Firework Emojis & Symbols

⡈⠃⠈⠀⠀⠁⠘⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠁⠔⢀
⠀⠀⢀⠑⠌⢀⠂⡀⠐⣁⡀⠀⠀⠀⠀⠠⡄⠃⠈⡀⢀⠀⠐⢁⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠⠀⠀⠄⠠⠀⠡
⠀⠡⠀⠀⠀⠁⠆⠀⠀⠠⠄⠀⠀⠀⡈⠂⠀⡐⢂⠁⠌⢀⠃⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⡄⢄⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠌⠃⡀⢠⠀⠂⠂⢀⠐⠂⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠄⠠⠀⠤⠄⠀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠠⠎⡡⠀⠁⠀⠀⠀⠀⠀⠀⠠
⡠⠀⠁⠐⠉⠀⢀⠰⣌⠙⠀⠀⠀⡀⠤⠀⠀⠔⠀⠠⠠⠀⣀⠒⢀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠊⡠⢀⠀⡀⣄⠠⠈
⠀⠊⠠⠀⡄⠰⠄⠓⠀⠀⠀⠀⠀⠐⠐⠋⡠⠀⠁⠐⠀⠂⠀⠀⢤⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠘⠄⠑⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⠀⡀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣰⣶⣠⣠⡄⣶⣶⠀⣤⣼⣿⣿⣀⣴⣴⡆⠀⠀⣰⣿⣾⣷⣦⠀⣀⢠⠀⣰⣿⡆⣀⣀⠐⣷⣀⣤⣄⣾⡧⣿⣴⣶⡦⠀⣧⣀⡀⣶⣶
⣿⣿⣿⣿⣇⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣇⣿⣻⣿⣿⣆⣿⣿⣇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⢀⠘⠋⠀⠠⡔⢲⠄⠀⠀⠀⠀⠀⠂⠠⢁⠀⣃⠀⠀⠀⢶⠆
⠀⠀⠀⠀⠀⡁⢉⠆⠠⣂⡆⠀⠀⠀⠑⠀⢀⠀⠉⠉⠁⠰⡙⠆⠀⠀⠠⠂⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠘⠐⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⠂⠀⢀⠀⠠⠄
⠀⠀⠀⠈⠀⢀⡀⠀⠀⠉⠁⠒⠠⡀⠀⠈⠢⠀⠀⠀⠈⠀⡐⠁⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⢰⡲
⠀⠀⠀⠀⠀⠑⠊⠀⠀⠠⠄⠀⡠⡀⠁⠢⠀⠀⠀⠀⠁⡐⠀⢀⠀⢈⠀⠀⠀⠝⠀⠀⠁⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⡀⠠⠀⠀⣀⠀⠀⠒⠂⠀⠀⢘⠉⠘⡲
⠀⠀⠀⠀⠀⣀⠀⠀⡨⠉⠀⠀⠀⠀⠁⠄⠀⠀⡐⢀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠛⠀⠀⠀⠀⢎⠆⠈⠈⠚
⠀⠀⠀⠐⡈⢙⠤⠀⠁⢀⡀⠤⠀⠂⡀⠈⠀⣀⠀⠠⠀⢀⠀⠄⠀⢀⠀⠀⠉⠁⠒⠠⠄⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠊⠙⠀⠀⠈⠀⠀⢀⠤⠀⠀⠐⠈⠀⠀⠁⠀⠀⢈⠀⠀⠂⢀⠀⠀⢞⡰⠀⠀⠈⡑⠀⡀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⡀⠐⠀⠸⠹⠀⡐⠁⠀⠘⠀⠈⠆⣆⡲⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠸⠗⠀⠀⢀⠌⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⡖⡢⠀⠀⠀⢫⣀⣩⠃
⠀⠀⠀⠀⠀⠀⡐⠣⡈⠀⠄⡠⠂⢀⠔⠁⠀⠐⠀⠀⠀⣶⠄⠀⡀⠀⢔⢲⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠒⠢⠁⠀⠈⠀⠐⠁⠀⢠⠠⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠁⠀⠀⢄⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠄⡀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠘⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠡⠰⠁⠄⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠛⠐⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠠⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠀⠀⠀⢣⠀⠀⡇⠘⠀⠇⠀⠀⡠⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⢇⠀⡇⠀⡜⠀⢀⠜⠁⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠆⠇⢠⠑⠠⠋⠀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠉⠉⠉⠉⠀⠒⠂⠠⠀⡀⠱⢄⣀⣶⣔⣴⢀⢈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠁⠀⢀⣀⡀⠠⠤⠤⠤⠄⠈⣀⡀⣰⣿⣿⠛⠘⢟⣫⡤⠀⠀⠒⠒⠀⠀⠉⠉⠉⠀⠐⢀⠀⠂⠀⠰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⠣⣼⣿⣧⣀⣀⢙⠿⠄⢀⠂⠒⠐⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡠⠒⠊⠁⠀⣀⠤⠰⠆⡉⠘⡽⡟⣻⡟⠿⢧⡀⢠⡌⠁⠢⢄⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⢀⡀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⣠⠔⠋⠀⢀⡴⠊⡁⢊⡄⠠⠂⢉⠁⣄⠀⠠⡀⠑⢤⡀⠉⠢⣀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠀⡔⠁⡜⠀⡙⠀⢠⠀⠈⢆⠀⠈⢢⡀⠙⢦⡀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠔⢁⠞⠀⡜⠀⢀⠃⠀⢸⠀⠀⠈⢆⠀⠀⠱⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠊⠀⢰⠁⠀⢸⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠱⡄⠀⢀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⡎⠀⠀⠸⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠾⠀⠀⠀⡀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠎⢀⠘⠀⢦⠁⠃⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⢀⠎⠀⡀⠀⠰⠀⠀⠁⡀⠀⠒⢀⡈⠀⠐⠀⣁⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠂⠂⠈⠁⢀⠁⠈⠀⠄⠁⠀⢠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⠐⣀⡁⢀⠀⠘⠀⡀⠀⡀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠂⠀⠆⢀⡁⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠂⠀⠠⡀⠱⠈⠀⠀⠠⠀⠰⠀⠄⠀⠠⠀⠀⠈⠀⠀⠀⠂⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠠⣀⠀⠸⡄⠀⡇⠀⡰⠋⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⠈⠳⡀⠃⠀⡇⠘⡴⠊⢀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤⡙⠄⠸⠀⣪⠔⠊⣁⣠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠉⣉⣉⣀⠀⠀⠀⠀⠈⠀⠤⠥⣤⣀⣀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠁⢀⡠⠒⢠⠀⠀⠀⡐⠲⠤⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡴⠋⠀⡰⠃⠀⣇⢠⠘⣆⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡸⠁⠀⠀⡿⠈⣇⠈⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⡀⠀⠀⠀⡇⠀⠹⠀⠀⠈⠁⢀⡀⠀⠢⡀⢠⠀⡇⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠠⢠⠂⠐⠃⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠤⢈⣑⠢⠑⠀⠆⢀⠎⠠⠔⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠁⠘⡀⢂⠎⠔⠊⠀⠀⠀⠀⣤⠀⣶⠀⠀⠀⠀⣀⣀⠨⠀⠀⠀⠁⠤⠬⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠌⠀⠀⠀⠐⣊⣁⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠔⠊⢀⠀⠀⡂⢄⡒⠢⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡪⠔⡀⡀⢀⠐⠠⠀⢀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠠⠀⠀⢀⠆⡄⠇⠘⢆⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠀⠇⠀⢂⠑⡀⠈⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⠄⠠⠋⠀⠇⠀⣀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡏⠀⢀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⣦⠀⠀⠀⠀⢸⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡

⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠑⠀⠀⡠⠈
⠀⠀⠀⠀⠀⣅⠈⠃⠆⢈⠰⠁⡁⠅⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠴⠀⠀⠂⢀⠄⠋⢀⠀⢄⠀⠀⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤
⠀⠀⠀⠂⠩⠖⠒⠄⡇⠀⠴⠀⠀⢀⠐⡠⠒⠄⠁
⠀⠀⠄⠈⠰⠂⠄⡀⠀⠁⡁⡐⢀⠈⠀⢀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠁⠀⠀⠀⠁⡄⠠⠀⠠⠀⣀⠐⠈⠃⠁⡀⠀⠀⠀⢄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠈⠈⠀⠂⠀⡐⠀⠰⠠⢀⡁⠀⢀⠁⠀⠀⠀⠠⠆⠂⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠄⠄⠐⠃⠁⠀⠄⠁⠀⠁⠀⠀⠀⣠⣬⣑⠂⡀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠠⢀⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⢲⠐⠣⠘⡀⠠⡀⠀⠠⠁
⠀⠀⠀⠤⠨⠀⠄⠁⠀⢁⠀⡦⠀⠨⠂⢈⡄⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠄⠀⠑⠄⠂⠀⠂⠈⠀⠘⠀⠢⠂⢀⠥⠉⡀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣒⠀⠉⠄⠀⠅⠀⠀⠀⢀⠈⠀⠌⠁⠀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⣤⠀⢸⠀⡶⢀⡀
⠀⠀⠀⠉⢁⠠⡈⠀⡄⠀⠀⠀⠈⡁⢀⡠⢀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡲⠙⣤⡡⠀⡏⣶⠁⠎⡴⡰⠂
⠀⠀⠀⠂⣂⠀⠂⠀⠐⠀⠀⠄⢀⠢⠄⡀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢕⡙⠆⠈⢿⡀⡿⠀⠋⣸⡾⠔⣃⠴
⠀⠀⠀⠀⠁⢐⠀⠁⠠⠇⠘⠀⠐⠓⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⢑⡢⠻⠶⢤⠤⠁⢠⠂⠉⣡⣴⡟⠀⢴⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡆⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢺⡭⠵⢶⢶⡀⠀⠀⢐⡚⠠⠤⣤⡬⠭⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⡰⣶⠠⢈⡄⠆⢐⠄⠑⠦⣤⠜⢡⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣜⡋⣶⢈⢀⡖⠘⣆⢡⣡⣼⣣⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠴⠁⡈⠿⡅⠀⠏⢡⣏⠺⠟⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠗⠘⠀⠀⠋⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣟⣻⣉⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣯⣿⣽⣿⣿⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠠⠤⡀⠰⣄⠀⠋⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⡤⠀⠀⠰⢄⠘⠀⠈⠀⣐⠊⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⢠
⠀⠀⠀⠀⠀⠀⣤⠄⠑⠀⠀⡄⠐⠋⠁⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢆⢀⠁⢀⢄⠔⣁
⠀⠀⠊⢀⡤⠂⠀⢀⠒⠒⠀⠀⠚⠀⠤⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢦⣴⣤⣇⢄⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡀
⠀⠀⠠⠏⠀⠐⠋⠁⡠⠂⠀⠁⠀⠢⡄⠀⠀⠈⠃⠰⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠒⣾⣿⠟⢿⠋⠄⠀⠠⠀⠀⠀⠀⠌⠂⠀⠀⠁⠩
⠀⠀⠀⡴⠁⡰⠀⠀⠀⠀⠆⠀⢶⠀⠀⠀⢀⠘⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠔⠨⠪⠁⢻⠠⠱⠑⠄⠒⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠭
⠀⠀⠀⠀⠰⠃⡔⠀⡆⠀⠀⠀⠀⠀⢸⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠘⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⡀⠢⠁
⠀⠀⠀⠀⠀⠸⠇⠀⠀⢸⠀⠉⢀⡆⠈⠀⠀⠁⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⣤⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠴⠒⣂⠀⣄⠐⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⣇⠀⠀⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣩⢭⣺⡴⠥⠄⠉⠓⠀⠀⠀⠀⢀⣀⠀⠘⠳⣄⠀⠿⠀⠆⢠⠟⠀⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡰⢊⡌⡿⡑⠂⢢⡀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠀⢀⠀⣀⠄⠀⠐⢀⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢁⠘⠀⡇⠃⣤⠀⠁⠀⠀⠀⠀⠀⠉⠉⢉⡁⠀⠤⢵⠷⣔⠂⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⢀⠀⠸⠀⠀⠉⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡄⠀⣦⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠐⠄⠈⠄⠀⡁⠀⠀⠀⠀⡞⠀⠀⡇⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢢⡀⢁⢀⠀⡼⠀⣶⠁⠂⠀⡀⠀⠀⠀⠀⠀⢠⢳⠘⠹⠸⠀⠃⠏⠜⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢄⠘⠦⡗⢴⡸⡀⠁⣬⢁⠀⢀⣪⠔⠀⠀⠀⢤⡙⠆⠁⠀⡀⡀⡄⡀⠀⢀⠞⠐⢋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠤⠐⠈⠒⠸⠔⠀⠀⡄⠒⡒⠬⢉⣀⠙⢮⠁⢇⣎⣔⣀⠂⠁⡀⠀⠀⢀⣓⠒⠄⠀⠀⢠⡁⠙⠀⠀⠂⠠⠖⠀⠤⢖⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡄⠀⡉⠉⠀⠠⡇⢌⠁⠂⣉⣤⣀⣬⣭⠽⡖⣻⣿⣿⣋⣠⠖⠚⠀⠀⠀⢈⣉⣉⠀⠀⠙⠂⢀⡄⠂⠀⠀⠀⠀⠀⠀⠵⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⠁⢐⠉⢀⠐⠀⠊⡀⢛⠙⠋⣧⠠⠀⣘⢶⢪⣋⡁⣙⠛⠳⢄⠒⠀⠠⠴⠖⣂⣁⡀⠀⣋⠀⠀⠀⠆⠀⢀⠠⠄⠀⢀⣒
⠀⠀⠀⠀⠀⠀⠠⠐⠀⠰⠈⢦⡀⠄⠀⠀⠂⠀⠡⠄⠐⠛⣻⡔⠀⡁⡘⣩⠙⡉⠤⠕⡀⠨⢐⡠⠄⠐⢛⣧⢋⠀⣠⢕⠀⡀⡀⣤⡐⡌⠓⠀⢀⡲⢤
⠀⠀⠀⠀⠀⠀⠬⡁⠈⠀⠂⠐⠀⠀⢉⠀⠘⠈⠐⠘⠨⠏⡳⠆⢈⡔⠀⠋⠈⠁⠸⠈⣵⢄⡀⠙⠃⡀⢩⠞⡧⣠⡔⠃⡐⠃⡇⠉⠁⣅⣢⣠⡱⡝⠂
⠀⠀⠀⠀⠀⠀⠀⡄⢊⡈⣰⣌⠤⠈⢈⠁⡈⣁⠉⠀⠄⠲⠐⠀⠘⠁⠀⠀⠄⠀⠈⠆⠐⠄⠠⢈⣡⣍⣥⠛⡹⣏⡴⢾⢡⢰⠀⢰⢤⠁⣇⠃⠓
⠀⠀⠀⠠⡄⠢⡄⢱⡜⠸⡿⠑⣆⢷⠒⡀⣀⢠⠂⠁⡀⠂⢠⠀⢠⠀⢠⢀⠀⣀⠀⠂⠦⠐⠢⡿⣵⣿⣿⣿⡟⢂⢁⠙⠛⠙⣤⡘⣾⠐⡆⢠⡄
⠀⠀⠀⠄⡈⠢⡝⢠⡄⣏⠗⣦⢇⠮⣰⣮⡽⠶⠀⠀⠁⠈⠄⠂⠀⠄⠃⠎⠔⡡⢊⡤⠲⠈⠁⣖⡿⣿⣿⣿⡯⣛⡀⠰⣮⡛⣿⣧⢹⢠⡇⡼⢡⡿⢠⡄
⠀⠐⢒⡂⠌⣁⡈⠣⡁⣽⣼⣴⣡⠂⠁⡀⢀⣀⠀⠨⢉⣑⢊⡓⠄⠀⠀⢈⣨⣀⣀⠐⠂⠒⠀⠫⡄⣡⠟⠯⣃⠉⡹⢷⣬⣛⢮⣿⣾⣿⣿⣵⡫⢐⣥⡆
⠀⢀⡀⢀⠤⠬⠬⠟⣻⣿⣿⣻⣧⢞⠋⠀⢨⡥⢖⣂⠈⠭⢙⠉⠂⠇⢰⠟⠋⢽⡋⣯⢽⡓⠈⠁⠤⠉⢠⡄⠱⢈⠻⢾⢷⣯⣿⣿⣿⣿⣿⣿⣿⣭⣴⣶⣏
⠀⠒⠈⠀⠤⠐⣨⢹⣣⣯⣁⢬⢻⡛⢖⠃⠂⠿⠋⣠⠖⢋⡉⠁⠀⠀⠀⢠⡭⡑⡷⢌⡙⢿⠀⠋⠀⠀⠦⠀⠀⢘⣷⠾⠿⣛⣿⣿⣿⣿⣿⣿⣿⣒⠶⠶⣄
⠀⠀⠀⡠⠔⠁⡀⡘⢹⠈⡇⣠⢀⡈⠺⣷⠒⠀⠘⢁⠄⣿⠀⡀⠀⠠⠀⢠⢹⢸⡕⢤⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣶⣿⢟⡽⣻⣿⣿⣿⡿⣮⣙⠻⣖
⠀⠀⠈⠠⠀⠀⡴⠁⠍⡼⠛⢸⡀⠙⠦⠈⠠⠀⠀⡟⠀⡇⢰⡇⠀⠀⠀⠛⡁⡀⣧⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡌⠤⣾⣡⣿⢸⡏⣧⢻⡌⢿⠳⠈
⠀⠀⠀⠀⠀⠁⠱⠆⠀⠿⠀⣄⠳⣄⠐⣃⢤⡀⠀⠃⠀⠧⠸⠓⡀⡠⣦⢰⡄⠀⠋⠤⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠀⠘⢹⢇⣾⡖⡿⢚⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⣤⠶⣴⣆⡌⣀⠰⠦⣀⠋⠀⠀⢀⠏⠰⠞⣂⠘⠀⠅⠂⣀⠼⠐⠀⠀⠰⠦⢍⠙⠓⠒⠳⢦⠀⡀⠀⠀⢀⡔⣁⠠⠔⠂
⠀⠀⠀⠀⠀⠋⠰⠆⠘⠢⣿⣬⣷⣿⣿⣿⡿⠿⣀⢀⠀⠋⠐⠏⠠⣀⢩⢉⠀⠁⠌⠠⡁⠘⠈⠑⠂⢀⡠⠤⠘⠛⠓⠀⠢⠡⠁⢠⣏⠝⣋⠙⣒⡒⠤
⠀⠀⠀⠀⠀⠀⠀⣤⠌⠁⣐⠶⣻⣿⣿⣿⡯⡑⠋⠀⠀⠟⠁⠀⢤⡀⠘⡈⢀⠈⠁⠉⢠⠈⡄⠀⠸⢁⣔⡋⣩⡤⠖⠒⠂⠀⠀⠀⠀⠂⢭⣣⠑⠪⣕
⠀⠀⠀⠀⠀⠉⠀⠀⣠⠀⢼⠋⠈⢋⣩⣍⢷⠘⠻⠂⠰⡎⠙⡃⠂⠐⠄⠰⢀⠀⠈⠀⡀⠔⠀⡀⠋⠅⢀⠖⠁⢠⡞⢀⠀⠀⠀⠀⡘⢎⢲⢭⠙⠦⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⡄⠙⠀⠎⠁⠘⠑⠂⠀⠆⠰⢤⠀⠀⠐⠀⡂⠀⠀⡄⠀⡁⢈⠀⡁⠂⠈⠃⠀⢠⠎⢸⠃⣸⠀⠀⠀⠀⣽⠸⠘⡇⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠐⠂⠈⠁⣀⠀⠀⠀⠈⣈⣁⢃⠰⠀⠠⠅⠤⢁⠈⠀⠀⠸⠌⠁⠀⠞⠀⢸⠀⣿⣰⠀⡄⡄⡅⡄⠄⢣⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⢂⠐⡀⢠⢀⡠⠖⠉⢀⠘⠀⠀⠀⠀⠀⠈⠀⠻⠁⠀⠁⡇⠸⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠈⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡇⠀⠀⠀⠀⠀⢰⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠘⠛⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⡄⠀⠀⠀⣀⣄⣄⠀⠀⢀⡟⣾⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣦⠀⠀⠀⠀⠀⠈⢷⣳⡀⠀⠀⢻⣿⠛⠀⠀⢸⢇⡏⠀⠀⢰⣿⠁⠀⠀⢀⡴⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⢀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣸⠁⠀⠀⠟⠁⠀⠀⣠⢋⡴⠋⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢦⡀⠀⠀⠀⠈⢻⣇⠀⠠⡿⡄⠀⠀⣿⡏⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⢀⣴⣮⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⠀⠀⠀⠀⢻⣆⠀⢧⢱⠀⢠⣿⠀⣰⢿⠀⢀⣴⠟⠁⠀⠀⣴⣤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠻⡄⠘⣿⡄⢸⠇⢀⣿⠏⠰⠋⠁⠀⠀⠀⠈⠿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢭⣝⣓⡶⢤⣄⣀⠀⠙⢦⣑⣆⠉⠀⠘⠃⠀⠀⠘⠁⠀⢀⣠⣶⡿⠇⠀⢀⣀⣠⡤⠴⢖⣒⣛⣩⡭⠽⠇
⠀⠀⠀⠀⠀⢠⣴⣶⣒⣦⡄⠀⠀⠀⢠⡤⢬⣉⡙⠛⠛⠿⠷⣶⣬⣉⡃⠀⠀⠀⠀⠀⠀⠀⠐⠋⢩⣥⠶⠶⠿⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢖⣒⡿⠿⠛⠃⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠⣈⠉⠓⠲⠾⠃⠀⢰⣷⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢛⣉⣥⠴⠖⠛⠉⠀⠀⠀⠀⢀⢔⡿⠃⣠⠆⠀⢀⠀⠀⣷⡀⠈⠻⣷⣄⡀⠀⠀⠀⠈⠛⠋⠁⠙⠻⣿⣒⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⣀⣄⣄⠀⠘⠋⢀⣴⠏⠀⠀⢸⡆⠀⠹⣿⠀⠀⠈⢳⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣧⠀⠀⠀⠀⢻⣿⠓⠀⠀⣰⡿⠃⠀⣴⠀⠈⣷⠀⠀⢉⣄⣄⠀⠀⠙⢦⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠀⢀⣠⡤⠀⠀⠀⢠⢞⡟⠁⠀⣸⣿⠀⠀⣿⡆⠀⢸⣿⡟⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟⠀⠀⠀⣰⣫⠏⠀⠀⢀⣇⡇⠀⠀⢹⣷⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠻⣦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢰⡿⠃⠀⠀⠀⠸⠾⠁⠀⠀⠸⣿⡆⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠸⣞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠄⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⡄⠀⠀⠖⠃⠀⠀⠀⣜⣀⣀⠴⢤⢦⠀⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠪⢣⠀⠀⠁⠀⢀⡠⡴⠞⠂⠀⠈⠉⠛⠲⠤⡀⢣⠀⢄⡴⢀⡡⠴⠂⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠶⠶⠶⠦⠤⠄⠀⠁⠀⠀⠀⣀⣚⡶⠤⠀⠀⠀⡈⠀⠄⠀⡤⠀⠀⠫⠦⢓⡒⠛⠛⠛⠃
⠀⠀⠀⠉⠀⠀⠠⠔⠒⠀⢀⡀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠁⠁⠠⠄⣁⠄⠀⠀⢀⠢⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠴⠋⠀⠄⠀⠀⠀⢄⠈⠲⢄⠀⠀⠈⠀⠀⡀⠀⡀⠀⠃⠆⠀⢣⠀⢰⡀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡘⠀⠀⠀⡆⠀⢢⠐⢦⡁⡬⠀⢀⡞⠀⠀⠉⠀⠀⠀⠐⠀⢣⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠙⣧⣠⠏⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣷⠳⣄⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⡴⠃⠠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡰⠁⠢⢄⠀⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡠⠖⠀⠀⠁⠂⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⢁⡌⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠀⠐⠀⠐⠀⠀⠄⠐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⠌⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠃⠀⢠⠄⠀⠁⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠂⣁⠀⠁⡐⠀⠀⠀⠀⠀⠀⢤⡒⣿⣈⣤⣁⢏⡞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣤⡑⠄⣈⣄⡀⠀⢁⠀⠀⠀⣘⠒⢽⣾⣿⣿⣿⣏⡤⠔⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⣿⣶
⠀⠀⠀⠀⠒⠊⡉⡿⠇⠤⣌⠁⠀⠀⠠⣬⣭⣽⣿⣿⣿⣿⣿⣿⣉⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠿⠿
⠀⠀⠀⠀⠀⠀⠓⡑⠂⠀⠀⠀⠀⠀⠀⣡⣶⢟⡿⣿⣿⣿⢿⣛⢶⡈
⠀⠀⠈⠀⠀⠄⠈⠀⠀⠀⡑⠀⠀⡀⠀⠀⠐⢋⣼⠃⡇⡏⣣⠹⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠄⠀⠂⠀⠄⠀⠀⠀⠈⠈⠀⠁⠀⠀⡈⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢀⠁⡐⢀⢢
⠀⠀⠀⠀⠀⠀⠈⡀⢈⡀⢂⡓⡈⠂⢂⡀⠠⠐⠀⠀⠀⠀⠈⠀⠀⠈⠀⠰⠠⡃⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠈⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠐⠠⠀⠄⣴⣁⣼⣷⣼⠷⠀⠀⠐⠀⠀⠀⠈⠀⠠⠀⠁⠀⠀⠈⠀⠁⠀⡑⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠠⠖⠉⠂
⠀⠀⠀⠀⠀⢀⠀⠄⠁⡰⡆⣻⣿⣟⠀⠋⠁⠐⢀⠀⢈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⢀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠅⠀⠖⠾⡃⠉⠀⠂⠀⠀⠀⠀⣀⠀⠈⠄⠀⠠⠀⠀⠀⠐⠐⠀⠀⠈⢁⠀⡀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠰⠈⠠⠀⠂⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡘⢡
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣛⡹⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣬⠑⠀⠀⣠⣿⣼⣇
⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⢠⠿⠿⠁⠀⠀⡀⠀⠀⠀⢀⡡⠤⠀⠀⠀⠀⠐⣤⠇⠸⢿⠀⠂⠔⣿⣟⡠⠞⣷
⠀⠀⠀⠀⠀⠀⢸⡰⡆⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⣳⡜⠀⠀⢘⡁⢠⡦⠀⡀⠀⠸⡆⡾⠀⠣⠈⠠⣼⣿⠟⠁⠀⣠⡇
⠀⠀⠀⠀⠀⣴⡾⠀⠀⠀⡀⠀⠀⠚⡉⠀⠀⠤⡄⠀⡶⢰⡖⣠⡜⠃⠀⠁⠘⢇⣠⡴⠇⠽⢤⣀⠀⡇⠿⢃⣤⠶⠋⠁⣿⠀⢸⡀
⠀⠀⠠⠁⣿⣿⠟⢉⡁⢈⣯⡠⠰⡿⠇⠀⢀⣶⡇⢠⣧⣼⡅⠘⠀⣤⣼⡟⣴⣿⣁⣀⣀⣀⣤⡬⠷⠁⢴⠛⣵⠀⣀⠴⠀⢀⣎⢸⡄
⠀⠀⣇⢰⣏⡩⣶⢁⠀⡂⠀⡱⣤⠁⠸⠿⠤⠙⠁⡞⠁⠈⣧⠀⠀⠏⠙⠃⣾⣅⡀⣀⡀⣀⡄⡠⣾⣷⠈⢆⣿⠊⢉⠄⠀⢘⡁⢀⣙
⠀⠀⠸⡢⣿⣧⡜⢂⣉⠔⣤⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠀⠀⢻⣯⣽⣯⣼⣧⠯⠻⢿⠇⠀⠀⠡⣔⠉⠀⠀⣫⡀⢀⣈⣇
⠀⠀⠀⠘⠻⢿⡿⠧⠁⠈⠔⠁⠀⠀⢀⣼⣤⣀⣀⠀⠀⠀⠀⡟⢃⠀⠀⢀⠀⠙⠶⣶⠶⠖⢒⡾⠋⠀⠀⠀⠀⠀⠀⣠⣾⣯⣥⣤⣤⣭⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣏⠉⢄⠀⠀⢰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠉⠂⠘⣧⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠌⡌⠐⠀⠆⠱⠈⠆⡆⠀⢘⠀⠠⠋⠰⠈⠀⠘⢠⠁⠚⠛⢠⢰⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

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



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

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


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


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


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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⢀⠀⠀⣸⠀⠘⠛⠛⠛⣧⠀⢰⡆
⠀⠀⢀⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⢠⠄⣀⠀⡀⠀⡄⢠⠀⠲⠈⠁⢀⣿⡇⠀⢠⣤⣄⠈
⠀⠀⠈⣡⡤⢠⠄⠀⣴⡇⠀⠀⠀⠀⠀⢠⡄⠀⡤⡀⢄⠀⠁⠀⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠹⠿⠟⠀⠀⢀⣄
⠀⠀⠀⠀⠰⠈⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠰⡿⣄⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠉⠁⠈⠉⠀⠁⠡⠶⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠐⡅⠀⢠⠃⠀⠀⠃⠈⢀⣴⣷⡀⠛⠛⢁⣀⣀⡀⠀⢀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠑⢸⠘⠀⠀⠐⠰⠾⣿⡿⠆⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⢛⡉⣉⢳⡀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣀⠀⠀⢠⣈⣠⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠖⢳⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⠙⠀⠀⠘⠖⠃⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⢀⣠⣶⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢄⡒⠀⠀⠸⠀⠀⠀⠚⠁⠀⠛
⠀⠀⠀⠛⠛⠿⠇⠀⠛⠋⣤⡶⠀⡀⠀⠀⠈⠥⠀⠘⠂⠀⠀⢄⡐⠀⠀⠀⠸⡀⠀⠀⠀⡀⠀⠀⠛⠀⢀⢀⣀
⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠻⣿⣿⣿⣄⠀⠀⣶⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠸⠇⡌
⠀⠀⠀⠻⠿⢿⣿⡷⠾⠛⠀⠀⢨⣯⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⡎⠀⠀⠀⣌⠀⠤⠀⠀⢠⡄⣬⠀⠀⢠⡆⠅
⠀⠀⠀⠈⠁⠈⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉

⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠿⠿⣿⠿⠗⠀⠀⠀⠀⠉⠀⠀⢀⣴⣄⠀⠹⠇⢀⡀⠀⢰⣿⣿⣷
⣿⡀⠀⠀⣿⣿⣿⠄⠀⠆⠀⣴⡁⠀⠀⠀⣾⣿⣷⠄⠦⠀⣾⣿⣿⠆⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠉
⣿⣷⡀⢴⣿⣿⣿⣧⠀⠀⣼⣿⣷⡀⠀⣠⣿⣿⣿⡄⠀⠰⣿⣿⣿⡷⠀⢀⣄⣀⠺⠿⢿⣿⠿⠟⠂
⠻⠋⠁⣼⡿⣿⣿⣷⠀⢀⣼⣿⣷⡀⠀⣹⣿⣿⣿⡏⠀⠼⠿⣿⠿⠿⠄⣹⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢈
⠀⠠⠄⠀⠀⠙⢠⡄⠀⢉⣿⣿⣿⡉⠀⠛⠛⣿⠛⠛⠂⣄⢠⠘⠀⠀⠰⣿⣿⣿⠧⠀⠉⣀⠀⠐⢻⣤⡞
⣤⣤⣤⠄⠀⠀⣾⣿⡀⠚⠛⣿⠛⠛⠂⠀⠀⠉⠀⣸⡄⣏⢹⠀⣼⡆⠼⠿⣿⠟⠷⢀⣾⣿⣷⡀⠿⠛⣿
⠿⢿⢿⠀⠀⣼⣿⣿⣧⠀⠀⠉⠀⢦⡼⣆⠀⠃⢠⣿⣧⠈⠉⣸⣿⣿⡀⠀⡉⠀⠀⣸⣿⣿⣿⡇⠀⠀⣿
⠀⠸⢸⠀⣰⣿⣿⣿⣿⣇⠀⠋⠀⣾⡿⠉⣀⠀⠛⢿⠿⠓⢰⣿⣿⣿⣷⠀⠉⠀⠰⢿⡿⣷⣿⡿⠆⠀⠏
⠀⠀⣰⡀⠛⠛⢻⡿⠛⠋⠀⠀⠀⠙⠶⠿⢫⣾⣿⣄⠀⢀⣿⣿⣿⣿⣿⣇⢰⡆⢰⣿⣿⣿⣿⣿⡆
⠀⣰⣿⣷⡀⠀⡀⡀⠀⠀⣴⣶⣶⡀⠀⠀⢿⣿⣿⣿⠆⠀⠀⠉⠻⠉⠁⠀⣾⣷⡀⠀⠀⠟⠀⠀⠀⠀⠈
⠀⣹⣿⣿⡉⢰⡍⣵⠀⢈⣿⣿⣿⡅⠀⣰⣿⣿⣿⣿⢧⠠⢶⣀⡴⠃⠀⠾⢿⡿⠷⠀⢀⡄⠀⣼⣶⣶⡀
⠴⣿⣿⣿⡿⠆⠉⠁⠀⢾⣿⣿⣿⡿⠄⣹⣿⣽⣿⣽⣯⠀⣾⢿⣷⣀⣁⠀⢀⡀⠀⢠⠀⠀⢠⣿⣿⣿⡄
⣰⣿⣿⣿⣷⣄⠀⠂⢀⣾⣿⣿⣿⣷⡄⠛⠛⢻⡟⠛⠛⠃⡄⠀⣿⣿⣿⣿⣿⠀⢠⣿⣧⡀⢻⣿⣿⣿⡟
⠀⠀⢻⠁⠀⠀⠀⠀⠈⠁⠀⢿⠀⠀⣄⠀⢄⠈⠁⢀⠀⢀⣿⡀⡟⡇⠀⢸⢸⠀⣠⣿⣿⡀⠟⠛⣿⠛⠛
⠀⣧⠀⠀⠂⣰⣶⣶⡀⠀⠃⠀⠀⠀⣸⣶⣏⠁⠀⣀⢀⣾⣿⣧⠀⠁⠀⠈⠈⠘⣻⣿⣿⡛⠀⠀⣉⠀⠤
⣼⣿⣆⠀⠀⣽⣿⣿⡏⠀⣶⣶⣶⣶⣿⠋⠙⠁⢠⣿⣎⠙⠟⠉⠁⢠⣾⣦⡀⠘⠛⢻⠛⠛⠂⣴⣿⣷⡀
⠻⡿⠟⠂⢾⣿⣿⣿⡿⠄⡟⡟⠛⢻⣿⠀⠀⠐⢻⣿⣟⠂⠀⠀⢰⣯⣿⣿⣷⡀⠀⡈⠀⠀⢠⣿⣿⣿⡅
⢠⡄⣀⠀⣼⣿⣿⣿⣿⣄⠧⠃⣤⠘⠟⠀⢀⣠⣿⣿⣿⣦⡀⠀⣴⢿⣷⢿⣿⣄⢰⡟⣳⠀⣹⣿⣿⣿⣏
⢾⣽⡅⠈⠁⠀⢹⠁⠀⠀⠀⣸⣿⡆⠀⠤⠀⣰⣿⣿⣿⣆⠀⠸⣿⡿⣿⣿⢿⡿⠀⠓⠃⡄⠉⠉⢿⠉⠉
⣤⣙⡟⠀⠐⠂⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠘⠋⠉⣿⠉⠉⠃⣰⣿⣿⣿⣿⣿⣿⡆⠀⣸⣿⡀

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣿⡇⠀⠀⠀⠀⠀⡇⠰⠖⠘⡸⢙⡤⢤⢐
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠋⠀⠀⠀⠀⠘⠐⠻⠈⠒⠀⠱⢎⣀⢒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⠀⠀⠀⠀⣰⣀⡀⢠⡴⡴⢤⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠖
⠀⠀⠀⠀⠀⠀⠀⣿⣾⢿⣽⠀⠀⠀⠀⠩⠸⠿⣿⡖⣲⡀⠿⡗⠳⠗
⠀⠀⠀⠀⠀⠀⣴⣯⣿⠿⣷⠆⠀⠀⠀⢴⣶⢶⡂⣟⣸⣶⣶⡶⠲⠶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠐⣿⣯⣿⢿⣿⣾⠄⠀⠀⢸⡿⣢⣴⣷⣶⣶⣶⡔⠤⠖⠀⠀⠀⠀⡼⠀⠀⠀⠔⠀⡰
⠀⠀⠀⠀⠀⣼⣹⣹⣿⣿⢻⣿⣦⠀⠀⠐⣪⣼⣿⣿⠟⢻⣿⡇⠄⡀⠀⠤⠀⠈⠑⠀⢀⣴⠃⢀
⠀⠀⠀⠀⢠⣟⣻⣿⣿⢿⣿⢿⡾⢀⠀⠈⠁⠐⣿⠁⢀⡈⢻⣇⠈⡇⢀⡰⢄⣠⣦⣾⢟⠋⢀⠄
⠀⠀⠀⠀⡷⣿⣿⣿⡏⠈⣹⣗⣿⠟⠢⣤⡀⠈⡿⡬⠿⠧⣿⡇⠀⠃⠀⠀⠈⠀⠁⢸⠁⣆⠊⣀⡀
⠀⠀⠀⠀⢛⠻⠁⢘⠟⢱⡏⠛⠀⡟⢰⡄⢀⠠⡴⣦⣾⡧⠾⠭⣦⠀⠀⠀⠀⠀⠀⠈⡇⡃⠀⠈⣤⠰⡃
⠀⠀⠀⠀⢷⡤⠀⣰⠀⠈⠀⢀⣿⡟⣾⠁⣸⡇⠠⠾⠿⠷⠶⠶⠶⠶⠺⠁⠀⠂⡤⠈⠁⠀⣿⠀⢻⠞⣧
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠐⠄⠃⠔
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠭⢹⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠄⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠒⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠀⠀⢰⠄⠀⢀⠀⠀⠠⢠⠀⠀⠀⢀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠐⠀⠀⠀⠀⠠⠉⠀⡀⠀⡄⠀⡀⠘⠀⠀⠘⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⢀⡈⡴⢶⡎⣀⠀⠠⠄⠀⠔⠁⠑⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⡚⠣⡀⠀⠀⠀⠀⠢⠀⠠⠃⠀⠀⠀⠀⠁⠀⠀⠲⠀⣨⠡⡠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢴⣟⣳⠡⠠⠤⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⢀⠀⠀⣠⠐⠫⠁⠃⡄⠀⢠⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠠⢔⡀⠄⠀⠀⠤⠀⠌⢢⣀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠐⢨⢇⠜⡕⠂⠀⠀⣀⠀⠀⠈⠑⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⠀⡱⠒⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡇⠀⠀⠀⠀⠀⠀⠀⣾⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⣸⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡳⢦⡀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⢀⣤⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣦⡀⠀⠀⢀⣠⣤⠤⣤⣤⣀⠘⠁⠀⠀⠀⢀⣤⠾⣋⣵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣠⡾⢋⡥⠶⠶⠶⢦⣍⡛⢦⡀⢀⣴⣿⡷⠛⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡴⢋⡴⢖⣚⣒⠶⣬⡻⣆⠻⣆⠉
⠀⠀⠀⠀⠀⠀⠿⣭⣉⣉⣉⡛⠛⠶⠶⢤⣀⠀⠀⡟⣸⢡⡏⡼⣫⠥⣭⡙⣮⢳⡜⣇⢻⡄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⣠⡀⣇⢻⠸⡞⣟⢧⢾⡆⣷⢸⡆⡇⣿⢸⡇⠶⢿⣿⣿⣯⣭⣭⣭⣭⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⡽⣎⢷⣙⢮⣽⣭⠾⢃⡾⣱⢇⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠻⣌⠳⣭⣓⠲⠖⢚⣋⡴⢋⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣦⠀⠈⠳⣌⡛⠦⣭⣍⣉⣩⡥⠞⣋⡴⠋⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⣥⠞⠁⠀⠀⠀⠀⠉⠓⠶⠦⠤⠶⠖⠛⠉⠀⠀⠀⠈⠻⣍⡳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠠⡶⡄⠀⠀⠀⠀⠈⠙⢦⣉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡟⠀⠀⠀⠀⠀⠀⢷⠹⣄⠀⠀⠀⠀⠀⠀⠉⠳⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⠇⠀⠀⠀⠀⠀⠀⠘⣇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢹⣿⣿⣿⡇⠙⣿⢸⠃⠇⠈⢸⡏⣻⡏⣿⢿⣿⣿⢛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢟⢿⣿⣷⠀⢹⣿⠻⡅⠀⢹⠘⠀⠀⠀⠸⠀⢃⠀⡿⠣⡾⠁⠠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣎⠳⡀⠂⠫⠃⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠜⡰⠱⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢿⡉⠻⣯⡂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⣹⠿⣿⢿⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠻⣤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⡕⠋⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣍⠻⢦⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢋⢴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣪⠛⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢉⣿⣿⣿⣿⣿
⣿⣿⣾⣍⡋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣟⣿⣿⣿⣿
⡷⠷⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣞⣿⣿⣿
⣿⣯⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠏⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢛⣻⣿⣿
⣾⣯⢤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠀⠈⠹⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣠⣿⣿
⣿⡿⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⢠⡀⠀⢹⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣿⣿⣭
⣿⣿⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠘⠀⠈⢳⡄⠀⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢬⣭
⡿⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠿⣿
⣿⣖⣛⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⡶⢶⣮
⣿⣿⡻⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡞⣷⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣙⠿⣿
⣿⣮⣡⣀⣄⣤⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⣷⣿⣿⣿
⣿⣿⣿⣿⡟⠍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣽⣻⣿⣿⣿
⣿⣿⣿⣿⣾⣛⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣉⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢴⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾⡣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⢢⣀⢵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⢀⣠⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⣰⠇⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠐⡀⣄⣆⢰⣄⠰⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⡿⡕⠀⣼⠀⣴⣧⢎⡄⢸⢠⡄⣇⠀⡀⡈⠀⠀⣿⡄⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣹⣾⣿⣿⡄⣾⣼⣧⣿⡆⣷⣾⣇⡰⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⣀⣤⠶⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠤⠤⢀⢀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠄⡀⠂⠀⠄⠀⢀⠀⢘⡀⠀⠀⠀⡠⠀⠀⠨⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡀⡋⠁⠀⠈⠂⠀⠀⢠⠃⠀⠀⠉⠀⢤⠈⠀⠀⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⢄⠀⠀⠀⢐⢯⠀⠀⠀⠀⠖⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣶⣾⣧⣜⢦⠀⠀⣞⠀⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠁⠀⠀⠀⠈⠙⢦⣠⠻⣧⣾⠇⠀⠀⠀⠀⡀⠀⠠⠂⢀⠀⠀⠀⠺
⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠇⠀⠀⠀⢰⣧⣼⡦⢿⣦⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠠⠀⠀⠀⠀⠁
⠀⠹⢄⠀⠀⠀⡄⠀⢳⠀⠀⠀⠀⣠⡆⠀⣨⣍⣭⠖⣩⡿⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⠶⠁⠀⠀⠐⠁
⠀⠀⠀⠛⠢⡈⢧⠀⠘⠀⠀⠀⠀⠉⢃⠀⠙⠛⢿⣶⣿⡇⠀⠀⠀⢀⠔⣙⣀⡚⣀⢠⠀⠀⢀⣠⡦⣉⣠⠊
⠠⡄⠀⢀⠻⣤⠿⠗⠀⠘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⢸⡷⠀⣠⡴⠟⠛⠛⠙⡁⠉⣠⣦⣴⣿⢿⠔⣠⠃
⠀⠀⠀⠀⠄⠻⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄⣦⡀⠸⢿⠟⠢⢀⠀⠐⠗⠀⠻⠛⠋⣹⣿⡿⠀⢀⡿⠤⠄
⠀⠀⠀⠄⠈⠂⢒⣇⠀⠀⠀⠠⠀⣼⣷⠄⠘⠿⠟⢹⣶⣿⠂⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⡟⢐⠀⠈⠁
⠀⠀⠀⠀⠐⠌⣻⣿⣦⡀⣠⢤⡾⠋⠀⠀⠀⣶⣤⣷⡟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⡤
⠀⠀⠀⠀⠀⠀⠀⠹⣍⡻⠦⠈⠁⠐⠒⠀⠀⠈⠉⠉⣶⣤⣿⠀⠀⠀⣀⠀⠀⠠⠐⢀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⣶⡿⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠛⢠⣤⣀⠀⠀⠙⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠁⠀⢸⡟⡤⠄⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⠣⣀⣀⡈⢒⠀⠐⠀⠀⠀⡀⠀⠊
⠠⠒⠂⠀⣰⠏⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⡾⠀⢀⣄⣶⣤⣀⣦⢀⡾⠁⡌⠸⠛⠉⠠⠘⠋⠀⠀⠄⠘
⠀⠀⠀⠐⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢈⣻⡿⠍⢻⣿⡊⠀⠀⠀⠊⠁⠠⢄⠀⡠⠒⠀⠉⠛
⠀⠀⠀⢇⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡁⣨⡴⠚⠍⠉⢐⠦⣄⠈⠑⢦⡀⠀⠤⠒⠉⠉⠑⠒
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠍⠀⢾⣦⡷⠻⣾⡿⠀⠀⠀⠁⠀⠢⣤⣞⡁
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠷⠲⢤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢬⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⡸⢣⢇⢔⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢱⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⠀⠈⠀⢀⠴⠙⢻⣶⠖⠀⠀⠀⠀⠐⠀⢀⠀⠀⢉⢶⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠀⠀⠀⠀⢠⢡⣛⠻⠿⣧⠀⠀⠀⠀⠸⠋⠘⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢀⠐⠿⣳⡆⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣢⠇⢰⡄⠀⠀⢩⠶⣝⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠌⠀⠀⠀⣠⠀⡌⠣⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡴⣰⢰⡇⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⡀⠀⠀⠀⠈⠀⠠⢦⣄⠉⠀⠂⠀⠁⣊⢞⢔⣭⣠⠄
⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠒⠲⢿⡢⠀⠀⠀⠜⠁⠄⡽⠷⠭⠤⠀⠄
⠀⠀⠰⠄⠀⠈⡹⢦⠀⠀⠀⢀⠀⠄⠀⠋⠸⣄⡄⠂⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠨⠙⢒⣨⣍⡙⠃
⠀⠀⠀⣤⢀⠀⢨⠷⠠⠀⠀⠐⠻⠀⠀⠀⠁⡤⢿⣥⠀⠀⠀⠨⠀⠀⠠⠄⢀⠀⢀⠀⠀⠲⡤⡙⢾⣛⠅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠶⡶⠀⠄⠀⠀⠠⠂⢴⡧⡎⠀⠸⠀⠁⠀⢘⡛⠓⠭⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠓⠁⠃⠀⠀⡟⠋⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⣶⠀⣤⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠸⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢤⣄⢣⠀⣰⢷⢸⢀⡴⢃⡤⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⢇⡖⡆⢰⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢱⢀⡄⠀⠰⡰⠃
⠀⠀⠀⠰⠦⠭⠓⣰⠃⠈⣇⣙⣚⠁⡀⠀⠀⠀⠀⠠⣄⠀⣈⣓⣀⡼⠀⠸⣄⣁⣊⠀⣀⡤⠀⠀⠀⠑⠂⠈⠳⢌⡞⢹⡀⠜⠁⠀⢀⠤
⠀⠀⠀⣀⡛⠯⣉⠁⠀⠀⠈⠀⣠⠞⡥⠄⠀⠀⠀⠀⠀⢈⠣⢄⡀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠛⢉⡿⠛⠛⢿⣛⠿⠃⢀⣀
⠀⠀⣠⣤⠴⠆⣼⠀⢀⣀⠀⢸⢑⡒⠶⠤⠀⠀⠀⣀⠨⠍⢐⠂⡏⠀⣀⡀⠹⡄⡊⠭⠁⠀⠀⠀⠀⠲⠶⠓⢨⠛⣠⣴⠚⣇⠴⢤⣄
⠀⠀⠈⠀⡴⢁⣧⠖⣋⡈⣑⢦⡇⠻⡆⠀⠀⠀⠀⠁⠀⠘⠉⠸⡤⠞⠡⢨⠲⠿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⠊⠁⡀⠁⠺⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢰⢹⡇⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠛⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡹⡄⢠⡿⣆⠀⣴⢢⡶⠀⠀⠀⠀⠀⠀⠘⢦⡘⣧⠀⣠⠀⠀⡟⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣦⠀⡀
⠀⠀⠀⠘⠓⠶⠕⢀⣞⠁⠽⡄⠋⠭⠖⠂⠀⠀⠀⠀⠰⠶⣬⡳⠙⣰⣿⡆⠘⠐⣫⣤⡆⠀⠀⠀⠀⠀⢀⣀⡴⣣⠏⠈⢧⠹⠦⠤
⠀⠀⠀⠐⠻⣟⠋⡉⠱⠄⠀⠟⠉⣻⠖⠀⠀⠀⠀⠀⠀⠀⣤⢤⣶⣿⣿⣿⣦⣤⣤⠄⠀⠀⠀⠀⠀⠀⢶⡚⠋⠁⠀⠀⠈⠉⠉⣲⠆
⠀⠀⢈⣛⣳⠎⢳⠋⠀⣀⢉⡂⣾⢁⠮⣥⣄⠀⠀⢀⣀⣀⡈⠹⣿⣿⣿⣿⣿⠟⢡⣤⣤⠀⠀⠀⠀⠀⠤⣍⢲⡀⠀⠀⠀⢠⣞⡵⠂
⠀⠀⠉⢉⡴⠃⣾⣠⠟⢛⢶⣄⣿⠈⠳⠀⠀⠀⠀⠈⣁⣴⠂⢠⣿⠟⠋⠻⣿⠀⢬⠳⣶⠄⠀⠀⠀⠀⠀⠻⢸⢀⡴⣛⢦⣸⡏⠇
⠀⠀⠀⠀⠀⠀⠟⢁⡞⣿⠸⠙⠻⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⣴⢹⡆⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠚⠉⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⣤⠐⠣⠉⠄⠋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠦⡑⢠⠃⠸⡌⢠⢊⡄⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠀⡤⠀⢃⠔
⠀⠀⠀⠂⢀⠀⠨⠥⠃⣀⠘⠬⠥⢈⡁⣀⠀⠀⠀⠀⠀⢠⡤⠥⠒⠋⠀⠀⠓⠶⠦⣤⠄⠀⠀⠀⠀⠠⠦⡀⠱⠈⠑⠀⣀⢈⠔
⠀⠀⠀⠤⠈⢂⡀⠀⢻⠟⠃⠀⢀⠜⠅⡀⠀⠀⠀⠀⠀⠐⡈⠓⡄⠀⠀⠀⠀⡠⠚⠡⠄⠀⠀⠀⠀⠀⢄⣘⠆⣀⣹⣶⣇⡀⢜⣡⣆
⠀⠀⠀⠀⠶⢃⠃⠀⢀⠌⡁⠀⢁⠻⠇⠀⠀⠀⠀⠀⠉⠩⠔⢸⠁⣠⠔⢦⡀⢹⡀⢝⠲⠀⠀⠀⠀⠈⠉⠒⠀⠈⠀⠿⠀⠁⠠⣒
⠀⠀⠀⠀⠞⠸⠤⡂⢱⣆⠈⡂⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⡠⢰⢠⡈⠲⠇⠀⠀⠀⠀⠀⠀⠀⠠⠆⠙⡃⠁⢰⠀⡙⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠙⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠘⠈⠋

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

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀
⠀⠀⠿⠯⢠⣾⣧⡀⠐⠀⠀⣾⠁⢨⡷⠀⣴⢒⣦⠀⢉⡀⢰⢿⠂⣰⡿⣛⠻⣇⠀⡞⠀⠈⢳⠋⠀⠙⡆
⠀⠀⠀⣰⣿⡟⣿⣷⡀⠀⠀⠹⢤⣀⡀⠀⢻⣌⣉⢰⠫⣽⠂⠀⠀⠹⣷⣭⣾⡏⠀⠳⡀⠀⢺⠀⠀⡸⠃
⠀⠀⣴⣿⣷⡅⣥⣿⣿⣄⠀⣶⠆⢨⠟⣉⠉⠉⡉⠙⢳⡀⠀⠃⠀⠐⢶⠭⠶⠆⠀⠀⠙⢦⣸⣠⠞⠁
⠀⠈⢉⣽⡿⠇⡿⣿⣏⠉⠀⡀⠀⠘⠦⠿⠀⠀⣉⣀⣰⣧⣄⣀⣀⡘⠻⠖⠿⠃⢀⣤⡀⠀⠙⣡⡶⣤⡀
⠀⠠⠾⢿⣿⡆⣾⣿⡿⠧⠀⡁⢀⠀⠀⣀⣶⣀⠙⣿⣿⣿⣿⣿⡿⠟⠀⠄⠀⠀⠈⠛⠃⠀⠸⣕⡿⣫⡇
⠀⠀⣠⣿⣯⡃⢋⣿⣷⡀⢸⣎⣹⡁⠐⣺⣿⣗⠂⢸⣿⣿⡟⠁⠀⢠⡄⢶⢦⣤⠀⠸⣿⠟⠀⢉⣉⠉
⠀⠐⢛⠛⠛⣷⡟⠛⠛⠛⠈⠑⣋⡁⠀⠀⠛⠀⠀⢸⣿⣿⣧⠀⢸⡗⢠⣶⣦⠐⣷⠀⠀⠀⣰⢿⣿⡷
⠀⠀⣉⠠⡄⢉⠁⠀⣠⡀⠠⣾⣿⣿⣆⠀⠀⠙⠀⢸⡿⡟⡿⣧⠘⢫⡄⣩⣡⣬⠋⠀⢼⣿⣇⣠⡿⠃
⠀⢠⣭⡷⢳⣯⣄⠘⠿⠏⠀⠘⢿⣄⣸⣿⣯⠄⢀⣿⡁⠀⠀⣽⣧⠀⠀⠉⠁⠀⠀⠄⠀⠀⠉⣉⠀⢠
⠀⠀⠴⢋⡏⠳⠀⠀⢀⠀⠀⢀⣀⣉⣉⣉⣤⣶⣿⡿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣦
⠀⠀⠀⢠⣤⡄⠘⠁⠘⢷⣾⣿⣿⣿⠿⠻⣻⣿⡃⠀⢐⣻⣿⣿⡿⠛⠉⢀⣿⠏⣿⡆⢠⣾⣯⣩⣿⣷⡀
⠀⢰⣿⡟⣙⢻⣷⠄⠀⢸⣿⣿⣿⣧⣀⢀⢸⣿⣷⣦⣷⣿⡿⠋⠀⠘⠃⢸⡿⠀⣿⠇⢀⣼⣿⢙⣿⣧⡀
⠀⠀⢽⣧⣭⣾⡏⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣁⡤⢤⣀⠀⣰⡞⠁⣴⠟⠀⠀⣼⣟⠛⣿⣇
⠀⢰⣶⣭⢀⣭⣶⡆⠀⢰⣿⣿⣿⣿⠋⠉⠀⣠⣀⠀⡼⢃⢮⣷⡂⢧⠈⡀⠀⢡⡀⠀⠈⠉⠉⡿⠉⠉⠁
⠀⠈⠻⠿⠿⠿⠛⠀⢠⣿⢣⣿⡟⠁⠖⠀⠀⠛⠋⠀⠸⣆⡛⢟⣂⠏⠈⠁⣰⣿⣿⡄⢀⡄⠀⠠⡞⢳⠄
⠀⠀⠠⠀⠀⠒⣠⣴⡿⠃⣼⡟⠀⣰⠚⣶⣴⣾⣶⡀⠀⠀⣍⢉⠀⠀⠀⠐⣿⣧⣾⡟⠂⠀⢀⡀⢉⠉
⠀⢠⡶⣲⢶⣰⡿⠋⣠⣾⠟⢁⠀⠹⣾⣿⣿⣿⡿⠀⠐⢶⡿⢻⡷⠂⠀⠰⣿⣧⣾⡿⠂⠐⠶⢟⡻⠶⠂
⠀⠸⣞⣿⣳⠇⠀⠀⡿⠋⠐⣏⣱⠀⠘⢿⡿⠋⠀⠆⠐⠛⡿⢿⠛⠃⠀⠰⠛⢧⡾⠿⠂⠐⢋⡶⢾⠙
⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⡾⠋⠛⣷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⣠⣄⣿⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡄⠻⠧⠛⢁⣾⣁⣀⣀
⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⣛⣉⣉⣁⣀⣀⣀⣉⣉⣉⣙⢻⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⢻⡏⠛⠷⢦⣤⣀⡀⠀⠈⣿⢋⡭⠥⢄⠀⡀⠈⠉⠉⣉⣉⡉⣿⣁⣀⣤⣤⠴⠶⠞⠛⠋⢉⡿⠀⠀⠀⢀⣤⣦
⠀⠀⠀⢀⣀⣤⣤⣿⠀⠀⠀⠀⠉⠛⠻⢾⡏⡆⠀⠀⠘⠈⡇⠉⡇⠈⠀⠀⠈⡿⡏⠉⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⣷⣿
⣠⣾⣆⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠇⠀⠀⠀⠁⡇⠀⡇⠀⠀⠀⠀⢇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣄⡀
⠉⠛⠛⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠈⠀⡇⠀⠃⡆⠀⠀⠀⠘⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠃
⠀⠀⢀⣤⡴⠾⠛⠀⠀⠀⠀⠀⠀⠀⢰⠇⡂⠀⠀⠀⠀⠀⡇⠀⡆⡇⠀⠀⠀⠀⠇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⠀⠀⠀⠀⠀⡇⡇⠀⡇⡇⠀⠀⠀⠀⠸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⢀⣹⡧⠀⠀⠀⠀⠀⠀⢰⠇⡆⠀⠀⠀⠀⢠⠇⡄⠀⡇⡇⠀⠀⠀⠀⠀⡇⢻⡄⠀⠀⠀⠀⠀⠀⠰⣿⣀
⠀⠀⢠⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⡞⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠰⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡦
⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⣸⢣⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⢿⡆⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⣹⡷⠀⠀⠀⢠⠏⡎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⣠⣶⠛⠁⠀⠀⠀⠀⣾⢠⣁⠀⠀⠀⠀⠀⠀⡂⡸⠀⠀⡇⢢⠀⠀⠀⠀⠀⠀⢸⠄⣿⠄⠀⠀⠈⠻⣦⡄
⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠹⡄⢀⣉⠉⠑⠒⠀⠒⠀⠓⠠⠤⠃⠘⠦⠤⠴⠒⠚⣉⣁⠀⡿⠀⠀⠀⣀⡴⠟⠁
⣀⣠⣤⣤⡄⠀⠀⠙⣷⠄⠀⠀⠹⡼⡄⠀⠉⠉⠉⡆⠀⡖⠒⠒⡆⡰⠒⠉⠉⠀⠀⢀⡌⡼⠁⠀⠀⠺⣯⡀⠀⠀⢾⣿⣿⡆
⢻⣏⣼⠏⠀⢀⣤⠞⠁⠀⠀⠀⠀⢻⡱⡀⠀⠀⠀⢰⠀⡇⠀⠀⠃⡇⠀⠀⠀⠀⢀⠎⡼⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⠁
⠈⠋⠁⠀⠀⠛⠛⠛⠛⢿⡆⠀⠀⠀⣷⠱⣀⣀⠀⢸⠀⣇⠀⡘⢰⣀⣀⠀⠀⡠⢂⡼⠁⠀⠀⠀⢠⣶⠶⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⠶⠛⠻⣷⣤⠬⠭⠍⠀⢈⣉⣀⣀⣀⣀⣀⣀⣀⣾⣁⠀⠀⠀⣠⣄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣅⣀⣀⡀⠀⠀⢀⣀⣀⣀⣬⣿⠏⠁⠈⠛⠶⣤⡏⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣈⣉⣉⣉⣉⣉⣥⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠠⣄⠰⡄⢠⠒⢠⡇⡸⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠈⡐⠪⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⢈⡄⠀⠀⠈⠆⠀⢀⡀
⠀⠀⠀⠀⠀⣀⠙⠀⢈⠂⠹⡸⠄⡸⠀⠅⢁⣠⠆⠀⠀⡀⠀⠀⠀⠒⠈⠀⣈⠙⠆⠢⠀⠀⢸⠀⠀⠂⠄⠀⠀⠀⠠⢄⠀⠈⠋⢁⣀⣀⠂⢀⠴⠁⢡
⠀⠀⠀⠀⠀⠀⠙⠓⢦⣅⡨⠊⠉⠙⠢⡶⠋⢀⠤⠾⠛⠁⠀⠀⠀⢀⣀⣀⠀⠠⠂⠀⠁⠂⠁⡠⠀⡀⡄⠀⠀⠀⠇⠀⠉⠂⡔⠁⠀⠀⠈⢣⠊⠁⠀⠄
⠀⠀⠀⠀⠒⠀⢒⣀⣀⣼⠁⠀⠀⠀⠀⢱⠠⠤⠤⠤⠄⠀⠀⠀⡪⠊⠀⠤⠀⡀⠀⠀⠀⠀⠀⠤⠄⠈⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⢨⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⣠⡔⠌⠣⣀⡀⣀⡠⡳⠤⣀⠀⠀⠀⠀⠀⠘⠁⠀⠆⣀⠄⠑⢄⢀⡀⠔⠐⠂⠀⠀⠡⠀⠀⢢⡀⠈⡧⠀⠉⠦⠄⡠⠔⠃⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠈⣩⠀⢠⡼⠁⣇⠉⢀⠑⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣄⠠⡀⠀⢀⠑⠒⠐⠊⠀⠀⠀⠀⠳⠈⠀⠀⠊⢠⠀⣄⣸⡀⠀⠄⡐
⠀⠀⠀⠀⠀⠈⠀⠀⣩⠀⢸⠃⢸⠀⠇⠀⠙⢆⠈⠂⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠑⢆⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡆⠀⠈⠉⠁⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⣍⣙⣒⠲⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣤⣄⣀⣈⠉⠉⠛⠲⡄⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠘⢃⡆⠰⢀
⠀⠀⠀⠀⠀⠀⣠⠞⢁⠴⣫⠖⠙⠋⠉⠉⡙⢶⠀⢳⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢻⠦⠼⣧⣴⢋⡄
⠀⠀⠀⠀⠀⢺⠁⡴⡋⠚⠁⠀⠀⠀⠀⠀⣷⢸⡇⠘⡇⡛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣤⣾⣙⡴⡆⣹⠶⡶⠆
⠀⠀⠀⠀⠀⠘⡆⢷⢻⡀⠀⠀⠀⠀⠀⠀⠸⠀⣧⠀⣷⠛⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⣿⠶⣤⠾⢷⣅
⠀⠀⠀⠀⠀⠀⢻⡘⡇⢃⠀⠀⠀⠀⠀⡀⢘⡴⠋⣰⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡼⠇⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠈⣧⠹⠮⣤⣀⣦⣠⢞⡵⠋⣠⢞⣿⣃⡶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⢤⣄⣉⣉⠉⣠⣾⣵⣋⣼⣿⠂⡼⠸⠇⠈⠉⠙⠓⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢰⠀⠀⠀⣾⠁⠘⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡿⠓⠀⢬⣿⠾⢥⣴⡋⣿⢲⠶⠦⣭⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣷⢤⣀⣰⢿⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⣿⣛⠛⢯⣡⠏⢘⣤⣄⣀⡀⠉⡟⣆⠀⠀⠀⠀⠀⣀⠀⠀⣸⠀⡉⢁⡈⠋⢴⡁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡏⠀⠀⠀⣼⠁⠀⠀⢻⣟⣲⡿⠀⡏⢹⠉⠉⠓⠛⢦⣤⡀⠀⠀⣁⣠⣾⣁⡀⢡⡌⡵⠀⢠⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣠⡀⢁⡟⠰⣠⣼⣯⣉⡐⢶⠇⠀⠀⠀⣿⠯⠉⣝⣾⣡⡆⣠⠒⡶⣦⣤⣇⣷⡀⠈⠉⠀⠀⠀⣿⢀⣄⠀⢀⣈⣳⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠦⢹⡷⠞⠷⣾⠫⠷⢄⣀⣹⡿⠴⠄⣀⣸⠃⠀⠀⢈⣧⠤⢿⣟⢀⡇⠸⣀⣄⣉⠉⠛⡶⣄⠈⠁⣿⠋⠈⠳⣼⡅⠉⠙⠳⣤
⠀⠀⠀⠀⠀⠀⣨⡴⠿⣩⠜⠆⢽⠛⡒⠒⠀⢸⡋⠙⠓⢮⡏⠀⠀⠀⡼⠛⠃⠰⣿⠿⣶⣿⣇⢸⡏⡏⠙⠓⠿⠤⣤⡏⠀⠀⢀⡘⣇⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠒⣦⡞⠳⣥⠀⠀⠀⠉⠛⠛⣿⣛⡓⠠⣴⠃⠀⠀⢀⣿⠯⠉⣹⣦⣞⡠⣠⠶⡶⣤⣄⣘⣹⡄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠼⠧⠀⠘⠂⠀⠀⠀⠀⠐⢯⣁⠉⣳⣟⣀⠀⠀⣼⠁⠀⠀⢸⣇⣈⣿⡟⢀⡇⠿⢀⡈⠉⠙⢳⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠈⠉⣽⠯⠬⣄⣳⡇⠀⠀⠀⡾⠓⠂⢨⣿⠾⢴⣧⡏⢹⠛⡗⠺⠷⢧⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⣧⡀⠁⢰⣇⠀⡴⠙⢦⣤⢤⣿⣒⠂⢠⣼⠃⠀⠀⢀⣿⣛⠛⢿⣅⡜⢀⢁⠤⣄⣀⡀⠹⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣷⣄⣸⢻⣀⣠⣴⠟⠁⠰⣏⡉⠉⣳⡏⠀⠀⠀⣼⠁⠀⠀⢹⣯⠽⢷⣮⠀⡟⢹⠉⠙⠛⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣦⣀⣠⡽⠈⣁⠀⠉⢽⣁⣀⣉⣀⣀⡉⠉⣽⣯⣍⡐⢶⠇⠀⠀⢀⡿⠛⠀⠰⣿⣼⣡⡞⢠⡆⠴⡀⠀⠋⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⢦⠠⠄⢉⠘⠃⠀⣠⠞⠛⠉⠉⠁⠶⠷⣤⣀⣹⡿⠶⠄⣀⣸⠃⠀⠀⢠⠧⠜⣿⢭⠿⣷⡾⣧⡾⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣃⡤⣌⠀⡤⠦⠬⣷⣄⡀⠀⠀⠀⠀⠀⠀⢸⡋⠙⠓⢮⣏⣀⠀⠀⡼⣃⣴⣏⣒⢲⠄⣷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡾⠋⠀⡈⢳⣇⠀⠀⠀⠮⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⠭⢭⣜⣳⠃⠁⠠⢼⡷⢦⣴⠿⢮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⠼⠋⠀⠀⠀⠘⠃⠀⡿⠄⠀⠹



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⢠⡄⠀⠀⠀⢠⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠿⠀⠀⣀⣀⣀⣀⣀⠀⠈⠃⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠃⣀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠛⠳⢦⣄⠀⠰⠞⠋
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠻⠆⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠈⠙⠻⠷⣦⣄⣀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⢀⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠲⠶⠶⠶⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⢠⠶⠶⠞⠛⠛⠉⠉⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠁⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠈⠛⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠈⡉⠛⠒⠶⠶⠶⠶⠖⠛⠋⠁⠠⣦⡀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡇⠀⠀⠀⠀⠀⢰⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠘⠛⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⡄⠀⠀⠀⣀⣄⣄⠀⠀⢀⡟⣼⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣦⠀⠀⠀⠀⠀⠈⢷⣳⡀⠀⠀⢻⣿⠛⠀⠀⢸⢃⡇⠀⠀⢰⣿⠃⠀⠀⢀⡴⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⢀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣸⠁⠀⠀⠟⠁⠀⠀⣠⢋⡴⠋⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢦⡀⠀⠀⠀⠈⢻⣇⠀⠠⡿⡄⠀⠀⣿⡏⠀⠀⠀⠀⠀⣠⣾⠗⠁⠀⠀⠀⠀⢀⣴⣮⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⠀⠀⠀⠀⢻⣆⠀⢧⢱⠀⢠⣿⠀⣠⢿⠀⢀⣴⠟⠁⠀⠀⣴⣤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠹⡄⠘⣿⡄⢸⠇⢀⣿⠋⠰⠋⠀⠀⠀⠀⠈⠿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢭⣍⣓⡶⢤⣄⣀⠀⠑⢦⣑⣆⠉⠀⠘⠃⠀⠀⠘⠁⠀⢀⣠⣶⡿⠇⠀⢀⣀⣠⡤⠴⢖⣒⣛⣩⡭⠽⠇
⠀⠀⠀⠀⠀⢠⣴⣶⣲⣤⡄⠀⠀⠀⢠⡤⢬⣉⡙⠛⠛⠿⠷⣶⣬⣙⡃⠀⠀⠀⠀⠀⠀⠀⠐⠛⢩⣥⠶⠾⠿⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢖⣒⡿⠟⠛⠃⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠⣈⠉⠓⠒⠾⠃⠀⢰⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⣉⣥⠴⠒⠋⠉⠀⠀⠀⠀⢀⢔⡿⠃⣠⠆⠀⢀⠀⠀⣷⡀⠈⠻⣷⣄⡀⠀⠀⠀⠈⠛⠃⠁⠙⠻⣟⣒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⣀⣄⣄⠀⠘⠋⢀⣴⠏⠀⠀⢸⡆⠀⠹⣿⠀⠀⠈⢻⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣧⠀⠀⠀⠀⢻⣿⠓⠀⠀⣠⡿⠃⠀⣴⠀⠈⣷⠀⠀⢉⣄⣄⠀⠀⠙⢦⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠀⢀⣠⡤⠀⠀⠀⢠⢞⡟⠁⠀⣸⣿⠀⠀⣿⡆⠀⢸⡿⡟⠀⠀⠀⠀⠙⢦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟⠀⠀⠀⣰⣫⠏⠀⠀⢀⣇⡇⠀⠀⢹⣷⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠹⣦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⢰⡿⠁⠀⠀⠀⠸⠾⠁⠀⠀⠸⣿⡆⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠘⡎⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠄⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣋⡤⠖⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡞⠁⠀⢠⡄⠀⠀⠀⠀⠀⢀⡤⠖⣒⣚⡓⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢲⡄⠀⠀⠀⢸⢸⠁⠀⠀⠀⠀⠀⣤⡄⠀⣴⠟⠊⠉⠀⠀⠉⠙⠶⣌⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡞⠀⠂⢀⡀⠸⣿⡀⠀⠀⠀⠀⠸⠋⠀⠜⠁⠀⢀⡴⢶⣶⡄⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠈⠃⠀⠙⠷⠀⢀⡤⠴⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢧⠀⠀⠰⣲⡀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠳⣄⡀⠈⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠉⠉⠉⠉⠛⠲⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠭⠷⠶⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠻⢟⣦⠀⠀⠈⠳⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⡤⠀⠀⢀⣀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡤⣌⠁⠀⠀⠀⠀⠻⠛⠁⠀⠙⢦⣀⠀⠀⠀⠀⣀⡴⠋⠀⠠⣤⡀⠀⠈⢳⡄⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⣄⠀⠀⠀⠀⠀⢀⣠⠄⠀⠈⠉⠛⠛⠉⠁⠀⠀⠳⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⣝⣒⣒⣶⠿⠛⠁⠀⢀⠀⢀⡀⠀⣴⠀⠀⢀⠀⠀⠀⠀⢷⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠋⠀⠀⠀⣴⡏⠀⠀⣼⠀⠀⠀⠀⢸⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⢊⠞⠁⠀⠀⠀⢀⡄⠀⢀⡾⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠬⢭⠭⠴⠚⠁⠀⠀⠀⠀⠀⣀⡤⠖⣫⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⣧⢸⣸⡸⡰⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠌⣀⣈⣤⠀⢀⠀⠀⠀⢬⣓⣬⣾⣿⣿⣟⣥⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡆
⠀⠐⠀⠀⠁⢡⣙⠃⠒⠤⠀⠀⠀⡦⠶⣿⣿⣿⣿⣿⣿⡭⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠠⠀⠀⠀⠄⠁⠀⡀⠀⠀⠀⠐⢛⡩⢻⢿⢿⢟⢮⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢀⠀⠀⠀⠈⠐⠻⠸⠸⠘⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⡈⣐⡚⣼⣄⣤⠁⠀⠠⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠐⠂⠄⠀⠀⠀⠀⠄⠪
⠀⠀⠀⠀⠀⠀⠀⠂⡩⠙⣿⣿⡁⠖⠀⠠⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠄⡡⠢⢓⠉⠀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠻⢀⠘⡀⠃⠀⠶⠧⠊⠃⢡⡴⠀⠶
⠀⠡⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⠁⠀⠠⣤⢠⣆⣃⠦⢯⢡⠑⣄⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠉⠓⠁⠈⠀⠀⠘⠑⠀⡄⠉⠉⢠⠀⠊⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠍⠩⠁⠀⠒⠐⠊
⠀⠀⢠⡀⣠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⡀⠡⠀⠀⠀⠂⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣦⢤⡶⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⡨⠂⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⢰⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡤⠔⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠠⢀⠀⠀⠀⠀⡀⠀⢀⠀⠐⢠⡄⠀⠀⠀⠠⣸⣀⠤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢄⣸⣠⠄⠀⠀⠀⢀⡄⢂⠀⡀⠀⢀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠱⠘⠀⠀⠀⠠⠄⣻⠄⠑⠆⣲⢒⡐⠂⠀⠐⠛⡝⠒⠀⠈⠒⣀⢀⠰⢀⠄⡠⠎⠀⠐⠊⡍⠓⠀⠀⠀⢂⡚⢖⠀⠎⠡⣞⠠⠄⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠀⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠲⢈⡁⠆⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠐⠀⠀⠈⠁⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠠⠀⠀⠀⠘⢘⡠⢣⢜⡳⠜⠀⠁⠁⠈⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠀⠀⠄⡹⠃⡭⠀⠀⠀⢀⠐⠑⠠⠍⠂⠑⢦⡀⠀⠀⠨⢐⠟⡠⠀⠀⠛⠀⢀⠀⠀⢠⠀⠀⠀⠀⡀⠠⠄
⠀⢀⠀⢿⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠂⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⡠⠀⠀⠀⠀⠀⠂⣼⠆
⠀⠀⠂⠠⡄⠀⠀⡀⠀⠀⠠⡇⠀⠆⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠆⢨⠅⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠤⠢⠀⢠⠀⠀⠐⠀⢰⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⡠⠀⠔⠤⠤⠄⠀⡄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠒⠀⣷⠀⠀⠀⠑⣄⠀⣀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⣀⠌⠀⠀⠀⣴⠀⠔⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠒⣀⠋⠰⠀⠀⠙⠛⠀⢣⠆⠀⠀⠀⡄⠀⠀⠐⡞⠂⠛⠊⠀⠀⠒⠘⣀⠐⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⡄
⠀⠀⠀⠀⢤⠘⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠌⠀⠀⠀⠀⠀⠘⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⣠⠁
⠀⠀⠀⠀⠀⡀⠊⢠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠤⠑⢂⠄
⠀⠀⠀⠀⠀⢀⠐⠆⢀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠘⠢⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠔⠛
⠀⠀⢠⡄⠀⠀⠀⠉⡈⠂⡑⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⠐⢃⡈⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠤⠄
⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠
⠀⠀⠀⠄⠄⠡⠄⠤⠀⠀⠠⠀⠀⠂⠀⠀⠀⡈⢀⣀⠀⠄⢂⠀⠀⠀⠀⣀⡰⠤⡀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠃⠀⠀⠀⠀⠂⠀⠄⠀⠀⠤⠠⠤⠀⠠
⠀⠀⠀⠐⠈⢀⠂⠀⠀⠀⠀⠘⢣⣽⡀⣁⢒⢡⡤⠭⠒⢠⠊⠉⠀⠀⠀⢉⣇⣀⠟⠀⠀⠀⠘⡙⡄⠐⠭⠤⡌⠐⣀⢀⣼⣔⠃⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠡⠐⠋⣕⠉⠉⠀⡃⠠⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠘⡉⢢⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠔⢲⢺⠀⡉⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡗⢒⠢⠔⠂⠀⠀⠀⠠⡄
⠀⠀⠀⢈⣰⠀⠀⠀⠀⠂⠒⢋⠁⡈⠐⠀⠀⠀⠀⠀⠀⠀⠗⠔⠃⠠⠄⠀⡀⠀⠀⠃⠘⠀⠃⠌⠀⠀⠀⠀⠀⠀⠈⠐⢉⠀⡉⠒⠀⠂⠀⠀⠁⣦⠀⠆
⠀⠀⠀⠈⡃⡄⠀⠀⠀⠈⠄⢨⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⡁⠠⠁⠀⠀⠀⢁⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠃⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠀⠐⠀⠀⠀⠄⢰⡈⠣⢀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠓⡄⠀⠀⠀⠀⠐⠂⢲⠀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⠀⠀⢀⠞⠁⠃⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣷⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡟⣆⠀⠀⢿⡆⠀⠀⣧⡟⠀⠀⠀⠀⢠⡞⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠹⡜⡆⠀⢸⣿⠀⠀⠿⠁⣴⠀⠀⣠⣿⠁⠀⢀⡴⡿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠳⣷⠀⠙⣧⠀⢸⡿⡇⠀⠀⢸⣿⠀⣰⢯⡇⠀⣠⢏⡞⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠈⠁⢠⡄⠀⠈⡇⢿⠀⠀⣸⡏⢰⠏⡾⠀⢠⠿⢋⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠲⣤⣤⣄⡀⠀⠀⠀⠀⠈⠛⢿⣦⣄⡀⠀⠻⠆⠀⣿⠸⣇⠀⠈⢠⠏⣼⠃⠀⢀⣴⡿⠁⠀⠀⢀⣀⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⣍⡛⠶⣤⣀⠀⠀⠀⠙⢮⣝⠶⣄⢀⣤⠿⠛⠛⠛⠛⠻⢶⣏⠀⠀⠚⠉⣀⣤⠴⣺⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠿⠷⣦⠀⠀⠀⠈⠳⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⢳⣤⠴⠛⣩⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⠋⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⣿⣿⣿⣟⣛⢛⡛⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠀⣤⣤⣀⣉⠙⠒⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢄⡉⠒⠒⠒⠖⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⡿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⣄⣉⡑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣫⡴⠞⠋⢀⣼⠋⣻⠶⣤⣄⣀⣤⣤⡞⠋⢶⣄⠀⠉⠙⠓⠾⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⢠⡾⢡⡾⠃⠀⠀⠀⠈⣧⠀⣷⠀⠈⢧⡙⢦⠀⠀⠀⠀⠀⠉⠙⠛⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⡴⠋⠀⠀⣴⠀⠀⠀⠸⣇⢸⡆⠀⠀⠻⣌⠳⡄⠀⠀⠳⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠀⠀⢀⣼⡿⠋⠀⠀⠀⡞⡿⠀⠀⣦⠀⠹⡆⣷⠀⠀⠀⠈⠛⢿⡄⠀⠀⠈⠙⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠉⠀⠀⢠⡾⠋⠀⠀⠀⠀⢸⡿⠁⠀⠀⣿⡆⠀⢹⣿⡆⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⣧⠀⠀⢻⣧⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢻⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠈⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⣿⠀⠀⣿⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠱⣱⠀⢸⡇⠀⠋⣰⠀⢀⣾⠁⢀⢴⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠙⠆⠘⠀⢸⢹⠀⠀⣿⢀⢿⠇⢠⡿⠃⠀⠀⠞⠉
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠈⠻⢶⣄⡀⠘⠦⠘⡏⣇⠀⢁⠎⡞⠀⢈⡴⠃⠀⢀⣀⣤⠖⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠬⣝⣲⣄⡀⠀⠙⢯⡲⣤⠖⠋⠉⠉⠙⠺⣅⠀⣉⡠⢔⡺⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢿⡭⠚⠉⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠶⠶⢾⣾⣛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⢤⣌⣙⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣞⠲⢬⣉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⠭⠚⢡⠟⣦⣤⣀⣀⣠⡴⢫⣌⠉⠓⠺⠽⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣠⢏⠞⠁⠀⠀⠸⡄⢷⠀⠳⡕⢄⠀⠀⢀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⣴⡷⠃⠀⡴⡇⠀⡀⠹⡼⡆⠀⠈⠪⣧⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⢠⡾⠋⠀⠀⢰⠟⠀⠀⣷⠀⢻⣷⠀⠀⢦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⡀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⡯⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣙⣳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡙⠿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣋⣤⣴⣿⣷⣆⠈⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠻⠟⢻⣿⠿⣿⣿⣿⣿⣶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣠⠴⠛⠃⣤⣾⣿⣿⣿⣬⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⣧⠄⢀⣴⣿⣅⢀⣿⣿⣍⡻⡟⣳⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⢆⢀⡷⣼⣿⣿⡿⠟⢁⡰⠎⣩⣿⣿⠏⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢿⣿⢿⣿⣿⡟⠉⣃⢲⡛⠛⠛⠻⢆⣈⣤⣤⠴⠋⣹⠇⠀⠀⢀⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢀⢉⡼⠋⠁⢠⣾⣿⣯⠝⢶⡤⡴⠾⠿⠟⢽⢳⣾⣥⣤⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢶⠞⠛⣿⡀⢀⡀⣀⣾⣿⣿⣿⣶⣤⣤⣤⣷⣶⣶⡘⣟⣿⢿⣿⠿⢿⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣁⢀⣤⠂⠀⢀⣨⣷⣨⣿⣿⣿⣽⣿⣿⣿⡇⠀⢹⣿⡟⠿⡿⢧⣿⣶⣤⣴⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣒⠉⠙⠓⠲⠧⢬⣁⠛⠉⣫⣼⣄⡠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡿⠛⢹⢿⣻⣽⠟⠋⢱⣾⠿⢿⣦⡽⠟⠛⠿⣿⡷⣶⡄⢠⡼⢋⢀⡀⠀⣠⣶⢶⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡂⣀⠠⣦⠰⠟⠉⠀⣀⣠⣾⣿⣄⣼⣿⣖⠶⢤⣤⡬⢿⣶⠊⠁⠙⠿⣿⣿⣶⣟⣁⣾⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⡆⣉⢩⣅⠀⠀⠘⣧⡀⣠⣾⠟⠛⠋⣠⣦⠀⠛⢿⣦⣆⡀⠀⠀⠙⠿⣷⣠⣤⣀⠈⠉⣉⠉⣭⣁⣴⣶⣾⠇
⠀⠀⠀⠀⠀⡸⢸⣿⣿⣦⡆⠀⠙⠣⣾⠟⣿⡷⢀⣷⣷⡟⠾⠁⣀⣴⣿⠧⣿⣷⡀⠀⠙⣿⣿⠂⠀⠀⡖⠉⢻⡟⣿⣿⣶⣿⣶⡏⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠐⣷⣾⡿⢣⡟⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⢻⣿⣥⣿⠒⢿⣿⡇⠀⠀⠈⢿⡿⣿⣇⠰⢲⠞⠀⠀⠙⢿⣇⡁⠀⠀⠀⠀⠀⣠⡄⢰⣞
⠀⠀⠀⠀⢀⡿⠙⢱⡟⠀⣴⣶⣶⣶⠀⣠⣴⠿⠋⢀⡰⣷⣾⣿⣿⠿⢿⠦⢾⣿⣷⣶⠀⢀⠈⠙⠻⢿⣿⣛⢿⡷⢦⣄⣠⣈⢉⠓⢦⣤⣤⣾⢣⢿⣼⣿⡇
⠀⠀⠀⠀⢸⠃⠀⡾⢸⣿⡘⣿⣿⣿⡟⢉⠀⠀⣰⣿⣷⡸⣿⣷⣿⣤⣴⣄⣴⣿⣟⣻⣾⣿⡆⢰⣶⣾⣯⠉⠳⣄⠸⠟⠛⠛⢾⣿⣤⣦⣤⣿⣿⡜⠛⡿⠤⠴⠂
⠀⠀⠀⠀⢸⡆⢸⡇⠀⣿⣧⠹⣿⣿⣿⡘⢷⣿⠟⢛⣉⢷⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⠙⣿⠇⣾⣿⣿⡟⢀⡼⠋⣀⣀⠀⠀⠀⣽⢻⡽⠿⣿⡍⠀⢸⠷⠿⠂
⠀⠀⠀⠀⢸⣇⠈⢷⡖⠛⡿⠃⠉⣀⣀⣰⣞⢳⣼⣿⣿⠿⠿⢿⣿⣿⡇⠀⢀⣤⣤⣄⢸⠟⠀⠿⢿⣿⣧⣾⣵⣿⠟⠻⣿⡆⠀⣷⢰⣇⣴⡟⣠⢆⡇
⠀⠀⢀⡴⠾⣷⡀⠈⢿⡾⣧⣴⣿⣿⠋⠉⣿⣿⣿⣿⡇⠀⠀⠸⡏⢿⡇⣰⠿⠋⠉⢻⡟⠶⠦⠶⣦⣿⣿⣿⣿⠀⠀⠀⢹⣿⢠⡷⠖⢛⣫⣾⣡⣾⣀⡀
⠀⠀⠈⢰⣿⣿⠧⡀⢨⢷⣿⣿⠷⠛⠀⠀⣸⣿⣿⡏⠤⠀⠀⠀⣿⡘⣹⣿⠀⠀⠀⣼⠀⠁⠀⠀⣜⢹⣿⠟⣿⠄⠰⠆⣼⣾⣯⠶⢒⣻⣿⣟⣥⣤⢀⡉⠁⣀
⠀⠀⠀⠀⠉⠃⠀⢻⣿⣼⣟⢣⣀⠐⣠⢤⣿⣿⣿⣿⠔⣄⠶⢰⣿⠇⢻⣿⠣⡜⠃⠻⡇⠶⠀⠀⠉⣻⣟⢦⡀⠶⣤⠴⠂⣠⢿⣾⡟⠋⢠⡅⠈⡿⠏⠛⠃
⠀⠀⠀⠀⠀⣼⢻⡏⠙⢯⠙⠿⢿⣯⣤⡞⠁⣉⣿⡀⠀⠀⠑⠉⠉⠀⣸⡈⣳⣶⣶⡾⠿⢆⠰⡶⠚⢿⣿⣿⣿⣶⣦⣀⠶⠋⣀⠬⠛⢁⡾⠶
⠀⠀⠀⠀⢰⡇⡀⠃⣀⢈⣷⣀⣀⠈⢩⡙⠚⠻⠿⣷⣤⣀⣀⣀⣄⣰⣿⣿⣯⢿⣿⣇⢀⡜⠉⢱⣄⣼⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣸⣧⣄⠀⠈⡄
⠀⠀⠀⠀⣸⢟⣡⠋⣹⣿⣿⣿⡿⢣⢸⡏⡷⣶⠀⠀⠉⠉⠻⠿⠿⢿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⠀⠀⡧
⠀⠀⠀⢀⡾⢹⡇⠀⢿⢻⠝⡏⠀⠀⢸⡇⡇⣿⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⣤⢸⠆⢶⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣠⡄⣲⠴⢷⠀⣸⡿⢥⣠⠔⠋
⠀⠀⠀⢘⣷⠟⢳⡀⢀⡟⣰⠀⠀⠀⠘⠃⠗⠿⢸⡏⢸⡇⢸⡇⢰⡆⡆⠀⣿⠀⠀⢼⠐⡆⣷⠁⣷⠛⣤⣿⢸⣿⣿⠷⠟⠃⠈⢠⡏⠀⢠⡗
⠀⠀⠀⢸⡏⠀⢸⣿⣼⠁⠈⠉⠛⠲⠦⠤⣤⣀⣀⡀⠈⠁⠈⠃⠈⠃⡇⠀⠙⠀⠀⠚⠚⠃⠛⠀⠉⠀⠉⠀⠀⠀⣀⣀⠤⠤⠒⠉⢷⣠⠟
⠀⠀⠀⠈⢿⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣄⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⢴⡦⠶⠶⠖⠙⠃⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠜⠈⠢⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠉⠢⡀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⣄⠀⠀⠀⢹⠃⠀⠀⠀⠰⠆⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⢸⡏⢿⡄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⠇⠈⢿⣄
⠀⠀⠀⠰⢤⠐⠋⠈⠦⣀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠙⠳⠶⣦⣤⣤⣤⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠱⡄⡔⠋⠉⢀⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠀⠀⢿⠢⠤⠤⢺⠏
⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠉⠛⠛⠛⠶⣦⣄⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡤⠤⠤⢬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣷⢀⣾⠁⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠑⠤⣤⠄⠀⠀⠀⠀⢀⡾⠀⠙⢦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢄⢠⠊⠀⠀⠀⢠⣴⣚⡉⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢠⢰⣖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⣤⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⡀⠀⠀⠀⢽⣦⠄⠀⠘⢉⣿⣖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢢⣌⠈⠀⢁⠝⠳⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠂⣸⢰⣾⢏⡞⣼⣷⠀⡠⠀⠖⠀⠀⠀⠀⢉⢿⣭⡅⠀⡀⠀⡀⢠⢠⢠⡆⡀⠀⢀⣉⠋⠁⠀⠀⠐⠿⣝⠿⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡙⢦⠡⣔⠈⡏⡾⠐⡿⣫⠞⣠⠾⡃⣷⡟⠰⠀⠈⢷⠿⠷⢤⡈⠃⠳⠈⠋⣘⢿⢔⣅⣤⡄⢆⣠⠀⡀⠀⢦⣛⢿⡃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣖⠌⢀⠁⠘⠀⠃⠀⣠⠖⡡⠎⣲⡿⢷⣛⡯⠀⢰⠁⠎⠀⠒⠾⢿⠎⠀⠀⠐⢁⠤⠿⠿⢾⢵⠟⠇⠌⠃⣀⠘⢏⠛
⠀⠀⠀⠀⠀⠐⠛⠛⢺⣿⡢⠶⠁⠀⠀⠀⠔⠁⠀⢴⣩⣵⣾⣯⣶⣤⣤⠀⠀⠀⢀⠰⠆⠀⠀⠀⠀⠀⠐⠉⢹⣥⣭⣉⠀⠀⠀⠀⠇⠘
⠀⠀⠀⠀⠀⠀⣂⣀⠀⠈⠉⢀⠀⠉⠀⠀⠀⢐⣚⣢⣬⣤⠤⠶⠶⠶⠶⠤⠀⠀⠀⠀⡀⢚⣤⡆⢠⡀⠀⠙⢦⣍⢾⣕
⠀⠀⠀⠀⢀⣩⠴⠒⠂⢀⡠⠄⠀⠀⠈⠀⠀⠀⢈⠄⠀⠤⣽⡿⢶⣦⣤⡀⠀⠀⠀⠈⠐⡿⡻⣠⠈⠇⢀⠀⠸⣌⠛⠂
⠀⠀⠀⠀⠀⠔⠪⠀⠀⠜⡴⡀⣢⡄⠄⣀⠀⠀⠀⠑⢧⣤⡉⢙⣯⣓⠶⠄⠀⠀⠀⢠⠀⡇⣥⡟⣦⣶⣿⢿⡷⠈⡀
⠀⠀⠀⠀⠀⠠⢒⡥⢆⣴⡾⣣⣾⠃⠀⢿⡄⠘⠀⠀⢀⢰⡾⣷⢭⡛⠗⠀⠙⢦⣄⠲⡙⡆⢸⠛⣽⢃⣿⡿⣠⠞⢁⣤
⠀⠀⠀⠃⠀⠀⢉⠔⠹⣿⡟⣹⠏⢠⠀⠉⡇⠀⡐⠀⠀⢳⣧⡀⠑⢽⣲⢦⣐⠢⠙⠧⠙⡆⢸⠀⠁⠐⢋⡼⣫⢖⣫⣤⣀⣠⠤
⠀⠀⠀⠀⠠⠀⠀⠀⠔⠙⠰⡝⠰⢀⠇⠀⠅⠠⣧⠂⢈⣆⠉⢳⣀⣤⣄⣙⣶⡕⠠⠦⡀⠀⠈⠀⢀⠼⠋⠜⣉⠵⢚⣫⡭⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠆⠄⠀⡆⡆⣴⣿⣄⠘⡜⠃⠀⠉⠰⠾⠻⠿⣍⠺⠃⢀⡀⠀⠐⠋⠀⢀⠚⣶⠾⠿⠿⠿⠿⠶⠶
⠀⠀⠠⡀⡀⠶⢲⣧⡀⠀⡀⠈⠳⣅⢘⠏⡏⠏⣽⣣⢊⡤⠀⢀⣀⡩⠤⠀⠀⠀⠀⠤⠀⠀⠐⠈⠀⠨⣍⡽⠶⠶⣖⣚⠛⠛⠛⠻⠆⠀⢠
⠠⠭⣧⡄⠀⠀⠚⣉⣿⣞⣛⢳⡄⢈⠀⠃⠁⢠⠖⠕⡹⢾⡶⢯⡤⠖⡛⠋⢉⡠⠄⠀⠀⠀⠁⠀⠀⠀⢀⠠⡀⠰⢶⣽⠻⠷⣶⣤⡄
⠀⠴⠀⠀⠀⠀⠈⠛⢪⣭⣛⠛⠿⠃⠠⠀⠀⠁⢠⣓⡚⣛⣛⣳⣖⠩⢒⠀⡴⡠⠂⢘⣔⠠⠂⡆⠀⠀⠀⠙⢮⣦⣄⠩⣻⢭⣓⢶⣄⢀
⠀⡀⣺⣴⠂⡆⠀⠙⣾⣿⡿⠂⢀⠀⠀⠀⠀⠀⠙⠈⠩⣵⢶⣤⣩⢖⣥⠖⣠⣶⢏⣼⡿⠀⠀⣷⠀⠘⠆⠀⢀⠨⣪⣷⣮⣝⠿⡿⠋⡛⢦⣆⡀
⠀⠀⠋⠃⠀⠀⣰⠠⡙⠊⠃⠰⢶⡀⣦⠀⣄⠀⡀⠙⢶⣌⡹⣿⡓⠙⡡⢊⣿⣵⢏⡿⠁⠀⠀⢻⡇⠀⠀⡀⠀⠱⣽⡈⠛⢿⡳⠆⠈⢠⣞⡿⣷
⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠊⢴⣿⢺⠃⠀⢻⠀⠀⠀⢸⣏⠻⡪⠁⠈⠀⡠⠫⢃⢮⢃⠆⢣⠀⠈⡇⠀⣇⠇⠀⣦⠙⠻⣏⡀⢀⠀⠀⠀⣄⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠎⠂⡇⠀⠀⣿⠀⣦⠙⢆⠀⠀⡀⠀⠁⠀⠈⢎⢊⢀⠊⢠⠀⠁⣰⣿⠀⠈⡞⡧⠐⠻⣿⡟⠐⡇⠀⠨⡟⠪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⡘⠀⢸⢸⠀⠹⠁⠀⠀⠈⠀⠀⠀⠀⠆⠀⠀⠇⠸⠌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣶⠀⠀⠀⠀⡞⠳⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⡄⠀⠀⣿⠀⠀⠀⣸⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⣄⠀⠀⠀⠹⡄⠀⢹⠀⠀⢀⡾⢷⣶⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⢃⣄⠀⠀⠘⣄⢸⠀⠀⡸⠀⣠⠋⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢼⣸⠁⠑⡤⠖⠉⠉⠉⠉⠓⢶⡁⠀⠀⣀⡴⠚⠁⠈⣇
⠀⠀⠀⠀⠀⠀⢸⠓⠲⠤⣄⣀⠀⠉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣶⠊⠁⢀⣀⣀⣠⡼⠦
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⢉⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠉⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⢙⣦⡀⠀⠀⠀⠀⠀⣠⠞⠳⣄⠀⣠⡿⠋⠙⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⢶⠊⠉⠀⠀⢀⡴⠋⠀⣹⠛⢲⠒⠲⡏⠳⡄⠀⠀⠑⢿⡁⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡠⠊⠀⠀⢰⠇⠀⡿⠀⠀⢧⠀⠘⢆⠀⠀⠀⠙⠢⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⢠⣯⣤⡤⠇⠀⠀⢸⡄⠀⠈⢣⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠚⠋⠉⠉⡇⠀⠀⠀⣇⠀⢀⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⡀⠀⡇⠀⠀⠀⢻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⡄⠀⠀⠀⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⠐⡄⠀⠀⡇⠀⡄⠀⠇⠀⠜⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠁⠀⠀⢦⠀⠁⢠⠀⠀⠀⡇⠀⠀⠀⠀⢠⠃⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠀⠀⠈⠳⠀⠀⠀⠘⣧⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠦⡀⠀⠀⢢⡘⣇⠀⢿⠀⢸⠀⠀⡾⠀⢀⡴⠁⠀⠁⣠⠖⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠙⢦⣄⠀⠙⢦⡱⠈⠆⢸⡄⠈⠀⣸⠃⢠⠞⠀⢀⡴⠛⢁⠴⠊⠁⠈⢀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠈⠑⠦⡈⠳⣄⠈⠀⠇⠀⢠⠇⡰⠋⢀⠔⠋⠀⣀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠒⠶⢤⣄⡈⠁⠈⠣⡀⠀⠀⠎⠘⠀⢀⣠⠴⠞⠋⠀⠀⣀⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣄⣀⣀⡀⠀⠉⠙⠒⠤⠈⠀⠀⠀⠔⠚⠉⠀⠀⠐⠂⠉⠉⠉⠁⠀⣀⣀⡈⠉⠉
⠀⠀⠀⠀⠀⠈⠉⣉⣁⡀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠀⠀⡀⠀⠀⠀⠀⠄⣀⡐⠒⠒⠲⠶⠶⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠥⣒⠂⠀⢀⡴⠊⢠⠇⠀⢣⠀⠀⠀⠉⠙⠲⠦⣭⣑⠀⠀⠀⢀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⢀⣠⡤⠖⠋⠁⣠⠞⠋⡠⠃⡞⢰⠀⡀⢧⠈⢦⡀⠑⢤⣀⠀⢀⠀⠀⠀⣀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠁⠀⠀⠀⠚⠁⢀⡞⠁⣼⠁⢸⠀⢃⠈⢧⠠⡙⣄⠀⠈⠳⢦⡉⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣠⠏⠀⢰⠃⠀⣿⠀⢸⡀⠈⢇⠙⠌⠳⡄⠘⠦⡉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢀⠔⠀⠰⠃⣰⠁⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⠀⠁⠀⠀⠀⠀⠁⢀⠀⢿⠀⠀⠀⢡⠀⠠⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠎⠀⢀⠃⠀⠀⠘⠀⠈⠀⠘⡄⠈⠃⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⡆⠀⠀⢰⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢰⠖⠟⠳⢲⡆⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢰⣶⣶⡆⢱⣶⣶⡆⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠾⢽⢯⠷⢀⢀⠆
⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡷⠀⠀⢸⣿⣿⡇⢸⣿⣿⠁⠀⠀⢾⣦⡀⠀⠀⠀⠈⠀⢰⣿⢾⣿⣄
⠀⠹⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⠀⠀⣸⣿⣧⣤⣄⠀⠀⠐⢿⠿⠀⠿⠿⠁
⠀⠀⠀⠉⠉⠉⠀⠀⠸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠸⠿⠿⠇⠸⠿⠿⠀⠀⠿⠟⠛⠉⠛⠛⠃⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡁
⠀⠀⠀⠀⣸⣇⠀⠀⠀⠈⣚⣷⡴⠀⠀⢦⣴⣗⠚⠀⠋⣤⠀⠀⠀⠀⠀⢈⡉⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢀⡻⢟⡀⠀⠀⠈⠁⢖⣿⣶⣶⣾⣳⠋⠁⠀⠈⢃⡄⠀⠀⠀⠀⣈⡠⠄⠀⠸⠿⠆⠀⣀⠂⠀⡀⠀⠺⠿⠂
⠀⢻⣿⣸⣿⣿⣇⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣤⠄⠀⢀⣈⣁⡤⠖⠀⠀⠀⠀⠀⠈⠉⠹⣷
⠀⠈⠿⠋⠀⠀⠙⠻⠋⠀⠀⠈⣿⠛⠛⢻⠏⠀⢠⣦⠀⠀⢡⡆⠀⠈⣡⣀⡠⠵⠚⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⣾⣶⣶⣧⣄⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠀⠎⠸⠂⠀⠈⠈⠁⠀⠂⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣠⣶⣿⠓⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⣾⣿⣿⠟⠃⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠐⠻⠿⠿⠀⠀⣤⣄⣻⣿⣿⣟⣠⣠⠀⠀⠀⢀⣴⣄⡘⠇
⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡀⠂⠀⠀⠙⢿⣿⣷⣆⣹⡿⠋⠀⠀⣴⣿⣤⣬⣿⡆
⠀⠰⠿⠿⠿⠿⢿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄⠀⠀⠀⣿⣿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠋⠈⠿⢿⠷⠀⠀⠿⠿⠀⠸⠿⠇
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⢀⣬⠁⠱⠆⠀⠀⠀⠀⠀⠀⠀⣔⣰⣶⣠⣾⣧⢀⣤⠀⠀⣴⡟⠛⠉⠉⠙⢳⣆⠀⠀⢀⣴⣾⣦⡀
⠀⠀⠘⢆⡛⣡⡿⡿⠳⠇⢀⠀⠠⠀⠀⢀⣹⣷⣽⣿⣿⣿⣿⠃⠀⢘⣿⠀⠀⠀⠀⠀⠀⣯⠀⢠⣿⡿⠟⢻⣿⡆
⠀⠘⠛⣤⠢⣤⠷⢆⠈⣘⠋⠀⢇⠀⠀⠸⢿⣿⣿⠿⠿⠟⠃⠀⠀⠀⢿⣤⣀⡀⢀⡀⣰⡟⠀⢺⣿⣭⢀⠰⣿⣿
⠀⠀⠀⠉⠀⠀⠀⠘⠁⠙⠁⠀⠀⠑⠂⠤⠤⠤⠤⠤⠄⠂⠀⠀⠀⠀⠀⠉⠙⡿⡿⠛⠉⠀⠀⠈⠻⢿⣿⣿⠟⠃

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

⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢡⢠
⠀⠀⠘⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠆⠰⠈
⠀⠀⠀⠰⠀⠀⠀⠁⠀⠀⠛⡘⠛⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠰⡇⠀⠀⠠⠤⠖⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠠⠄⠀⠀⠠⠠⠄⡄⠀⠀⠀⠀⡂⠆⠅⠀⠀⠀⠰⠰⠀⠀⠀⠀⡀⠀⠀⣠⢭⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠰⠠⠀⣃⣀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⡀⠀⠀⡀⢀⢀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢸⣇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠒⡀⢇⣃⠸⡤⡀⣧⣅⠈⣆⠀⠀⠀⠁⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⡀
⠀⠀⣩⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⢀⡄⡄⠀⣄⠀⢠⠀⡀⡀⢠⡀⠀⡄⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⢀⣿⡇⠀⠈⠫⣶⡽⠃
⠀⠀⡡⢖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠣⡀⠐⠇⠧⠀⠷⠄⠸⠀⠬⠄⠀⠧⠀⠧⠉⠆⠮⠐⠦⠰⠥⠀⠀⠠⠻⠛⠃⠀⠀⠀⣿
⠀⠀⠖⠉⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁⠈⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⠁⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢄⠐⠀⣠⠆⠀⠀⠀⡆⠀⡆⠀⢀⢀⠀⠀⠀⢀⣀⡀⠀⠀⣄⠀⠀⠀⢰⡿⠁⠀⢈⠀⠄⠀⠀⠁⢈⠄
⠀⠀⠀⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⡀⠠⡀⠈⠀⠄⢀⠀⠁
⠀⠀⠀⢀⠀⣐⠈⠓⠔⢁⠣⠆⠀⠨⢀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⣀
⠀⠀⠀⠤⠀⠀⠲⠀⡠⠘⠀⠀⠁⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣂⣄
⠀⠀⢀⠄⢉⠖⠀⠨⢵⠀⢠⠆⠀⠒⡀⢀⡤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⡀⠂⢠⠄⡈⢀⢁⠈⠀⠀⠀⡄⢁⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠂⠄⠀⠉⣀⠠⢠⠘⠀⢁⠀⠄⠑⠀⢂⠂⠀⠀⠀⡀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠐⠀⠁⠔⠀⠀⠆⠀⡆⡀⢘⠁⠀⡐⠀⠀⠀⠀⢀⡠⠌⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⡐⠀⢀⠉⠀⠐⠁⠀⠀⠀⣀⣐⠂⠄⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⡀⠈⠁⡀⢀⠄⠦⡂⡇⠀⡀⠀⠀⣈⠉
⠀⠀⠀⣀⠐⡀⠑⠫⠠⠁⠀⢠⡀⠁⡪⠠⢊⡀⠀⠠⡂⠀⡠
⠀⢀⡀⠀⠣⣀⠨⡀⢄⠄⠃⢀⠇⡠⢀⠀⠙⡒⠂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠤⠀⠂⠀⠀⣢⠄⠀⠀⠀⠀⢂⣀⠀⠚⠀⠬⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠀⡄
⠀⠀⠀⠀⢲⠌⠠⠂⢀⠀⠀⠀⠀⠒⢀⠂⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠄⡘⢙⢠⣇⡴⠃⠞⣀⢠⠄
⠀⠀⠐⡀⠰⠉⡊⠀⢉⠌⠀⠌⠀⠨⡂⠙⢈⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡲⠓⢕⠈⢳⡎⢸⣟⢃⠎⢐⣵⣡⠄⣀
⠀⠀⠀⠀⠒⢀⠆⠔⢀⣰⠀⡄⠐⡤⠀⠐⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠦⢌⣳⣄⣐⢀⡳⠘⢁⠠⠴⠋⣩⡴⠋⣁⡀
⠀⠀⠀⠀⠀⠐⢁⠄⠀⠉⢠⠀⡄⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⣶⠆⣁⣉⣁⠁⠀⠀⢐⡐⠋⠉⠁⠐⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠛⣉⡩⢉⠖⢀⠀⣈⠒⣄⡉⢉⡻⠏⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠞⡿⢂⡠⢚⢉⠆⣮⠀⡨⠉⢿⡌⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⠖⡹⠁⡖⣼⠀⢨⡧⠹⠾⣳⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⣴⡜⢉⡇⣌⠁⢰⣳⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣸⡟⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋
⠀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⢀⣿⠃⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⢿⣄⠀⢀⣀⣤⣤⣶⣶⠶⠾⠿⠿⣿⡿⠂⠀⠀⠀⠀⣀⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠈⢿⠿⠟⠋⠉⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⢠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠈⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣴⡦⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⣶⠿⠛⠿⣷⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⣀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

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

⠀⠀⣤⣤⣀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⢀⣀⣀⡠⠀⢤⣤⣤
⠀⠀⢹⣿⠋⠀⠹⣿⡏⠀⠹⣿⡯⠉⢽⣿⡷⠀⠲⣿⡶⠂⠰⣾⡶⠂⠰⣟⡶⠃⠈⢻⡿⠏⠈⢻⡿⠇⠀⠛⣿⠇⠀⠐⢿⠏
⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠛⠀⠀⠈⠛⠀⠀⠀⠻⠃⠀⠀⠸⠃⠀⠀⠸⠇⠀⠀⠈⠏⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣀⡴⠄
⠀⠀⠀⠀⢛⣼⡺⠀⠀⠀⠀⠀⣻⣿⣿⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣿⣿⡟⠁⠀⠀⠀⠀⢠⣆⣀⠀⢿⣿⡘
⠀⠀⠀⠀⠀⠉⠁⠐⣶⣾⣇⠀⠈⠀⠉⠀⣾⣿⣿⠀⠀⠀⠀⠀⢴⣿⣿⡃⠈⠁⠈⠁⠀⠀⣀⠀⠘⢻⣿⣿
⠀⠀⠰⠖⠀⠀⠀⠰⠿⢿⡏⠁⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⣷⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⡞⡹⠇⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠘⠿⠾⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠐⠒⠀⠀⠀⠀⠀⢀⠀⠁⠁
⠀⠀⠀⢀⡾⠿⠞⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣦⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠖⠄⠉⠃
⠀⠀⠀⣿⣧⠀⠀⢈⣿⡇⠀⠀⣀⣀⡀⠀⠀⡀⠀⡀⠀⣀⡀⢘⢋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡀⢀⡀⣀
⠀⠀⠀⠻⣿⠀⠔⢺⡿⠃⠀⠨⢛⣧⣧⠀⠀⡟⠶⢻⠀⡧⠄⢸⢴⠃⣯⢼⠁⢱⠎⠀⠀⠈⠁⠁⠀⠀⢛⠋⣉⣡⣟⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠁⠀⠈⢀⠃⠃⠈⠀⡁⠁⠈⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠊⠀⠀⠀⠀⠙⠁⠘⠃⠑⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠈⣠⣤⡀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣂⠀⠈
⠀⠀⠀⠰⣾⣷⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡄⠀⠀⠐⠽⠿⠯⠛⠄
⠀⠀⠀⢀⣝⣛⡿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⡖⠀⠀⠠⣄⣀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠉⠹⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠠⡾⠃⠀⠀⠀⡞⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠤⠄⠀⠀⠠⠤⠀⠄⠀⠀⠀⠀⠿⠿⠶⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣀⡀⢮⣷⡄⠀⠀⠀⠀⢀⡴⣆⣠⣄⣤⣀⡄⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢮⠅⠘⠛⠀⠀⠀⠈⠀⠠⢤⣀⠀⢠⣀⣈⡀⠀⠁⠠⠄⢀⣠⡼⠛⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠀⠀⠀⠁
⠀⠐⠀⠀⠄⠤⠀⠀⠀⢀⣠⡝⠁⡈⣿⠇⠀⠀⠀⠀⠀⠀⢠⣦⣴⣦⣴⣦⣤⠀⠀⠀⠀⢿⡏⠋⠁⠀⠀⠀⠀⠒⠒⠲⠆⠐
⠀⠀⠀⠀⡀⠀⠙⠿⠛⠛⣿⣇⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠒⠒⠒⠘⠋⠙⠀⠀⠀⠀⠀⠐⠋⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⡠⠒⠊⠉⠉⠙⠲⣄⠀⠀⠀⡠⠔⠂⠀⠀⠒⠢⡀⠀⠀⠀⠀⡠⠔⠒⠒⠒⢤⡀⠀⠀⠀⢀⠔⠊⠉⠉⠙⠢⣄
⡜⠀⢀⠀⠀⠀⣀⠀⠈⡆⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⢀⠎⠀⠀⠀⠀⢀⡀⠙⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢧
⡇⢀⠉⠀⠀⠀⠉⠀⠀⡇⢸⠀⠀⠀⠻⠀⠋⠀⣠⠀⢸⠀⠘⠀⠙⠁⠀⠀⠈⣁⡀⢸⠀⢸⠀⢤⢀⣀⠠⡦⢸⡄⢸
⢡⠀⠢⢄⣀⣀⠴⠃⢠⠃⠈⡄⠘⠤⠄⠤⠠⠆⠚⠀⡌⠀⠸⡀⠻⣯⡯⣯⢽⡽⠃⡸⠀⠘⣄⠘⢦⣁⣀⣠⠞⠀⡼
⠀⠑⠤⢄⣀⣀⠠⠔⠁⠀⠀⠈⠢⢄⡀⠀⠀⣀⡠⠊⠀⠀⠀⠙⠦⣈⣉⠉⣉⡠⠔⠁⠀⠀⠈⠒⠤⣀⣀⡠⠴⠊
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡠⠚⠉⠉⠉⠉⠓⢄⠀⠀⠀⣠⠔⠊⠉⠉⠙⠲⣄⠀⠀⠀⢀⠔⠂⠉⠉⠉⠲⢄⠀⠀⠀⢀⠴⠊⠉⠉⠉⠑⢦
⡘⠁⠀⢀⠀⢠⠀⠀⠈⢇⠀⡰⠁⢀⠀⠀⠀⣀⠀⠈⣇⠀⢰⠁⠀⠠⠀⠠⠀⠀⠈⢧⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢣
⡇⡄⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠈⠁⢀⣀⣀⣀⠀⣸⠀⠆⠀⠀⢀⣀⠤⠴⣲⠀⢸⠀⢸⠀⠰⠆⠀⠀⠠⡶⠀⢸
⠣⡑⢄⠀⠀⠀⠀⡠⢣⠇⠀⢣⠈⢯⡙⠚⢒⡲⠃⢠⠇⠀⠸⡄⠐⠡⠃⠀⠀⠀⠁⡜⠀⠘⣄⠀⠀⠋⠙⠀⠀⢠⠎
⠀⠈⠢⠬⠭⠭⠭⠒⠁⠀⠀⠀⠑⠦⢌⣉⣡⠤⠖⠁⠀⠀⠀⠈⠢⠤⣀⣀⡠⠴⠊⠀⠀⠀⠈⠓⠦⠤⠤⠤⠚⠁
⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⢀⡔⠉⠀⠀⠀⠀⠉⠢⡀⠀⠀⣠⠊⠁⠀⠀⠀⠉⢢⡀⠀⢀⡔⠉⠀⠀⠀⠀⠙⢦⠀⠀⠀⡠⠊⠁⠀⠀⠀⠈⠙⢦
⡎⠀⢰⣄⠀⢰⡆⠀⠀⢱⠀⢰⠃⠀⣀⡀⠆⣀⡀⠀⢣⠀⡘⠀⠀⠀⠀⠀⠂⠀⠈⡇⠀⢰⠁
⡇⠀⠀⠀⠀⢀⡠⡤⠀⢸⠀⢸⠀⠈⠀⢀⣀⠀⠀⠀⡼⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠠⣤⣤⠤⠔⠒⠂
⠘⢄⡀⠀⠀⠀⠉⠁⡠⠃⠀⠈⢦⡀⠀⠈⠋⠀⢀⡴⠃⠀⠈⢢⡀⠀⠖⠉⠂⢀⡴⠁⠀⠈⠣⣀⠘⠜⠀⠀⠀⢀⡴

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣛⣉⣛⠂⠠⡄⢆⠄⡴⢃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣶⠿⠛⠋⠛⣷⢀⣿⡾⠈⣼⠟⠁⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡟⡕⠁⠀⣀⣠⠏⣼⠃⠁⠘⠃⣠⡘⢖⡒⢊⣥⡶⢶⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⡀⠀⠀⠀⠰⡟⣹⣇⣿⡀⣿⡵⡿⢡⣿⣯⠴⠟⠁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣉⣉⣿⣛⠛⠲⣄⠀⣿⡏⡋⠀⠛⠀⢃⢿⣇⠀⣠⢄⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣱⢞⣭⡶⠶⠦⠀⠀⣿⠀⣈⣁⣤⠤⢄⣀⡈⠉⠻⠷⠾⠟⠋⢀⣴⡇⡴⢂
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⡏⠀⠀⠀⢀⣼⠋⣼⣿⢻⣿⢿⣶⣦⣭⣉⣀⣀⣠⣤⣾⣿⡟⠘⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠿⠶⠶⠿⠋⣡⣾⣿⣧⣿⡏⣴⢫⠟⣭⢻⢏⣿⣯⢫⣿⣯⣶⢶⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠒⠒⠮⣭⣓⠿⣶⡿⢍⣎⣼⠸⣇⠻⢟⣽⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣛⠻⠿⠿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠖⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⢸⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠹⣷⡀⠈⡇⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢻⣧⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⣄⡀⠀⠐⠲⢤⣀⠀⠈⢻⣷⡀⠀⣿⠀⠀⠏⠀⠀⠀⠀⠀⣠⣶⡿⠋⢁⣠⣤⠤⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠈⠳⣄⠀⠹⣷⠀⢹⡇⠈⠀⢀⡖⠀⢠⣾⠟⢁⡴⠚⠋⠁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠒⠢⠄⡀⠀⠙⠻⣦⡀⠀⠈⢳⡄⢹⣇⢸⡇⠀⣠⠟⠀⣴⠟⢁⠞⠁⠀⠀⣀⣤⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢢⠹⡄⣿⠀⠁⣰⠏⢀⡾⠋⠀⠁⠀⣠⣴⠿⠛⠉⠀⢀⣀⣠⣤⣤⣤⡤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠿⢷⣶⣦⣤⣀⡀⠀⠂⠈⢷⡀⠀⠱⢸⡇⢠⠏⢠⡞⠁⠀⣀⣴⠟⠋⠁⠀⠄⠒⠉⠉
⠀⠀⠀⠀⢀⠀⠀⠀⢀⣁⣀⣀⣀⣀⠀⠀⠉⠙⠛⠷⣦⣀⠀⠻⡄⠀⠋⡇⡜⢀⠟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⢶⣤⣄⡀⠒⠉⠳⢦⡙⡄⠀⢰⢀⠎⢀⡜⠉⠠⠀⠀⣀⣠⣴⠶⠟⠛⠉⠉⠁⠤⠤⠤⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⠶⠶⠶⠶⠶⠤⠤⠉⡙⠳⠦⣄⠀⠑⠄⠀⠀⠈⠠⠋⢀⣠⠴⠚⣛⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠈⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠡⠒⠛⢉⣉⡉⠉⠉⠙⠛⠛⠛⠿⠶⠄
⠀⠀⠀⠀⠁⣀⡴⠖⠋⠉⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠒⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡉⠉⠉⠙⠛⠻⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⣠⣴⠾⠛⠉⣡⠄⠂⠀⠀⢀⡠⠀⠁⡠⠀⢀⠀⠀⠀⠀⠐⠢⣌⠙⠷⣦⣄⡀⠀⠀⢀⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠂⢀⣴⡿⠟⠁⠀⣰⠞⠁⠀⠀⢀⡴⠋⠀⣠⠞⠀⢀⠎⠀⠀⡌⠀⠰⡀⢈⠙⢶⣄⠙⠻⣶⣤⡀⠉⠓⢦⣄⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⢀⠞⠁⠀⠀⠁⣠⠏⠀⠀⣼⠃⠈⢀⡞⠀⠀⠀⠸⡀⠀⠹⣆⠀⠀⠈⠻⣦⡀⠙⠻⢦⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⣾⠁⠀⠀⣼⠃⠀⠀⠀⠀⣧⠀⠀⠘⣧⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣾⠇⠀⠀⢸⡟⠀⠀⢀⠀⠀⢸⡆⠀⠀⠘⣷⡀⠀⠀⠀⠹⣿⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠁⠀⠀⣸⡏⠀⠀⠀⣿⡇⠀⠀⢸⠀⠀⠘⡇⠀⡄⠀⠘⣷⡄⠀⠘⢆⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢠⣿⠁⠀⠂⠀⣿⡇⠀⠀⢹⠀⠀⠀⠃⠀⢷⠀⠀⢹⣷⡀⠀⠘⣧⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢻⡇⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡇⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⠀⠀⠀⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡇⠀⠀⠰⠀⠀⠀⣼⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⢧⠀⠀⠃⠀⠀⠸⠀⠀⠀⡀⠀⠀⠋⠀⢀⡆⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⡄⠀⠈⠀⠀⢸⡀⠀⢰⠀⠀⢰⡇⠀⠈⠁⠀⡈⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⢳⡀⠀⠐⣆⠀⠀⠀⠀⠇⠀⠀⡄⠀⢸⠁⠀⠀⠀⣸⠁⠀⠠⠏⠀⢠⠖⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠹⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⡰⠋⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠘⢦⡀⠀⠡⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠒⢀⡀⠀⠉⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢁⡀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠐⠲⢄⡀⠀⠈⠲⢄⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⢀⡴⠚⠁⠀⠀⡀
⠀⠀⠀⢤⣀⡀⠀⠀⠉⠐⠢⢀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⢀⣠⠴⠂⠉
⠀⠀⠀⠀⠀⠉⠓⠲⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠈⠀⠀⢀⣀⡤⠴⠂
⠀⠀⠀⠂⠰⠀⠤⠄⣀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠖⠀⠈⠉
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠖⠒⠒⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠀⠈⠑⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⣀⣀⣀⣀⣀
⠀⠀⠂⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⣀⠀⡀⠤⠤⠴⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠉⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠒⠒⠦⠤⣤⣀
⠀⠀⠀⠤⠐⠚⠉⠁⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠠⣄⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠙⠲⢄⡀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠚⠉⠀⠀⡀⠄⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⡤⠊⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠈⠰⣄⠀⠀⠙⠦⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢀⠜⠁⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠳⡀⠀⠈⠳⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠞⠁⢀⡖⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⡆⠀⠀⠀⠁⣀⠀⠈⠂⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⡀⠃⠀⢠⠞⠀⢠⠄⠀⠏⠀⠀⡤⠀⠀⢰⠀⠀⡇⠀⢹⡀⠀⠦⠀⠈⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢠⠏⠀⢀⡟⠀⢰⠆⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⢀⡀⠀⢡⡀⠀⠹⠄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⠀⠀⡼⠁⠀⢸⠀⠀⠀⡆⠀⠀⢸⠀⠀⠸⡆⠀⠈⢧⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠀⠀⠀⠇⠰⠀⢸⠀⠀⠀⠇⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣭⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠉⢱⣿⣿⣿⡿⣄⣴⣶⡖⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣴⠾⣿⢻⣟⢛⣿⣾⠟⢻⣷⣟⣩⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⡀⣀⠑⠾⣍⠈⣶⣾⣿⣾⣿⡟⣵⣢⣶⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⣢⡅⠐⣿⣣⣤⠞⣟⠷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣥⣾⣖⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣄⠀⠀⠘⣿⠁⢸⣿⡤⡴⡆⠈⡇⣿⣿⣿⣿⡿⣿⣶⢮⠙⠡⠷⠈
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣧⣿⡟⣀⣠⣯⣾⠿⣿⣿⣿⣿⣧⡜⠋⡀⣰⠆⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠐⢻⡿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠟⠁⠸⡦⠚⣋⢤⣿⢿⣿⣿⣿⣿⣟⡿⢛⣿⣿⣿⡛⣟⠒
⠀⠀⠀⢀⠀⠀⠀⠠⠇⢙⢿⣿⣿⣿⣿⡿⠋⢀⣰⠓⣲⢶⣶⣇⣈⢀⣾⣿⣿⣿⣯⡾⢛⡋⢒⡀⠀⠈⠛⠁
⠀⣤⣶⣿⣿⣆⡀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠴⠛⡷⣤⣌⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠿⠛⠁
⠀⢿⣿⣿⣿⣿⣷⠻⣧⠀⣤⡜⣿⣿⣿⣿⡤⢬⡛⠻⠟⣿⡟⣿⣿⣿⣿⣿⣿⣿⠉⡜⠉⢩⠓⠂⣠⣤⣤⣀⠀⢀⣀
⠀⠈⠻⢿⣿⣿⣷⣄⣿⣾⡏⣰⣿⣿⣿⣿⣗⠛⢨⡿⠷⣬⣥⣤⣿⣿⣿⣿⣿⣿⣶⣿⡶⣾⡂⣼⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⡇⡋⢀⣻⣿⣟⣻⣿⣿⡿⠛⣻⠿⠻⣿⣿⣯⡥⡀⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⠉⠀⢿⣿⣿⣿⣿⣿⡾⠋⣟⣼⣟⣻⣿⣿⡇⠀⣿⠀⢀⣿⣿⣿⣫⠥⢈⠀⠀⡉⣉⣀⣾⣿⡿⠿⢿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⣿⣿⣷⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡶⠢⠁⢠⠚⠙⠛⢛⣿⣿⠁⠀⢨⣿⣿⣿⣿⣏
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣘⡇⠀⠠⠐⠴⠿⠾⠛⠛⠁⠀⠀⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢻⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡿⣷⢾⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣷⣤⡀⣷⣶⣂⣠⣾⣧⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢘⣿⡿⣿⣿⠁⠠⢼⣧⣿⣿⢟⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⡽⠿⠻⡅⣟⢀⠀⢸⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢰⣿⡏⣿⡟⠀⢸⣿⠁⠸⣿⣰⡶⠛⠙⠁⠀⣮⠀⠀⢸⠟⠇⠸⣀⠟⠛⢿⣛⣿⠀⠀⢰⡇⠁⠀⡇⢸⠀⠀⢸⣿⣇⢸⣿⣷
⠀⠀⠀⠀⠈⣿⣹⣿⠇⠀⢾⣿⡀⢴⣿⣏⠁⠀⠀⠀⠀⣿⠰⠄⣻⠶⠀⠄⣿⠀⠀⠀⠿⠀⠀⠀⢸⡇⠀⠀⡇⠈⠀⠀⠸⣿⡟⠸⠿⣿⠇
⠀⠀⠀⠀⠈⠛⠻⣿⣷⣄⠈⢿⠄⠀⠸⠿⠀⠀⠀⠀⠀⠿⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⠿⠃⢤⣾⡿⠇
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⠤⣤⠤⣤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤

⣿⣿⡗⠀⢸⣿⣿⣿⠀⢹⢈⡇⠀⠀⠀⠀⡆⠀⠀⢸⣿⣿⣿⣿⣿⣯⣉⣿⡿⣿⣿⣿⣟⡋⠁⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢰⣿⣿⣿⣿⣿⣿⣷⢸⡇
⣿⣿⣧⠀⠈⣿⣿⣿⠀⣾⡾⢣⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣏⣹⡏⣿⠉⠁⠀⠙⠓⡂⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣾⣿⣿⣿⢸⣿⣿⣿⠀⡇
⣿⣿⡏⠀⡀⣿⣿⣿⠀⣼⡇⠛⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣬⠹⠿⣿⠇⢹⡦⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⡟⣼⣿⣿⣿⢀⡏
⠹⣿⡇⠀⢹⣿⣿⣿⡀⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣟⣥⣤⣄⢿⠀⣶⡀⣀⠀⠀⠀⠀⠀⠀⢠⣴⡄⢀⣀⣀⣤⣤⣺⣿⣿⡇⠈⣿⢿⣿⣷⡇
⠃⣿⡁⠀⢸⣿⣿⣿⡃⣿⡷⠀⠀⠀⠀⠀⠃⠀⠀⠺⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣹⠇⡄⣿⢸⣿⢹⡇
⠀⣿⡇⠀⢸⣿⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⡘⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢹⣿⣿⣿⣿⣯⣥⣾⣿⣿⣿⣯⢸⣦⣡⡏⢸⣿⢸⡇
⠀⡿⠃⠀⠘⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⢰⣿⡅⠹⣿⣿⣿⣿⣯⣉⣀⣰⣿⣿⣿⣿⣿⣿⡗⠘⣿⡿⠿⢯⣉⣉⣽⣿⣿⣿⣿⢰⣿⣿⡇⢸⡏⠈⡇
⠀⡇⠀⠀⠀⣿⣿⣿⣼⣿⡅⠀⠀⠀⠀⠀⢰⠀⢠⠀⣿⣿⣷⡶⠛⠉⠁⠷⠾⢷⡷⠶⠿⢟⡋⣹⣿⣿⡿⠀⢿⣿⠛⠿⣤⣬⣭⡟⣻⣿⣿⢸⣿⢿⡇⠈⡇⠀⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣿⣿⡟⠀⠘⢿⣆⠀⠀⠉⠁⢺⣿⣿⡟⢘⣿⣼⡇⢠⡆
⢸⡆⠀⠀⠀⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⣿⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⡶⢞⡛⢿⣿⡋⠀⠀⢸⡿⣿⣦⣀⠀⢸⣿⣿⡇⣸⣻⣿⡏⠘⡇⢸⠂
⠸⣅⠀⠀⠀⣿⣿⣿⡇⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡟⠀⢀⣐⣶⣿⣿⢛⣩⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⢿⣿⣆⣽⡿⣿⡇⣼⣿⣿⣧⠀⠇⣼
⢠⣿⠄⠀⠀⣿⡏⢿⡇⣿⣿⠀⠀⠀⠀⠀⢸⠀⢻⡇⢹⣿⣿⠧⣿⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⢿⠀⡆⣿
⢸⡿⠀⠀⠀⣿⡇⣨⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⢸⡇⢸⣿⣿⡆⠷⢣⣿⣿⣿⡿⠿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣻⣿⢸⠆⠁⣿
⢰⣏⠀⠀⠀⢺⣧⢹⡇⢸⡇⠀⠀⠀⠀⠀⢘⠀⢸⡄⣸⣿⣿⣿⣾⡘⣟⢻⣿⣿⣿⣿⣏⣹⠋⢛⠉⡏⠙⡏⢿⣹⣿⣿⣿⡿⣻⣿⣖⣯⢀⣿⣿⣿⢀⣧⠀⣿
⢸⣿⡄⠀⠀⢸⣿⢾⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⣿⣴⣿⣿⣿⣿⣿⣷⡙⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢃⣯⡨⣿⣻⣿⣾⣿⠀⣿
⢸⣿⡇⠀⠀⢸⣿⢸⡇⢸⣿⠀⠀⠀⠀⠀⢸⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣌⠸⡿⣿⣎⣩⣙⣋⣯⣯⣽⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣼⠇⠿⣿⢻⣿⣿⣿⠀⡟
⠸⣿⡇⠀⠀⢸⡇⢸⡇⢸⡟⠀⠀⠀⠀⠀⠘⡂⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣠⣌⠻⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢠⠄⣿⢸⣿⣟⣟⠀⡇
⠀⣿⡇⠀⠀⢸⡇⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣜⣿⣿⡿⣿⣿⢿⣿⣏⣿⣿⣿⣿⣿⣿⡟⣿⣸⠘⣿⢸⣿⣿⢿⣳⡇
⢸⣿⡇⠀⠀⢨⡇⢸⡇⢸⢿⠀⠀⠀⠀⠀⢠⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣋⠁⣀⣼⣧⣽⣿⣿⣿⣿⣿⣿⡷⠠⣿⣿⠛⣿⢸⡟⢸⢸⢻⡇
⢸⣿⡇⠀⠀⢸⡇⢸⡇⠘⠸⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣿⣿⢸⣿⣼⡇⠘⢸⢺⡇
⣼⣿⡇⠀⠀⢸⡇⠸⣇⠀⣱⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣟⣿⣷⣸⣶⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠶⢶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⣤⣶⡶⠾⠿⠿⠿⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣰⡿⠻⣷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⣿⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠸⣿⠀⠀⠀⢀⣾⠇⠀⠀⣿⠇⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢻⣇⠀⢀⣾⠏⠀⠀⣸⣿⣶⡶⠾⠟⠛⠛⠉⠉⠀⠀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠈⢿⣦⣿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣀⣀⣀⣀⣀⣀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣿⣿⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⢶⣶⣶⣤⣤⣶⣶⡶⠾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡅⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠠⠄⠀⡇⢠⢄⠀⠠⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀⢀⠈⢷⠀⢠⠀⡇⠀⡄⢀⡏⠠⠂⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠢⠠⠈⣆⠈⠀⡇⢰⢀⡞⣀⠑⢀⡴⠃⡀⠀⠀⠀⠀⠀⠰⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠐⠈⠀⢈⠳⣄⢣⡸⣾⣇⣧⡇⡼⡰⢂⡴⠋⢀⠁⠊⢀⢀⡀⠤⠀⣰⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣅⣓⢮⣳⣷⣼⣿⣿⣿⣿⣵⡯⠞⣉⣤⠴⠚⠋⡁⠀⠀⣴⣿⣶⡖⠈⡓⣤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠤⢬⣙⣛⣿⣿⣿⣿⣿⣿⣿⣾⡯⠥⠄⠂⠀⠀⠁⢀⡞⠉⡿⠛⠓⠼⣉⡽⠈⠑⠢⢤⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠋⠉⢉⣉⣭⣿⣿⣿⣿⣼⣿⣿⣿⡿⠯⣛⣉⠉⠉⢉⣱⣏⡄⠀⠀⣤⠴⡆⠉⠀⣶⣾⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣀⣡⠴⠚⣩⢷⣿⣿⣿⣿⣿⣿⣟⠯⣓⠦⣄⣈⠀⣲⡟⠀⣙⠦⠀⠧⢄⡜⠃⠀⠛⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠒⠉⢀⠀⡢⢋⡴⢫⢾⡏⣿⡟⡿⡌⢯⡳⣌⠓⠀⢈⣽⠉⠉⠙⠃⠀⠀⠀⠈⠀⠰⡖⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢈⡴⠋⠐⠁⡞⠰⠞⡇⠺⠹⡄⢂⢈⠳⢤⣽⣽⣿⣯⠀⠀⠀⣶⣿⣤⠀⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠈⢀⠀⠂⡼⠁⠂⠀⡇⢀⠁⠱⡀⠡⣰⣯⡄⠈⠋⢉⡀⠀⠀⠉⠻⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠸⠁⠐⡰⠀⡇⠘⡀⠀⠡⡰⠳⡴⠃⠀⠠⣞⠉⢏⠀⣠⠞⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⡇⠀⠀⠀⣜⠁⠀⠀⢀⣀⡀⠘⠋⠉⠀⠈⡷⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⣏⠙⠢⣄⠾⣿⠧⠀⢐⠖⢶⡜⠁⢸⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⢄⡙⠳⢄⡀⠈⢱⣿⠈⡁⢸⠀⠩⠀⡼⠀⠄⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠟⠒⢤⣉⡶⠧⠘⣆⢱⢸⡄⠇⣼⢁⠕⢁⠾⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⣰⢇⢄⡘⠀⠈⡙⢮⣳⡘⣿⣾⣿⣸⣧⢣⡔⣫⠠⠈⢀⡠⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡴⠁⠀⡀⣉⠓⠲⢬⣶⣽⣿⣿⣿⣿⣿⣷⡿⣊⡥⠖⣚⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠞⢀⣀⣀⣁⣀⣈⣉⣶⣾⣿⣿⣿⡿⣿⣿⣿⣿⣟⣋⣁⣀⣉⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠏⠀⠀⠀⠀⡄⠀⠐⢔⣺⡿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡛⠢⠄⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⠃⠀⠀⠀⢀⢀⡤⠔⠚⣉⡤⢺⠿⣿⡿⣿⣿⡟⢿⣯⡻⢍⢓⠲⢤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡜⠁⠀⠀⠀⠀⠈⠁⠀⠐⠨⣈⠜⠣⡊⡿⠹⢿⠙⡽⡌⠣⠙⢦⡁⠠⠂⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⢀⠈⣸⠁⠸⢸⠀⠡⠹⡄⠊⡂⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⠃⠀⠄⢸⠀⠢⠀⢱⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⣠⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣄⡄⣤⡀⠀⢐⠻⠂⠀⢩⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢶⠄⠁⠘⣩⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡐⣰⠀⡟⡼⢹⡿⡴⢋⣼⣰⡤⢀⠀⢪⣿⣆⠀⢦⢢⠻⠟⣿⣄⠄⡐⢂⢀⠀⠀⢉⠿⣯⠅
⠀⠀⠀⠀⠀⠚⠷⣮⡀⠑⠈⠇⠃⠀⣩⢚⠵⣵⣶⣿⣷⠈⠖⠨⠂⠡⢽⡦⠀⠀⠘⣡⣽⣿⣿⣾⡟⡘⢀⡀⢟⠛
⠀⠀⠀⠀⠐⠻⠷⢿⡷⠯⢀⠀⠀⠎⠁⠴⣬⣷⠿⠷⠦⠤⠀⠀⠀⠰⠂⡀⠀⠀⠀⢋⠻⣯⣭⡁⠁⠀⠘⠀⠃
⠀⠀⠀⠀⠠⢤⣆⣀⠀⠀⠀⢀⠀⠀⠬⡝⠲⠶⣚⣛⠛⠓⠂⠀⠀⢠⣼⣷⡏⢰⠀⠈⢳⠮⣿
⠀⠀⠀⠀⣒⢍⠁⢀⣂⠀⡀⡀⠀⠀⠀⠠⣌⡙⠿⣽⢿⣗⠂⠀⠀⠀⢸⢙⣶⣄⣤⣧⣎⠣⠀⠀⡀
⠀⠀⠀⠀⢀⢄⡠⢉⣵⣪⡟⠀⢾⠀⠢⠀⠙⢯⣾⣝⠷⡆⠐⢦⡀⢌⢴⢸⡿⣻⢻⣿⢏⠔⢁⡀
⠀⠀⠘⠀⠀⠩⠊⣿⡟⡿⠀⡄⠙⡇⢀⠆⠈⢺⣄⠑⢽⣶⣄⡢⠙⠆⠻⠀⠆⠃⢘⡱⢻⣖⣭⣄⣠⠄
⠀⠀⠀⠀⠀⠀⠐⠉⠘⣧⠃⠇⠀⠃⣼⠃⢸⣦⠘⢦⠴⢤⣽⣯⣒⡂⠀⠀⠀⡠⠋⢐⡩⣚⣯⣿⣚⡁
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠡⡠⢠⣵⣷⣿⡷⡠⠋⠀⠀⠌⠉⠉⠛⠌⠀⠒⠀⠀⠀⠠⠮⣙⣛⣩⣭⣭⣭⣅
⢀⣢⣙⠑⠉⠟⢷⣤⠶⣄⠙⠈⠎⠉⣸⠟⢶⣥⣤⣊⡩⠭⠖⢀⡀⠁⠀⠐⠀⠀⠉⠋⡉⢭⣵⣶⣦⣄⣀⠀⠘
⠠⠌⠁⠀⠀⠘⢻⣿⣛⠻⠟⠀⠀⠐⠁⣔⣾⣿⣾⣷⡢⠀⢠⢭⢆⣰⡄⠄⡀⠀⡀⠑⢶⣤⣉⢻⣿⡻⢥⣀⡀
⠠⢤⣷⠇⡆⠀⢳⢿⡿⠂⠀⠀⠀⠀⠈⢉⠹⣷⣦⡤⣦⡴⣢⣾⣯⣼⠇⠀⣿⠀⠐⠀⠀⡸⡾⣷⣽⡿⠟⠹⢷⣦⠄
⠀⠈⠹⠀⠀⠇⠪⠡⡡⣘⣷⡾⠁⣆⠠⠈⢻⣦⣿⠮⠠⠊⢹⡿⢻⡏⢀⡀⠉⡇⢠⣠⠀⡘⣷⣬⠙⠉⠀⠠⠻⣿⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⡃⡆⠙⢰⠀⣌⢦⠈⠁⠀⠀⠋⠁⠻⡼⠠⠃⠀⠃⣼⡇⠀⣷⡀⢹⣶⡶⢠⠀⠑⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠙⠀⠁⠀⠂⠀⠀⠀⠈⠈⡄⠀⠀⠀⠟⠁⠀⠁⠁⠀⠉⠇⠀⢲⠰⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠁⠀⠀⣤⠋⢰⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⣀⡀⢘⡄⠀⠀⠀⠀⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠆⠈⢁⠄⠀⡄⠢⡀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠰⠒⠚⠃⠀⣠⠒⡄⠀⠀⠀⠀⡠⠄⠀⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠑⠚⠀⠀⠀⠀⠀⠀⠀⡆⢑⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⢀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠔⠁⠀⠀⠐⠉⠀⠀⣀⠠⠤⠐⠒⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⣀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠁⠀⡐⠁⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠰⣛⡆
⠀⠀⠀⠀⠀⠀⠀⢎⡹⠆⠀⢀⣀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠈⠂⠐⠀⠃⠀⡼⠀⠂⠀⡀⠄⠊⠁⠀⠀⡒⡦⠀⠀⠘⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠉⠀⠰⠹⠀⠀⠀⠈⠀⠄⠀⠀⡀⠀⠰⠀⢀⠄⠊⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⠜⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⡀⡈⠀⠀⠁⠐⢀⣀⠠⠔⠒⠀⠈⣠⡀⠀⠀⠉⠉⠀⠀⠀⠀⢈⣂⡀⢈⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⠉⠀⠀⡀⠀⠉⠉⢉⠉⠀⠀⠀⠄⠀⠀⠀⠠⠀⠊⠁⠀⠄⠀⠀⠀⠀⠛⠋⠀⠀⡀⠀⠀⡞⢳⠀⠈⠀⠑⠚
⠀⠀⠀⠀⠀⡤⠴⢻⣀⠀⠀⠇⠸⠀⠀⠀⠁⣀⡀⠤⠀⠒⠐⠂⠈⠀⠈⠀⠀⠀⠀⠈⠉⠍⠉⠁⠐⠒⠒⠠⠤⣀⡀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡱⢀⡠⠊⠁⠀⠀⠤⠄⠒⠉⠁⠀⠠⠄⠀⠀⡠⠔⠀⠁⠌⢰⢀⠂⠠⡍⠂⠀⠐⠂⠀⠀⠀⠀⣀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⡀⠀⠀⣀⠤⠒⠀⠀⠐⠁⠀⠀⠂⠌⠀⠀⠀⠀⢂⠀⠀⠀⠑⠄⡀⠀⠀⠸⣅⠗⠀⠀⠀⠀⣈⠑⢄⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⡠⠄⠀⠰⡉⡳⠀⢀⠊⠠⠀⠘⠀⠀⠀⠆⢠⠒⢢⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⢈⣤⠀⠀⠀⠀⠀⡠⠃⠀⡄⠀⢠⠀⠀⠀⠘⡈⠓⠁⠀⢀⡀⠈⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡤⠊⠑⠶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣉⠆⠀⠀⠈⠛⠁⠀⠀⢀⠜⠁⠀⡘⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣤⠗⠀⠀⠀⠀⢨⣇⠤⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠠⣀⠀⠰⠀⣀⠔⠁⢀⠴⠁⠀⠀⠀⠁⠀⠀⠀⢴⣷⠀⠀⢰⠀⠀⢰⠋⢳⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢐⠁⠀⠠⠊⠁⢀⠔⠁⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⣀⡠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠳⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣀⠀⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣀⠜⠢⢤⠀⠀⠀⠀⠀⠀⠸⡿⠆⠀⠀⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⡤⠤⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⡀⣿⠀⠀⢸⡇⢀⡀⠀⢠⡶⢶⡀⢀⡾⢩⡗⠀⣀⣤⡄
⠀⠀⠀⠀⢠⡟⠀⣿⡇⠀⢀⡟⠀⠈⣅⠀⢸⣄⠾⠀⣸⡷⠋⠀⣼⠋
⠀⠀⠀⠀⠈⠁⠀⢹⡇⣤⡟⠁⠀⢸⣿⡀⢀⡞⢳⣾⡋⠳⠤⠾⢁⠀⡄⢶⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄⠀⣿⠸⣧⡾⢁⡾⠉⢷⠀⠀⡦⠘⡷⣴⠘⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⢷⣴⠇⠀⠀⠀⠸⣇⣀⡾⠀⠀⣗⠳⠑⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢠⣤⡄⠀⠀⠈⠉⠀⠀⠀⠉⠀⣰⠏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⣄⠀⠀⣿⠀⣿⠀⠀⠀⠺⠃⠀⠀⣶⢰⡏⠀⣸⠃⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢸⡇⠀⣿⢠⡇⢀⣀⠀⠀⣴⡄⠀⣿⣿⠀⢠⡟⠀⣾⣁⣠⠟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⢹⣿⠁⡟⠙⣇⠀⣿⡇⢸⡟⣿⠀⣾⢁⣼⣿⠉⠁⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣀⣀⣠⡞⢻⣄⣷⠀⣿⢀⡟⢷⣼⠀⠉⠰⣧⡾⠁⠈⠛⠛⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⣧⠀⠙⠛⠀⠹⡾⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢦⡴⣟⠢⣶⣤⣌⣤⠞⣠⣄⡰⢦⢀⠀⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣶⣿⠦⢤⡄⣀⣀⢅⣀⣰⣸⡀⡄
⠐⣻⡅⠋⠑⠿⡟⢫⠈⢨⢈⣟⢫⠉⣿⠓⣹⣩⢇⡀⡀⠀⣤⠀⠀⣀⣀⡼⢀⠮⠂⢪⡇⣿⣣⡉⣿⡿⢁⠺⡘⣯⠼⡦⢿
⠈⢇⢓⡦⡟⡾⢹⡼⢗⣙⢈⡷⣈⡻⠖⢢⠒⣶⡐⣿⡟⣿⡙⢿⣿⢽⡿⣺⣍⣌⣇⣰⣆⠺⠧⡑⠾⣷⠈⠠⡌⢓⢂⡟⡶
⠀⠀⠼⡆⢉⠗⢜⠓⠎⠴⢖⣄⡹⠟⢵⣡⠟⡀⢌⡙⢶⠉⣐⠈⠷⠠⠃⠄⡂⣹⣧⢧⢸⠌⣣⡘⢲⢦⠈⠇⢉⠘⠾⠑⢹
⠀⠀⢠⠀⡌⠁⠄⡐⠀⠀⠈⠀⠁⠚⠂⠛⠀⠸⠾⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠄⢄⠉⠠⡌⠳⠶⠌⠀⠁⠈⠈⠂⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠁⠀⠑⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠚⠏⠀⠀⠀⣄⣀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠛⠿⣶⣄⠀⠀⠀⠚⠻⠁⠀⠀⠠⠴⢿⡟
⠀⠀⣠⡾⠛⠉⠀⠀⢀⣠⡤⠶⠚⠛⣋⣉⣩⣭⣭⣭⣛⣦⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠁
⢠⣾⠋⠀⠀⢀⡴⠞⠉⢀⡤⢖⣪⠭⠒⠒⢋⣩⡭⠿⠛⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠏
⣿⠃⡎⣖⡆⡞⠀⢠⠞⡡⠚⠁⢀⣠⠶⠛⠉⠀⠀⠀⠀⢀⣀⣠⣤⣶⠟⠁⠀⠀⢀⡾⣻⠏
⣿⡄⢣⠳⠃⠳⢤⣏⣞⣀⡤⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⢛⣿⠉⠁⠀⠀⠀⠀⢀⡞⣰⠃
⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠁⣠⢎⣿⡄⠀⠀⠀⠀⢠⡞⣴⠃⢀⣸⣦⠄
⠀⠈⠻⢷⣤⣀⣀⠀⠀⢀⣀⣠⣴⡾⠛⠉⢀⣠⠴⢊⡵⢋⠘⣧⠀⠀⠀⢠⠟⡼⠃⠀⠀⠀⠙
⠀⠀⠀⠀⠈⠉⠛⣿⣛⠿⠿⠯⠗⢒⣒⣉⠥⠔⠊⡥⢖⡡⠂⠹⣆⠀⢠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⡩⠔⣡⠀⢻⣴⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⣢⣴⢃⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠚⣵⢣⡞
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣠⣤⡴⠶⠛⡿⢡⠏⠀⠀⣰⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣾⣿⠏⠀⠀⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⣠⡾⠁
⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣿
⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠁⠀⠀⢹⣇
⠻⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⠳⢄⣀⡀⠤⠄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢠⡤⠄⠤⠃⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠗
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡸⠁⣀⠀⠀⡤⠖⠶⠞⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⡾⠀⣿⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠾⠓⠊⠉⠳⣄⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠁⠚⠳⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⣇⣶⣤⡤⠀⠀⠀⠀⢴⡞⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⣿⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠈⡷⠀⠀⠀⠀⠈⢻⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣴⠋⢀⣤⠞⠃⠾⠀⠀⢰⡟⠒⠲⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⠀⠀⠀⠀⣀⣀⣀⠠⣴⠈⣧⠀⠀⠀⠀⠀⣸⠃⢠⡾⢻⣧⡄⢀⣤⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⢿⡆⢸⣇⠸⣆⠀⠀⠀⢰⡏⢀⡟⠀⠈⢉⣧⡾⠋⠹⡿⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣼⣯⡄⢻⡄⠀⠀⣾⠋⣼⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣰⠇⢸⣗⢀⢻⡄⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣼⠃⠀⠀⢿⡄⡌⢷⡀⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣾⠃⠀⠀⠀⠈⣷⠰⠈⢿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⡏⠀⠀⠀⠀⠀⠸⣧⠁⠈⢳⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⣷⡀⠀⠀⠀⠀⠀⢹⡆⢀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠹⣷⡀⠀⠀⠀⢀⣼⢿⡀⠄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠈⠙⠓⠶⠖⠛⣁⡾⣧⠰⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⣤⣤⡶⠾⠋⠀⢹⣇⢃⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⡄⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠰⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢁⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠠⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢣⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠆⠈⢷⡀
⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡛⣾⣦⡾⢃⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣰⠏⠙⢿⣆⠀⠀⠀⠀⣠⡶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣦⣀⠀⣼⠋⠀⠀⠀⠙⢷⣤⣤⠾⠋⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠛⠛⠋⢉⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠙⠛⠁⠀⠀⠀⢀⣀⣤⠤⠶⠖⠚⠛⠛⠛⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣼⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠈⠉⠉⠛⠛⠻⣶⠆
⠀⠀⢠⣤⣤⣶⡶⠾⠃⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢼⣯⣀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠙⠷⣦⣄
⠀⠀⠀⠀⠀⢙⣷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣹⣿⠆
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⣼⢻⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⣶⠞⠛⠉⠉
⠀⠀⣴⣿⣁⣀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣶⠤⠿⢧⣤⡿⢿⡤⣾⠁⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠈⢿⡄
⠀⠀⠀⠉⠉⠙⠛⢻⡆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⠛⠲⢤⣀⣀⣤⠿⠦⣤⣤⣤⣤⣼⡇⠀⢀⣀⣤⠴⠞⠉⠀⠀⢀⣀⣀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠉⢷⡀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠉⠀⠀⠀⠀⠀⠀⣼⠏⠉⠛⠛⠷⠾⠟
⠀⠀⠀⠀⠀⠠⣿⣴⠶⠾⠛⠛⠉⢹⡇⠀⠀⣠⣴⡟⠀⠀⠀⠀⠀⠀⢀⣼⣦⣀⠀⣰⣶⣄⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣴⠞⠋⢈⣿⠆⠀⠀⠀⠀⠀⢀⣿⠀⠙⠿⠟⠀⠉⠻⢶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⣷⣤⣄⣀⣀⣠⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡆⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣾⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⣠⣾⡇⠀⠀⠁⠀⠀⠀⠀⠀⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⠀⠀⠹⣦⡀⠀⠀⣠⡿⣧⣀⣠⡾⠋⠸⣧⣀⣀⣠⠄⠀⢀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠁⠀⠀⢻⡟⠶⠾⠛⠀⠈⠉⠁⠀⠀⠀⠈⠉⢻⡇⠀⠀⠀⠀⠀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣀⣼⠇⠀⣀⣤⠶⠖⠛⠛⠲⠶⣤⡀⠀⠈⠻⠶⠶⠶⠶⣲⡿⠋⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⠀⣸⡇⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⢰⡟⠀⠀⠀⠚⣉⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⣟⠛⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠘⢧⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⢀⡿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢠⡟⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣷⡀⠀⠈⠙⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣾⡃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢈⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢠⡾⠋⠉⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⢀⣼⡀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠀⢠⡾⠻⢧⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢹⠄⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠀⠀⣠⣟⣤⡴⠶⠲⢦⡀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣤⣀⠀⢸⡆⠀⠀⠄⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠸⠷⠶⣦⠀⣴⠟⠉⠙⠿⠁⠀⠉⠻⢦⣷⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⡇⠀⠀⢠⡆⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⠀⠀⠀⠺⠇



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠰⠀⠀⠠⠄⠀⠀⠀⠀⣁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⡙⠀⠀⣃⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡂⠀⠘⡀⠀⠀⠀⠐⣟⣿⡶⠾⣿⠈⠀⠀⡀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢈⣁⣀⡙
⠀⠀⠢⢙⠉⠉⡋⠄⠀⠀⠀⠀⠐⠀⢰⠃⠁⠀⠀⠀⠌⡉⠉⢙⠡⠂⠀⠠⠰⠍⠁⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⠛⢁⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣁⣄⡹⢏⣄⣈⡇⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡤⠀⠀⠀⠀⠐⠀⠂
⠀⠈⠀⠀⠀⠀⠄⡈⠁⠀⠀⡀⠒⠒⠲⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠲⢤⣤⠔
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠚⡀⢀⠃⠀⠀⢠⡤⠀⠤⠀⠠⠄⠰⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠈⠀⠀⠀⠈⢒⡀⡀⡐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣇⢀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⣀⠀⡀⡀⠀⠀⠀⠀⢡⠤⡌⠀⠀⠀⠀⠀⠉⠀⡀⠉⣀⠀⠀⠀⣠⠂⢁⡉⠑⢂
⠀⠀⠀⠀⠛⠋⠀⠂⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⠀⠈⠉⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠋⠡⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠂
⠀⠀⠀⠒⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠆⠀⠀⠂⠀⠠⢀⠀⠀⠀⠀⠂⠀⠒⡀⠠⠀⠀⠈⠻⠏⠘⠿⠋⠀⠀⠀⠀⠛⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠚⠛⠚⠀⠂⠀⠀⠁⠀⠚⠙⠂⠠⠀⠀⠀⠂⠀⠂⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣁
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⢯⡀⠀⢠⢍⠀⠀⠀⢰⢥⡀⠀⣠⢕⠀⠀⠀⡣⠄⠐⠂⠀⢔
⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣤⠀⢠⡄⠀⠀⠀⠾⣿⣶⠶⣶⣾⡷⠀⠀⠀⢀⡀⠀⢠⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⣈
⠀⠀⠀⠄⣀⡀⡄⠀⠀⠀⠀⠀⠋⣠⠘⠃⠠⠀⠀⠀⠈⠁⢠⠈⠁⠤⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠈⢀⣄⠈⠀⠀⠀⠀⠀⢬⣀⣀⡥
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠈⠀⠀⠀⠐⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠥⠐⠀⠀⠀⠀⠀⠀⠨⠅
⠀⢈⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠠⣀⠀⠀⢀
⠀⠈⠉⠤⠀⠀⠒⠠⡆⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⡀⢤⠀⠀⠀⠀⠔⠛⠿⡿⠟⠓⠄⠀⠠⠰⣀⠀⠀⢀⠂⠄
⠀⠀⢾⣧⡄⢤⢼⡇⠀⠀⠀⠀⠉⠀⠀⡄⢰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠐⠀⠠⠀⠀⠀⠴⢀⣀⠸⠄⠀⠀⠀⡀⠈⢄⠀⢍⢀
⠀⠀⠊⠲⠦⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠁⢌⣃⣂⠫⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿