Titan cameraman skibidi toilet Emojis & Symbols

⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠐⠒⠒⢲⠰⠆⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢛⠀⠀⢸⠂⠠⠀⠀⣀
⠀⠀⠀⠀⠀⠨⠚⠉⠉⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠈⢁⡠⠔⠀⡒⠋⠈⢓⡂⠸⢄⣐⠁⠠⠄
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⡀⠀⠀⡀⠀⠠⠀⠀⠄⠀⠉⠀⠀⢀⠀⢐⡎⠁⡆⠀⡀⠀⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠁⠁⡤⠀⡄⠀⡀⠀⠀⠀⠀⠠⠀⠀⠉⠹⠇⠨⠀⠀⠀⠀⠀⠀⢀⡄⢀⡀⠘⠀⠀⠇
⠀⠀⠀⠀⠀⡀⠎⠂⠀⠀⠂⠄⠃⠐⠡⣲⣗⠂⠠⠀⠀⢠⢈⠀⠄⠄⢐⢠⠀⠀⠠⠠⢬⣷⢬⢂⠀⣁⠀⢀⡀⠀⣀
⠀⠀⠀⠘⠱⠃⠀⠀⠀⠀⠀⠀⣸⠤⠊⠈⠁⠁⠐⠂⠀⠀⠄⢠⠀⢤⠀⠄⠀⠀⠖⡒⠈⠑⠁⢦⠄⠀⠀⠠⠄⠁⠈
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⡀⠃⢦⠀⠀⠐⠀⠀⠈⠉⠋⠑⠈⠀⠈⠸⠙⠉⠀⠀⠐⠈⠃⡀⠠⠂⠀⠀⢈⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠘⠀⠂⠊⠀⠀⠈⠈⠀⠀⠀⠠⣆
⠀⠀⠀⠀⠀⠀⠀⠠⡆⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢠
⠀⠀⠀⠀⠀⠀⠨⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠁⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⢐⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢰⡇⠀⢀⣀⣀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠐⠁⠀⣀⠦⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣼⠅⠀⠀⠇⠇⠇⠜⠣⠏⠿⠀⠀⠀⢀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣿⠀⠀⢏⣡⠿⣼⠷⢧⣏⡿⣇⡼⠆⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣬⡏⠀⠀⣦⣶⣰⣆⡶⣴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢰⣿⡇⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠀⠀⠀⠀⠀⠀⠀⠂⡰⠀⠀⠀⠀⢿⠆
⣤⣬⣿⣥⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣤⣤⣤⠀⢤⡤⣀⡤⠀⣤⡄⢤⣶
⠟⠉⠀⡰⠊⠁⠀⠀⠀⠠⠀⢁⠀⠀⠀⢄⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⢰⣦⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⢰⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴
⠘⠉⡀⠀⠁⠀⠀⢈⠀⠀⠀⢀⠖⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙
⣲⣤⣦⠄⠀⠄⠀⠜⠀⠀⡀⠂⠄⠁⠐⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴
⡟⢻⠥⠀⠀⠀⠀⠀⠀⠀⠁⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙
⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣠
⡿⠛⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠈⠂⣶⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⡿⠟⠋⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠔⠒⠒⠒⠚⠒⠒⠢⠤⠀⠀⠀⠀⠙⠟
⢀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⢻⣯⣿⣿⣿⣷⣽⣇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣷⣿⣿⣿⣿⣷⣿⣾⣄
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣿⣿⣿⣿⣿⡧⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣼⣿⣿⣿⣿⣯⣤⡟⠛⠿⣿⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠒⠒⠒⠀⠀⠀⠀⠀⢀⣿⣿⠟⢿⡿⣿⣿⣿⣿⣿⣿⢿⣿⠇⠀⠀⠀⠉⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡦⠤⠤⠤⠤⠤⢭⡥⢀⠠⠊⠁⢹⣿⣿⣿⣿⣿⠉⠠⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣾⣦⣼⣿⣿⣿⣿⣿⢠⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠲⠀⢀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⠀⢠⣷⣤⣾⡿⢋⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣋⣠⣾⣿⣿⣟⣉⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠀⠀⢀⣼⣿⣦⡄⢀⣹⣿⡀⠀⠀⠀⠹⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠈⣿⣿⣿⡇⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢻⣿⣿⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠆⣿⣢⡿⠀⣿⠐⣿⢻⣧⢸⣿⢸⡟⢻⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⡄⣿⣿⣇⠀⣿⠀⣿⠻⣧⢸⣿⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠾⠃⠿⠋⠿⠀⠿⠐⠿⠾⠛⠸⠿⠸⠷⠾⠃⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠋⣼⡟⣿⡆⣿⡆⣿⠆⠀⣿⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⣿⡇⣿⡇⣿⠃⠀⣿⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠙⠷⠟⠁⠿⠃⠿⠷⠆⠿⠶⠂⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⢀⡐⠊⠁⠀⠀⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠁⠀⠉⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠠⢄⣀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠠⡄⠐⡿⠀⠀⣀⡤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⡉⡲⡦⣀⠤⠜⠓⠦⣤⣄⢁⡤⠔⠀⠈⠀⠀⠀⠀⠈⠁⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⢄⠀⠀⠰⢀⣃⣤⡇⠀⠀⠀⠀⠀⡉⢛⣮⡆⠀⠘⠤⣄⡀⠀⠐⠩⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠚⡴⢠⣏⣽⠛⢴⠁⠑⠢⠤⣀⠀⠈⠅⢀⡁⢸⠀⢀⣀⠴⣈⢨⡖⣰⠾⡉
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⡵⠸⠀⢸⣀⣠⣴⣧⢇⣼⣻⣺⣿⡀⢠⠋⠁⠀⠀⠀⠨⣫⠙⠀⢰
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠈⢆⣷⠠⠀⣼⣿⣿⣿⣿⣆⢻⡿⣿⣿⣇⠇⠀⠀⠀⠀⠀⠄⣧⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣇⡿⢰⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠸⡏⣆⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢹⠇⠀⡀⠀⢱⡀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢧
⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡇⢀⠁⢡⡀⠘
⠀⠀⠀⠀⠸⠄⠤⠘⠃⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡗⠀⠀⠀⠀⠀⡇⢸⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡿⣿⣿⠾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⡇⠀⠀⠀⠀⠀⡇⠊⠀⠀⠸⠊
⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠶⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⠁⠐⠴⠋⠁⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡆⠙⠋⠁⢻⣿⣿⣿⣿⡿⠛⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⢀⡤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠉⠀⠂⢃⠀⢀⡀⢾⡟⣫⣭⡻⢛⡤⣷⠒⢦⠀⢠⠏⣠⢿⠃⣼⢃⡼⠋⢲⡏
⢠⠀⠀⠀⠀⣀⣤⡄⢁⣤⣶⣦⡄⠀⢘⣴⡿⠃⣠⢞⡹⢫⡏⣫⣰⣯⠴⠋⢠⡏⣰⠏⢾⣾⠃⣞⣀⣴⡯
⠰⠀⠀⢠⡞⠩⠞⢡⡞⢡⢋⡾⠀⢀⡾⠁⠐⢲⡏⠞⣳⢏⡼⢱⠏⠙⢦⣠⠟⠠⢏⠀⠛⠁⠀⠉⣱⠏
⠰⠁⠀⡟⠀⣠⡆⢾⣀⣠⠞⣵⣶⠾⠷⠶⠶⢊⢛⣛⠡⣼⠷⣈⠆⣀⢀⠑⡤⣀⣸⠀⠀⡀⠀⠘⡁
⢀⠀⠀⠙⠚⠉⠀⠈⠉⠤⠵⠆⢠⠀⠀⢀⡨⣶⡰⡠⠚⣷⠞⡹⢡⠯⡑⢒⠃⠤⣙⢢⡄⢠
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠤⠰⠇⠛⠑⠊⠀⢫⣥⣴⣧⣀⣀⡀⠀⠀⠀⠀⠈⠢⠐⣈⡡⠥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣲⣶⠂⠀⠠⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣻⡿⠷⣤⣇⣼⣿⣷⣶⠏⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣇⡀⣸⣿⠶⠟⢫⡍⠻⣿⣧⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡫⢵⡂⢠⠀⢠⣬⣯⣱⣷⢾⣠⣤⣊⢠⣾⣁⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠒⠈⠑⡞⠀⠉⠉⠘⠃⢙⠒⠂⡼⠋⠿⠋⠉⣀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡠⠂⠀⠀⠀⠀⠀⣆⢘⡷⠛⠌⠛⠇⠰⠋⠙⣦⢈⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡌⠡⡶⠂⠈⠣⠈⠀⠀⢣⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢴⢠⡑⠄⢠⢆⠀⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠐⡇⠀⠀⠀⡆⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣀⣰⠀⠀⠀⠀⠁⢀⣀⡄⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠧⠀⡀⢻⠉⠳⠾⠐⡄⠀⠀⡞⢹⣿⡔⣆⣀⠀⠂⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠠⠕⠊⠀⠁⠀⠉⠀⠈⢭⡄⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⢀⠀⢀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠻⣦⡀⠄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡄⠠⠳⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠇⢠⡀⣠⣄⠄⠀⠀⡟⠔⡈⠆⢀⠤⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⡇⠀⣶⠈⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡸⢧⠿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠀⠐⠘⠀⠀⠀⠀⠀⠃⠀⡟⠀⠀⣠⠓⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠁⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢡⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⡠⠀⠀⠀⠸⠀⠀⠤⡠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢺⠀⠀⠀⠀⠀⡆⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠐⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣀⣀⣤⠤⠴⠦⠝⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣿⣿⡿⠿⣿⠿⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠉⠉⠀⣴⠆⠀⠀⠀⠀⠀⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡋⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⣇⢠⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢹⣆⠀⢀⣀⣀⠀⠀⣽⡛⣾⣾⣯⣇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⡄⢸⣿⣿⡋⠻⣯⣽⠂⢘⢿⣻⡝⠑⢶⡤⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⣷⣾⣿⣻⣿⣿⡥⢗⢿⣿⣿⠻⣿⣿⣄⣴⣿⢛⠟⢲⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⡾⣾⠉⢿⣦⠄⢃⣎⡿⠾⠛⠫⠽⣿⢟⣿⣾⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡶⣾⣤⡔⣫⡉⢩⡰⠀⠀⠂⠴⢊⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⢾⡋⣿⠩⠀⠀⠐⠇⠀⠀⠀⠀⢸⢼⡟⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢣⣙⣧⣀⠨⠣⣀⠀⠀⠀⠀⠘⣾⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⢻⣿⣷⡭⢉⣥⡰⡀⠀⠄⠀⠀⠀⠀⠧⠀⠰⡀⠀⢀⠴⢒⣓⡄⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡈⠀⠈⠉⣠⣔⢻⣿⡤⡁⠀⠂⠀⠀⠀⢰⡏⣇⢴⣼⣧⡔⣶⣿⣀⢡⠀⠀⠀⠀⠀⠀⢸
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡟⣿⡡⡶⣿⣷⡇⠈⠀⠀⠀⠀⣻⡏⣟⢨⣯⣿⣷⣷⣛⡅⢸⣧⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣰⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⠟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⣼⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣼⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⣿⡟⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⡆⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠁⣼⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⣿⡿⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⠿⠟⠉
⠀⠀⣸⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠁
⠀⠀⠈⠉⠋⠛⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠈⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡦⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣠⠀⠀⢰⣾⣿⣖⡾⢗⣶⣾⣶⡆⠀⠀⠀⣐⣂⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⢻⣿⢧⠀⡼⣷⡿⣿⡀⣠⡿⣿⣿⡆⠀⠀⣼⣹⡿⡩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢶⡽⣦⢶⡁⢛⣤⣿⣉⣁⣷⣭⡁⠀⢀⡴⢡⣿⡿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡷⠿⠶⡿⠂⣯⣑⡈⢈⠉⢀⠙⢶⡿⢧⣾⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⣏⠀⠐⠃⠀⠉⠀⠀⠘⠀⢠⠃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠤⠀⠀⢀⠃⠀⠀⢀⠸⡅⠐⢲⠋⠉⠉⢣⠀⣠⠏⠀⠀⠀⠀⠀⢳⠉⠉⠙⠒⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠂⠀⠀⢀⠉⡄⢧⠘⣾⡆⠀⢉⣾⠊⡞⠀⢠⣧⡀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠈⠀⠀⢠⠋⠀⠀⢰⢸⠄⣟⠻⠤⠟⣋⡄⠃⠀⢸⢝⣧⠀⠀⡄⠓⣲⡄⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⣤⠶⡇⠀⠀⠀⠸⣀⣀⣀⡜⠀⣇⢹⠈⢸⠀⡍⣿⠀⠀⢸⠀⠘⣆⠀⢣⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠚⠉⠀⠀⠘⠲⠶⠶⠖⠋⠀⢸⠀⠀⢉⣿⣶⡎⡶⠛⣧⠀⠀⢸⡀⠀⠹⡄⠈⢧⠀⢀⣂⡷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣼⠈⠘⠆⠇⠀⢹⠀⠀⠈⣇⠀⠀⢳⡀⠈⠻⣔⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡼⠸⠀⠀⠀⠀⠈⡆⠀⠀⢹⡀⠀⠈⢣⡠⠤⢬⠹⡔⢄⠀⠀⠀⠺⢿⣶⣤⠀⢶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡗⠓⠦⠤⠶⠒⠛⢻⡄⠀⠀⢱⠀⠀⠀⣇⠀⠀⢀⠙⠼⠂⠀⠀⠀⠀⠈⠛⣀⣀⡈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸⠁⠀⢀⡤⣄⠀⠀⠀⢳⠀⠀⠀⢣⠀⠀⠈⠳⠴⠞⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⢈⣿⣿

⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⣷⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣶⣤⣀⡀⠀⠀⠀⠉⠛⢷⣤⡀
⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣦⣄⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⢿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠈⠙⠛⠦⣄⠀⠀⠀⠉⠂⠀⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠐⢶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠉⠛⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⣶⣴⠂⠀⠀⠒⡒⠒⠦⣄⡀⠀⠀⠀⠀⠀⢀⣸⣦⠆⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣸⣦⡆⡀⠚⠈⠀⠀⠀⠀⠠
⠀⠹⠉⠃⠀⢀⠠⣌⠙⠢⣄⠙⠳⠀⠀⠀⠀⠀⠹⠋⠃⠀⠓⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠘⠋⠁⠀⠺⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢱⡀⠑⣄⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠡⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣠⠤⠤⢤⣄⣀
⠠⣿⣿⣡⠰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⡂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⢾⣿⡇⠀⠀⠹⣟⣒⠲⢦⣌⠁
⠀⠈⠱⠆⠀⡅⠈⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠁⠢⡑⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢳⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢄⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿
⠠⣿⣾⡳⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣋⡼
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢷⣴⡾⠛⣿⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠀⠀⠀⠀⢸⣇⠀⠈⠻⣦⡀⢀⣀⡀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣯⣅⣀⠀⠀⠀⠀⠀⠙⢳⣦⡀⠙⣷⡄⢻⡟⠓⠶⠞⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⣴⠟⠛⠛⠋⠙⠁⠀⠈⢿⣄⣿⠄⠀⠀⠀⠈⠛⠳⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠋⢀⣀⠀⠀⢠⡶⠞⠋⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣄⠀⣀⠀⠀⠀⠀⠀⠸⣿⡟⠛⠋⠉⠳⣄⠸⣧⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⢷⣄⠀⠀⠀⠀⣈⣿⣦⡀⠀⠀⠘⢿⣿⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢷⠶⠞⠛⢩⡟⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠃⠀⠀⠀⠀⠀⣠⡟⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣯⣉⡀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⡄⠀⠀⢀⣀⣀⡀⠈⠛⣷⡄⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣰⠿⠋⠉⠛⠛⠛⠛⠛⠂⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣄⡀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠈⢿⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⢻⣆⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⠀⠀⢿⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢿⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢿⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⣿⢀⣄⠀⠀⠀⠀⠀⠈⣉⣹⣶⣦⣷⣤⣶⣿⡟⠉⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣶⣤⣄⣠⣴⣤⣤⣤⡀⣀⢀⡶⠛
⠀⠀⠀⠈⠉⠙⢷⣄⠠⠀⠀⠀⠀⢀⠛⠋⠁⠀⠀⠀⢀⣀⡤⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠻⠛⠛⠛⠛⠋⠛⢻⣿⠛⠛⠻⡿⠃
⠀⠀⠀⠀⠀⠀⠠⠞⠓⠀⡂⠰⠦⣈⡿⢧⠄⠀⠀⠀⠀⠉⠓⠦⢀⠀⠐⠛⠠⡄⠀⠀⠀⠀⠀⠠⣄⠀⠀⠒⠐⣤⢄⣠⣤⠀⡄⠀⡐⠸⣿⡄⣠⠤⠟⠀⠘⢇⡀
⠀⠀⢀⢀⣀⡖⠖⣀⢀⠀⠠⡐⢶⣄⢀⡾⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠳⠶⣔⠃⠀⠀⠀⠀⠰⠗⠈⣷⠀⠀⠸⠀⠀⢉⠇⠈⠁⢠⠇⢤⣿⣧⡏⢀⠀⣠⡄⠀⠛
⠀⠀⣠⠔⠁⠀⣸⡇⠈⣷⠂⠉⢀⡈⠛⢤⣅⣨⠀⢠⡀⢰⠀⢀⠄⠀⠀⡀⠈⢳⠀⠀⠀⠀⢀⣴⣿⣼⢧⠀⠚⠤⠰⠦⡀⠀⠀⣾⠰⣆⣰⢉⢀⡉⣠⠈⠳⣄⠤
⠀⠞⠁⠀⢠⣼⣿⡇⠀⢻⠀⡀⠈⢃⣦⠀⠙⠃⠀⣾⣿⡀⠀⠛⠀⠀⢠⡇⠀⢸⢀⣀⡈⠛⠛⡿⢻⡁⡌⣀⠀⠀⠀⠐⣱⠀⢺⡇⢀⢡⡏⢻⠀⠁⠙⠃⠀⠀⠤
⠀⢀⠀⠚⠈⡿⢿⡁⠀⠈⠀⠁⠀⠈⠆⢰⡄⠀⠈⡜⠻⠀⢀⡈⠀⠠⠊⠀⢰⣾⣿⣿⣏⡆⠀⠘⠈⣟⣠⡟⠐⡆⠠⡤⠟⠀⡿⢀⡈⣧⠀⠀⠰⢦⠀⠟⠙⠓⠖
⠀⢻⣿⠀⢰⠀⣼⠋⠀⢀⠀⠠⠀⠀⠈⣿⣦⣤⠀⢰⡄⠀⠋⠙⠒⠇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠘⡇⠉⠿⠟⢻⠶⡷⠀⢰⠀⣶⠞⠆⠀⠙⠳⣎⠙⠆⢰⠘⣥
⠀⢸⣿⡆⢸⠆⠙⠃⠀⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠁⠀⠀⠀⠐⠉⣀⡈⠛⠿⠛⠿⠟⠓⢀⣤⠴⡷⠦⣀⠀⢠⡦⠀⢨⣤⣤⣥⠀⠀⠐⠲⠿⠊⠁⠀⠀⠈
⠀⠘⣿⡇⢸⠁⣠⡀⠀⣀⡀⢠⣄⢀⣤⣆⠀⢀⣀⡀⠚⠓⠠⡄⠲⣤⡋⣡⣤⠄⠀⠀⠀⢀⣀⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢿⣿⡄⠀⢸⡄⢠⡭⠷⢶⣿⣿⣿⣷⠄⠠⠤⡉⢉⠐⠶⡌⠃⠙⠁⠛⣋⢀⠀⠤⣄⠉⠉⠁⠀⠀⠀⠀⢀⠄⠀⠢⡰⠄⠀⠀⠶⠀⠈⠁⠀⠀⠀⢠⠶⡴⠶
⠀⣿⣾⡷⠛⢠⣿⣡⠀⠒⠐⠂⠀⠶⠠⣤⢄⠀⠀⠸⠀⡈⣯⣄⠀⠀⢠⣌⡉⢶⡜⢶⡌⠀⠀⠈⠀⣀⣀⣘⡴⠄⠀⠂⠐⠲⠖⠉⠁⠠⠌⠉⠀⠀⠰⠏⠀⠀⠐
⠀⣿⣿⣷⡀⠸⠋⣀⡀⢠⣤⣄⢤⣄⣀⡀⠀⠉⠐⠓⠤⠀⣀⠀⠀⠀⠀⠈⠀⠀⠽⠀⠀⣀⣀⣀⠲⣿⠛⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠀⠭⢐
⠀⣿⣿⠉⠀⢶⡈⠉⠈⠁⠀⠁⠀⠉⠉⠀⢀⡀⠠⠤⠐⠈⠉⠀⠀⠀⠀⠀⠀⠛⠀⠤⣀⡉⠉⠙⠀⠈⠃⠀⠦⢀⣀⣀⡀⠀⢠⠖⠀⠀⡀⠀⣠⠄
⠀⢻⡏⠀⣸⠒⠛⢤⠀⠀⠀⠀⠀⠀⡠⠶⠨⠦⢀⠀⠀⠀⠀⢨⣨⣥⣤⣄⣷⠀⠀⠠⠙⣿⡇⠀⢀⣠⣄⢀⣀⠀⠀⠀⠈⠁⠘⠃⠲⠿⠀⢈⠃⢀⢠⠠⠘⣰⠆
⠀⠟⠙⠀⠹⠞⠁⠐⣿⡷⠖⣠⢤⠀⠀⠂⣀⣀⣀⣀⣉⣀⠰⠄⠀⠀⠀⠀⠀⠖⠀⠀⠉⠀⠀⠀⠈⠉⠋⠀⠛⠂⠀⢔⠒⠀⣀⣐⣦⣠⠀⠈⠉⠉⠓⠒⠂⠘⠂
⠀⣤⠄⢀⣀⣀⣀⠈⠠⠀⠒⠙⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠰⠀⠀⠠⠒⠳⠦⣀⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠉⢁⠀⠀⢀⠤⠄⠀⣠⣤⣂⠝
⠈⣿⠾⢛⣛⣉⣉⣀⡀⠀⠀⠀⠀⠀⢠⣄⣀⣙⢦⡌⠀⠀⠀⠀⠀⠀⠀⠾⠿⠶⢶⡖⢶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⠀⢀⡀⢀⣉⣛⣉⡾
⠀⣿⣿⣿⣿⠿⠃⠶⢤⣄⠀⠈⠉⠑⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠦⡤⠀⠀⠀⠀⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠄⠈⢁⣠⣤⣤⣤⣬
⠀⢿⠿⠏⠀⠀⠀⠀⠀⠈⠑⢦⣄⠘⠃⠚⠃⠀⠀⠀⠐⡀⠃⠀⠤⠀⠀⠀⠰⣆⣀⣀⣤⠴⠦⢈⡆⠀⠀⠀⠀⠀⠂⠠⣤⡄⠀⠀⡀⠂⣤⣶⣾⣿⣿⣿⠟⠻⠿
⠀⢈⠀⠀⠤⠤⠀⠠⠤⠴⠶⠄⠤⠂⠀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠁⢴⣀⠄⢸⡏⣀⣈⣶⡞⠛⠠⠾⣆⣿⡀⠸⠧⣼⡿⠛⠛⠉⣁⢔⣀⣀⡀
⠀⠈⠁⠀⠀⠀⣀⠀⠀⢀⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⣄⣈⡀⣡⠀⡀⠀⣁⡀⠴⢟⠉⠋⠀⠷⠗⢚⣂⡄⠀⠈⣷⢠⠀⣀⣀⡀⠰⠇⡈⠁⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢤⣤⡟⠓⠜⠛⣤⣀⣀⠀⠉⠉⠀⠰⣶⠀⠀⠀⣉⣤⡴⠋⠀⠀⠛⠛⠻⠿⢿⣷⣶⣶⣆
⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠴⠁⠻⠏⠙⠳⠾⠒⠦⢠⡏⠀⠘⠣⠤⢄⣀⡀⠉⢸⠗⢛⠉⠉⠹⢶⡆⠀⠀⠀⢀⠤⠒⠊⡁⠂⠁⠀⠀⠀⠀⠘⠛⡷⠾⠿⣿⣿⣿
⠀⢀⣩⡿⠳⢤⣄⠀⠀⠀⠀⠀⣀⣀⣀⠰⠰⠄⠀⢸⡇⠀⡀⠀⠀⠀⠹⠁⠚⠛⠁⠈⠀⠀⣀⡀⠦⠄⢊⠀⠤⠐⠊⠀⠀⠂⠀⠀⡀⢤⠴⠞⠈⠁⢠⣦⣤⣼⣟
⠀⢀⡱⢶⣉⠙⠻⠂⢤⣤⣄⠀⠉⠁⠉⠃⠀⠀⠀⠀⠛⢶⣬⣙⠓⠀⠀⠀⠀⠰⠒⢈⣉⣉⠠⣤⣈⣁⣀⣤⡤⠄⠈⠉⠉⠙⠙⠛⠻⢶⡄⠂⠀⠀⣠⣴⣶⣿⣿
⠀⠈⠍⠉⠀⠀⢀⡀⠀⠀⠹⢤⡤⠐⠶⠀⠀⠀⠀⠐⠂⠁⠈⠛⠛⠛⠋⠋⠉⠉⠙⠁⠄⠋⠉⠉⠀⠀⠀⣄⠀⠀⠀⠉⠉⠘⠃⠦⡄⣀⠓⣀⣀⠀⡀⠚⠛⠻⠟
⠀⠀⠂⠀⠀⠀⠾⠷⠷⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠐⠀⠀⠠⠀⠀⢸⡇⠔⠉⠀⠀⠀⠀⢸⣆⠀⠀⢻⣿⣷⡞⠀⡀⠀⡄⠀⠀⠈⠘⠫⣏⣿⡟⠥⣐⠢
⠀⠀⠶⠈⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠆⣠⡀⠠⠆⠀⠀⠀⠀⠠⡞⠁⠀⠀⢰⡆⠀⠀⠘⣁⣠⠄⠀⠹⣏⢻⡄⠀⠈⣁⣀⠀⡇⠀⠀⠈⣿⠙⢦⡈⠻⡆
⠀⢀⠰⠉⠉⠉⠛⠛⠋⠢⣀⠀⠀⠀⢀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡀⠀⠙⠀⠀⠈⠛⠻⠆⠀⡀⢳⡄⢹⠀⠐⢉⠛⢡⡾⢢⡄⡀⣿⣆⠈⣿⢆
⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⠈⠻⠉⠶⢈⡷⠀⠀⠀⢀⡈⠂⠀⠀⠉⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠈⢻⡀⢷⡀⠘⠀⢰⢁⠞⠀⡀⣿⣿⠇⡸
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⣤⠀⢠⣴⡛⠀⠀⠀⢀⡈⠤⠈⠀⣤⠐⢤⠀⠠⡌⢧⠘⣧⠄⠀⠘⠁⠀⠀⡟⢃⣸⠀⠙⠁
⠀⠀⠀⠀⠰⠶⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡌⠉⠁⠀⣤⠛⠉⠀⢰⡶⠛⣋⠀⠀⣀⠀⠋⠘⡄⠙⣦⠘⠇⢀⠀⠀⡇⠘⣿⢀⣀⡀
⠀⠴⠂⡀⠀⠀⠀⠀⠀⣉⠉⡁⠲⠦⢤⣴⡦⠴⢦⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⢠⡴⠛⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⣿⠀⢿⡄⠀⠐⠦⣤⡇⠀⢟⠁⠘⠒
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠂⠀⠐⠒⠛⠻⢿⣿⣦⡀⢸⡆⢸⡇⠀⡈⣷⢈⠁⠀⠸⢫⣤⣀
⠀⠀⠀⠀⢀⡀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠠⠄⠲⠾⠟⠛⠛⠿⠿⠿⠿⠿⢿⣶⣌⣿⣷⣸⡇⠀⣷⠀⠄⠀⣀⡀⠐⠛⢣⣈⢏
⠛⠛⠛⠛⠀⠁⠀⠀⠈⠉⠀⠀⠀⠀⠖⣁⠀⠀⣤⣀⠀⠀⠀⠠⣤⡴⠆⠑⠀⢶⠶⣶⣶⣶⣶⣤⣀⣀⣠⣶⣾⣿⣿⣿⣿⡇⠀⢻⣀⡤⠀⠤⠄⣀⠐⢦⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡻⠀⠀⠀⠀⠀⠀⢀⣀⠐⠃⠀⠀⠀⠀⢠⣤⣬⣍⣛⣛⡻⠿⣿⣿⣯⣼⣯⣿⣿⡇⠀⠘⣯⣡⡖⠰⣂⡈⠋
⢀⡔⠂⠀⠘⠋⠀⠀⠀⣀⠀⠠⡚⠡⠘⠃⠀⠀⠀⢀⡤⠲⠹⠅⠀⣤⣤⡄⠄⣰⢆⣀⣩⡍⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠈⡉⠉⠒⠛⢃⣠⣤⣿⣦
⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠙⠋⠉⠁⠀⠉⠈⠉⠋⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠘⠃⠀⠛⠛⠻⠿⠿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡉⣡⣉⢿⡁⣸⠉⣉⣭⠋⣸⣽⠋⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡒⡂⠀⠀⠀⠣⠝⠀⠀⠀⢔⢲⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢠⢄⠀⠈⠀⢀⢤⠀⠀⠀⠀⠤⡀⠀⠁⠀⠤⡄⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠈⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⢤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⢸⡆
⠀⠀⠀⢀⣠⡼⠶⠚⢛⣉⣉⣭⣤⡤⠤⢶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠤⠤⣤⣭⣉⣉⡛⠓⠶⢧⣄⡀
⢀⣴⠞⣉⡤⢶⡞⠋⣉⠭⠋⠁⠀⣀⣀⠈⢆⠀⠀⢀⡀⠀⠀⠀⡇⣀⣀⠀⠉⠙⠬⣉⠙⢳⡶⢤⣍⡳⢦
⣾⡵⠋⠁⠀⢸⠗⠊⠀⠀⠀⠀⠋⠁⠀⠀⠀⠑⠦⡼⠉⠓⠲⠦⠇⠀⠈⠙⠀⠀⠀⠈⠑⠺⡇⠀⠈⠙⢮
⠹⣦⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣴
⠀⠈⠙⠶⢤⣼⠀⠀⠀⠀⠀⠸⠋⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠙⠇⠀⠀⠀⠀⠀⣧⡴⠖⠋
⠀⠀⠀⢀⡞⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢳
⠀⠀⠀⠀⠳⣄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠞
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⠉⠓⠢⠤⠤⠔⠚⠉⠑⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏
⠀⠀⠀⠀⠀⡠⠒⠁⡇⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢸⠈⠒⢄
⢀⡠⠤⠐⠊⠀⣠⠤⣇⢀⡄⠀⠙⢙⠓⠶⠤⠤⣤⣤⣤⡤⠤⠤⠶⠚⡉⠋⠀⢀⡀⣸⠤⣄⠀⠑⠂⠤⢄
⢎⣀⠔⣦⠀⢀⡵⠀⠀⢨⠃⠀⠀⠈⠙⠲⢤⠔⠃⡀⠀⠑⠦⠤⠖⠋⠀⠀⠀⠘⡅⠀⠀⢮⡀⠀⣴⠢⣀
⠀⠑⠊⠘⢤⣈⠆⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠰⣅⡤⠃⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠉⠁⠐⠒⠂⠀⠠⠀⠀⠄⠀⠐⠒⠂⠈⠉⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠒⠒⠒⠶⠃⠘⠖⠒⠒⠒⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠤⠤⠤⡦⠀⠀⢤⠤⠤⠤⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠉⠓⠢⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣶⣶⣶⣟⣻⣿⣿⣏⣀⣀⣹⣿⣿⣟⣿⣶⣶⣶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣆⠀⣠⡄⠀⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⣾⣿⣶⣿⣿⣿⣿⣿⣆⣴⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⠿⠿⢟⣫⣶⣿⣿⣿⢭⣽⣛⡝⠂⠩⣭⣛⡛⠻⠿⠿⠿⢟⣛⣫⣵⣿⠟⣿⡿⢟⡪⣔⣮⠳⢍⡙⠛⢫⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣑⣃⣀⣠⠄⣐⣬⣽⢟⣋⡭⠷⠦⢶⣢⣤⡉⢔⣲⣭⣿⣿⣷⣮⣭⣿⣿⣿⣯⣙⣶⠾⠫⢾⣿⣿⣭⣖⣿⡶⠿⢛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠙⠋⣉⣉⣭⣭⣅⣛⠻⢭⣛⣫⡴⢮⣽⠷⠾⠿⠿⠶⡾⢿⣿⠿⣭⣷⣶⣮⠭⠽⠿⠛⠛⣒⣙⣫⡵⠾⠛⣉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⠻⠷⠶⢖⡫⠽⣛⣴⣬⠭⣿⣛⠤⣶⠾⢝⣟⣭⣝⣿⣿⣾⣷⣽⣍⣋⣙⣀⣈⣊⣛⠽⣵⣒⠴⢞⣋⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⣭⣭⣭⡭⢽⣓⠶⢿⣻⣶⣬⡵⢞⣛⣯⡥⢶⣿⣥⠯⠽⣟⣿⣶⠭⢭⣭⡉⣉⣩⣭⠭⢴⣞⡯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢭⣿⣶⣢⢌⣉⣑⡒⠒⠂⢘⣫⢭⠒⣉⣽⣖⣛⣩⣭⣽⣭⣭⣽⣛⠤⠮⣌⡕⠀⠚⠯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣭⣛⡻⠿⣙⣻⣤⣤⠈⠶⣯⣝⡻⣛⠭⣑⣻⣧⣶⣾⣿⡿⣛⡿⢾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⢿⣤⣞⠿⠯⠉⣭⣯⣿⡶⠾⠧⣬⣽⣿⢥⣼⣟⡻⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠟⠛⢭⡴⣬⠴⠾⠿⠟⠟⠋⠛⠈⠁




⣶⣶⣶⣶⣶⡾⢶⣶⣶⡾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣾⢿⡾⠶⡶⠶⢾⣶⡾⠾⠾⠶⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡉⣉⣶⢤⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠁⠀⠀⠂⠀⠀⠉⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢠⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⢠⠴⠒⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⠒⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣏⠙⠋⠓⠒⠶⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⣠⣤⣴⣶⠾⠛⠋⠉⠙⠿⠿⠟⠛⠛⠉⠙⢿⣿⣦⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⣴⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠞⠉⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⠀⠀⢀⣈⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠰⣏⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠘⠁⠀⠀⠈⠇⠀⠀⠀⠀⠠⢁⠈⠀⠐⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⣀⡄⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣄⣀⠀⠠⠒⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠀⠙⠅⠒⠢⠤⠤⠤⢤⣤⡐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡐⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⢦⠀⠀⠀⠀⢤⠀⠀⢀⡄⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠶⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠈⠳⠀⡀⠂⠀⠀⠀⠁⠈⠣⡬⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⠀⢀⠔⠁⠀⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⠆⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣵⡀⠀⠀⠁⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠈⢂⠀⠀⠇⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠊⠙⢷⣄⠀⢀⠃⠀⢀⣉⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠈⡁⣯⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⣀⠠⠌⠀⠀⠀⡿⢛⠃⠀⠀⠀⡁⠘⠀⢀⠃⠀⠀⠀⠀⠀⢁⠀⠃⢀⠁⢰⡀⠀⢀⡤⠞⠁⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠞⠀⡆⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⡗⠉⠁⠀⠀⠀⠀⠀⠘
⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠓⠀⣀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠾⠀⠀⠀⠀⠈⠑⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡔⠁
⠀⠀⠀⠀⠐⢄⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠀⠀⠀⠀⡇⠈⠉⠉⠛⠛⠛⠒⠒⠒⠒⠓⠒⠚⠋⠉⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢸⡀⠀⠉⠐⠂⠠⠤⠤⠠⠤⠴⢧⠀⠀⠐⠒⠂⠉⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠋⠒⢶⡀⠀⢎⠙⠋⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡈⠐⠒⠀⠁⠃⠰⠈⡀⠀⠀⠀⣐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠑⠴⠤⠆⠘⠁⢸⠀⠁⠈⠙⣀⠈⠁⢠⠄⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠒⠂⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠇⠤⠀⠀⠀⣀⣀⡀⣀⣀⠀⠠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣦⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣶⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡄⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣤⣶⠿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡿⠋⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋
⠀⠀⠀⠀⠀⣄⣋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣁⠀⠀⠀⠀⠀⠀⠀⢀⣸⡋
⠀⠀⠀⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠺⡿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣖⣭⠵⠶⠆⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⡋
⠀⠀⠀⠀⠀⠠⣿⣗⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⣠⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠇
⠀⠀⠀⠀⠀⠠⣴⣦⠁⠀⠀⠀⠀⠀⠀⠀⣴⣷⠍⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⠀⣤⣦⠍
⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⡯⠂⠀⠀⠀⠀⢀⣰⣋⡀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣶⣯⠀⠀⠀⠀⠀⠀⠀⢀⣠⣜⠁⠀⠀⠀⠀⠀⠀⢠⣤⡄⠈⠈⠀⠀⠀⠀⠀⣴⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠟⠓⠀⠀⠀⠀⠀⠀⠀⠈⠟⠏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⣄⠀⣠⣠⣤⡄⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣄⠀⠀⠀⠚⢻⣷⣝⣿⣿⣄⣿⣿⣷⡀
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣷⣿⣿⣿⣷⡄
⠀⠉⠉⠙⢟⣿⣛⣺⣶⣿⣷⡄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣾⡿⣿⣿⣿⣿⣿⣿⣟⣿⡆⠀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡛⢿⣿⣿⣿⣿⣿⡇
⢐⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢠⢻⣿⣿⣿⣿⣿⡟⠛⠁⢠⣽⣯⣭⣿⣿⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡾⢿⡿⠷⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⢹⣿⣿⡦⢉⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠛⠛⠋⠀⣻⣿⣿⣿⡄⠀⠀⠀⠀⢠⣧⡤⢻⡀⢈⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣿⣘⣧⣸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⡿⡇⠘⡇⢸⣿⣿⣿⣿
⠀⠀⠀⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡜⠀⣿⣿⣿⠋⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⡇⡇⠀⢣⣸⣿⣿⣿⣿
⠀⠀⠀⡜⠀⡇⢷⠈⠋⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢠⠁⢀⣿⣿⠋⠇⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⡍⣙⠁⠀⠈⣿⣿⡟⢿⣿⡄
⠀⠀⡼⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⢸⣿⡿⠀⢡⡀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠈⢿⣿⠀⠀⠀⠀⠈⠁⠋⠀⠀⠀⢹⣿⡇⠸⣿⣧
⠀⡸⠃⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⠀⠁⠀⣾⣿⠃⡄⠈⡀⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠸⣿⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿
⢠⠃⠀⠀⠀⠀⠀⢾⣿⣿⠿⣿⣿⣯⠩⣿⠇⠀⠀⣴⠀⢀⣿⣿⢾⣁⠀⢡⠀⠸⣿⣇⠀⠀⠀⠀⣠⣼⣿⡇⠀⠀⣿⣧⠀⠀⢠⠇⢠⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠘⠤⣶⠿⠟⠉⠀⠀⠀⠀⠀⠉⠀⠙⠿⠇⠀⠀⠉⠙⠀⠀⢻⡿⠃⠀⠀⠀⠈⠉⠉⠁⢠⣾⠿⠿⠀⠀⠈⠃⢺⠶⠂⠠⠶⠾⠿⠇⠘⠛⠛



⠀⢀⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⣰⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⠀⢀⣀⡀
⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣽⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⢀⡀⠀⢀⣶⣿⣷⡀⠀⠀⠀⢠⡤⠶⠶⠶⣿⣏⣿⣿⣿⣷⣆
⠠⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣘⣷⣾⣯⡿⣿⣿⣷⣤⣄⠀⠀⢰⣶⣾⣷⣾⣿⣿⣿⣿⣿⡏
⢰⣿⣿⣿⣿⣆⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠛⢛⣿⡿⠃⣼⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣾⣿⣿⣿⣿⠉⠁
⠀⠹⣿⣿⣿⣿⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡝⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠠⣹⣿⣿⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⣿⣿⡿
⠀⢀⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣯⣤⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⣽⣿⣿⣿⡇
⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣼⠏⠩⡉⠉⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠺⡟⢻⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢇⣸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢠⡄⢸⣿⣿⡇⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⢈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⡄⠀⠀⠀⢸⠃⠀⠀⣸⣿⣿⠃⢿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⠀⠀⠀⢿⠀⠀⠀⣿⣿⡇⠀⠘⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⣧
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⣀⣀⣴⣿⡇⢸⣿⡇⠀⢀⡟⠀⠀⠀⣿⣿⠇⠀⠀⢻⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠻⠿⠿⠿⠗⠀⠘⠧⢄⡀⠀⣿⣿⢀⡆⠘⠿⣿⡆⠀⠀⠀⠀⣿⡏⣸⣿⡄
⠀⢸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠚⢷⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠘⠀⢿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆⣤⣤⠐⣲⡿⠁⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⣀⠀⢸⣷⣮⣿⡯⣹⠋⠀⢀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠈⣿⣾⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠢⡤⡘⣿⣿⣷⣌⢻⣿⣿⢽⢿⣤⣌⠁⣈⡿⠆⠀⠀⠀⢨⠁⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣫⡿⣿⣿⣷⣿⣿⡅⠁⠉⠉⠉⠉⠉⠉⠁⠀⠈⢸⠳⢴⢃⡘⠈⠻⠋⠑⠉⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⣿⠟⠉⠓⠒⣲⠖⠒⠒⠒⠒⠲⡖⠒⠚⠢⡀⠙⠷⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⢀⡴⠞⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⢄⣀⢝⢶⣫⣤⣾⣿⣶⣤⣤⢀⠀⢀⠀⢀⠙⢦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⣿⣿⣿⣿⣿⡇⠄⣩⣵⣶⢻⣻⣷⣾⢣⣿⣿⣿⣷⣷⣷⣷⣾⡏⣽⣿⣶⡆⣴⠀⡦⢤⡄⢠⡶⠀⠀⠀⡀⠀⠘⢿
⣿⣿⣿⣿⣿⣿⣿⣛⠿⠟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⠁⠺⠦⠻⣅⠠⠔⠈⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢒⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠤⠤⠤⠀⣑⡉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢂⠀⠀⠀⢀⢀⣒⠒⠀⠩⠝⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡈⢀⡆⠀⠀⠀⠄⠒⠤⢌⡹⠐⠠⣀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⡟⠁⢀⠀⠀⠀⠐⠆⠀⠀⢣⡠⠦⡀⠑⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠈⠀⠀⠀⠀⢀⡀⠀⠈⢑⣁⠆⡠⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣄⠀⠀⠰⡶⠂⠉⡇⠀⣤⣡⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠓⠢⠤⣬⠭⠍⢀⣠⠖⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⡤⡔⣤⡠⡗⠋⢹⠿⠡⠤⢄⠀⠀⡿⡐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢮⠠⡢⣱⣱⠟⠈⠙⠉⠓⠬⠼⣁⠁⠢⡑⡜⠀⠘⡁⠂⢭⡲⡤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⢻⣦⢱⡞⠓⣬⡙⡉⢆⠀⠀⠀⠀⠀⢀⢴⣟⠀⠀⠀⣎⡱⠁⢰⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡹⠞⣧⣀⢹⣧⠛⢾⣉⣉⣹⠟⠉⠁⢁⠶⠬⣔⣒⡤⣷⣀⠇⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡲⠾⠌⢉⠉⠑⠢⣄⠀⠀⠀⠀⠁⠈⢹⠒⢇⣂⣀⠠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⠤⣀⠀⠑⢄⠀⠀⠑⢦⣀⣀⣀⣀⡸⠶⢶⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠊⢐⠢⡀⠱⡀⠈⣆⠀⠀⠀⣀⠤⠋⢄⠐⠁⣸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣀⠀⠉⢦⢄⣊⢠⣀⠌⢼⡴⠧⠊⠑⢌⠉⠀⠀⠀⡁⢸⣴⢾⣟⠓⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠳⢦⡈⠛⣧⡰⠃⡠⠊⠀⠀⠀⠀⠀⠉⠒⠒⠒⠧⠊⢹⠟⠉⠻⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⠻⣄⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣉⣈⡳⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⣄⣀⠀⠀⠀⣀⡴⠚⠋⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠉⠳⣄⡴⠃⠀⠀⣀⣤⣄⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡴⠚⠓⢦⠀⠀⠙⠁⠀⢠⡞⠁⠀⠀⠹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⣇⠀⠀⣸⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⠇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠁⠀⠀⣼⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⣴⣶⣶⣦⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⡇⢀⣀⣀⣀⡀⣠⠞⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴⠋⠉⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⣄⠀⠀⡇⢸⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠟⠀⠀⡇⢸⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⡇⢸⠀⠀⢸⡇⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢧⡀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣀⡿⠀⠀⡇⠘⠒⠒⠚⠃⠻⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷⠀⠀⠀⠀⢰⡛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡀⢀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣸⡇⢸⣷⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⠃⡇⢸⡇⢧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⠇⠀⡇⢸⡇⠈⢧⠈⣇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠏⠀⠀⡇⢸⡇⠀⠘⣇⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡏⠀⠀⠀⡇⢸⡇⠀⠀⠘⣆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⡞⠀⠀⠀⠀⣧⣸⡇⠀⠀⠀⠹⣄⣹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⡉⣩⡦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⡁⠋⠀⠀⠀⠰⡄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠠⠁⠀⠀⢀⣀⣀⠨⠤⠤⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠤⠘⠂⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠉⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣀⡒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⢀⣀⣠⣤⠤⠶⠖⠚⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣠⠴⠖⠛⠉⠩⡄⠀⠀⠀⠀⠀⠀⠀⢀⠲⣦⣀⠀⣦⡈⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠉⡽⠟⠾⠋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⣠⡄⠀⢀⣠⡄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣦⠖⠛⠈⠓⠦⡀⠐⠟⠀⠀⠠⠀⠙⠁⠐⠀⠛⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⢲⣄⠀⠉⠀⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⣀⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣦⣄⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢿⣿⡿⠿⣿⡿⠿⢇⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠁⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠫⡓⠢⠤⣈⡀⠀⠀⠀⠀⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣀⠀⠈⠀⠀⠀⠀⠀⠀⠜⢡⠶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡤⠚⠁⠀⠀⠀⠀⠈⢆⠀⠀⠠⠚⢃⠀⢠⠚⢧⡀⢸⠀⠀⠀⠀⠀⠀⠀⠔⠃⠘⠢⡀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠸⡀⠀⠀⠀⢀⠄⠀⠀⠀⠓⢴⠂⠀⠘⡤⠁⠀⠀⠙⣎⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡃⢀⡶⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠑⢄⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⡠⠀⠀⠑⠦⠐⠁⢪⡄⠤⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⠀⡜⠁⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⡆⠰⠀⠉⠀⠀⠀⡀⠀⠀⠀⠸⣅⢀⠔
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠱⣄⠀⠀⠀⠀⠌⠀⠀⠙⣷⣄⡜⠀⠀⠰⠤⢴⣄⠀⡸⠀⠀⠀⠀⠀⢣⠀⢀⡦⠠⠄⢡⠀⠀⠀⠀⢀⡼⠉⠢⠤⠤⠔⠉
⠀⠀⠀⠀⠐⠀⡀⠃⠀⠀⠀⠈⠣⡄⠐⠚⠀⠀⠀⣠⠏⢰⠁⠀⠀⠀⠡⢀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠠⠀⡅⠄⠀⢸⣀⣀⡤⠚⠁
⡀⠀⠀⠁⠀⠀⠀⠀⠰⠀⢀⠔⠈⠠⠀⠀⠀⠀⠘⢃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠈⠀⢀⡄⠀⠂⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠂⠐⠀⠀⠀⠈⡄⠀⠈⠛⢄⣰⠀⠀⢸⠉⠂⠴⠹⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⢄⠀⠀⠀⠃⡄⠐⠀⠀⠀⠱⠒⠋⠀⠀⠀⠀⠃⠈⡿⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠁⠀⣀⣀⡠⠤⠲⡏
⠀⠀⠀⠀⠀⠳⠀⡠⠀⠀⠀⠀⠀⠀⡈⠋⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⠀⠀⠘⠀⠀⠀⢀⠌⠀⠀⠀⢰⠀⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢇⡀⠀⠀⢀⠌⠀⠀⠀⠀⠸⡀⠀⠀⠁⠐⠂⠠⠤⠤⠤⠀⠛⡆⠒⠒⠂⠀⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣤⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡛⠛⠛⢻⢦⠀⠸⡉⠛⠉⠈⠩⢇⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡌⠁⠘⠂⠈⣰⠀⢦⣈⠀⡀⠀⢠⣜⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠛⠀⠆⠂⠓⠉⠰⣇⠀⠉⠉⠏⡀⠀⠀⡢⠄⠒⠒⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠐⠢⡁⢀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠁⠎⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠠⠤⠤⠤⠤⠤⠀⠀⠂⠀⠒⠂⡀⣉⠀⠀⠃⠂⠠⠤⠀⠀⠄⠀⠤⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡬⠩⠖⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⢀⣀⣀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡠⠀⠂⠒⠉⠁⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠂⠀⠀⢀⣀⣀⡀⠀⠤⠤⣤⣤⣬⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠈⠁⠐⠨⠄⠠⡂⢄⠠⢄⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⡄⠀⠀⠀⣀⣀⠠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⣍⠛⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⡁⠀⠀⢀⠄⠀⠑⢤⠈⠀⢠⠂⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠈⠄⡤⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣇⠀⠐⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠠⠀⠈⠂⠂⠀⠤
⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠘⠻⣦⡀⡰⠀⢀⠁⠀⠀⡀⠀⠀⠀⠄⠀⢀⢀⢫⠀⠀⠀⢀⡴⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠂⠀⠀⡼⢫⠁⠀⠀⢀⠁⠠⠁⠀⠀⠀⠈⠀⠁⠀⠈⣄⣠⠔⠋
⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⠀⢀⠀⠀⠀⠀⠀⠄⢀⠀⠀⡓⢀⡰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⢄⠀⠀⠀⠀⠀⢉⢠⡜⠁⠀⠀⠊⢙⠂⠂⠤⠄⣀⣀⠀⠀⡀⣀⣀⠤⠔⡖⠁
⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠸⠀⠁⠂⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⣀⡀⠀⢸⣤⡠⡤⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠣⠀⠀⠛⠄⡐⠈⠐⠐⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠢⠀⠤⠘⠠⢉⠁⠒⢂⠙⠂⠤⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠂⡠⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠃⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠐⠂⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠠⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢅⠀⠐⠀⠀⠀⡀⠀⠔⢀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠢⠀⠀⠀⠀⠀⢀⠘⢀⠀⠀⠀⠐⠁⠠⡀⠀⠄⠐⠠⢄⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠄⠀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠑⣀⠌⠀⠀⠀⠈⢀⣤⣴⣶⣶⣿⡿⣷⣶⡶⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠴⠶⠿⠟⠻⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⡿⠷⠿⠿⠿⠷⠤⠄⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⡐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⢀⠀⠀⠀⢀⣀⠀⢀⠀⠀⠀⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⡏⠙⣷⢸⣷⠀⡖⣿⠁⢠⣿⡇⠀⡦⠉⣿⠁⣾⡇⠀⣸⣼⣿⠉⢷⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣷⠀⣿⠈⣿⣴⠇⣿⠀⢸⣿⣿⢸⠇⠀⣿⠀⣿⡇⢀⡇⣿⣿⣠⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⣿⢸⣿⢀⡟⠀⢻⣿⠀⣿⠖⢸⡏⢻⣿⠀⠀⣿⠀⢻⣧⡾⠁⢿⣿⠻⡄⢸⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠋⠉⠀⠀⠈⠉⠀⠙⠃⠈⠁⠈⠁⠀⠀⠉⠀⠈⠉⠁⠀⠈⠁⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⣀⣀⣀⠀⠔⢢⠀⠀⣀⠔⠂⠀⡃⠀⠠⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠈⠑⠑⠀⠁⠊⠁⠀⠊⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠠⠐⠒⠒⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠈⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡠⣶⣤⠀⠀⢸⣿⠃⠀⣠⠚⣿⣿⣦⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣷⣿⣿⣧⠀⢸⣿⡄⠀⢾⣨⣿⣿⣿⡇⣨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣿⣿⣾⣿⣆⣿⣿⣷⠀⠈⠻⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣿⣟⣁⡀
⠀⠀⣤⣤⡀⠀⠀⠀⠀⢀⣿⣻⣿⣹⣿⣿⣭⣭⣭⣭⣽⣯⣽⣯⣍⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⢀⣀⣀
⠀⢠⣤⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣇⣿⣏⣿⣿⣿⡯⣯⣠⣏⣻⣿⣿⣿⣿⢿⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠈⠻⠟⠁⠈⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣞⣿⣿⣿⣿⡿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⣿⣾⣿⡿⢿⣿⣿⠿⠿⠿⠿⠿⢇⣿⣿⣿⣿⣿⣿⣿⡇⠸⣾⣀⣙⣻⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡝⠷⠮⠉⠉⠙⢷⣤⠀⠸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡿⣿⣿⣿⣾⡏⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⠘⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠠⠆⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡿⠛⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀
⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣼⣿⣿⣶
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠛⠛⠋⠉⠉
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣿⣿⣿⡿⠁⡰⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿
⠸⣿⣷⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⡰⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⣿⡇
⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⣹⣿⣿⣧⡀⠀⠀⢸⣿⠇
⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠛⠁⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⣼⣿⣿⢿⣿⣷⡄⠀⢸⣿
⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⢤⣀⡀⠐⠛⠛⠋⠉⣉⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⣴⣿⣿⣿⠋⠀⠹⣿⣿⣆⣿⡏
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⣈⠑⠪⠍⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠒⢉⣠⣶⣿⣿⣿⠟⠁⠀⠀⠀⠈⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣦⣤⣄⣉⣀⡐⠒⠒⠒⢂⣈⣉⣠⣤⣶⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡛⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠆⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀⠉⠛⠛⠻⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠂⠀⣤⡀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⢀⡀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠾⠿⠛⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢉⣤⠖⠂⣀⡀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠶⠖⠀⠀⠀⠲⣶⡶⠈⠀⠀⠀⠀⠉⠲⣆⡈⠙⠶⢀⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠎⠉⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠀⠈⠙⠦⣀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠁⠀⢀⣀⠀⠀⠀⢀⡀⠴⠶⠟⠀⠀⠀⣀⡀⢶⣦⡀⠀⢀⠀⠿⣆⡀⠀⠀⠈⠁⠀⠘⡿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⣠⠶⠈⠉⠁⣀⠀⠀⠈⠉⠐⢶⣦⠉⠁⠀⣶⠀⢀⡠⠶⠉⠠⣄⡈⠉⠙⠛⠷⣦⠈⠣⡄⠀⠀⠀⠀⠐⣶⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣰⠞⠁⣠⣴⠆⠈⠉⠙⠿⠟⠀⢦⡀⠉⠢⣀⠀⢰⡶⠈⠁⣠⣾⠷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⢀⡘⠁⢠⡄⠛⠃⢠⡞⠉⢀⣀⣀⣀⠀⠈⠣⡀⠉⣠⠀⠀⠀⠀⠛⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠸⠃⢀⡄⠀⠀⠀⠈⠁⣰⡿⠿⡿⠿⣷⣦⠀⠋⠀⠸⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠸⢿⡀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⠀⢸⡇⠀⠀⠀⠀⠀⠏⠀⡄⠀⣀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠁⠀⣰⣶⡟⢿⡆⠀⠀⠠⡇⠀⢃⡀⠀⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠈⠁⠀⠀⠆⠀⠀⠀⠠⣇⡈⠻⣿⡿⢿⡟⠀⢀⠀⠀⠀⠀⠠⠀⠀⢠⠈⢿⣿⣿⠇⣸⡇⠀⠀⠀⠃⠀⠈⢳⡤⠙⠋⠙⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠘⢷⣆⠀⠀⠀⠀⠀⠘⠛⠀⠈⠁⡦⠁⢀⠛⠀⠀⠀⠀⠀⠀⠀⠛⠓⢠⣤⣄⠘⠋⠀⠀⠀⡀⠀⢀⡼⠋⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡜⠛⠻⣷⣄⠀⠙⠃⣤⣄⠀⠀⠀⣠⣤⠐⠁⢀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡄⠋⠀⣀⡞⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡈⠀⠈⠙⠂⣀⣀⠙⠿⣦⣤⠀⠀⠀⠀⠀⠀⢀⣤⡴⠛⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⡦⠀⠀⢀⠟
⠀⠀⠀⠀⣠⠞⠛⠓⠀⣀⠀⠀⠀⠙⢣⡀⠘⠏⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟
⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠻⢧⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠐⢶⣿⣇⣀⣴⠃⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢀⣤⡴⠟⠁
⠀⠀⠀⢾⠁⠀⠀⠒⢀⣤⡀⠀⠀⢠⡶⠂⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⢀⣀⡀⠘⠒⠀⠀⢀⡹⠃⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠈⠁
⠀⠀⠀⠀⣶⣄⡀⠀⠀⠉⠳⢄⣀⣼⣧⣤⠾⠉⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠛⠁⢀⣀⡀⠶⠋⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⣀⡀⠀⢀⠿⣦⣀⠈⠉⠹⠏⠁⠀⠀⠀⠀⠉⠷⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠀⣀⡴⠾⠋⠁
⠀⠀⠀⠀⣉⠓⠲⠿⠆⠉⠉⣀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠶⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠊⠉⠁
⠀⠀⠀⢀⡟⠀⠀⠀⢀⡶⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⣶⠖⠒⠀⠈⠉⢻⠃
⠀⠀⠀⡿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡶⠆⣀⠀⠀⠀⠀⠀⢿⣶⡶⠦⣀⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠶⢶⣾⠋⠀⠿⣀⠀⠿⠀⠀⠀⠀⡀⠼⠋⠀⠀⠉⣿⣇⡀
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠀⠉⠉⠀⠀⠀⠛⡀⠀⠀⠙⠿⠀⠀⢠⡴⠈⠉⠀⠀⠀⢠⠚⠁⠉⠉⠲⣦
⡀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣴⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠷⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣧⠀⣾⠀⠀⠀⠀⠺⠀⠀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠙⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯
⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠳⣤
⠀⠈⢷⣤⡀⢀⣤⣤⣤⡤⠔⠛⠛⠛⠻⠇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠛⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⡘⠋⠀⠀⢀⡴⠛⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡼⠟⢀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡴⠋⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⡀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⠀⣀⣀⠀⠀⠲⠶⠖⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠲⠶⣶⣄⠘⢧⡴⠃⠀⠀⠀⠀⢀⣀⠴⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⡊⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣏⠰⠎⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠶⠶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠰⢿⡟⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠶⠂⠀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣶⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⢠⣿⠀⠀⣶⠀⠀⢀⣀⣠⣄⡀⠲⠾⢿⡟⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠈⠉⠁⠀⠙⡿⠁⠀⠁⠀⠀⠛⠓⠺⣿⠁⠉⠁⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⣇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣿⠟⠁⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢾⣿⡷⢠⣤⠄⠈⠋⠀⣿⠀⠀⠀⠀⠀⠀⣤⡴⣿⡦⠤⠄⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠀⠀⢀⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢈⣤⠀⠀⠀⠀⢀⠘⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢘⣇⠀⢀⣤⡞⠛⢷⠀⠀⠀⠀⣴⠛⠛⠁⠀⠀⠀⠛⢃⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠻⠧⣤⣤⠀⠀⣘⠛⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⣠⣼⣇⡀⢠⣄⣴⣶⡀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠉⠉⠉⠙⠓⠀⡀⠀⠀⠻⠿⠶⠟⠛⠛⠻⣿⠁⠀⠀⠀⠀⠀⠉⣿⠟⠓⠀⠀⠀⠀⠙⠃⢀⠙⠋⠁⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⣿⡄⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠒⠾⠛⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⣀⣀⣀⣤⣄⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠲⠖⠘⠛
⠀⠀⠀⠀⢿⣇⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠴⠶⠶⠖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⢦⣀⡀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣠⡿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠆⠀⣀⣀⣀⣀⣀⣀⣀⡀⠰⠶⠖⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣇⣦⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣯⣼⣿⣿⡷⣄⡘⣦⠻⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢻⢿⣿⣿⣿⣡⡱⣾⡝⢦⡈⠛⠛⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠈⠫⠳⣄⠻⢿⣿⣝⣾⣿⣷⠙⠲⣴⣷⣦⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⣛⠛⠛⠉⣠⣴⣾⣰⣤⡴⠶⣤⣀⠀⠉⠛⠿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣿⣿⣿⣿⡿⡋⣠⣦⡈⡛⠿⣷⣾⣴⣴⣴⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⢀⣀⣀⣀⣀⡀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠘⠛⠛⠛⠛⠃⠻⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⣠⣶⣶⣶⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣈⣛⣛⣛⣛⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠋⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⠄⣠⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣤⡈⣿⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⠸⣿⣿⣿⣭⣭⣽⣯⣭⣭⣿⣿⣦⣬⣴⣿⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⡿⠉⠉⠀⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣠⠙⠿⠿⠋⣠
⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⢿⣿⡿⢁⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⣶⣶⠀⣿⣇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡙⠁⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⣿⣿⠀⠹⣿⡆
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡉⠀⠀⣿⣿⠀⠀⢹⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⢻⣿⡀
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⣿⣿⠀⠀⠀⠈⢿⣷
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⣿⣧
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠸⣿⣇
⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠾⠿⠛⠛⠛⠿⠿⠷⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠋⠁⠀⠀⠠⠐⠆⠀⠀⠀⠠⠒⠄⠀⠉⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠛⡙⠂⠀⠀⠀⠈⠀⠀⢀⡀⠀⠉⠀⢀⠔⢆⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠤⠀⠀⠀⠀⠔⣱⠆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠐⠀⢀⣀⣠⣤⣤⣤⣶⣶⡾⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⣿⣿⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣀⣤⣴⡶⠾⠿⠛⠛⠉⠉⠁⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡈⠉⠛⠻⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠋⠉⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣶⣤⣄⡉⠻⣷⡄
⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠉⠻⢷⣌⣿⡆
⠀⠀⢀⣴⡿⠋⣁⣤⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⡿
⠀⢠⡿⠋⣠⡾⠟⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣾⠇
⢠⣿⣡⡾⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠀⠀⣴⡿⠃
⠸⣿⡟⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠂⢻⣏⣀
⠀⠹⣷⣄⡴⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⣼⣿⣿⣧
⠀⣴⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠉⠈⠙⠻⠟⠁
⠀⠘⠛⠛⠛⠓⢛⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢶⡀⠀⠀⠀⠀⣿⣿⣿⠟⠓⣄
⠀⠀⠀⠀⢠⡶⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⡟⠀⠀⠀⠀⣿⣿⣇⣀⣾⣿⣷
⠀⠀⢀⣶⣿⣧⠀⢹⡟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⠇⠀⠀⠀⢀⣿⠃⠀⠙⠿⣿⡿
⠀⠀⠸⣿⣿⡿⠛⠋⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣤⡀⠀⠀⠀⠀⣠⣤⠞⠋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠔⠛⠉⠛⠛⠿⢷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠟⠻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⡁⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀⠉⠉⠉⢉⣹⡟⠉⠹⣧⣤⣤⣾⡇⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠁⠀⣸⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠐⠀⠐⠀⠀⠀⢻⣧⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣴⠞⠛⠉⠙⠛⢺⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡁⠉⢷⡄
⠀⠀⠀⠀⠀⠀⣰⠟⠀⣠⡾⠁⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⢀⡀⠀⡀⠀⠘⠀⠀⠀⢹⣟⠱⣦⠀⠙⠶⣄⣀
⠀⠀⠀⠀⣀⡶⠏⢀⣴⠟⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠠⠤⠠⠀⠤⠀⠤⠤⡄⠀⠀⢀⡄⠀⠀⠀⠈⣿⡄⠈⠛⠶⣄⣀⠉⠛⠦⣄⣀
⠀⠀⣴⠟⠉⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠈⠉⠳⢦⣤⡈⠉⠉⠛⠷⣦⡀
⣀⡼⠃⠀⡀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠂⠀⠀⠀⡁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠛⠶
⢻⣤⣤⡾⠻⣦⣼⠃⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢠⡾⠿⣶⣶
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠂⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠙⠛⠻⢿⣆⠀⠀⠀⠀⠀⢀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣀⡀⠂⠠⠈⣿⣧⠀⠀⠠⠀⢀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠻⢷⣦⣤⣽⣿⣷⣀⣠⣾⠟⠋⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠀⢀⣼⠏⠙⠋⠀⠻⠟⠛⢷⡄⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠁⢀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⡋⠉⠁⢀⣠⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣶⣤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⣿⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⡾⣿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⢻⡟⠉⠉⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⣿⣿⣳⣝⢛⡿⣿⣟⣻⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢋⣷⣿⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣻⠿⣗⣙⠿⢹⣷⢿⣳⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⣼⢿⣟⡥⠖⠋⠁⠈⢻⣿⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣟⠿⡿⣿⣿⡿⢾⣿⠿⢿⣟⣿⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣴⡧⣫⣵⣿⣤⣤⣤⡰⣿⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⡻⣿⠿⣺⣫⣾⣿⣿⣨⣭⣽⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣿⣿⢛⡿⣿⣿⣾⣿⣿⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠾⢿⣟⣿⣽⣿⣿⣿⣿⠱⢟⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠉⠘⠛⠛⠛⠛⠏




⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⣠⡆⠀⠀⢠⣴⡆⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠻⡆⠀⠀⠘⢿⡇⠀⠀⠿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⢶⣻⣿⣿⢶⣶⣶⣶⠀⣶⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣳⣿⠻⣿⣿⣷⣽⣿⡿⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣙⣀⠀⣀⣤⣴⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢫⣾⣿⣾⣿⣿⢻⣿⣷⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣵⣟⣿⣭⣭⣟⣾⡍⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣹⣟⣛⣿⣱⣾⣿⡯⠀⠀⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣿⣿⣿⡯⣽⣷⣻⣝⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣗⣹⣯⣅⣛⣼⣿⣼⢟⣻⣟⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣿⣮⣾⣿⣿⢸⣷⣿⣯⣟⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢩⣿⢿⣿⣿⣿⣹⣿⣿⣿⣗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣻⢿⡿⣿⢿⣻⢟⣾⣟⣻⣵⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣾⡷⣿⣿⣿⠿⣻⣾⣛⣻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠑⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠏⢹⡀
⠀⠀⠀⠀⠸⡟⠁⠓⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠉⠁⠀⠈⠓⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠰⠗⠢⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠦⠎⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠷⠶⠚⠶⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⢠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡇⠀⠀⠀⠀⠛⠉⠉⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠴⠛⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⠤⠤⠤⣤⣤⣤⡴⠋⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⣨⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠛⠳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⠀⢀⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⢀⣀⡤⠴⠒⠉⠉⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⢀⡠⠔⠚⠉⠀⠀⠀⣀⣀⡠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣠⠔⠊⠁⠀⢀⣠⠤⠖⠚⠉⠁⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡠⠖⠉⠀⣀⠤⠖⠋⢁⣀⡠⠤⠖⠒⠛⠉⢹⠏⢀⣀⣠⡤⠶⠞⠛⠳⣄⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠔⠋⢀⡤⠖⠋⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡠⠞⢁⡤⠚⣁⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼⡇
⠀⠀⠀⠀⠀⠀⢀⠜⡡⢊⡠⢚⡡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣠⣫⢊⢔⡫⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢣⡀
⠀⠀⠀⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠜⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣀⢠⠟⠁
⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⡬⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙
⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠲⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠠⠒⠶⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠀⠀⠀⠀⠀⠀⢀⣵⡼⣶⣿⠀⠀⠀⣤⣤⣀⣀⣀⣄⣀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠒⠲⠶⣾⢟⢭⣴⣶⣿⣏⠁⠒⢶⡟⠀⡫⠅⠉⠛⡶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢉⠃⣾⣿⠟⠙⠓⠈⠐⢄⢻⡄⠋⠀⠀⠘⠞⣦⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠂⢀⣒⣤⣄⡌⢠⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡷⡀⢰⠚⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣉⡠⠤⠐⠛⡭⡙⢀⢎⠎⠀⣦⡀⠀⠀⠀⣼⡟⠛⢻⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⠴⣻⣿⠀⠀⠀⠀⢠⠁⣌⠃⠀⠀⠈⢿⣄⠀⠀⠙⠇⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⠁⡀⣿⡏⣀⠄⠀⠀⣼⡞⣤⡴⠈⡲⢟⣛⠿⠄⠐⢲⣾⢎
⠀⠀⠀⠀⠀⠀⠀⣿⢀⠇⠀⢸⣿⠏⢁⣀⢠⣤⡿⣿⠩⠔⠁⠀⠉⠉⠀⢢⣄⠀⢧⠸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⣼⣿⠟⠉⠀⠀⠹⢷⡝⣥⠀⠀⠀⢠⣦⠚⠀⠹⣄⠀⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡀⢠⢊⠄⢀⠀⠀⡅⡟⠂⠀⠀⢹⠏⠀⠀⠀⢻⣷⠀⠀⠀⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣿⣿⣧⣤⠁⣠⠎⠀⠀⠀⠀⣤⣼⠿⣦⣀⡀⠀⠈⠓⠤⣀⠀⠀⠉⠻⢶⣖⡈⠒⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢝⠻⣧⣾⣧⣄⣀⣀⢀⣀⠿⢏⡀⠈⠓⢮⣳⠶⢤⣀⠀⠈⠁⠒⠢⢤⣈⠻⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡉⠀⠀⠀⢘⣶⣦⣴⡞⠁⠀⠀⢀⡞⠀⠀⠀⣽⢧⠀⠀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠐⣹⢿⡇⣿⣷⡄⣀⣴⣿⣡⣤⣴⠤⠉⣸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠟⡘⠻⢿⣿⢀⠏⠈⠓⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠃⠇⠀⠀⠈⠁⠀⠀⢶⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟⢿⡟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⡾⢧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡿⢄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠠⣷⣤⣤⣤⣦⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠉⠩⠁⢀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠐⣀⣡⢴⠶⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠒⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡿⣷⢸⠀⠀⠈⠹⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⢠⠆⢀⣀⣀⣴⢨⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠛⠛⠛⠛⠋⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠘⠿⠷⢖⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣂⣈⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠁

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣀⣿⣷⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⢿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣿⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡉⣽⠦⠤⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠡⠁⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⣁⣠⡤⠤⠐⠒⠒⠒⠒⠺⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠴⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠉⠀⢀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣖⠒⠒⠒⠺⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⣴⣶⡾⠛⠋⠉⠉⠛⠛⠛⠋⠉⠈⠻⣿⣆⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣁⠴⠚⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⢙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠠⣏⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠃⠈⠈⠋⠀⠀⠘⡆⠀⠀⠀⠀⡀⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⣷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠁⠀⠀⠀⠀⣅⡀⠀⠀⣀⡀⠀⠀⠀⠀⣾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠹⠿⠿⠆⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⣄⠀⠀⠀⠀⠈⠁⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠃⠈⠈⠑⠒⠢⠶⠶⢖⣋⠁⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠊⠀⠀⠀⠘⢄⠀⢀⠐⡆⠀⠔⢤⠀⡀⠀⠀⠀⠀⢀⠄⠐⠛⢟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢁⠀⠀⠀⡀⠀⠀⠈⠰⠆⠀⠰⠄⠀⠀⠹⡅⠀⠀⠀⠀⠆⠀⣄⣀⣨⠁⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠑⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⡀⠄⠣⠀⠈⠉⠁⠀⢈
⠀⠀⠀⠀⠠⠂⠀⠘⢆⠀⠀⠀⢀⠈⠙⢷⣄⢀⠂⠀⣨⢉⡀⠀⡒⠀⠀⠀⠐⡂⢀⡈⡩⢹⠀⠀⠀⠀⡤⡄⠀⢠⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠳⣄⠀⠂⠀⠀⣠⠋⠏⠀⠀⠀⠀⡃⠀⠁⠀⠀⠀⠀⠁⠈⠥⠀⢸⣀⣠⠔⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⡀⠃
⠈⢄⠀⠀⠀⠀⠀⠀⠅⡄⠀⠀⠀⡴⢄⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⡀⠀⠀⠀⡀⠀⠈⠉⢠⠴⠓⠀⠉⠘⠑⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡔⠂
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢁⠀⠉⠉⠉⠛⠛⠓⠒⠚⠚⠉⠉⠀⢠⠃
⠀⠀⠀⠀⠀⠈⠒⠄⢀⠀⠁⠀⠀⡐⠀⠀⠀⡆⠘⠄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠠⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠳⢄⠀⠀⠈⠁⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠒⠲⢦⡀⠸⠳⢖⠚⢻⣋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠁⠐⠂⢉⡃⡦⢁⣀⢀⠠⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠈⠁⠁⠉⠉⠀⠣⡀⠀⠉⠄⡀⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠈⠢⡔⠈⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⣠⣴⠞⠋⠁⠀⠀⢀⡤⠊⠀⠀⠄⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⡴⠞⠋⠉⣴⣷⡶⠟⠉⠀⢀⡠⠒⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠺⣿⣿⠋⠁⠀⠀⠀⠀⠘⠉⠃⣠⡴⠞⢉⡤⠞⣁⠄⠀⠀⠠⣷⡆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⣀⣤⣶⠟⡉⣠⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⠾⣿⣿⡋⠀⠐⡿⠏⣠⠞⠁⠀⠀⠂
⠀⠀⠀⠀⠀⢲⣶⣶⣿⣧⣀⠀⠋⠀⠁⠀⢀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠋⠀⢰⣄⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠘⠋⠉⠻⣿⠀⠀⠰⢿⣿⣿⡄⠀⠀⠀⢀⠠⠀⠀⠀⢾⢿⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣟⢿⠿⢿⣿⠻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣿⠁⠩⡿⠸⣷⢺⢴⣎⢿⡣⢶⡜⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⣻⡷⡇⣨⣤⣥⡖⣿⣷⣷⣿⣧⣵⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣻⣿⣿⣯⣿⣿⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣯⣿⣿⡿⢿⣿⣿⣿⡏⠁⠀⠀⠀⡠⠤⣤⣽⣿⣿⣿⢧⡤⠤⠴⠶⠒⠒⠿⠛⠅⠀⠀⠘⡆⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡏⠀⢢⠈⢻⣿⡄⠀⠀⠀⠀⠠⢾⠉⠙⣽⡅⠠⠠⠀⠀⠀⠀⠀⠂⠒⣋⡑⠀⠂⠒⣟⡓
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣿⣿⣿⣿⣷⡀⢘⡄⠀⠻⡷⠀⠀⠀⠀⠀⠈⠿⠟⠿⡷⠶⠶⣤⣤⣤⣤⣤⣶⣾⣰⣇⣀⣀⣀⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣌⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣈⠄⠀⢸⡇⠀⠈⠉⠉⠛⠛⠛⠛⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⡀⢀⡴⠋⠉⢋⣹⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠒⠶⠖⣻⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⣧⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿⣿⣖⠤⢀⡀⠀⠀⠀⠀⢰⣤⣀⡀⣀⡠⠞⠀⠀⢀⠴⢺⣷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⡉⠛⣻⢦⣌⡁⠒⠒⠲⠼⢿⣤⠀⠀⠀⠀⠀⢠⠃⢹⣹⠏⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣿⣿⣷⣾⣿⣷⣦⡀⣠⠞⠍⣇⠀⠀⠀⠀⣨⠀⠞⠁⢀⡿⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣯⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⢷⣄⡀⢺⡄⠀⠀⠀⡏⠀⠀⠀⣿⠁⠨⣺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⡿⡍⠿⡀⢈⢧⠣⢭⣛⣿⣿⡆⣿⡷⣦⣷⡀⢀⡀⣇⠀⠀⠀⠙⠖⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡛⣴⣷⡘⣿⣆⠃⡣⣙⢻⣿⣿⣿⡮⣹⣼⣿⣷⣿⣟⠻⣄⠀⠴⡆⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⡒⢌⢻⣿⡞⢿⣳⡔⣹⣿⢿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣷⣌⡟⡿⢷⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡛⡹⣭⣻⣩⣿⣎⡿⣽⣞⡹⣶⣿⣿⠏⣽⡿⣿⠿⣿⣿⣫⣻⣿⣷⣶⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡼⣏⣿⠿⣤⡹⣿⣿⣳⡬⢿⣿⣿⡿⣿⣿⣼⣿⡷⢝⢾⣿⡿⢳⡿⣛⡞⡿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣁⢻⡽⣌⢿⣿⣣⡺⠳⣿⣿⡽⣿⣻⡻⣾⣫⣷⣽⣷⣯⣟⡟⡼⠁
⠀⠀⠀⠀⠀⠀⣿⢾⣿⢯⢿⢞⢾⢿⣻⣽⣇⢻⣿⡷⡴⡹⣽⣿⣿⣷⣷⠣⠛⣯⣻⣿⣜⣏⡜⠁
⠀⠀⠀⠀⠀⠀⣿⡽⣿⡿⢻⣧⢳⡠⣻⡻⣯⣷⣿⣿⣟⣵⡜⣿⣿⣿⣧⡆⡀⠙⢻⣿⣟⠞
⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠁⠁⠁⠈⠁⠁⠋⠛⠙⠛⠋⠉⠈⠈⠛⠛⠉⠙⠘⠂⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣠⣤⣤⣄⣀⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣿⣿⣅⣿⣿⣾⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣶⣼⣶⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢶⣶⢶⣶⡶⣶⣶⡶⣶⣶⢶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⠛⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⣿⣿⣿⣯⣾⣿⣯⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣼⣿⣦⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⣿⣿⡛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⢻⣿⣿⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣤⣄

⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠠⢀
⠀⠀⠀⠀⠀⢀⠆⠠⢤⠀⠠⠄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⡄⠀⠤⡀
⠀⠀⢀⡀⢂⡈⠁⠀⠀⠀⠈⠉⠉⣉⣁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠎⠀⠀⠀⠀⢀⠀⠑⠈⢊⠂⠀⢂
⠀⠀⠋⠀⢸⠠⢯⡟⢴⢂⢤⡭⠟⠦⠈⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⡎⠄⠀⠀⠉⠉⠉⠀⠀⠸⣄⠀⠀⠆⠃⠀⡆
⠀⠀⢠⠀⠀⣾⠘⠿⠃⠀⠀⠶⠖⢠⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠄⣲⡲⡀⢤⡐⣦⡜⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠑⠤⣟⡃⠀⣀⠀⠀⠀⢀⣟⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣯⠈⠘⢷⡷⣶⠈⢶⠃⡀⢠
⠀⠀⠀⠀⠀⠈⠙⢃⣄⠀⣠⠴⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠄⠀⠀⠀⠀⠀⠁⠀⢀⠺⠀⠁
⠀⠀⠀⠀⣰⠂⠐⠀⢇⠀⠚⠀⠉⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠂⡀⠲⠖⢛⡠⠞⠃⠀⠀⠠
⠀⠀⠀⠔⠈⠀⠘⢆⡠⠳⡱⢧⣀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠀⡒⢈⠏⠀⠄⡀⡔⠉⠉⠂⢹⠟⣇⡀⢠⠀⠁⠀⡄
⠀⠀⢈⠀⠀⠀⢰⠀⢱⣀⣽⡧⠌⠆⠀⠀⡈⠢⡀⠀⠀⠀⢠⠌⠸⠀⣠⣤⠖⠂⠄⣈⡄⢂⠀⡁⠉⢈⡀⠱⠄⡀
⠀⠠⠀⢀⣢⡄⠀⡰⠋⠈⢸⣧⠀⠀⡔⠘⠄⠀⠈⡆⠀⢠⣵⠂⠀⠈⢏⢸⡒⠐⢄⠘⠀⠀⠃⠀⠀⠀⢳⠀⠐⠁
⠀⢃⠀⠀⠀⢹⢽⠀⢀⠶⢥⡜⠉⠀⠂⠐⠀⠀⡰⠀⠀⠀⠙⠳⠾⠀⠈⠁⡝⠛⠛⠀⠀⠀⠀⠆⢀⣐⠁⠢
⠀⠀⠀⠀⡅⠀⡍⠀⠀⠀⠀⠂⢀⡄⠙⠂⢀⠔⠀⠀⠀⠀⠀⠀⠐⢀⡀⢰⠁⠀⠀⠀⠀⠀⠰⠀⡠⠁⠀⡀
⠀⠀⠀⠀⢃⠀⢙⡒⠂⠐⡂⢻⠈⠗⠖⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⡗⢀⠔⠊
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡘⡄⠀⠐⡊⠄⠀⠹⡆
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠒⠐⠁
⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⡐⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠠⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⣅⣀⡀⠁⠀⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠢⠠⠀⣀⢀⠄⣀⡀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⡀⠀⠈⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠤⠤⡁⠀⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀
⠀⠀⠘⡖⠔⠂⠀⠀⠀⠠⠄⢠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢰⠀⠀⠀⠀⢸⠆⠘⣦
⠀⠠⠐⠉⢐⠀⠀⠀⠀⢠⡀⢀⣀⢉⣉⠑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠧⡔⠈⠃⠀⠀⠀⠈⠓⠠⠓⢕⠄⡀
⢠⡥⠀⢄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⢀⡠⠢⠃⠀⠀⠀⠀⠀⠢⡀⠂⡠⠚
⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⣉⣀⣀⡀⠉⠉⠙⠻⣷⣄⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⣴⣾⠿⠛⠋⠙⢳⡀⣤⣤⣤⣼⣗⠋⠍⡉⣩⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢻⠩⠀⠠⠐⠊⠁⠀⠀⠈⠻⣧⣼⡇⠒⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣨⠂⠁⠀⠀⠀⠀⣰⡿⠟⠂⠈⠻⠇⢃⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣧⠀⠀⠀⠀⠠⠟⢡⠖⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣟⣿⠿⠗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠿⠿⠛⠛⡳⠃⠀⢀⢿⠀⠀⠀⠀⢀⠀⠀⠀⠀⢉⣮⡢⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠧⣀⠤⣮⠈⠒⠉⠦⡊⠁⠀⠀⠀⣰⣿⣿⣿⣟⣄
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠛⢿⣯⣦
⠀⢠⢤⣴⣶⣶⣿⣧⣶⣾⣿⣏⠓⠦⡀⠀⠀⠀⣷⣞⣕⣦⣄⣀⡠⢔⠟⠁⠀⠀⠀⠀⢿⣿⣧
⠀⢸⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣀⠀⠈⠑⠤⡀⣿⣹⠋⣼⣿⢃⠜⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠘⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣏⡓⢄⡀⠀⠀⠙⠣⣀⣿⠟⠳⣄⠀⠀⠀⠀⡠⠊⢀⣾⣿⣿⣿⡆
⠀⠀⣟⣿⣿⣧⣀⣀⣀⣼⣿⣿⣿⡠⠄⠹⠦⣀⠀⠀⠈⠀⠀⠀⢈⡣⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⡿⢟⣁⣀⠠⠂⣬⡗⠤⣀⡀⣀⠔⢻⣿⡿⠿⠟⠛⠉⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠈⠓⠛⠛⠋⠉⠉⠁⣹⡷⣄⣀⣀⡠⠤⢿⣦⢿⣿⣿⡇⠀⢸⣿⡦⠤⠼⠴⠋⢻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣼⡱⠀⠠⣱⡄⠀⢻⣿⣿⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣾⢿⡇⠀⢸⡟⢾⢆⠀⠹⡟⣿⣇⠀⢸⣿⣿⣶⣤⣶⣾⣟⠯⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠇⢸⢇⣀⡼⡇⠈⢻⣢⣶⣿⠟⠛⠻⠽⠿⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢡⡁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠁⠀⠤⠀⠂⠀⡀⠀⠀⠐⡄⠀⠀⠀⠀⠉⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⡀⠄⠂⠁⢀⠠⠀⠂⠉⠄⠀⠀⢠⠜⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⢀⠄⠊⠀⡀⠔⠈⢀⠄⠀⢁⠠⠐⠁⠠⠆⠀⠂⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⠔⠁⠀⡠⠊⠀⡠⠊⠀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠁⠀⡠⠊⠀⡠⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠊⠀⢀⠈⠀⢀⠄⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⡠⠁⠀⠠⠁⠀⠠⠂⠀⢀⠂⠀⢀⠊
⠀⠀⠀⠀⠀⠰⠁⠀⠠⠁⠀⠠⠁⠀⢀⠂⠀⢀⠂
⠀⠀⠀⠀⢀⠃⠀⢀⠃⠀⠀⠂⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⢀⠁⠀⠰⠀⠀⠀⠁⠀⠀⠆⠀⠀⡄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⣤⣀⠀⠀⣠⡴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠞⠂⠀⠙⣧⡾⠃⣤⠶⠛⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⡏⠀⠀⠀⠀⠀⢸⡇⣼⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⡾⣧⡀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣶⣤⣤⣤⣶⣿⣤⣼⣿⣦⣤⣤⣤⣾⣯⣤⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣤⣶⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢨⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⡿⠛⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⡇⠀⠀⣾⠉⠉⠉⠉⠉⢩⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⢽⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⣿⣷⣤⣀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣿⡇⠉⠙⠻⢷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢸⡄⠀⠀⡇⠀⠀⡄⠹⢿⣿⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⣿⣴⠀⣿⣇⠀⢰⣧⠀⣦⣧⠀⢀⠀⠀⠀⢀⣷⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⢀⣿⣿⣿⡴⣋⣠⡕⠺⢿⢀⣿⣿⣤⣿⡄⠀⠀⢸⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⢀⠜⣉⣙⣿⣿⣿⣿⣵⣶⣆⡬⣿⣿⣿⣿⡇⠀⢄⠹⣿⡅⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⡙⡟⢁⣚⡟⢫⣾⣿⣿⣿⣿⣿⣿⡇⠙⣿⡟⢻⣿⡤⠀⠀⢹⣿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣿⢀⣿⡿⠿⠀⡾⣿⡷⢮⡽⠿⣿⡿⡷⢾⣭⠀⣤⡬⣏⣀⣀⠖⢿⣀⣙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠃⣚⠋⢘⠃⣾⠆⣼⠇⣿⢁⡚⢀⣡⡿⢀⡖⢸⡟⢰⡿⢠⡟⢠⡟⣰⠆⣿⠁⡣⡮⢶
⠀⠀⠀⠀⠀⠀⠀⢀⠏⢸⠁⠇⢾⣦⣵⣤⡵⣦⡴⠃⠑⠬⠭⠦⠞⠣⠬⠲⠬⣴⣬⢥⣬⣴⣿⠬⠕⠤⠭⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠁⠀⠧⠚⠙⢿⣿⣷⣼⢻⣷⡀⠀⠰⡢⢔⠆⠀⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣬⣻⣦⡈⠠⠄⣠⣾⣿⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⢻⣶⣾⡿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣏⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣊⣉⣵⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠁⠁⠀⠀⠀⠢⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠀⣀⡠⠤⠐⠒⠒⠒⠒⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⠔⠂⠉⠠⠁⠀⠀⠀⠀⠀⠀⠠⠠⠠⠦⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⠀⠃⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣴⡤⠶⠤⠤⠥⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣤⣤⣶⠾⠛⠛⠛⠿⠿⠿⠛⠛⠙⢿⣿⣄⠀⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡤⢶⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠚⠁⠀⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠴⢿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⠿⠟⠀⠀⠀⠀⠀⠀⢴⠆⠐⠐⠷⠀⠀⠱⡄⠀⠀⠀⢀⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⠂⠄⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠉⠀⠀⠀⠀⢹⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⠀⠒⠀⠀⠀⠀⠀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠈⠉⠉⠠⠄⠀⠀⠀⢀⡜⠁⠀⠀⠁⢠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠶⠠⣀⡀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠘⡀⠄⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠈⣄⠀⠀⠀⢀⠉⠉⢙⡱⠒⠀⠀⠀⠀⠀⠀⠀⠐⣠⣤⣌⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⠁⠀⠀⠀⠀⠈⢆⠀⡐⠀⠇⠠⠊⠱⣄⠄⠀⠀⠀⠀⠠⠂⠀⠉⠁⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠀⡠⠂⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠈⢆⠀⠀⠀⠀⡁⠀⠲⡤⠤⠂⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠁⠞⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣆⠀⠄⠂⠑⠀⠀⠂⠈⠈⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠑⡀⠀⠀⠀⠄⠀⠙⢷⣤⡌⠀⠀⠦⢠⠀⢠⠁⠀⠀⠀⠈⡄⢀⡄⠔⢰⠀⠀⠀⢀⡔⢲⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⠀⠈⠀⠀⣠⠎⡰⠀⠀⠀⠐⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡦⠤⠚⠁⠀⠘
⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⢈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠐
⠈⠢⠀⡀⠀⠀⢀⠀⠰⠤⠀⠀⠀⢐⠣⢀⡸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢄⠀⠀⠘⢀⠀⠀⠉⠱⠤⠞⠀⠀⠀⠉⠰⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡖⠁
⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⡀⠀⠈⠉⠉⠉⠛⠛⠙⠉⠉⠉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠑⠄⢀⡀⠁⠀⠀⢀⠃⠀⠀⢠⠀⠳⠄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠈⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠶⠶⣆⠀⢸⠲⠖⠚⢻⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡌⠁⠒⠐⠹⠠⡄⡃⠀⠀⢠⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠒⠒⠒⠊⠰⢁⡈⠉⠉⠄⡁⠐⠒⠒⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠈⠉⠁⣄⠄⠊⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠤⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣤⣴⣶⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡷⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠈⠉⠉⠠⣶⠀⠀⠈⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠘⡿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠂⠀⠉⠀⠀⠀⢠⣦⡄⠀⢲⣿⡖⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠶⠀⠀⣀⣄⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⢠⡀⠀⢀⠀⠀⣻⣿⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⣛⡛⢻⡛⣻⠿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⣶⣤⡀⠀⠈⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠙⠿⣷⣤⣀⣀⣈⡹⠿⠶⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣾⣿⣿⣦⣀⠀⢀⣙⣿⠷⠤⠔⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⠟⠁⠀⣠⣾⡿⠁⠀⢀⣴⡿⠋⠀⠀⣰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣤⣤⣤⣾⣿⣧⣤⣤⣶⣿⣯⣤⣤⣴⣿⣿⣤⣤⣤⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣻⣿⣟⣻⣿⡆⣷⣿⣾⣿⣛⣿⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢶⠶⣶⣶⡶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣭⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡄⠀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠴⠖⠒⠒⠒⠊⠉⠉⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡤⠤⠾⠖⠒⢚⡙⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠙⠻⠶⣤⣀
⢀⠤⠤⠴⠶⠒⠒⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⠐⡖⠒⠒⢤⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤
⡆⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⢠⠀⣴⠴⠶⠶⠆⢶⣄⠀⢸⡀⠀⠘⡇⠀⢸⡄⠀⠸⡄⢻⣠⠴⠚⠀⢸⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢹⢾⡀⠀⠀⢰⣆⠀⠀⠀⣏⠙⢦⠘⣆⠀⡌⠀⢻⣀⣀⣀⠀⢸⡍⢷⡈⣇⠀⠀⢧⠀⠈⢧⡀⢸⠃⢸⡟⢦⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠘⣿⣇⠀⠀⢸⠘⣆⠀⠀⢹⡀⢘⡇⠹⡄⡇⠀⢸⡇⠀⠀⠀⠈⡇⠀⠙⢿⠀⠀⠸⠄⠀⠈⠙⠃⠀⠀⠃⠀⠙⠂⠀⠉⠉⠉⠁⠀⠀⠀⡠⠖⠁
⠀⢿⣿⠀⠀⡷⠖⠘⣆⠀⠈⣇⠜⠁⠀⢻⠁⠀⠀⠷⠶⠶⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠊
⠀⢸⣿⡀⠀⠃⠀⠀⠙⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⠀⠠⢤⣤⣤⣤⣶⣶⣦⣤⣤⣴⠶⠶⠶⠶⠟⠛⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⣤⣴⣖⣲⠶⣶⠶⠶⠖⠻⠟⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⢙⣳⣾⣤⣐⠶⠶⠮⠿⠛⠓⠛⠊⠉⠉⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠳⠀⠀⠀⠸⣤⡆⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠐⡄⢠⠀⠀⠀⢀⡿⠀⠋⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⢆⠘⢆⢇⠀⠀⣼⣷⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠣⠘⡞⠀⡈⣿⢿⣀⠞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡉⠪⠐⠄⢹⠷⣗⣨⠁⣁⠀⠀⠲⠊⠁⠀⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠈⠁⠠⠤⠭⠤⠄⠀⠐⠟⠛⠒⠚⠛⠒⠒⠒⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣤⣤⣤⣄⢀⣀⣀⣀⡀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⣿⣿⣿⣿⡿⠈⠉⠉⠉⠁⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢁⣾⣿⣿⣿⣷⣶⣾⡆⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⢰⣶⣶⣶⣶⣶⣶⣦⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⣩⣭⣭⣭⣭⣥⣾⣿⣿⣿⣿⣿⣿⣿⢠⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⡛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡖⣠⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠰⠆⣻⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣧⡙⠿⠿⠶⠶⠿⠶⠶⠿⠿⠷⠾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⠛⠟⠸⠿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠗⣈⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢃⡘⠿⡿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠻⣿⡟⣡⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣶⣶⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣌⠀⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⠸⡿⠁⣿⣿⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⣿⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣿⣿⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣭⡉⠀⠀⠀⣿⣿⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠹⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠛⠛⠛⠋⠉⠉⠙⠛⠛⠛⠒⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠛⠒⣿⠃⠰⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⡴⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⢤⣄⣀
⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣀
⠀⠀⣿⠙⠶⢚⡟⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⢴⣟⣁⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⢹⣆⡞⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠦⣄⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⣶⠀⠠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⡄⣀⣻⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⣦⠸⡦⠀⠀⠃⠚⠃⠀⠰⣉⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⡼⠈⢀⣀⣀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠓⠃⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡙⠂⡀⠀⡏⡏⠀⢀⠀⠀⠀⢺⠆⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠃⠀⡀⠀⠀⠑⠬⠶⠋⠀⣀⡀⠀⠀⠀⠈⠀⣴⠄⠀⠀⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢍⠛⠁⠀⠟⢀⣤⠀⠀⠀⠉⣰⢻⢳⡠⠖⡆⠀⠀⢈⡀⠈⠁⠀⢚⣁
⠀⠀⠀⠀⠀⠀⠀⢐⣊⠁⢀⠀⡠⠋⡏⢧⠐⠀⡰⠃⡜⠀⢁⡴⠁⠂⣠⠚⡟⣆⠀⡀⠙⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠚⠁⠘⣅⡸⠳⡞⠀⠸⠵⠂⡞⣞⠱⠘⠹⣤⠇⢈⠢⠀⠐⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠺⠄⠀⢼⡧⠀⠈⠁⠀⠘⠄⠀⠀⠀⠘⣌⡆⠑⠀⠈⠀⢾⠦⠀⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣺⣟⠀⢠⣿⡄⠀⢰⠒⠦⠤⢦⡈⠇⣰⣷⡀⠐⣿⣗⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⢽⡿⡁⠰⣿⡢⢠⠋⠓⠤⢎⢿⣱⡄⢞⣿⠆⠨⢾⡮⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣻⣏⡂⣪⣿⢝⠀⠭⠍⠑⠚⠉⠥⠀⡻⡿⡅⢐⣽⣝⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠉⢔⣿⡳⠄⣱⣆⢩⠍⣴⡌⠠⢚⣟⡢⠉⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢿⠌⠂⢽⡷⡀⠨⣾⢮⠘⠵⡷⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠈⢆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠈⢆⡀⣈⣷⠤⠶⠶⢶⡶⠶⢲⡶
⠀⣀⣠⣤⠤⠶⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠏⠀⢀⡾⠁
⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⢠⣞
⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢠⠏⠉⠳⣄⡀
⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⣏⠀⠀⠀⠈⠻⣦⡀⢀⡤⣶⣤⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠈⢧⡀⠀⠀⠀⠈⠙⢾⣧⠆⠀⠉⠁⣰⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠳⡄⠀⠀⠀⢠⡞⠁⢀⠀⠀⠀⢈⡻⣤⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⠞⠁⢉⡹⠟⠲⠦⣤⣀⣀⠙⣄⠀⠀⠙⣄⠀⠀⠈⠉⠳⡆⠷⢠⡿⠷⣥⠾⠃
⠀⠀⠀⠀⠀⣾⠀⢀⡴⠋⠀⢀⣴⠋⠀⠀⠀⠀⠘⢧⠉⠉⠛⠓⠚⠂⠙⢦⠀⠀⠀⠀⠻⠞⠛⠳⣄
⠀⠀⠀⠀⠀⣧⣴⣩⣤⡤⠴⠋⠙⢷⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠁⠄⠀⠹⣄⠀⠀⠀⣀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠻⣄⣾⠹⠉⠳⢦⣀⣠⠴⠊⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠈⢦⣴⢛⠋⠡⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡆⠀⠀⠈⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣦⡔⠻⠓⠲⠾⡧⠂⠀⠀⠱⠤⠠⠤⠼⢶⡄⠀⠀⠀⠀⠀⢸⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠶⠦⣤⣀⡤⠖⠛⡇⠀⠀⠀⠀⠈⢷⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠲⡀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢿⡀⠆⠀⠉⠀⠀⠠⣇⡀⠀⠀⠀⠀⠈⢳⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠙⣄⠀⣾⣉⠀⠀⠀⠀⢆⠀⠀⢀⣿⠲⠶⠶⢤⡶
⠀⠀⠀⠀⠀⢘⡷⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⣷⠀⠅⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⢦⠀⠉⠉⠛⠳⣆⠈⢆⠀⣼⠇
⠀⠀⠀⠀⣴⡮⠤⠄⠠⠄⠀⢀⣶⣠⠤⠟⠀⠀⠀⠀⢠⡇⠘⠀⠀⠀⣠⡔⠒⠤⢀⠀⠈⢳⡀⠀⠀⠀⢣⡀⠀⠀⠀⠘⢧⡈⣵⡟
⠀⠀⠀⠀⠀⠀⠉⠻⣦⠘⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣇⣀⣴⠊⠁⠈⠙⠒⢤⣌⣁⡲⠷⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠉⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠹⣆⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⡞⡛⠑⠦⣄⡀⠀⣠⠔⢻⡀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇⠁⠀⠀⠀⠉⠛⠁⠀⡞⠱⡀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢘⡷⠊⠀⠀⠀⠀⠀⠀⠀⣇⡀⠱⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⡝⢷⣄⡠⢶⡶⠀⠀⠀⠀⠈⢧⢀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠳⡀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⡋⠀⠀⠠⠀⣾⠁⠀⠀⠀⠀⠀⠘⣟⠲⢤⡉⠑⠀⠀⠀⢠⣖⣐⣒⣒⣰⡾⠃⠹⡄⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⠇⠀⣀⢀⡙⣦⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⡆⢷⠀⣰⠋⢩⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠶⠋⠛⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⢷⠀⠈⣷⡤⠟⠁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣀⡷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣤⡴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣤⡶⠚⠛⠉⠉
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣶⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣤⣾⣿⣌⢿⡏⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⢋⣉⠛⠛⠛⠛⠿⠿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠡⢟⡻⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣋⣀⣀⣀⣀⣀⣈⣛⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣶⣿⣷⡘⠿⢰⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⡘⣿⣿⣿⣿⣿⣿⠟⣴⣿⣿⣿⡿⠿⢒⣋⣭⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⡇⣿⣿⣿⣿⣿⠏⠼⢛⣋⣭⣴⣶⣿⠿⠟⢛⣋⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⡇⣿⣿⣿⣿⠰⣶⣿⠿⠟⣛⣩⣥⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⠟⣸⣿⣿⡇⠻⠿⢿⣿⡇⣡⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣷⣶⣦⢰⡆⢰⣶⣾⣿⣿⣿⡇⢺⣿⡈⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⢸⣇⢸⣿⣿⣿⣿⣿⣇⢸⣿⡇⣿⡇⣿⣿⣿⣿⡇⣴⣬⣙⠻⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢸⣿⣿⣿⣿⣿⣿⣬⣥⣼⣿⣿⣿⣿⣿⣿⢸⣿⢠⣿⡇⣿⣿⣿⣿⡇⣾⡿⠟⣋⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣸⣿⡇⣿⣿⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠁⠉⠉⠁⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣄⣀⣄⣄⣀⣰⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠙⣡⡁⠀⢀⣉⠂⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠛⠛⠛⠛⠹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡆⠉⠁⠀⠈⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡤⢖⠂⠀⠐⣉⣒⠹⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠙⠟⠀⠈⠛⠉⢸⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠏⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠠⠄⠀⠊⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⠂⢀⠀⡀⠓⠰⠀⣦⠄
⠀⠀⠠⡀⠀⠀⠀⠈⢣⣀⣷⣣⠀⠀⠀⠘⠂⠀⠀⠀⠨⠐⢅⢀⣀⡴⠁⢄⣀⠐⠁⠈⠐
⠀⠀⠀⠈⢢⣀⠔⠰⠋⠉⢻⡅⠀⠃⠐⠀⠀⠀⠀⢠⠴⠀⠀⢿⡰⡒⠀⠀⠛⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢈⣿⠀⠠⠢⠤⠋⠀⢀⠀⠀⠀⠀⠀⠀⠑⠛⠃⠀⠁⡝⠓⠋⠀⠀⠀⠐⠀⣤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠨⠍⠡⠸⠀⠁⠘⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠼⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠄⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣉⡐⠂⠀⠀⠀⠐⠀⢔⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⣒⠀⠀⠀⠀⡃⠘⡦
⠀⠀⠀⠿⠃⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠋⢀⠀⠀⠀⠀⠁⠐⣿⣦⠢⡀
⠀⠰⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠉⠤⠖⠈⠀⠀⠀⠀⠀⠐⢬⡁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣠⠞⠡⠈⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠲⢾⣷⠒⢿⣥⠤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣻⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⣩⠟⠁⠀⠈⠑⢬⡹⣍⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡜⢁⡾⠃⠀⠀⠀⠀⠀⠀⠑⡌⢦⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⢀⡞⢠⡟⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⡾⠷⠶⠶⠶⠶⠶⠿⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣞⣠⣿⣠⡤⠶⠖⠚⠉⠉⠁⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣉⣙⣛⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡤⠶⠛⠋⠉⠉⠀⣀⣀⣤⣤⠴⠶⠖⠛⠛⠉⠉⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⢀⣀⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣴⣤⠀⣀⣿⡿⠟⢻⣿⢿⣿⣿⣿⠿⣿⡷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣀⣤⣴⣾⣯⣥⣀⠀⠀⢶⣒⠂⠀⠀⠀⠀⠀⠀⣴⠋⣿⡶⠔⢛⣭⣍⠁⢁⡿⠁⣰⠋⠙⣷⠊⣳⠀⡴⠋⠙⣷⢂⣳
⠀⠀⠀⠀⠀⠀⢠⣾⣁⣤⣶⢿⣿⣿⣿⠛⠁⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣴⠾⡿⠁⢸⡇⣸⠃⢠⡇⢀⣄⢸⡄⢼⢠⠃⣠⡄⢸⡄⢸⡆
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢺⡛⠃⠀⠀⢠⡟⠀⣿⠀⢸⡇⠸⠏⢸⠃⢺⢸⠀⠻⠃⢸⠃⢹
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢼⢷⡄⠀⠀⠘⣧⡀⢻⡀⠈⢧⠀⢀⣼⢠⡏⠘⣇⠀⢀⡾⣂⡿
⠀⠀⠀⠀⠘⠻⠿⠿⢿⠿⠿⠿⠿⠟⠛⠛⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣠⠾⠖⢻⡟⠛⢷⣤⣬⣿⠿⠷⠛⢦⣄⣹⣿⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⡾⠋⠀⠶⠋⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣤⠞⢁⡴⠋⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣴⠟⢁⣠⣾⠁⠀⠀⣶⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣶⣆⢸⣿⠙⢷⣴⠟⠉⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⠶⢻⡟⠁⠈⢻⣄⣸⣿⣶⣤⣄⣀⣀⣀⣤⣴⠛⠓⢶⠞⢻⣷⣤⣤⣤⣤⣤⠶⢶⣤⠖⠋⢉⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⢻⡟⠀⠀⠀⠀⢻⡿⢹⠿⣄⠉⠉⢉⣉⣽⢿⡇⠀⣿⠀⣾⠤⣤⣤⣤⣤⣤⣶⣾⠇⢈⠻⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⢿⠄⣾⠀⠹⡟⠛⠋⢩⡇⢸⡇⢠⡇⠀⣿⠀⠀⠀⠀⠀⠈⢀⡤⠀⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣿⠀⠀⠀⠀⠸⣷⡴⠾⠋⠁⣿⢠⡟⠀⠀⣿⠀⢠⡞⣷⠸⣇⠸⠷⠞⠛⠀⠀⠀⠀⠀⠀⠈⠛⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⢀⣼⠇⣼⠃⠀⠀⢸⣧⠟⠀⠸⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣇⣴⠞⣡⡾⠁⠀⠀⠀⢸⡏⣀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⢰⣿⣋⣤⠞⠋⠀⠀⠀⠀⠀⢸⡆⣉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠛⢀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢨⡄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠚⠛⢻⣏⢀⣀⠀⢀⣀⣀⣀⣀⣀⢀⣿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣦⠴⠞⠛⠉⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⣿⢯⣭⠿⠈⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠃⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣼⣇⣀⣀⣀⣀⣀⣠⣄⣤⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠿⠿⠛⠛⠋⠋⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠹⡄
⢀⣀⣀⣤⣤⣤⣤⡤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⣀⣀⣀⡀
⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⡆
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣅⣀
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠈⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠲⣄⡀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢸⠃⠀⠀⢀⣠⠴⠚⠉⠀⠈⠉⠳⢦⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢸⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣰⠟⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣧⣀⡀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠖⠋⠹⣄⠀⠀⠀⣀⡼⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⣶⣶⢶⣶⠶⠶⠶⠶⢶⣶⡀⠀⠀⠀⢰⣿⠃⣴⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡷⢾⡇⠰⠶⠶⠆⢸⣿⡇⠀⠀⠀⠸⣿⡄⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠿⠷⠾⠷⠶⠶⠶⠶⠾⠿⠛⠀⠀⠀⠀⢈⠛⠓⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⢀⣉⡙⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡆⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⢀⣀⡀⠀⠀⠀⢴⣿⣿⣿⠏⣰⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⢸⣿⣿⣿⣿⣷⣾⣿⡿⠃⣼⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉⠉⠙⠛⠛⠛⢡⣤⠀⣿⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣠⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⣉⠉⢉⡁⠀⠀⠀⠀⠀⠀⢈⣉⣉⣉⣀⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠻⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿

⠀⠀⢴⣶⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⢀⣼⣷⢶⠖⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣦⠀⣨⠿⣄⠀⠀⠀⠀⠀⢠⣬⡷⠞⠁⣿⠀⠀⠀⠀⠀⠀⢠⣶⣬⡉
⠀⢸⣝⣿⣧⢶⣄⠀⣼⡇⠀⠀⠀⠀⠿⢷⣼⠿⣥⡀⠈⠀⠀⠀⠀⠀⣾⣏⡛⠋⣼⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⠶
⠀⠜⠁⠀⠻⣆⠈⣴⣿⡇⠀⠀⠀⠀⣠⠞⠉⢿⣬⣿⡄⠀⠀⠀⠀⠀⢸⡏⠻⣠⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⢻⡄⡀
⠀⠘⠀⠀⠀⢉⣼⣿⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢘⣣⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠁

⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⢄⡀
⠀⠀⠀⠀⣴⣷⣤⣄⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⡠⠊⠁⠀⠀⠀⠀⠀⢘⣛⠀⠀⣛⡃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠐⠠
⠀⢐⡶⣤⣿⣷⣴⡾⠷⠄⠀⠀⠀⠀⠀⣀⡸⠫⣄⣀⠀⠀⠀⠀⣠⣴⣿⣯⣷⣼⣿⣽⣦⡄⠀⠀⠀⠈⢛⣧⡴⠟
⣼⣟⣻⡯⠿⠿⠏⣾⠿⣷⡄⠀⠀⣤⣾⡿⠃⠀⠻⣿⣷⡄⠀⠀⢎⣭⡝⠭⢭⣭⠯⠯⠭⠅⠀⠀⠀⠀⠌⠻⣷⣶⣦⣄
⠈⠛⠛⠁⠀⠀⠀⠛⠿⠛⠀⠀⠀⠙⠋⠀⠀⠀⠀⠈⠛⠁⠀⠀⠘⠋⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠉

⠀⠀⠀⢀⠠⡠⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⡀
⣴⣔⣊⣹⣞⣓⣼⣦⣤⣄⠀⠀⠀⠉⠱⠀⢸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⡀
⠻⣿⠿⣿⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⢧⣼⣷⣿⣿⣶⡄⠀⠀⠀⠀⣠⣿⣿⠹⣷⡀⠀⠀⠀⠀⣶⣀⣀⣠⣿⣻⣃⣀⣠
⠀⠻⠶⠟⣁⣀⣈⠻⠶⠟⠀⠀⠀⠀⠀⣿⣿⠉⠀⠈⠉⠀⠀⠀⣀⣼⣿⣿⣿⠀⠙⣿⣄⡀⠀⠀⢙⡛⣛⣛⡛⣛⣛⡛⣛
⠤⠶⠿⠿⠿⠿⠿⠿⠶⠦⠀⠀⠀⠀⠤⠴⠶⠶⠶⠶⠤⠄⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠁⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⢺⠂⠀⣠⣶⠄⠀⠀⠀⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣝⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆⢠
⢀⣀⣤⣤⣿⣷⣾⣭⣄⣀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣉⠳⠂⠀⠀⠀⠀⣀⣀⣼⣿⣲⣴⣷⣦⡀
⢨⣍⣩⠭⣭⣩⡭⣭⣩⡥⠀⠀⠀⠀⠀⠀⠀⠶⢼⡃⠀⠀⠀⠀⡾⠉⠙⣮⢿⣉⡞⠉⠙⡆⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⡄⠀⠀⠻⠤⠴⠋⠈⠁⠳⠤⠴⠃⠀⠀⠈⠉⠉⠉⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⣀⡀⠰⠄⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠀⣀⢸⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠤⠄⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠟⠃
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣤⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⠀⠠⠀⡀⠀⠠⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣤⣤⠁⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠉⠉⢉⡉⠉⠣⠘⠻⠀⠉⠃⠐⠒⠒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠊⠐⠀⢀⠀⠖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⣠⠇⠀⢀⡄⠀⠀⠀⠀⢄⠀⠀⠁⠐⠀⢀⠀⢀⠔⠁⠠⡆⠀⠀⠀⠀⠀⢠⠈⠰
⠀⠀⠀⠀⢠⡏⠀⢠⡟⠀⠀⠀⡀⠀⠀⠑⠠⡀⠀⠠⠈⠁⠁⢀⠈⠀⡇
⠀⠀⠀⠀⢸⠁⠀⡾⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠃⠀⠀⠀⡏⠀⠀⠁⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⡟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠁⠀⡰⠄
⠀⠀⠀⠀⢸⠀⠻⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⢈⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣿⠀⠀⣸⠿⠶⢦⡄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢈
⠀⠀⠀⣰⠏⠀⠀⡗⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠐⣇⠀⠀⠀⠗⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠁
⠀⠀⠀⠈⢙⠇⠀⠀⠀⠀⢠⣶⣤⣤⣤⣤⣤⣤⠀⠀⠀⢰⣶⣶⠏⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡔⠀⠀⢀⣴⠂⢢⠀⠉⢹⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢧⢀⣴⠏⡋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠓⠀⢠⣄⣀⣀⣀⠀⠀⠀⠀⢀⠀⠛⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⢸⡋⠉⠉⠉⠙⡟⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⢠⠉⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⡄⠀⠀⠸⡀⠐⠂⠀⠂⡿
⠀⠀⠀⠀⠀⠀⠀⣧⠘⠒⠒⠁⢀⠃⠀⠀⠇⠀⠀⠀⠸⠆⡀
⠀⠀⠀⠀⡀⠀⠀⠘⠂⠀⠀⠀⡌⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠇⠀⠀⠀⠉⠁⠒⠖⠒⠠⠤⡤⠤⢤⠰⠆
⣭⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿