀⠀⠀⠠⢿⠈⡛⠸⡯⡅⢀⣀⡄⣠⣶⣤⣴⣾⣽⣾⡿⠟⣛⣛⣋⣙⠛⠟⢿⣷⣿⡻⣅⡀⢠⡐⠄⠀⣾⣿⣯⣼⣿⠀⢵⣿
⠀⠀⠀⠀⢄⠈⠗⣧⠀⠀⢀⡿⠃⠀⢉⣟⣭⣿⢟⣫⣴⣾⣻⣯⣹⣿⣿⣿⡟⣷⣮⣍⣹⣾⣟⣏⢻⣮⠻⣿⣿⣠⣶⣹⡿⡀⠛⣀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠲⠀⠉⠀⢠⣯⣾⡛⣱⣿⠝⢛⣹⣉⢉⣉⣿⠿⢿⠙⠛⠉⠹⡿⣭⢿⣾⣳⡛⢧⠹⣿⣟⣫⡄⢀⣯⣀⡈
⠀⠀⠀⠀⠀⠀⣾⠏⠈⡁⢀⠀⢠⢏⣿⣟⣼⡟⣷⡽⣾⢇⡝⠻⠿⢿⣶⣿⣷⢠⣬⢻⡜⠛⢿⡩⣿⣹⡀⢳⣿⡍⢙⣥⠨⡟⠇
⠀⠀⠀⠀⠀⣨⣽⡴⠀⣯⣬⡶⣿⣿⣿⣿⡿⣿⣿⣧⣄⣀⡎⠀⠀⠀⡿⣿⣾⢷⣄⣀⠀⣶⣸⣧⢿⣛⣳⠀⡟⣅⢸⡿⠀⣳
⠀⠀⠀⠀⠀⢱⣶⡟⠛⣿⣯⢐⡇⣿⣿⣿⡭⣿⣿⣟⡟⠙⠗⠾⢶⣼⣁⣛⣿⢈⠻⣿⡉⣛⠉⣿⣸⣿⣿⣼⣿⣿⣿⡏⠀⣴⣶⡆
⠀⠀⠀⠀⠀⠈⣿⠃⠀⡟⢹⠸⡷⣿⡟⣷⡽⣿⣿⣧⣼⣿⣆⠀⢠⠏⣩⣿⣗⣦⠦⣭⣷⣤⣿⣿⣔⣯⣿⠉⣿⡏⢹⡟⠀⣿
⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠈⠀⣿⢿⣿⢻⣷⡿⣿⣼⣿⣿⣿⣷⡾⣾⣷⣟⣿⣿⡇⠀⠀⣹⢿⡿⣻⣿⣿⣿⡟⣷⢈⢠⣀⣨
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢄⠘⣷⣿⣯⢻⣷⣎⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣿⡿⢽⣿⣿⠻⣿⢱⡇⢸⣿⠿⣿
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⢸⣌⢷⠘⣿⣿⢳⡿⣿⣶⣾⣿⣿⣯⣿⣿⣿⡿⠟⢀⣤⣾⣿⢟⣵⣿⣴⢯⣄⢀⣿⣇⢸⠥⡂⢸⡀
⠀⠀⠀⠀⠀⠀⡇⣠⢀⠀⢸⣿⣦⢠⡈⠻⣿⣿⡾⢻⣿⣿⣿⣾⡏⢿⣡⣾⣷⣼⠿⣻⣵⣾⣛⡿⠃⠟⡁⠁⣼⡇⢸⠿⠈⣽⠁
⠀⠀⠀⠀⠀⠀⠓⠛⠈⠁⠚⡅⠘⣄⠙⠿⣿⡟⢿⣿⣿⠇⣽⣿⣟⢻⣿⣯⣩⣾⣷⣿⣿⢟⣁⠄⣀⠄⠀⣴⡿⠶⢼⠳⠿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠓⠐⠮⢍⠀⠈⢉⣓⠶⡿⢿⣿⡿⠿⠷⠛⠛⠉⠀⢚⡡⠈⠁⢀⠈⣽⣟⢱⢸⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⡁⠹⠀⠎⠀⠻⣶⣥⣤⣀⠀⡀⡀⠀⢀⣉⣙⣛⣙⣛⣛⣛⣛⣡⣤⠴⣾⠋⢀⣀⣰⣬⣿⣿⣿⣾⢉⣦⡤⠶⡏
⠀⠀⠀⠀⠀⠐⠖⠶⠒⠲⠶⠖⠀⠀⠀⠀⠐⠂⠀⠀⠀⠶⠬⠭⠭⠌⠥⠅⠩⣥⡤⢀⡀⠀⠩⠄⠀⠀⠀⠁⣴⠶⠲⠖⠶⣶⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠉⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠃⣶⠾⠛⠿⠆⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠟⣠⣴⣄⢁⣿⣿⡍⠻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠘⠛⠛⠛⣻⣿⣿⣿⡀⠀⠈⡉⠛⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣿⣧⠀⠀⠰⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣤⣶⡟⣰⣆⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣇⣽⣿⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣦⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣶⣾⣿⠿⠿⡿⠿⠿⠿⠟⠛⣸⣴⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣾⣿⢿⠉⠉⣀⣈⣀⣠⣠⣶⣶⣦⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣫⣶⣿⣿⡿⠿⠿⠿⠿⠿⠛⣿⣿⡿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⡇⢹⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⣿⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣿⣿⣿⣿⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⠋⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢹⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⢒⠺⠓⠢⠒⠘⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⣀⡀⠀⠀⡰⣴⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡤⠤⠀⠤⡴⠀⠀⢠⠂⠁⠀⢀⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡛⠚⠒⠐⠢⠐⠚⠁⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠠⠇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⠀⠀⠷⠀⠀⠀⢀⣠⠖⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠂⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢳⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠠⡴⠿⠁⠙⠉⠁⠀⠀⠀⠩⠆⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠙⠉⠃
⠀⠀⠀⠀⠀⠀⢐⠀⢓⠀⠀⠀⠀⠀⠘⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠜⡁⡐⠲⠂⠀⠀⠀⠈⠇⢀⣄⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⡀⣈⠙⠀⠀⢐⣖⣶⡞⠆⠀⠀⠀⠀⢤⠚⣁⡚⣠⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠌⣄⡀⠀⠈⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠯⣣⠅⠀⠀⠀⠀⠀⠀⠀⣩⠃
⠀⠀⠀⠀⠀⠈⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⢺⠠⠄⠀⠀⠀⠁⢀⣦⢤⣤⡤⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠰⠿⠒⠛⠋⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢤⡘⡛⡀⠜⠁
⠀⠀⠀⠀⠤⠴⠦⣐⡀⠁⣠⠦⠤⢀⣀⡸⠂⠘⠀⠙⠤⠖⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⡀⠀⠀⠆⣄⠈⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠙⣃⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠑⡐⠋⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠄⠀⠀⠀⠀⣤⢘⠃⠀⡀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠠⣶⢈⠀⣠⢫⠄⠀⠀⠀⠀⠒⠤⢄⣀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡌⠰⠀⠀⠀⠀⠀⠲⢿⡆⣀⡌⠀⠀⠀⠀⠀⠀⠐⠘⠛⡀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⣁⢴⡂⠀⠀⠀⠀⠀⢭⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣘⠉⠀⣚⠀⠛⣄⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠉⠉⠉⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⣶⣷⡀⠀⠀⠀⠀⣰⣿⣦⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⣿⣿⣿⣷⡄⠀⠀⣰⣿⣿⣿⣷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣔⠿⠛⠛⠻⢗⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⡏⣴⣿⣷⡌⢿⣿⣿⣿⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⠶⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠹⠿⠿⠃⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⠉⢨⡝⠻⣿⠀⠀⢸⡿⠛⣽⠀⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣾⣶⣾⣦⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣷⣄⢹⣿⣿⣿⢁⣼⡟⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⢠⣾⣿⣿⣿⣿⣧⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣺⣿⣿⣿⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣭⣙⣛⣛⣩⣥⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠟⠛⢿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣿⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣤⠀⠀⠀⠀⠀⠀⢠⡜⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣷⣿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⢁⡾⠀⣤⣦⡄⠸⣆⢻⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡘⣧⠈⠻⠿⠏⢀⡟⣸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠷⠈⠀⢠⣆⠀⠈⠰⠟⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⠁⠿⠋⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣸⣿⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢿⠀⠀⠀⠟⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠃⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢿⡤⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠄⠀⡌⠂⢠⠀⡀⠀⠁⠐⠶⠖⠀⠀⠀⡀⠸⡆⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⢀⠀⠒⠀⠄⣀⣸⣛⠁⣹⡽⡛⢳⡀⠀⣤⡆⠠⡴⠊⢀⣽⣎⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠴⠃⢄⣉⠁⠀⠰⢖⣫⢞⠛⢻⡞⢻⣿⠷⠾⣶⣷⡉⢀⣲⠀⠐⣠⠟⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠤⠀⠀⠐⠋⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠇⢻⣿⠀⠒⠛⠛⠁⠐⠀⠑⠛⠀⠀⢒⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣫⣶⣰⣤⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⢯⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢿⡿⠋⡼⣿⡟⢸⠇⠙⠀⠀⠁⠀⠉⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⡠⣄⡀⠀⠀⠀⣀⣴⣿⣿⣪⣴⠋⢀⠞⣴⠋⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣿⣷⡿⠝⠛⢻⣶⣾⢟⡿⣻⣿⠟⠁⡴⠋⣼⠋⠀⢀⣾⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⠺⣝⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣹⣏⣿⣷⣷⣤⣶⣿⣿⡿⣫⣾⣿⠁⢁⡜⢀⣾⣇⡆⢸⣿⣿⠀⢄⠀⠀⡆⠀⣿⣏⡆⠈⢦⡈⢻⣿⣦⡀
⠀⠀⠀⠀⠼⠿⣿⣿⣿⣾⣿⡿⢿⡟⠿⢿⣿⣿⣯⣾⠛⠹⠿⣶⡞⢀⠈⢿⣿⠁⣿⣿⣿⠀⢸⣄⣀⢱⢸⣿⠋⢹⢂⣤⣻⣮⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠻⠏⠉⠉⠀⠙⠲⣬⣟⠾⡟⠃⠀⠀⢠⣽⡿⠞⠀⠘⠉⠶⢽⣿⣿⠂⣿⣿⣿⡿⠟⠉⢦⠘⠋⢀⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⠶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆
⠀⠀⠀⠀⠀⠀⢹⡀⡄⠀⠀⠀⠀⠀⢀⣤⣠⣿⣿⣿⣿⣷⣠⣄⠀⠀⠀⠀⣼⠛⠏⠀⠀⠀⠘⠟⢷⡄⠀⠀⠀⠀⠀⠀⡼⠁⠈⢦
⠀⠀⠀⠀⢀⡆⣼⣇⣃⠀⠀⠀⠀⠀⠈⠛⢛⡏⢙⣿⡉⣻⠛⠋⠀⠀⠀⢰⣿⣶⣆⠿⠂⠺⢆⣶⣿⡇⠀⠀⠀⠀⢀⡞⠀⢀⡴⠉⢣
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣤⣿⡿⠾⢿⣯⣄⣀⠀⠀⠀⠀⢿⡉⣩⡐⠶⢆⣌⡉⣻⠇⠀⠀⠀⢀⠞⠀⢠⠎⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠋⠈⠻⠶⠛⠈⠙⠋⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⢃⣀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡰⠃⢈⣏⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⢎⡴⠛⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⣦
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⡰⠁⠻⠏⠈⠿⠃⠱⡀⠀⠀⠀⠀⢠⠎⠘⢿⣅⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⠋⠈⣿⡿
⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠛⠒⠀⠀⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠁

⠀⠀⠀⢀⣴⣶⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣾⣿⠿⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⡆⢀⡴⣩⠗⢄⠀⠀⠀⠀⠀⡴⠁⢀⣠⣄⡀⠈⢆
⠀⠀⠀⢸⣿⣤⡞⢳⣤⣿⠁⠀⠀⠀⠀⢀⣾⣦⠈⠟⢁⣾⡆⠀⠀⠀⠀⢠⠇⠀⢨⢁⠋⢀⡥⠞⣉⣇⠀⠀⠀⡜⢡⣦⣿⣿⣿⣿⣴⠌⢧
⠀⠀⠀⠀⢠⣹⡿⢿⢃⡆⠀⠀⠀⠀⠀⠸⣿⡿⠃⡀⠙⣿⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡨⠒⠋⠁⡿⠀⠀⠘⡄⠀⣀⣳⣾⣷⣞⣀⠀⣠⠃
⠀⠀⢀⣦⣈⡛⠿⠾⢟⣁⣴⡀⠀⠀⠀⠀⠙⠁⣼⣿⣆⠈⠁⠀⠀⠀⠀⠀⢣⡰⣿⡿⠀⠉⠨⠉⡹⠃⠀⠀⠀⠘⣌⠛⠉⠳⠞⠉⠛⡰⠃
⠀⠀⢀⣀⣈⡽⠗⠺⠯⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠥⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠈⠦⠤⠤⠤⠤⠔⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀
⠀⠀⢠⠊⠁⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⢀⣧⣴⣶⣶⣶⣶⣶⣆⠀⠘⠀⠀⠀⠀⠀⢀⣶⢸⣿⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⠀⠄⠀⡴⠉
⠀⠸⠈⠉⠉⠉⠉⠉⢻⣿⣦⠀⠃⠀⠀⠀⣴⣿⣷⣾⣯⡾⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠙⣿⣿⣿⡦⠀⠀⠀⠀⠚⠓⠀⠈⠁⠀⠀⠠⠄
⠀⠀⢣⠀⠀⠀⠀⠀⠈⠛⠛⡿⠀⠀⠀⠀⣿⣿⠿⠻⣿⣿⣆⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠐⠐⠈⡄⠐
⠀⠀⠀⠑⠠⠀⢀⡀⠀⠤⠊⠀⠀⠀⠀⠀⠈⠻⣦⣤⠿⠿⠋⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠈

⡿⠿⠿⠿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣿⣿⣿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣷⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣾⣿⣿⣿⣿⠿⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⢿⣿⣿⣿⣿⣦⣤⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⢹⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠙⠻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠁⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢠⣾⠟⠛⠿⣾⣿⣿⡟⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠘⣿⣿⣿⡾⠟⠛⢿⣦⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⠃⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠰⣿⣿⣿⠇⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⣿⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣄⠘⣿⣿⣿⣆⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢀⣾⣿⣿⡟⢀⡄⠀⠀⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢻⣦⣹⣿⣿⣿⣷⣄⠀⠀⠀⠀⢴⣦⠀⢀⣴⡆⠀⠀⠀⢀⣴⣿⣿⣿⣿⣡⣾⠃⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠿⠇⠸⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⢘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣶⠿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢷⣶⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠟⠻⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⡿⠿⢿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⠿⣶⣤⣤⣤⣶⡿⠟⠉⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠶⠶⠶⠾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠏⠀⠈⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠈⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀⢠⣾⣿⣿⣦⠀⠀⠹⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠙⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡀
⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀
⠀⣼⣿⣿⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⡄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡷⠀⠀⠀⡄⠀⠀⠀⠀⠀⢴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣏⡀⢶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢀⡿⠀⢠⡞⢁⡴⠆
⠀⠀⠀⠀⠀⢀⠴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⣇⠘⠀⡸⠃⡰⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠈⢠⠀⠀⠂
⠀⠀⠀⠀⠀⢡⡘⢗⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡙⡄⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⠀⡴⢰⠂⠀⢀⠀⠀⠀⠶⢶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠑⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢄⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠘⠧⠠⢤⣀⣤⡀⣀⡔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⡿⠇⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠤⠊⠰⠐⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠙⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⠈⠉⠑⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡁⠙⠃⠀⠁⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠢⠀⠤⢀⠀⠄⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡞⣠⣄⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠸⠻⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠦⠤⡄⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣄⣹⣶⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠂⠀⢠⠄⠀⠈⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠙⠢⠝⢀⣀⠀⠐⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠠⡿⠶⠶⠶⠀⠀⠀⣿⣴⢷⣤⠐⠀⠛⠙⠀⠀⠀⠀⠠⡶⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠤⠀⡄⠸⠛⠃⠘⠀⠘⠙⠣⡁
⠀⠀⢰⡶⠐⡒⠈⠁⠐⡂⠀⠿⠈⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠑⠄⣡⡙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠶⠁⠀⠈⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠉⢉⣠⠖⠀⠴⠦⠐⠀⠒⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢀⠀⣠⡄
⠀⠀⠈⠁⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠉⠂⠈⠤⠉⠁
⠀⠀⠀⢀⣀⡀⢆⡠⠄⠆⠐⠒⠢⡀⠤⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡠⠚⠃⠀⣤⣀⠀⠀⠀⢀⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠇⠀⠀⠀⠙⠋⠀⠀⠀⠈⠁⠀⢀⠇⠀⠀⠀⠀⠶⠀⠀⠀⢀⡀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠆
⠀⠀⠀⠀⠀⢦⣀⣀⡀⠀⢄⠠⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠠⠄⣠⢀⡆⠀⠀⠀⣍⡈⠙⠀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠼⠅⣠⡿⠿⠷⠷⠴⠶⠀⠠⠶⠟⠡⢬⢱⠾⢇⢀⣀⣿⣿⣿⣶⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠺⢇⣶⣾⢬⣼⣿⣿⡿⠟⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣶⣬⣿⡿⠀⠁⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡞⣿⣦⡙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣦⣿⡿⢩⣿⣿⣦⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡃⣼⣿⣿⣿⣦⢻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⣯⣿⣿⣿⣿⡿⢿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢹⣿⣿⣿⣿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡃⠿⠿⣿⣿⣿⣿⣿⣦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠦
⠀⠀⠀⠀⠶⠛⣻⠋⠓⢠⣀⠐⢻⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⡆⠀⠀⠛⠘⢿⣿⡛⣿⡟⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠚⠃⠴⢂⣈⣥⣤⡬⠷⣿⡿⠟⠻⠉⠀⠀⢀⡟⠇⠀⠀⠀⠃⠀⠽⣷⡈⢷⡄⠁⠀⢿⠛⠻⠟⠋⠉⠛⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢵⠀⠴⡓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⢫⣧⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⡇⠐⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣴⣾⠋⠀⠰⠷⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⣭⣵⣾⣯⡐⠷⠀⠀⡀⠀⣿⣿⣿⣿⣦⡀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠛⠉⣿⣦⣄⠈⠁⠀⠀⠉⠛⠿⣿⣿⣶⣶⢟⣿⠇⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠅⠈⠀⠃⡸⠋⡣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣫⣿⠃⢀⠀⠐⠜⠂⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⡿⢛⡛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠠⠀⠤⠜⠀⢀⡠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣌⢻⣿⣿⣿⠿⠿⢿⣦⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⡀⠀⠀⠐⠀⠀⠠⠄⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠵⡀⢄⣴⣶⣿⣿⠥⢀⠀⠄⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏⣿⡇⠀⠀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢬⣿⣿⣝⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⢰⣿⣿⠀⠻⣾⣿⣦⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠈⢿⣝⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣟⢇⠀⠀⠉⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠿⠟⢻⣮⡓⠦⡤⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣴⡿⠟⠿⣶⡀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣿⠃⣴⢿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠹⠦⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢠⣾⡿⠙⣷⠀⣀⣤⣤⡴⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣴⣿⠟⠀⢀⣿⣿⣿⠟⠁⢀⣤⣾⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⡲⠶⢶⣶⣶⠿⠟⠋⠀⢀⣠⣾⡿⠋⠀⣠⣾⣿⠟⠁⣠⣶⣿⣿⡿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⣝⡶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⣠⣴⣿⠿⠋⢁⣴⣾⣿⣿⠟⠋⠀⢀⣴⠶⠶⢤⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣛⠶⣯⣭⣍⣉⣩⣥⣤⡶⠿⠛⠉⢁⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⣾⡇⢰⣆⣼⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣍⣉⣉⣁⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣶⣶⣶⣄⠀⠀⣠⣶⣶⣶⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠙⠛⠛⠉⢀⡀⠉⠛⠛⠛⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⣴⣿⣿⡦⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢢⡀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⢀⡔⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⢳⡀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⢸⢀⡞⠁⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠸⠥⣙⡢⠔⠓⠤⠚⠓⠤⠚⠲⠔⣋⠬⠇⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣠⠦⢄⣀⠉⠙⠲⠤⢄⣠⠤⠒⠋⠉⣀⡤⠴⡄⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡹⠖⠾⣅⠀⠀⣀⡭⠖⠲⠤⣀⡈⠉⠒⠶⢭⣀⠀⠀⣨⠷⠲⢏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠊⠉⣀⡀⠤⠒⠋⠉⠈⠙⠒⠤⢄⣈⠉⠙⠁⠀⠀⠀⡇⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠈⢳⠀⠀⠀⢰⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡆⠀⠀⠀⡞⠁⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠘⢤⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡤⠃⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⢏⠉⠉⢹⠀⣀⣿⣇⣀⣨⡁⠉⢹⠓⠒⢤⣄⡀
⠀⠀⠀⠀⢀⣠⠖⠋⠉⢣⣀⡤⠼⠒⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠙⠒⠦⢄⡀⠉⠗⠦⡀
⠀⠀⣠⡔⠋⠀⢳⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣶⢰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣤⡿⠓⢄
⣠⠞⠛⢿⣦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⠑⢤⡊⠑⣄
⠧⡀⣠⠞⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⠀⢀⠞⡴⢋⠖⠀⠀⠙⢤⠊⢢
⢀⡼⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢏⢞⡴⠃⠀⠀⠀⠀⠈⢣⠀⢳⡀
⠞⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠤⠖⣂⠀⢣⡶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣴⣊⣁⡀⠘⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣖⠒⠀⢰⣀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡎⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢳⠢⡄⠀⢀⠎⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠣⠊⠀⠀⠄⠠⢀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠘⠆⠃⢀⡔⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢁⠀⠀⠘⠠⢇⠚⡄⠀⠀⡇⡄⡏⠦⠀⠀⢀⡠⠂⡠⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⢰⡆⠤⠀⠀⠀⠀⠀⣤⠐⡂⡩⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠒⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⡡⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠶⡖⠃⠰⠋⠰⠤⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⣠⡀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠈⢆⣀⠔⠒⠒⠤⡀
⠀⠀⠀⠀⢀⠤⠒⠀⠈⠀⠒⠴⠏⠀⡰⠁⠀⠀⠑⢆⠀⠀⠀⠀⠀⠁⠈⢣⢸⡵⠊⠉⠈⠑⡌⠄
⠀⠀⠀⠠⠃⡴⠊⠉⠁⠉⠙⢲⠀⠀⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⢀⠀⢨⠀⡆⠀⠀⠀⠀⢰⢸
⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⠀⠀⠀⣷⣿⣠⠤⠤⠦⠾⣾⠃⢸⢰⠋⠉⠑⣄⣀⢆⠆
⠀⠀⠀⢣⠸⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⡳⠴⠒⠋⠙⠀⠲⠄⠀⠰⠈⠃⠓⠺⡀⠀⠀⠣⣈⡉⠒⠢⡀
⠀⠀⠀⠀⠣⡈⠲⠤⠤⠠⠄⠐⣡⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢳⢆⠀⣠⠜⠓⠠⠈⠢⡀
⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠋⠰⡃⢀⣤⠶⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢂⠌⢣⠹⣥⠞⠉⠑⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣀⡀⠀⠀⠀⠀⠈⠙⠛⠉⣀⣀⠤⠒⠁⠀⢠⠀⠳⠔⠉⠂⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠉⠁⠒⠒⠒⠚⠉⠉⢁⠈⢦⠀⠀⠀⢘⠂⠀⠀⠀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠤⢄⣀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢧⣠⢤⠏⠀⠀⢠⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠈⡇⠀⠀⠀⠸⠖⠒⠀⠀⠀⠀⠉⢁⠀⠀⠈⡷⠋⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠐⢄⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠘⣧⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⡀⣩⢶⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢻⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⠋⠁⣨⠞
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠠⠄⣸⡄⢀⡞⠀⠀⠀⠀⠀⠑⠲⡄⠀⠀⣠⠏⠀⠀⠓⠒⠢⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠤⣀
⠀⠀⠀⡀⢔⠁⢈⠴⠂⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⢸⠴⣞⣁⣀⠀⠀⠈⠱⠒⠒⣭⠽⠀⠀⠀⠀⠀⡈⠀⠀⡀⢸
⠀⠀⠸⢥⡖⠒⢁⡠⢚⣁⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠈⠉⠉⠉⠙⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⢰⠃⠀⢠⠤⢄⣀⣀
⠀⠀⠀⠀⠉⠉⠁⢮⡬⠤⠖⠚⠉⠸⣄⣀⠀⣀⠀⣀⣀⣸⠁⠀⡔⠁⠀⠐⠒⢨⠅⠒⡀⠀⢀⠀⡀⠀⠄⣄⠓⠐⠣⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠙⠉⠉⠁⠀⠀⠑⠤⣀⠀⡠⠠⣁⡰⠆⢀⠐⠂⠐⢀⣀⠌⢑⠒⠊⠉⠉⠓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠠⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⢱⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠑⣴⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⢀⠄⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⠁⠐⣻⡿⠻⠾⣾⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠚⠋⣀⠀⠠⠼⠇⢻⠷⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠀⠉⠀⠀⠀⠀⠛⠉⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐


⠀⣆⣂⡀⣄⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑
⣿⣿⣿⣿⣿⣶⣷⣿⣶⣷⣴⣿⣷⣶⣎⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢴⡁⠀⠀⠀⡀⠀⠃⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⡏⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠋⠀⠀⠑⠄⢄⠀⠀⠑⢄⢤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⡀⠀⣄⡸⠀⠀⠀⢠⠞⠑⢤⣤⣶⣿⣶⣶⣷⡤⠤⠟⠀⢀⠀⠒⠒⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠋⠈⠀⠀⠀⠀⡰⠃⠀⠀⠀⠛⠿⠟⢿⣿⣿⢿⣆⠀⢐⣉⡠⢀⣀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠉⠉⠁⠉⠝⢢⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⡀⠻⣧⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠒⠀⠰⠀⠐⠊⠉⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣬⢷⡀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢈⠥⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠽⣧⢳⡄⠀⠀⠀⣆⠁⠀⢀⣠⣠⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠻⣄⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠠⠀⠀⠈⢀⠃⡀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠀⠀⠀⠀⣠⢃⠁⠀⠀⢸⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠘⣦⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⣀⡴⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠻⣷⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⣠⡟⠀⠀⠀⠀⢦⠀⠀⠀⠘⢆⠀⡀⠀⠀⠈⣝⡻⣝⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣠⠾⠋⠐⠀⠀⠀⣠⣾⠟⠁⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡀⠈⠀⠱⠈⣿⣯⡓⣬⡳⣄
⠀⠀⠀⠀⠀⠀⡴⠟⢁⣴⠟⠁⢀⡜⠀⠀⣰⣾⠟⠁⠀⠀⠀⣀⣾⡟⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⢹⣦⣀⡀⠀⣸⣿⣿⣾⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠑⢾⣏⣁⣀⣠⡞⠀⣠⡾⠟⠁⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡀⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠲⢦⣴⣴⣾⣿⣿⣿⣤⣤⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠻⠿⠿⢿⣿⣿⡿⠿⠿⠟⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⢸⣿⣷⣄⣀⣀⣠⣾⠟⠻⣷⣄⣀⣀⣠⣾⣿⡇⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⣿⣿⣿⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣷⣌⠙⠛⠻⣿⣿⣿⣾⣷⣿⣿⣿⠟⠛⠋⣡⣾⣿⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣟⠛⠛⠓⠀⠀⣿⢻⡟⣿⣿⢻⡟⣿⠀⠀⠚⠛⠛⣻⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠛⠷⣦⣀⠀⠀⠀⠈⠁⠉⠉⠈⠁⠀⠀⠀⣀⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⡄⠀⠀⣉⠳⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣀⡀⢰⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⣿⡆⠀⣿⣧⠀⢰⣶⡀⣶⡆⢠⣶⣾⣦⢸⣿⠛⠃⢸⡟⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⡇⣸⣟⣿⡄⢸⡿⣷⣿⡇⣿⡇⣴⣿⢸⣿⠿⠇⢸⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠁⠿⠋⠻⠷⠸⠇⠘⠟⠃⠙⠿⠟⠿⠸⠿⠿⠆⠸⠟⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡤⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⣀⡀⣠⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⢀⡀⠄⠀⠀⠀⠁⠀⠀⠐⢦⡤⠾⠋⠀⠘⣁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⡄⠀⠂⠀⠀⣼⠫⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⣠⠌⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠶⠤⠀⢄⣴⠋⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠈⢡⡄⠀⠀⠀⠀⠛⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡧⠀⠀⠄⣼⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠿⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠐⠀⠈⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠲⣌⠁⡰⠛⠋⠉⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣦⣀⠀⠈⠀⠀⣼⠀⢄⡀⠀⠀⣀⠀⠐⢦⣶⡾⠋⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣶⣶⣾⣧⡧⢾⣦⣼⣶⠿⠷⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡆⢾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠀⠀⠀⠀⠀⠀⢺⣿⠓⢶⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠂⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣿⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⣿⠏⠁⣤⠆⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⣛⣿⡿⠀⠀⣾⠠⣤⠀⠀⠀⠀⠀⡄
⠀⠀⢀⣤⣀⠀⠒⠀⠀⠔⠀⠀⠀⠳⠒⠶⠟⠷⢄⡀⣹⠀⠉⠀⠰⠄⠀⢀⣀⠀⠀⠀⠀⠀⠃
⠀⠀⣽⣽⣿⣷⣿⣤⣽⣤⣴⣀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠇⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠘⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠁⠙⠛⠖⠺⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠒⡀⠐⠒⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣌⡙⠛⠛⠛⠛⠛⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠉⠉⠉⠉⠁
⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⣶⣶⣶⣦⣾⣦⣾⣧⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠒⠀⠉⠀⠀⠀⠀⠐⢲⡤⠀⠀⠀⠀⠀⠀⠀⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢢⠀⠀⠀⠀⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠲⣦⠀⣷
⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡀⣀⡀⠠⠀⠘⠀⢀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⢇⡄⡀⠈⣠⠀⠈⢩⡔⠃⣀
⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠀⠆⠀⢀⠀⠀⠀⠈⠉⠀⠃⢉⡠⠏⠘⠉⠠⠴⠚⠁⠞⠃
⠀⠀⠀⠀⠀⢸⢻⣿⠀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⢠⣶⠀⠀⢸⠀⣿⠀⢸⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠤⡤⣤
⠀⠘⣿⠀⠀⢸⢠⣿⠀⠌⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣞⢷⡀
⠀⠀⣿⡄⠀⠘⢸⡿⢊⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠋⠀⢄⢸⢿⣧⣷⡀⠀⠀⣀⠀⣀
⠀⠀⢿⣧⠀⡞⢸⣿⠟⠁⢠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢺⡶⣋⡄⠀⣀⣼⠇⣾⣿⣛⢯⣿⣷⣾⣯⢁⠈⠢⣄
⠀⠀⠘⣿⣦⡗⢸⣿⠀⠀⢸⣼⡇⠀⣀⠀⠀⢀⠠⠀⢀⠎⠀⣼⡿⠋⠀⠀⡿⠋⢸⣧⡈⠛⢿⣿⡿⣿⣷⣿⣷⣀⣉⢻⡶⣦⣀
⠀⠀⠀⠘⢿⣇⢾⡏⢀⣄⢸⣿⠃⠀⠸⣷⡀⢉⡤⠚⠉⢀⡾⠋⠀⣰⣧⠞⠀⢼⠙⢿⣿⣦⡺⣿⣿⣮⣿⣿⣿⡿⠋⠻⣧⡿⣿⣿⣆
⠀⠀⢀⣶⠀⣿⢸⡇⢸⣿⢸⣿⡆⢀⣤⢿⡗⠉⠐⣠⡾⠋⠁⠀⣰⣿⢏⠄⡆⢠⠸⣄⠈⢿⣷⣿⣿⡿⠛⠉⠁⠀⠀⠀⣽⠿⣿⣄⡈
⠀⠀⠘⣿⣆⣿⣿⠁⣸⣿⣼⣿⡇⣿⣿⣿⣿⣶⠟⣫⣤⣶⠶⠋⠉⣠⠎⢀⡁⢸⡆⠨⣦⡈⠿⠟⠉⢰⢸⡇⠈⠁⠀⣰⣿⡀⠀⠉⠃⠑⠂
⠀⠰⣾⣿⣿⢿⣿⡇⠈⡻⣾⣿⠃⣤⠙⠿⠿⠗⠛⠛⢻⣃⣤⠈⣰⣟⣀⣾⡇⠘⠛⠀⠉⠀⠀⠀⣶⠸⢿⠁⣾⢠⣿⣿⡛⢻⣶⢤⡀
⠀⠀⠀⠀⣈⣿⣿⡇⠀⠙⢻⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣥⣾⣿⣷⠿⠋⠀⠀⠀⠀⢠⢠⣄⠀⢹⣄⣿⣰⠇⠈⠙⢻⣿⣿⣿⣿⣧
⠀⠀⢀⣈⣠⣿⣿⣿⡓⠶⣿⣿⣿⡿⠀⠀⠀⢀⣀⣀⡀⠀⠸⠿⠏⢠⡀⠀⠀⠀⠀⠀⠸⣇⣿⠀⠀⠙⡿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠻⠟
⢰⠂⠉⠉⠻⣛⡙⣉⣙⠓⠿⢿⣅⠀⠀⠀⠀⠨⠽⠟⠋⠀⠀⠀⠀⠈⣿⣦⣤⣀⣀⣤⣄⣸⣿⣤⡤⠼⢿⣶⣦⠙⢟⠗⣶⢷⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⠒⣘⠛⠿⠿⢷⣶⣴⣦⣤⡀⠀⢀⣀⠀⠀⠙⠿⠟⠛⠀⡈⢙⣿⠋⠀⠀⠸⣿⡿⣷⡆⠀⢀⣀⣼⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠁⠀⠉⣙⣯⠁⠀⠈⠛⢯⣤⣤⡤⠀⠀⠀⠀⠹⠿⡿⢦⣄⣤⢀⣿⠷⠛⠋⠙⠛⠿⠿⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠀⡠⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⣀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠊⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠀⠨⠄⠂
⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⡠⠒⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡀⠤⠀⠀⠈⠐⠀⠀⠈⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠁⠉⠉⠀⡀⠠⠔⣈⡀⠀⡀⠀⠠⠄⢂⢠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠤⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⢾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠨⠤⢄⣤⣬⣥⣤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠠⢔⣽⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⣀⠀⠉⠐⠒⠀⠄⠠⠤⠀⠀⠀⠀⠤⠄⠐⠷⢤⣤⣀⣀⣀⣀⣐⣐⣨⡧⢀⠠⣊⠔⠒⠉⠉⠉⠙⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠒⠠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⠀⡀⠀⡴⠃⢀⠠⠀⠀⠄⠠⢌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⢧⡔⡥⠚⠉⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠀⠀⠀⠀⠠⠀⠐⡀⠔⡯⠥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣟⠒⠤⠤⣤⠭⢤⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡀⠉⠉⠙⠛⠛⠛⠛⠛⢑⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⠖⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠄⠠⠈⠠⠀⠀⠠⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠁⠉⠉⠉⠙⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢰⣏⣤⣶⣶⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣶⣶⣄⢻⡄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⡜⢿⣿⣿⣿⣿⣿⣿⣿⢻⣮⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠘⢿⣝⢿⣿⣿⣿⣿⠿⠋⣼⣿⣿⡌⠛⠿⣿⣿⣿⣿⠟⣸⡿⠃⠀⠀⢀⣠⠤⠶⠦⣄
⠀⠀⠀⢀⣠⣼⡅⠀⠈⠙⢧⡄⠀⠀⢈⣿⣷⣦⣭⡀⠀⠀⢸⣿⡿⣿⡷⠀⠀⠀⢀⣤⣴⣿⣿⠁⠀⢀⡴⠋⠀⠀⠀⣤⣟
⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠙⠳⢦⣼⣿⣿⣿⣿⡇⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⡶⠞⠋⠁⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠉⠳⠦⠤⠤⠤⣤⣀⠀⠀⢸⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⠃⢀⣀⡤⠶⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡶⢤⣀⡈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢀⣀⣤⣾⡋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠴⠚⠉⠁⠀⠀⣈⣩⠿⠓⠒⠒⠒⠒⠒⠒⠿⢯⣉⠁⠀⠀⠉⠙⠲⢤⣄⡀
⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠉⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⣤⣀⠀⠀⠈⠙⠛⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠻⣤⡄⠀⠀⠀⢠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡄⠀⠀⠀⠀⣀⣀⣸⠇
⠀⠀⠀⠀⠸⣇⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣼⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉








⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣷⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠶⢀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⣡⡞⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⡇⠠⠀⣀⠐⠆⠀⣤⢀⣂⠀⠀⠀⠀⢈⠁⠀⠘⠓⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⠲⠀⣠⣬⡿⠿⠿⠷⠤⠤⠶⠄⠀⠠⣤⣦⠉⣤⢀⡉⣤⣼⡁⠀⠀⠀⣤⣤⣶⣦⣀⣴⣤⡟⣿⣧⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢠⡮⢐⠉⣈⠠⠆⢶⣶⣾⣿⣿⣿⠏⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠘⢡⡼⠇⣅⠾⣶⣽⣟⣿⡻⠟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠡⢂⣀⣵⣿⡟⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠟⢿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⡈⠃⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠂⣿⣶⣀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⢴⣶⡶⠃⢶⣿⣳⡀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢱⣿⡇⠃⠀⣿⣿⣿⣿⡀⠸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢛⡟⣱⣥⡟⣿⠀⠘⠻⡿⣿⣟⣿⡆⢹⣿⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⣼⠟⢚⣻⠞⣐⣿⣿⣷⣿⠀⢀⢰⣏⢹⣿⣿⣧⡌⢿⣿⣿⣝⣿⣶⣄⡀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠀⠁⠁⠀⢠⣚⠧⠼⠩⢈⢋⣵⣶⣿⣿⣿⣿⡇⠀⠈⣾⣿⡆⣿⣿⣝⡄⠸⣿⣯⣿⣧⣍⠻⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡴⣺⢶⡛⠃⡀⢈⡅⣵⣦⣶⣼⣯⣿⡟⠁⣶⠏⣸⠟⢳⣷⡘⢿⣿⣿⣦⠈⢿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⣀⣤⣴⡶⠀⢃⡀⠉⠊⢉⣀⠀⠌⠁⢸⣧⣿⣿⣿⣡⡿⣿⣥⣾⢃⠀⠋⠀⢸⡎⠹⢶⣝⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣽⣿⢿⣿⡛⠛⠿⠶
⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠲⠤⠀⠠⠺⡿⢛⢡⣖⡥⣪⣿⣏⠐⠙⢫⢋⡆⠀⠈⠀⠀⠁⠀⠺⠻⣧⠹⣿⡝⠳⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⡻⣍
⠀⠀⠀⠀⠈⠙⠀⠐⠀⢀⣀⢠⣤⣤⢄⠠⣽⣫⡽⠿⠛⠍⠀⠀⠀⠀⢸⢠⠇⠀⠠⠀⠈⠇⠀⠐⣿⣆⠘⢷⡄⠈⠃⠈⡻⠿⠿⣿⣿⡟⠻⠿⠮⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠉⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠈⠀⠀⠁⢀⣴⣿⣿⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠘⣀⣀⣀⢔⣾⠋⠉⢻⣟⡼⠋⠑⢻⣧⣤⣤⣤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢨⣭⣉⣈⡙⣿⡄⠀⢸⠿⠀⠀⢀⠈⠰⠿⠯⣩⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⠉⠙⠛⠦⠤⣀⠀⠀⠀⠀⠘⠟⠣⠾⠥⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣯⡆⠀⢀⣴⡺⠟⠶⢆⡑⢄⡀⠀⠀⠀⣠⠀⢠⣾⣿⡿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠛⠻⢳⡀⡀⣇⢀⣀⣀⣨⢻⡄⣷⠀⠀⠀⠘⠂⠊⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠗⣠⡤⠄⠁⡁⢸⣿⠈⠁⢰⠁⢳⢸⡄⠀⠀⠀⠀⠈⠹⣷⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢀⣀⠀⠁⠐⠀⠃⣾⠃⠀⠀⡏⠀⢸⡎⣧⡄⠀⠀⠀⠀⠉⠉⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠤⠀⡀⢀⣀⡀⣀⡿⠀⠀⠀⢻⠀⢨⡇⡯⠁⢀⣀⡠⠔⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠡⠂⠀⣶⣯⣿⣏⡁⠛⠓⠲⣶⢾⣤⣤⣷⠗⠚⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⣿⣿⣿⣿⣇⠀⠆⢰⡇⣴⣔⢠⡏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡀⣈⠿⣿⣯⣿⣿⣶⡗⣿⢸⣿⣿⣼⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⡅⠁⢰⣼⣧⣿⣿⣫⣷⣷⡞⣿⣿⣯⣿⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠁⢾⣛⢿⣿⣿⣿⣼⣿⣷⣿⣿⣿⠋⠘⠣⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡀⠀⣠⣤⣤⣄⡀⠙⠏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⣸⣧⡀⠙⠛⠛⠛⠁⠈⠋⠀⣀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠈⢻⡟⠉⠀⠀⠀⠰⠶⠀⠀⠀⠙⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⠃⠀⠈⠁⢀⣤⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⡀⠀⠀⠉⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠉⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⠀⠈⠋⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⣀⣤⣤⣄⣤⠤⠀⠀⠀⣀⠄⠘⠛⠉⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠈⠄⢀⠀⠀⠀⠀⠀⠄⡀⣄⠐⡌⠉⠉⠑⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠐⠆⠀⠄⠈⠑⠈⠀⠈⠑⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠤⠤⠔⠒⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠿⣦⡀⢠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠎⠈⠁⠀⠀⠂⡀⣀⠀⠀⢀⢻⠀⠀⠱⠈⢏⡳⠤⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢴⠀⡰⠃⠀⢁⠊⠕⠁⠀⢠⠋⠀⠆⠀⠀⠐⠀⠀⠷⢀⠄⢡⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⣁⢀⠔⠇⠐⠂⠀⠀⡸⠀⠀⠃⠀⠀⣴⣄⠢⠠⠤⠐⠤⣠⡔⠢
⠀⠀⠀⢀⠐⠁⠀⠀⠀⣠⠋⠀⡁⠀⡘⣀⠀⠀⢠⠄⢸⠀⠀⠐⠂⡰⠓⣌⢢⠐⠶⠀⠀⠢⠀⣀⡤⣈⠶⢤⡀
⠀⠀⠀⠀⠃⠀⢀⠐⡈⢀⡰⣊⠀⠈⠉⠉⢀⡴⠁⠂⠘⠀⠀⠀⠀⠤⠀⠊⢸⠀⠰⠄⠀⠀⠀⠈⠁⠀⠀⠈⣙⢦⡁
⠀⠀⢠⠀⠀⠀⠀⢀⠡⠂⠀⠁⠀⠀⠀⣠⠎⠐⠆⠀⢑⠀⠀⠀⠀⠀⠀⠀⢬⠄⠀⠀⠀⣠⠀⠀⠀⠈⠓⠀⠀⡀⠍
⠀⠀⠂⡠⣤⣀⠈⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⣸⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠼⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⣆⡠⣄⢠⠀⠀⠅⢠⡄⠀⡀⠐⢀⠎⠁⠓⠤⣀⠂⢀⡰⠚⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠄⢀⡠⠤⠤⠥⠀⠂⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡀⠋⠶⠴⠴⣄⡄⠀⠀⠧⢀⠀⡀⠑⢖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠒⠂⢠⢀⣤⠀⠀⣰⠀⠘⣧⡄⠐⠛⠁⠛⠄⠀⣅⠂⠬⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠠⡔⡖⢻⢀⠠⠒⣄⢼⠝⠏⠋⠀⠀⠶⠋⠑⠒⠚⠷⠂⢀⣀⠀⠂⠰⣌⣆⠀⡀⠈⢹⣄⡄
⠀⠀⠀⠀⠀⠀⢠⠹⣦⣼⣧⣶⡿⠟⠉⠀⢓⡳⠂⠡⣄⠀⠀⠀⠀⠘⣧⠀⠀⢉⡧⢀⠀⢹⡦⣀⠀⠈⢿⡇⠀⡀
⠀⠀⠀⡀⢸⠀⠎⢀⣸⣿⢳⣏⣤⠤⠚⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⣆⣷⢀⠁⠘⡧⢸⣦⡀⠎⢷⡴⢻⡆
⠀⠀⠀⣧⠀⡆⠀⡸⢋⡿⣾⣉⣆⢠⢠⡠⣴⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢿⠳⠷⣧⡄⣣⡑⡄⢼⣷⣾⠁
⠀⠀⢀⠸⡔⡉⢶⡟⣹⣱⡟⠓⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠂⠳⣄⣏⠘⠻⢷⣿⣀⣿⡃⣨
⠀⢳⠈⡦⢻⣦⡟⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣿⡝⣿⡷⡴⠂
⠀⠈⢷⡄⠈⢿⣾⢃⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⣿⡇⢻⣇⢽⠄
⣄⠀⣸⢿⣆⣼⣟⣱⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⢻⡷⣼⣿⣷
⠘⣧⡽⣎⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣸⣿⣼⣿⠏
⠀⠘⣧⣿⢸⣿⣿⢀⣄⠀⢠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⡏
⠀⢀⢹⣾⢾⣿⣿⣨⠋⠡⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⠀⡓⢾⣿⣿⢳
⠐⢾⡤⣿⣤⣿⣿⡄⠀⢸⣿⣫⡀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⡻⡟⣾⣿⣿⢸⠇
⠀⠸⣿⢏⢿⣿⣿⣧⠀⢒⢸⣟⡆⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇⢈⣿⣿⡇⢸⠀⠠
⠀⠀⢹⡥⡂⢻⣿⣿⣧⠀⢖⣿⢩⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⠥⣼⣿⣿⣇⡏⠀⠏
⠀⠀⠀⠘⢷⡈⣿⣿⣿⣷⡨⣯⣾⣿⢘⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀⢶⣷⣆⡀⠀⠈⢀⣤⡸⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣛⠛⣿⣻⣿⣶⣄⢀⠀⢀⠀⠀⠘⢝⢯⣇⢆⣇⡞⣿⠩⢿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⣿⣷⣾⠼⠿⠿⠿⠯⣄⣠⣤⡄⢠⠴⠓⢉⣩⣍⠙⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠦⠤⣼⣿⣥⠤⠄⣨⡤⠐⠀⠀⢈⠗⣅⠀⣲⣊⣹⣥⣾⣿⣿⣿⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠉⢻⣿⣟⣩⣹⣷⣶⣊⣠⠶⢻⣯⠟⠉⠀⠀⢤⣤⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠿⠏⠀⠊⠁⠐⢤⠞⠂⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⡿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⢀⣀⣴⣿⠟⡟⢿⣷⣄⣀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡏⠀⣷⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣯⠙⣿⣿⣷⣼⣿⣴⣿⣿⣿⠩⣿⣏⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠈⠛⢿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣠⣾⣿⣿⣟⣧⡁⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⣿⣿⡟⣼⠇⠹⣯⣼⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⡰⢟⢿⣿⣌⠃⣰⠋⣿⣿⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣠⣆⠃⢸⡿⢿⣇⠀⣿⣮⣙⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢀⣿⡿⣿⣟⡟⠻⢿⣦⣈⣻⣿⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣋⣽⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠁⣽⣿⡿⠁⠀⠀⠀⠀⠀⢠⣾⠟⢠⡿⢭⠃⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⣿⣿⣿⠟⢋⠉⣉⣠⣠⣤⢴⣶⣺⣿⢻⠀⠀⠀⠀⢀⣰⣾⡟⠹⣚⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣛⠛⠿⣿⣽⣛⠻⠚⠛⠛⠛⠉⠉⠙⢻⣶⣶⣿⣽⣿⣽⠂⢠⣾⣿⣿⠋⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣈⣝⣿⣶⣤⣀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣎⡷⠋⠁⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡀⠀⠀⠁⠄⠀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⢻⣿⠻⡿⢟⣻⠿⣿⢿⣷⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠿⣿⣦⣤⣄⣀⣀⡤
⠀⠀⠀⠀⢠⣿⣿⣹⡿⠋⠀⠀⠹⣷⣄⠈⠻⠉⢻⣆⠈⠉⢹⣿⡏⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⢿⡆⠀⠉⠉
⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⣹⡀⠀⠸⣿⣷⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⣷⠀⠀⠀⣀⣀⠀⠀⠐⠂
⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣿⠁⠀⠀⢻⣿⣦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⣶⣶⠿⡸⠛⠳⠟
⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⠃⠀⠀⠀⠀⢿⡧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠋⠁⠀⠁⠚⠀⢀⠀⠀⠌⠀⠂
⠀⠀⠀⣽⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣯⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⡷⣻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠔⠎⠊⠀⠁
⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣉⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠷⠶⢶⣶⣶⡶⠀⢀⠤⠒⠋⠡⠄⠀⠀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⡋⠁⢁⣉⣀⠐⢚⠃⠀⠀⠀⠀⠀⠰⠈⠉⠰⢀⡀⣀
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢙⣿⣷⣶⠶⣶⢦⣄⠠⠶⠂⡀⠀⠀⣈⣀⠄⠛⠉⠀⠐⠆⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠡⠄
⠀⠀⠀⢸⣿⣿⣦⠀⠀⠘⠒⠺⠿⢿⣿⡠⠉⠉⠉⠉⠉⠁⣀⡄⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢷
⠀⠀⠀⠈⣿⣿⣽⣀⡀⣀⡀⢀⠀⠀⠈⠀⠀⢀⠠⠚⠛⠛⠉
⠀⠀⣀⡀⢸⣿⣿⣎⠺⠛⠛⠚⠓⣆⠀⣀⡰⠃
⠀⠀⠀⠀⠈⢻⣿⣿⣳⣄⠀⠀⠀⠘⢷⣌⢳⣦⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣶⢤⣤⣤⣽⣷⣦⣤⣌⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠
⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠁⠀⠀⠠⠀⢀⡀⠁⠀⠀⡄⠀⠔⠁
⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⢀⠀⠀⠠⠤⠠⠆⠉⠀⡀
⠀⠀⠀⠀⠀⠐⠁⠠⠄⢀⠄⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡀
⠀⠀⠈⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⠄⠀⠀⠀⠐⠀⠄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⠇⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠃⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠰⡄⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡠
⠀⠠⠄⠀⠂⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⡉⠀⠀⠀⠀⠀⣀⠉⠤⠔⠉
⠠⠄⠀⠀⠀⠀⢰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠂⠐⡀⠂⠀⠀⠀⠀⠀⢄⣀⣈⣉⡀⠥⠤⢦⡠⠖⠋
⠀⠀⠀⠀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⡃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢀⠃⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠁⠒⠂
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠠⠀⠜⠁
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠉⠦⢠⠊⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⡀⡠⠒⠀⠀⠀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠣⢀⡠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠐⠤⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠙⣷⡎⠀⠈⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠀⠀⠀⡠⠤⠽⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣶⣾⣄⡀⢀⣸⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢙⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠶⠚⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⢀⣴⣦⢀⡞⠀⠠⠤⡀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠄⢀⡴⢋⡀⣿⣼⠃⣴⣄⠀⢈⡀⠄⡈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣆⠀⢘⣚⡭⠚⠻⠄⣙⠋⡘⠉⢻⣷⣿⠿⠶⠤⢀⡀⠹⠷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⡿⠛⣿⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠻⡇⠀⠀⠀⠀⠈⠉⠉⠉⠙⢶⣄
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷
⠀⠀⠀⠓⠒⠛⠉⠳⣤⣴⣿⣦⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣀⡀⢀⣠⣤⣴⣶⣿⣷⣦⣴⠿⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⠛⠛⠉⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢕⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀⢂⠀⠀⠀⠀⠀⠀⢀⠤⢒⡒⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢑⢄⠀⠀⢘⡀⠰⠤⣤⡤⣠⠔⢁⠔⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠑⣝⡦⠊⠀⠀⠀⠀⠑⠧⠤⠣⡀⢀⡠⠔⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢼⠘⠟⠛⠛⠺⢶⡆⢠⠀⡘⣉⠤⠖⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠈⠈⠉⠁⠒⠀⠄⣸⠔⢁⡥⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢶⠢⢄⡀⠴⣶⠉⠁⠀⢀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢃
⠀⠀⠀⠀⠀⠀⠚⣿⠃⣶⠀⣷⣶⠛⠃⠀⠀⠀⠀⡜⢀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⣿⢹⣏⣁⠀⠀⠀⠈⢿⠟⠁⠀⢀⣠⣤⠖⠛⠀⠀⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⡈⠉⠁⠀⣀⠀⠀⠀⠙⢭⡰⡇⢸⡇⠀⠀⠀⠀⠀⠔⢻⠟⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⢹⡿⡟⢻⡆⠀⠠⣴⡇⡁⠀⡇⠀⠀⢀⠴⠃⡠⠂⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⡸⡿⣧⣼⠃⠀⠀⠙⠗⠁⠀⣝⣲⣻⣯⠴⠊⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⡤⢠⣤⣤⠀⠀⠀⣷⠉⣧⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡦⠄⠀⢸⡄⠀⠀⠀⣿⣾⣿⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠘⠷⠖⠂⠸⠃⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣋⠀⠀⣠⡀⢀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣯⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⣿⣿⣿⣿⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⠌⠟⠛⣿⣿⣿⣷⣄⣠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⠛⠁⠈⠙⠿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣤⡘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⠛⣷⡈⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣿⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⢠⣾⣿⠀⣿⣷⡌⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠒⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠛⢐⣟⢻⣿⣭⣿⣿⣿⣆⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⣭⣭⣭⣭⣍⣭⣭⣭⣭⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢛⣛⣛⣛⣛⣛⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢹⣧⣷⣿⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢋⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠙⢿⣿⣇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⢿⣿⣿⠆⠀⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣋⣉⣛⣛⣛⣉⣙⣛⣛⣛⣉⣉⣉⣉⣉⣉⣙⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠋⠄⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡚⣟⣳⠀⠀⠀⠀⢀⡀⢇⣀⡠⠰⣃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣻⠻⢲⠖⣠⢤⣤⡔⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣳⡭⠼⠿⢷⣀⠀⠀⢀⡽⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠃⠈⠉⠁⠰⣄⠀⠅⠘⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⢿⠉⠙⡄⠀⠈⠻⠟⠖⠛⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⢿⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠈⠀⢸⡄⠀⠀⠑⠂⠠⡄⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⡄⢸⡇⠀⠀⡇
⠀⠀⢀⣤⣀⡴⠖⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢸⣰⠞⠙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡀⠀⠀⢿
⠀⠀⢍⢻⡏⠀⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⢸⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⢈⣸⣏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣷⠀⢀⣰⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠀⠀⠀⣿
⠀⠀⠘⢿⡏⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡁⣾⠿⣷⡾⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡀⡏
⠀⠀⠀⢸⣡⠂⢾⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⣿⣿⡟⣷⡾⣿⠿⠾⠃⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇⠀⢀⡇
⠀⠀⡇⢸⡏⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇
⠀⠀⣧⠀⣇⣼⣽⡇⠀⢀⡀⠀⠀⠀⣼⠀⠀⠀⠀⣸⣿⣿⣾⣿⡅⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⡇
⠀⢠⣿⢠⣿⣼⣿⠣⣀⠔⡴⠀⠀⠀⠆⡀⠀⠀⠀⢻⣿⣟⣿⢻⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢂
⠀⠀⢹⣻⡇⠻⣿⣷⣏⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠛⢡⠸⠙⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠘⡄
⠀⠀⢸⢸⡇⠈⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡎⢦⢃⡻⠀⠀⠤⠤⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠈⠀⠀⠃
⠀⠀⠀⠀⣹⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢈⣇⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢇
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢺⣿⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⣄⠂⢸
⠀⠀⠀⠀⢹⡇⢰⡀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⡟⢻⣿⡀⠐⠂⠰⠉⠀⠀⠀⠀⠀⠀⠀⣿⣥⡀⢸⣧⠈⣼
⠀⠀⠀⠀⢀⣿⠀⡇⠀⢰⡇⠀⠀⠀⠈⡆⠀⠀⠀⠀⠸⡿⠃⠈⠻⠆⠀⢈⡵⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⡇⢰⡿⠀⡏
⠀⠀⠀⠀⢸⡏⢰⠃⠀⠘⣇⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠐⠀⢀⢻
⠀⠐⠀⠀⠈⡇⠘⡄⠀⠀⢹⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠁⠀⠀⠀⠠⠀⠸⣿⡇⠀⠀⢿⣿⢲⡄
⠀⢀⠀⠀⢰⠇⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢘⣿⣜⣡
⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢋⡵⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠈⠀⠀⢀⠈⣿⣿⣋⠄
⣿⣿⠿⠿⡿⢿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠈⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣴⠃⠀⠀⣀⠀⠈⢾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠘⡟⠀⡽⠃⠀⠶⠛⠉⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠄⠈⠿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⣱⡄⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⠄⠀⠀⠀⢀⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠂⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣪⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⡔⠋⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠋⠁⠈⠉⠉⠉⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠴⣤⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡸⠀⠀⣠⣤⣀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡠⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠰⠁⢀⣌⠋⠀⠀⠠⠖⠀⠒⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⢰⠀⠘⠀⢷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠀⠄⠀⠐⠾⠟⠀⠀⡄⠿⠿⠇⠀⢰⡀⠆⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢊⠀⣄⠀⠀⠀⠨⠀⠇⠀⠀⠀⣠⠎⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠖⠀⡄⠈⢂⠄⠀⠘⠀⢀⠀⠈⢠⠃⠀⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠁⠀⠀⠘⠀⢸⠀⠀⠀⢁⠁⠀⠀⣸⢀⡾⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠈⣘⠳⣌⡉⠉⠉⣉⡴⠛⠉⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢡⡆⠀⠀⠀⠀⠀⠀⡧⠀⠀⠉⠉⠉⠁⠀⠀⢡⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠉⠓⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢀⡏⢳⣄⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⢀⣀⣀⠀⠀⢤⣤⠾⠯⣍⠈⡿⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠈⠀⠀⠀⡀⠠⡀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸⣆⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣧⠖⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⢀⣷⠀⠀⠀⡘⡆⠀⡆⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠙⠲⢄⣀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠁⠃⢈⡰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⣠⣞⡁⢀⢄⣤⠤⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣠⡾⢴⡆⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⢤⣤⡀⣉⣷⠄⣀⣀⠀⠀⢠⡟⠀⠀⠀⢠⡞⠉⠀⡼⠀⠀⠐⠇⠔⠚⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢱⡏⠀⠀⠀⢰⣏⣤⠴⠊⠁⠐⢦⣀⣀⣀⠀⠀⡀⠰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⢌⢳⠀⡷⠀⢹⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣉⣀⣀⡤⠖⠒⠒⢦⡀⠘⡄⠘⣜⡆⠳⠖⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⡇⢀⣇⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠐⠀⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠂⡸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡝⠻⢧⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⡏⢠⡎⠹⡆⠀⠀⠋⠒⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠡⡘⢷⣠⡇⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⠸⣿⡀⠀⠈⡢⣝⠛⠧⢀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠾⠮⣅⣉⡒⣤⣀⠁⠓⠺⢅⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⠞⠟⠓⣲⣦⣤⣄⡀⠈⠙⠺⣟⡲⣦⡂⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⢀⣽⡿⠛⠉⠈⠹⣆⠀⠀⠀⠹⡄⠙⢦⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⣸⣟⠂⠀⠀⠀⢠⡿⠀⠀⠀⠀⡇⠈⠈⢷⣁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡋⠉⠙⢻⠒⢤⣾⡟⠁⠀⠀⣠⠞⠀⢀⠀⢸⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢄⡈⢿⡻⠶⠃⠀⠃⢈⢿⠿⢷⣿⣅⡀⠀⠈⢀⣾⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⢹⡿⢽⣶⣄⣀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠶⢮⣈⡴⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣿⠁⠄⠈⠹⣿⣭⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣦⡀⠀⠀⠻⣷⡙⢦⡉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⢈⡄⠀⠈⡆⠉⢳⠢⠄⡘⢷⡼⠟⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⣝⢦⠈⠳⢤⣀⠀⠀⠀⢇⡀⠀⢱⣀⣨⠦⠖⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠈⠓⢄⣀⠼⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⢀⠴⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⡗⣊⣉⣦⢠⠤⠤⠤⠀⠛⠚⠉⠙⠛⠓⠒⠠⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣭⣭⡵⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠐⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠻⢿⣿⠿⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⣾⣎⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⣴⣿⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⡿⢿⣯⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣳⣿⡟⢀⣾⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⠿⢿⠿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⣿⡟⠀⠾⢻⣿⣿⣷⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣀⠛⠛⠞⠛⠋⣠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣽⣿⣿⣷⣶⢀⣾⣿⣿⣿⣿⡽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠙⠻⣿⣶⣤⣾⡿⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣾⣿⣿⣿⣿⢁⣽⣿⣿⣿⣿⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⡿⠛⠛⠻⣿⣶⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣿⡁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⣀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣀⣠⣼⣿⣷⣄⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣴⣾⣿⣿⣿⠟⠳⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣹⣿⣿⠟⣛⡛⢿⣿⣿⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣷⡹⣿⡇⣾⣿⣿⡆⣿⡿⣰⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠹⢷⣬⣙⣩⣼⠿⣱⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣙⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⠃⠀⠉⠛⠋⠁⠀⠻⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠉⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠠⠤⠤⢄⡀⠀⡀⠤⠤⠤⣀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠒⠒⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠩⠟⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠙⡯⠍⢢⠀⠀⠀⡔⠁⠀⣀⠤⠤⢄⠀⠈⢢
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢰⠉⢑⠀⠀⠀⠀⢐⠉⢳⠀⠀⡇⢀⢸⠀⠀⡜⠀⢀⠎⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢸⠏⢢⠀⠀⠀⠀⠑⠄⢸⡀⠀⠉⠁⠀⠪⠬⠂⠀⠉⠁⠀⢰⠃⠤⠃⠀⠀⠃⠀⡌⠀⡎⠙⡄⠀⢀⠃
⠀⠀⠀⠀⣸⣀⠀⡇⠀⠀⠀⠀⠀⠀⠑⡄⠀⠓⠄⣀⣀⣀⠤⠊⠀⡠⠃⠀⠀⠀⠀⢸⠀⠀⡇⠀⢣⡀⠈⠒⠁⠀⡔
⠀⠀⠀⡮⢔⡽⠏⡇⠀⠀⠀⠀⠀⠀⡠⠺⠲⢄⡀⠀⠀⠀⢀⣠⠚⡗⢄⡀⠀⠀⠀⢸⠀⠀⡃⠀⠀⠉⠒⠒⠒⠉
⠀⠀⡠⠋⠋⣡⡗⠁⠀⠀⠀⠀⢀⠜⠰⠁⠌⠀⠀⠉⠉⠉⠀⠀⠣⠈⢆⠈⠢⠀⠀⢸⠀⠀⡇
⣴⠊⣀⡠⢖⠁⠰⣄⠀⢀⣀⠔⠁⢠⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠆⠀⠑⡄⢸⠀⠀⠇
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⣀⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⡀⠀⠈⠎⠀⢰
⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠐⠊⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢄⠀⠘⣄⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡧⠊⢆⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢠⠀⡠⡺⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠈⠒⠠⠀⠀⠀⠠⠔⠈⠀⡰⡓⠉⢰⣁⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠈⠑⡤⠄⢀⣀⣀⠀⢤⠐⠉⠀⠈⢆⠀⣕⢃⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠢⡀⠀⠀⠀⢀⡤⠃⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠂⠀⢸⠀⠀⠀⢎⠀⠀⠛⠓⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠰⣄⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⢠⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠠⠀⣦⣠⠔⠀⡀⠀⠘⠆⠉⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠀⠼⠀⠀⠤⠀⠸⠛⢀⡀⠀⠁⠀⠀⠔⣈⠁⠀⠀⠀⠠⢖⣀⣰⠜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⡀⠀⠉⠈⢱⣌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⢿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⣛⣓⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡄⣸⣷⢸⣇⠷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⣬⠍⠀⠀⠈⠀⠀⠀⠆⠒⠋⠀⠂⠰⡤⠴⢚⡁⢰⠀⠩⢾⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⣏⠀⠀⠀⠓⣚⠁⠙⠂⢑⣂⠀⢁⠀⢤⠴⢖⣼⣌⡐⠆⢠⣿⡿⠿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⠠⣿⡈⢉⡳⢬⢟⣻⢿⡿⢿⡿⣶⢶⡿⢿⣿⣿⣶⠀⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣨⣿⠖⠙⣿⣷⠟⠷⠾⣰⠄⠸⣿⣿⠛⠷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⠒⠒⣧⡇⢤⣌⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢳⢶⡦⠁⣀⡌⠙⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⡗⡎⢈⣷⠘⡄⣠⣿⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢢⣿⣿⢹⠀⣅⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠻⠃⠺⠂⠀⠀⠉⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⢀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠘⣠⣤⣀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠤⠤⠴⠤⠴⠾⠿⠧⠴⠌⠛⠓⠲⠷⠾⣿⣟⡡⠞⠒⢚⣾⣿⣿⣶⣆⣀⣛⣛⣺⣷⣶⣶⣶⣶⣤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⢰⠆⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⢤⢰⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⢀⡎⠠⠀⢸⡁⠀⠀⠀⠀⠀⣄⠀⠺⢢⠚⠃⢀⡄⠀⠀⠀⠲⠀⣀⣀⠐⠃⠀⠀⠀⠠⠴⠀⣀⠄⠀⠀⠤⠀⠒⠂⠀⠀⠀⠈⡟⢻⠀⢐
⠀⠀⢶⣶⠟⡇⡏⠀⠀⠀⠀⠀⠘⡗⣬⣿⡹⡄⡯⠁⠀⢀⣐⠀⠃⢴⣄⠘⡁⢂⡀⠀⣰⣦⠀⣤⠟⠀⠚⡴⠂⠈⠀⠀⠀⠑⢘⣓⣘⡣⠊
⠀⠀⠨⣐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠗⠉⠀⠀⠀⠀⠀⠠⠧⣙⣁⠴⠑⠂⠀⠈⠘⠁⠀⠀⠉⣀⡘⠁⠀⠀⠀⢠⠀⠀⠀⠏⠹⠄⠀⠀⢀⡀
⠀⠀⠀⢿⡵⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠘⠖⠀⠀⠀⡀⠀⠀⠀⠀⢭⡥⠀⠀⠀⠀⣡⢣⠀⠀⢀⣀⠀⢠⠌⠙⠆
⠀⠀⠀⣘⢠⠀⠀⠀⢀⡷⢯⡀⠀⠀⠀⢀⢀⠀⠀⣀⠤⠄⡄⡀⠀⠸⠗⠀⠀⡀⠠⠀⡁⠠⠀⠀⠀⢰⡆⠀⢀⠀⡘⠔⢥⡏⠀⠨⠍⠀⢰⢚⠀⠈⠀⠀⡀
⠀⠀⠀⢸⡖⠀⠠⣁⠁⣷⣯⡇⠀⠤⠀⠘⢉⠀⠮⢰⡶⠳⣶⠹⡄⠀⡂⠀⠀⠀⠛⠀⡅⠘⠃⠀⠀⠈⣷⠒⠋⠀⠀⣄⣢⠀⠀⢀⣆⠀⠀⠙⠶⣀⡈⠟⠁
⠀⠀⠀⢰⢺⠀⢄⡅⢰⢾⠿⡇⠤⠄⠀⠸⠚⠀⣇⢹⣦⣤⣟⢁⠃⠈⠋⠀⠠⠀⣀⠈⠂⢀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠰⠖⠀⠀⠘⡞⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢬⡷⣾⠔⠡⠀⠀⢰⣠⠀⠀⠃⠠⡅⠄⠋⠀⠀⠀⠀⠀⠐⠁⠀⡀⠸⠁⠂⠀⠀⡟⠀⠀⠀⠀⠈⡏⠀⠀⢀⢦⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣴⠄⠀⢐⣸⠀⠐⠀⠀⢠⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠰⠇⠀⠀⠀⡏⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢐⠀⠀⠀⠘⠿⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠘⠦⠆⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡄⡄⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡆⠀⠀⢠⠉⠄⠀⠀⠀⠘
⠀⠀⠀⢸⢉⠀⠀⠀⠖⠐⢠⠁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢐⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠰⠀⢠⢠⠄⢄⠄⠀⠀⠀⠀⠀⠀⢠⢠⠄⠀⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠰⠒⠚⠀⠀⠀⠀⠀⠞⠀⠐⠀⠰⠠⠀⡀

⠀⠀⣸⣿⡟⠀⢠⣿⡟⠀⣰⣿⠟⠀⣴⣿⠟⠁⢀⣴⣿⠟⠉⠀⣀⣴⣾⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿
⠀⢠⣿⡿⠀⢠⣿⡟⠀⣰⣿⠏⢀⣾⡿⠃⢀⣴⣿⠟⠁⢀⣤⣾⣿⠿⠛⠁⠀⠤⠄⠀⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠈
⠀⣼⣿⠁⢀⡾⠿⠀⠸⣿⠃⢠⣾⡟⠁⢠⣾⡿⠃⠀⠀⠈⠉⠛⠁⠀⣠⣴⣇⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣷⣶
⢠⣿⡏⠀⣠⠀⠀⠀⢀⠀⠀⠘⠻⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠀⣀⣀⠀⠀⠠⠀⠈⢿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠈⠙⠻⢿
⢸⣿⠃⢀⣿⡆⠀⠀⠈⠣⠀⠀⠀⢰⣿⡟⠀⢀⠀⠀⠀⠀⠀⠻⣿⠟⠉⣠⣴⣿⣿⣿⠿⠆⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉⠻⣿⣿⣿⣶⣤⡀
⣿⣿⠀⢸⣿⠁⢰⣶⡄⢀⣀⡄⠀⣾⣿⠁⢀⣿⣦⠀⠀⠀⢀⡠⠋⣠⣾⣿⡿⠛⠉⠀⢀⣳⣄⣠⣦⣤⣤⣄⡀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿
⣿⣿⠀⢸⣿⠀⢸⣿⠃⢸⣿⡇⠀⣿⠏⠀⠘⠻⠇⠀⢸⣿⡿⠁⣴⣿⡿⠋⠀⣀⣴⣾⣿⡿⠿⠟⠛⠛⠛⠿⠿⢶⣄⣀⠀⢀⣤⡀⠀⠈⠙
⣿⣿⠀⢸⣿⠀⢸⣿⡀⢸⣿⡅⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⠁⢸⣿⡟⠀⢠⣾⣿⠟⠉⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠉⠙⠻⣿⣿⣷⣄⡀
⣿⣿⠀⢸⣿⡄⠘⣿⡇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠃⣰⣿⠿⠁⠀⠘⠻⠟⠛⠛⠛⠛⠛⠛⠁⠀⣴⣶⣄⡀⠀⠙⠻⣿⣿
⢸⣿⡆⠀⣿⣇⠀⢻⣷⠀⢻⣧⠀⢲⣿⠀⠀⠀⠀⠀⢿⣿⡆⢻⣿⠀⣿⠇⣠⡷⠀⠀⠀⢰⡶⠿⠿⣷⡆⠀⠀⠀⠈⠙⠿⣿⣶⣄⠀⠈⠻
⠈⣿⣷⠀⠸⣿⡄⠘⣿⡆⠘⣿⣆⠈⢿⣧⠀⢻⣿⡄⠘⢿⣿⡌⢿⣇⣿⢰⠟⣠⠎⠀⠀⣤⣶⣶⣤⣤⣀⡀⠀⠀⣽⣦⡀⠈⠻⣿⣷⣄
⠀⠘⣿⣇⠀⢹⡿⠀⠀⠀⠀⠘⢿⣆⠈⢻⠗⠂⢹⣍⠀⠈⠙⠛⠮⡻⣿⢸⣼⡇⠀⠀⠴⠶⢦⣤⣌⣉⠙⠻⢷⣤⡀⠙⢿⣦⡀⠈⠻⣿⣦
⣆⠀⠹⣿⣆⠀⠀⠀⢀⠀⢶⣦⡈⠻⣷⣄⠁⠀⢸⡇⠀⠢⡀⠀⠀⠀⠙⠻⣿⣿⡯⢭⣙⡛⠶⣤⣉⠛⢷⡦⠀⠙⢿⣦⡀⠻⣿⣦⠀⠹⣿
⣿⣆⠀⠘⢿⣷⡀⠘⢿⣷⡀⠙⢿⣦⣈⠙⠻⢶⣾⡇⠀⢀⣙⡂⠀⠀⠀⠀⠘⣷⣝⠲⣌⠛⢶⣌⠙⢷⣄⠀⠀⠀⠈⢻⣷⡄⠘⣿⣧⠀⠘
⢻⣿⣧⡀⠈⠻⣿⣦⡀⠙⠟⠃⠀⠉⠛⠿⣶⣤⣼⣿⣼⣿⣿⣿⠀⠀⠀⠀⡠⣷⢻⣆⠙⡷⠀⠻⢷⡀⠻⣷⡀⠀⠁⠀⠙⢿⡄⠘⣿⣧
⠀⠙⢿⣿⣦⡀⠈⠻⣿⠀⠀⠀⠸⠿⣶⡦⠀⢠⣿⣿⣾⣿⠿⠟⣀⡴⢂⣿⠃⣿⠈⣿⠆⠀⠀⠀⠀⣻⡀⢹⣷⡀⢳⣤⠀⠈⣷⠀⢹⣿⡆
⣦⡀⠀⠛⢿⣿⣦⣀⠈⠀⠰⣾⣶⣤⣀⢀⣴⣿⣿⣿⣿⣿⣦⡾⠋⣠⣾⠇⢰⣿⠀⣿⡄⠀⣴⣦⠀⢿⣧⠀⣿⡇⠈⣿⡆⠈⣿⡇⠀⣿⣿
⣿⣿⣦⡀⠀⠙⠿⣿⣷⣦⣄⡀⠉⢙⣿⣿⣿⣿⣿⠟⠛⠙⢻⣿⣾⣟⠁⣠⣿⠇⢸⣿⡇⠀⣿⣿⠀⢸⣿⠀⠸⠿⠀⣻⣇⠀⢻⣇⠀⢹⣿
⠙⠿⣿⣿⣶⣄⡀⠠⠛⠋⠙⣻⣿⣿⣿⣿⣿⣿⣥⡶⠖⠛⠋⠉⠉⠙⣿⣷⡍⢠⣿⡿⠀⢠⣿⡏⠀⣼⣿⠀⠀⠀⠀⢹⣿⠀⢸⣿⠀⢸⣿
⣄⡀⠈⠛⢿⡟⠁⢀⣠⣴⣿⠟⠋⣡⣿⡿⠋⠟⠁⠀⠀⣠⠂⠀⠀⠀⠟⠁⣠⣿⡿⠁⢀⣾⣿⠃⠀⠟⠋⠀⠘⠁⠀⣼⡏⠀⣸⡿⠀⢸⣿
⣿⣿⣶⣄⣠⣶⠾⠟⠛⠉⠀⢘⣷⣿⣿⣶⣶⠀⠀⠀⠀⠁⠀⠠⠐⢁⣠⣾⡿⠟⠀⠀⠾⣿⠃⢠⣀⡀⠀⢠⣴⠆⢠⣿⡇⠀⣿⡇⠀⣿⣿
⠈⠙⠿⣿⣿⣿⣦⡀⠀⠀⣠⣿⠋⠙⠛⠛⠛⠃⠀⠀⠀⢀⣀⣤⣶⣿⡿⠛⠀⠀⠀⢠⡀⠀⠀⢾⣿⠃⢠⣿⡟⠀⣼⡿⠀⠸⠿⠃⢰⣿⡏
⣤⣀⠀⠀⠉⠛⠿⢿⣷⣼⣿⣥⣴⣷⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠛⠁⠀⣀⣴⣦⡀⠀⠀⠀⠀⠀⠁⣠⣾⡟⠀⣸⣿⠃⠀⠀⠀⢀⣾⣿⠁
⣿⣿⣷⣶⣤⣀⠠⠴⠿⠟⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⢀⣠⣴⣾⣿⠿⠋⠀⣠⣾⣶⠖⠀⣰⣿⠟⠀⣴⣿⠃⠀⠀⠀⠀⣼⣿⠏
⠀⠉⠛⠿⢿⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⣴⣶⣿⣿⡿⠟⠋⠁⢀⣤⣾⣿⠟⠁⣠⣾⡿⠋⢀⣼⡿⠃⢠⣾⡟⠀⣰⣿⡟⠀⢠
⣠⣤⣄⣀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⢀⣠⣴⣾⣿⠿⠋⠁⣠⣾⡿⠏⠀⣴⣿⡟⠁⣰⣿⠟⠀⣴⣿⡟⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢽⡟⠞⠁⣯⠴⢖⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⣀⣠⣤⠴⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣠⡴⠞⠋⠁⠀⠀⠀⠠⣏⣤⠶⠞⠛⠛⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⣠⣤⡶⠶⠂⠀⠀⠋⠁⠀⢀⣀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢸⣧
⠀⠀⠀⢀⣴⠞⠛⠛⠻⢶⣄⢸⡇⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⠈⠻⠆⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢸⡏
⠀⠀⢠⡿⠁⣠⣴⡶⣶⡄⠈⢿⡁⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣾⡇
⠀⠀⢸⡇⣾⠏⣡⣶⢿⣧⠤⠞⠛⠛⠓⠂⠉⠁⢀⣀⣀⣀⣀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢠⣿⠁
⠀⠀⠘⣷⡀⠀⠙⢡⡞⠁⠀⠀⠀⠀⠀⠀⠠⣾⠛⣛⠉⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣼⡏
⠀⠀⠀⠈⠻⣶⣤⣼⡇⣠⡶⠃⠀⠀⠀⠀⠀⠈⠀⠉⠀⠋⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⢀⣠⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠹⣇⠋⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣴⡾⠛⢋⣉⣀⣀⣀⡈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠟⠁⣠⣾⠿⠛⠋⠉⢻⣿⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠉⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡀⠀⠀⢹⡄⢾⣿⠿⣿⣧⠀⠀⡾⠃⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⠀⠀⠉⠙⠻⠿⣷⣶⣦⣤⣤⣤⣤⣴⡶⠟⠉⠁⠀⠀⣸⢷⣄⠀⠀⠈⠁⠀⢀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⣀⣠⣴⠟⠉⠀⠉⠛⠻⠶⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣶⣶⣶⣶⣶⣶⣶⡶⠿⠟⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⡿⠟⠛⠛⠿⠿⠛⠛⠻⢶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⢟⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢛⠋⠙⠃⠀⠀⠀⠀⢀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡶⣋⣄⡀⠀⢀⣀⣠⣁⠀⠀⠀⠀⢈⠶⠀⠀⠤⡀⠀⠠⡀⠀⠀⠹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⠿⠘⢛⡿⠯⣤⠔⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⡀⠂⡀⠂⠉⠻⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣣⠁⢀⡔⠉⠀⢰⡏⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠑⢄⡮⡻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⡾⢣⠀⢸⡇⠀⢠⣘⣿⣄⡀⠰⣄⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠈⠈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣺⣿⣿⣷⣤⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣦⣤⣤⣤⣶⣤⣄⣀⣤⣤⡤⠀⠀⠀⠁⠀⠐⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⠿⠿⣿⣯⣭⣿⣿⣿⣿⠟⠛⠛⠛⠛⢻⢿⣿⣭⣭⣭⣿⠿⠿⠿⣷⣶⣶⢂⣠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠷⣝⣛⣯⣬⡻⣿⣶⣶⣿⣿⣿⣿⣿⢀⠀⠀⢀⡀⠀⣼⣿⣿⣷⣶⣶⣿⡿⠿⡿⣫⣶⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠛⠀⠀⢸⣿⣿⣿⣿⣜⣿⡟⠛⠻⣿⢿⣿⡏⠑⠚⠁⠈⢹⢿⠋⣿⡿⠛⢛⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠀⠀⠀⠀⠀⠈⡁⢈⠿⢻⡟⢿⣷⡄⠀⠹⢸⣿⡇⠀⠀⠀⠀⣼⠀⢰⡟⠀⣠⣿⣿⡿⢋⣴⣿⠋⠉⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣬⡻⢆⡙⢿⣆⠀⢸⣿⡧⠀⠀⠀⠀⣿⠀⠈⠀⣴⣿⠟⣡⡴⢛⠋⠙⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⣷⣤⡙⠢⢕⠄⠙⠇⣸⣿⡇⠀⠀⠀⠀⢸⡄⢀⡾⠋⡡⢚⡥⠤⠍⣤⣤⣤⣤⣤⣤⣤⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⣈⠁⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠁⠀⢐⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣯⣭⣟⣛⠛⠁⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠚⠛⣋⣩⣭⣽⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣸⣿⣿⣿⣷⡀⠔⠒⠒⢀⡠⠼⢆⡀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠐⠀⠀⠀⠀⠀⠰⣿⣿⠿⠿⢿⣿⣤⣤⣎⠉⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠊⠀⠀⠀⠈⠒⢶⣦⣤⣤⠌⠀⠀⠀⠀⠙⠿⠟⠿⠿⣶⣴⣿⠃⠚⠦⢤⣴⣄⣀⣀⣀⣰⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⠿⠿⢿⣶⣭⣭⣭⣽⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣽⣿⣾⣷⣾⣶⣿⠿⠿⠶⠶⠚⠛⠋⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢿⠛⡻⠻⣟⠟⣿⠿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⠀⠘⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣜⢹⣇⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦
⠀⠀⢸⡶⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠤
⢀⢀⡻⣧⠐⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⡿⠳⠆⡄⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠠⢠
⠁⠀⠁⢨⡯⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣤⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠣⠀⠇⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢳⢈⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⢴
⡏⠈⡱⠀⠆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⣿⡂⢠⠀⠀⢀⠤⠈⡇⠀⠸⠀⠀⠀⠀⠀⡷⠒⠀⠀⠐⠐⠛⡇⠀⠀⠀⠀⡸⠆
⢿⠛⠁⠀⠀⣔⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣯⣭⣽⣃⣻⡠⠒⠋⢣⣋⠀⡇⠀⠀⠀⢠⡇⠀⠀⡄⠀⠀⠀⣱⣾⠀⠀⠀⠣⣤⡓⢸⡀
⠈⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣈⡧⡆⠀⡀⠀⣠⡴⠘⠇⠁⠃⠀⠀⠀⠘⢧⠀⠀⡃⠀⠠⠀⣿⠟⠀⠀⠀⠘⠟⠅
⠀⡇⠑⢶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡏⠀⠉⠻⠦⠊⠀⢷⠀⠠⠀⠀⠀⠀⠀⠀⢻⠂⠀⢰⠀⢠⠀⢈⠀⠀⠀⠀⠀⠀⠀⠲⣶
⠀⣷⣀⣈⠆⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠠⣾⠉⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠄⠀⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢷⠀⠀⡆⠀⠀⠀⠀⠀⠀⢢
⠀⠅⠀⠀⠀⠈⠙⣥⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⣆
⠐⠀⠀⠀⠀⠀⠀⢛⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⡰⠆⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⠈⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠞⠀⠀⠁⠀⠀⠀⠘⠀⣀⠜⠀⣄⠀⠀⠀⠀⠀⠀⠂⠀⢀⠄⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⡀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⣦⠀⣷⠀⢻⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡿⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⡰⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢣⠀⠙⡆⠀⠀⠀⢰⡇⠀⢠⡇⠀⢀⡀⣾⠀⢀⡏⠁⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡆⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢰⣾⣿⣿⡿⣿⣿⡌⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢹⡄⢹⢀⣿⣧⣿⣿⠆⢸⠁⠇⠀⣾⡴⠃⠀⠀⢠⠏⣸⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠁⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢳⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⣟⠈⢆⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡷⢸⠀⡼⠁⢀⡞⠀⡪⣐⢩⠴⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠃⠘⠋⠀⠀⠚⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⣬⠒⠂⡀⠁⠀⠀⠁⠠⡀⠀⠀⠄⠀⠀⢄⠀⠈⠲⡀⠀⢀⠀⠈⠀⠀⠈⢇⠀⢹⡏⢻⣮⠹⣿⣴⣧⡿⠏⢉⡏⠀⡱⢋⠡⠂⢴⢁⠼⠋⠟⠀⣡⠞⠃
⣈⡀⠀⠀⠈⠠⠀⠀⠐⠀⠐⣄⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠶⢾⣎⡀⢣⡎⣼⠶⡏⠅⠀⢻⣆⡜⠀⡀⠁⠘⠀⠀⠀⠈⠀⢀⠠⠊⠀⠀⠀⠀⠀⢀⡴
⣍⡉⠓⠠⡀⠀⠀⠀⠄⠀⠀⣾⠛⠀⠈⠉⠉⢻⡶⢦⣤⡀⠀⣀⣸⡍⠂⠀⠛⠙⢠⣵⣁⡀⠁⠀⠠⢼⠻⠔⠿⠉⠛⠙⢳⠞⠋⠙⡟⠛⢳⣦⠀⠀⢀⠤⠚⠙⠋
⠾⠈⠀⠀⠈⠀⠄⠀⠀⠀⠀⣷⡚⠀⠑⣞⠉⠛⠁⠈⠀⠈⠘⠙⢹⡦⣤⡀⠀⠀⠈⠀⠽⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⠀⠀⢰⠇⠀⡁⢿⠠⠚⠁⠀⠀⢀⠨
⣍⡀⠀⠚⠒⠤⠄⠀⠀⠀⠀⣯⠁⡀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⣄⣀⣀⡀⠀⠀⠀⠀⢤⡼⠋⠀⠀⠀⠀⢀⠀⣰
⠉⠉⠓⠠⢀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠂⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠐⢠⠈⠀⠒⣿⠉⠀⢹⠆⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠈⠉⠉
⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⠷⣤⣄⠀⠀⠀⠈⠀⠈⠃⠰⠀⠄⠀⡀⠀⠀⢢⡔⢉⠠⠚⠁⠀⠉⠀⠀⠀⠀⠀⠘⠿⠀⠀⣤⠖⢓⡡⠀⠀⠀⠀⠀⠀⠀⠐
⣠⣤⣤⣀⡀⠈⠀⣢⠶⠛⠷⠂⠸⡄⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⠗⠛⠓⣦⣠⣤⡀⠈
⣀⣀⣀⡈⠉⠀⢠⡿⢖⠀⠀⣀⣠⠄⠀⢧⡀⠀⠀⠀⢀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠁⠙⠀⢹⡶⣖
⣤⣈⡐⠀⣉⣡⣾⠃⠀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠠⠶
⢉⣁⡶⠻⠀⠀⠙⠄⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠐⠂⠐⠀⠀⠠⠜⠛
⠀⢺⡁⣀⠀⠀⢀⡀⠀⣀⠀⠀⢀⡀⠐⠒⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠄⠀⢀⠀⠲⣶⣦
⠲⠒⠻⣭⡴⣥⡟⠂⠀⠻⠦⢠⡎⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⡀⢰⠀⠀⠀⠀⢀⠀⠀⠤⢀⠈⠂⠁⠀⠀⠀⠀⠀⠈⠁⢐⡀⠀⡤⠀⠀⠀⣀
⠡⠀⠀⠀⠀⠀⠙⢧⣀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠔⠀⠀⢀⠁⠈⠀⠀⠨⠀⠀⠀⠀⠈⠃⠀⠀⠀⠁⠂⠄⢄⠀⠀⠀⠀⠀⠀⠀⣠⣰⡇⠀⠠⠴⠿⠛⠅⢒⠒⠦
⣴⡶⠓⠀⠀⠀⠀⠀⠉⠛⠿⠚⢤⡀⠀⠀⠀⠀⠘⠤⡤⠶⠤⠂⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠠⠄⠀⠀⠠⠽⠀⠀⢀⠀⠀⠀⣸⡽⠀⠈⡇⠀⠠⢀⣀⠀⠉⠙
⡩⡁⠐⠀⠀⠀⠀⡠⠄⠈⠁⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠰⣀⣠⠆⠀⠀⠲⣤⠤⡀⠘⢆⠀⠀⠀⣠⡀⠀⢀⠀⠑⠒⠉⢙⣷⢛⠉⢀⣤⣾⠁⠀⢀⠀⠀⠁⠀⠈
⠔⠀⠀⢀⡠⠔⠁⠀⠀⢀⣴⡿⠚⠷⣴⣤⡴⠞⣆⣀⣀⣾⡍⢩⣁⡀⡀⢀⣿⡆⠡⠸⠾⣤⡴⣶⠋⠙⠖⠞⢧⣤⣤⡽⠟⠀⠉⠙⠛⠉⠀⠀⠀⠀⠈⠓⠄⠈⠂
⣞⡭⠊⠁⠀⠀⣠⠴⠛⡁⠊⠁⠀⠀⠀⠀⢀⠀⠈⠉⢁⡾⠀⡸⣏⣠⣤⣞⠙⢶⡆⠀⠀⠀⣴⠇⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠈⠛
⠁⠀⠄⢀⡴⠋⣠⡔⠋⢀⠀⣀⠔⣠⠄⡠⠛⣠⠂⠀⡞⢀⣶⡠⣎⢿⣜⡼⣼⣇⢙⠧⢹⣛⠁⠀⠀⠀⠨⡂⠀⢴⡀⠀⠢⠀⠀⠠⠀⠀⠀⠄⠁⠀⠀⠁⠢⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠈⠀⠀⢁⣒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⣀⠀⢀⢸⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠀⠀⣁⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣚⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣹⢉⡧⡁⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠐⠁⣸⡇⠀⢄⠀⢈⡑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⡠⠒⠀⣰⡀⡇⠀⠀⠑⠀⡽⣗⣬⣕⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠚⡁⢈⣤⢂⡠⠂⠀⡀⠉⣇⠘⢂⡀⡈⠛⢷⣤⡀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⢀⣤⣒⣚⣯⣄⡉⣒⣁⣸⣿⣿⣃⣢⣖⣜⣀⡩⠵⠟⠋⠁⢀⣀⢍⡙⣝⣢⣤⣀⣀⠈⣙⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣩⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡀⢉⣬
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠵⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⢒⣆⣀⠀⠀⠀⠈⠚⠻⡼⠀⠃
⠀⠀⠀⡀⣠⠁⣀⡀⠀⠀⠐⠀⠀⢻⡟⠋⠙⠛⣿⣿⣷⠀⠀⢀⣤⣤⡀
⠀⠀⠀⡶⣿⣾⣿⣿⡃⠀⠀⢀⣤⠏⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠉⠳⡆⠀⠀⠙⠓⠐⠄⠀⠀⠄
⠀⠀⠀⠘⠯⢿⡿⠿⢁⣶⣾⡽⠋⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣶⠶⠖⠛⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿