Wordnet Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⠉⠁⠈⠙⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⣶⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠀⢀⠄⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣦⣴⡦⠞⠁


⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⣀
⢀⣴⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆
⣼⠛⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣐⣀⣤⣤⣬
⠹⣶⣶⣶⣶⣶⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃
⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⢀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣦⣤⡀
⠀⠀⢰⠏⠙⠉⠉⠉⠉⢱⠀⣰⠿⡿⠿⠿⠿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠿⠿⠿⠿⠿⡆
⠀⠀⢸⣂⠀⠀⠀⠄⢀⣞⠀⣇⣀⡄⠀⠀⢀⣀⣜⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠂⡤
⠀⠀⠀⠻⢷⣿⣾⣶⡿⠋⠀⠘⢿⣿⣿⣿⣿⡿⠃⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣶⣷⣶⡶⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢸⠋⠀⠈⠀⠈⢈⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣄⣀⣀⣂⣠⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⣀⡈⠀⠀⠀⠉⠁⠀⠑⠦⠎
⡀⡄⠔⠂⠀⠀⠀⠀⠈⠡⠀⠈⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠈⠃
⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⡀⠆⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠐⠒⠈⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⡀⠀⠀⣈⠠⠐⠈⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⣐⣀⠀⠀⠀⠓⠀⠀⠀⠠⠀⠀⠔⠂⠀⠀⠀⠀⡀⠀⠀⠐⠀⠁⠐⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⡀
⠀⠀⢀⢁⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠲⠀⠀⠅
⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠓⠀⠐⠂
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢈⡀⠀⠀⠠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠰⠆⠉⠀⠀⠀⠠⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⡀⠄⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃
⠈⠀⠀⠀⠀⠀⠘⠉⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠚⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠂⠀⠠⠀⠴⠘⠀⠈⠀⠐⠄⠐⠂⠀⠤⢄⡀⢁⠀⠀⠀⠀⠀⠓⠶⠦⢈⣀⡀⠤
⠀⠠⠀⠉⠁⠀⠂⠁⠀⠀⠀⠈⣀⡈⠁⣁⡀⠀⠀⢀⠀⠀⠀⠉⢀⠉⠁⣀⡁⠀⠐⢀⠀⠠⠈⠁⠀⠈⠢⡈⠢⠀⠀⠀⣀⡀⣐⠂⠒
⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠉⠁⠀⠀⠀⡄⠀⠀⠀⠉⠙⠁⠉⠀⠀⠤⠠⠄⠄⠀⣀⠀⠀⠀⠈⢀⠀⠠⠤⠄
⠀⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠐⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠀⠀⠈⠑⠊⠲⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄
⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠚⠀⠀⠰⠀⠀⠀⢠⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⠁⡀⠁
⠀⠀⠀⠀⠁⡀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠠⢈⣁⡀⠀⠐⠂⠄⠀⠀⠀⠂⠤⣈⣀⡀⠀⠂⠉⠀⠀⠀⠐⠀⠁⠀⠉⠁⠘
⠁⠀⠀⠂⠤⠀⠀⡀⠀⠄⠠⠄⠀⠒⠐⠆⢌⠀⢀⠀⡀⠀⠰⠄⠑⠆⠀⠀⡈⠢⡀⠀⠉⠈⠲⠊⠁⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠠⠤⠀⠔⠒⠂⠀⠀⠒⠂⠀⠑⠤⠤⠀⠒⠐⠀⠀⠁⠒⠀⠈⠂⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠈⠀⠀⠀⠂⠂⠁
⡄⣀⠀⠈⢁⣀⣀⡐⢀⠀⠀⠀⠂⢈⠉⡀⠈⠁⠀⡄⢠⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠤
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠂⠠⠄
⠀⠀⣬⣀⡐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠸⡐⠂⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠤⠄⠀⠐⠀⠀⢀⡐⠗
⠔⠀⠀⠀⠁⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⠀⠐⠀⠀⠀⠀⠉⠂
⠤⠀⠀⠘⠢⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠂⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠄⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠁⠀⠂⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⣈
⠀⠀⠐⠄⠄⠀⣀⠀⠀⢀⡀⠀⠀⠀⠒⠀⠀⠀⣀⢠⡁⢈⡁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀
⠐⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠈⢀⣁⠈⠀⠈⠁⠈⡄⠀⠀⠀⠠⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢨⢠⠀⠼⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⣇⢤⢰⠆⠿⠀⠀⠀⢨⠩⠠⢨⠁⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠀⠀⠀⠀⠤⠬⢤⠶⠆⠄⠠⢤⠤⢤⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣀⣀⣀⣤⣠⣴⣀⡀⢸⢘⡀⡁⢸⠆⠂⣹⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⢿⣟⣿⣿⡉⣤⠁⣶⠸⣷⣷⣶⣶⣶⣶⣶⠀⠒⠠⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⢦⡠⡄⣤⡀⠄⡅⠤⠡⠈⡌⠱⣡⢸⣿⠀⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣉⣁⢈⣸⠀⣄⣥⣼⠠⢣⣥⣬⣬⣾⡿⠛⣭⠑⠾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢛⠓⠙⠛⡍⠀⠃⣿⠀⢶⣿⣿⣿⣿⣿⠀⠈⣩⣍⠉⢸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠐⠶⠾⡶⠲⢶⣷⠍⠏⢿⠂⠩⡿⠿⠝⠿⠿⠄⠟⠛⠣⠤⢸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢨⣧⣤⣴⣇⠆⠘⠀⡏⠁⠁⠀⠘⡴⠀⠀⠀⠀⠀⠀⢸⣿⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⡉⠙⠩⡍⠄⢡⠒⠂⣬⠰⠀⠂⠶⠀⠉⠛⠓⠀⠀⠸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⢠⣥⣤⣈⣥⣤⣌⣡⣴⣴⡆⡄⠰⠀⡀⠀⠀⣀⠓⠈⢰⣿⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠖⢸⣿⣿⡇⠎⠱⢹⠸⡏⠙⣁⢾⢠⢡⠉⠀⠀⠠⠄⠀⠀⡤⠈⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⢡⣼⣤⣦⣠⣧⣬⣽⣼⣮⡄⠈⠋⠉⣭⣄⡀⠁⢀⡀⡀
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠀⠀⠈⠀⠇⠀⠀⠈⠩⠉⠙⡙⠙⡙⢻⠋⠋⡃⠀⠡⠀⠙⠃⠐⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⡀⠁⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣠⡄⠀⢠⣄⠀⠀⢠⣄⠀⡀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠟⢻⣿⡿⢻⣿⣿⡟⢻⣿⣿⣿⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢿⠇⠀⠸⡿⠀⠀⠈⢿⠄⠀⠀⢿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣀⣸⣿⣇⣸⣿⣿⣿⣀⣿⣿⣿⣂⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⠀⢠⣤⣤⣤⡄⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣏⣿⣿⡇⠈⢹⣿⣿⠁⣾⣿⡟⢛⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣷⠀⢸⣿⣿⠀⣿⣿⡇⠻⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⢱⣿⣿⣿⡇⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠘⣦⢀⡸⡄⣀⣠⡆⠘⢶⡄⠀⣿⢤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢋⣿⠙⡿⣇⣿⣿⡟⣹⣧⡛⢻⣿⠀⡛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡇⢰⡟⢸⡇⠀⢸⡏⠓⠂⣸⡇⢠⣿⢸⡁⣶⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣸⣿⢠⡇⢸⣿⡇⢰⣮⣽⡇⣼⡟⢰⡇⣾⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⠀⠈⠃⠀⠀⠘⠂⠈⠋⠘⠃⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣷⣼⣿⣿⣧⣿⣷⣼⣧⣽⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢠⣿⡇⣿⡿⢷⣄⢸⡿⢷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⣿⡿⠠⢸⠁⢀⡉⢻⡇⢀⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢀⣿⣿⡇⣿⡇⢈⣿⢾⡇⠈⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⡿⠁⠀⢸⠀⢸⣷⠀⡇⢸⣷⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⠀⣾⣧⣿⡇⣿⣧⣾⠋⢸⡇⢀⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⠋⡀⣿⠣⠘⢀⢸⢇⠘⠁⣴⡇⢸⡿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⠿⠼⠏⠀⠿⠇⠿⠏⠻⠦⠸⠿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣸⣷⣀⣃⣰⣿⣀⣸⣀⣸⣄⣹⣇⣊⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠟⠛⠻⠟⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⢽⡏⠉⢙
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠛⠛⠓⠛⠛
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠂⢀
⠀⢸⣿⡉⠙⠏⢉⣿⡇
⠀⢸⣿⣷⠀⢰⣿⣿⡇⠀⠟⣧⠀⡿⠁⣏⡷⡿⠇
⠀⢸⣿⣿⣤⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠰⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⡀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⣠⠍⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠠⣶⢀⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⡉⣉⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⣀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠴
⠀⢀
⠀⠀⠈⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣾⣿⣽⣿⣶⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠿⠿⠿⠿⢿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢋⣠⣴⣶⣶⣿⣶⣶⣦⣌⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⢁⣴⣿⣿⣿⣿⠋⣀⠹⣿⣿⣿⣿⣦⡘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢠⣿⣿⣿⣿⠿⠃⣸⣿⣆⠹⢿⣿⣿⣿⣷⡈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣿⣿⠁⢤⣶⣶⣾⣿⣿⣿⣶⣶⣦⡄⢈⣿⣇⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣷⣄⡙⢿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢻⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⡆⢹⣿⣿⣿⡇⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡈⢻⣿⣿⠀⠟⢋⣡⣤⣈⠛⠷⢘⣿⣿⠟⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠙⢿⣷⣶⣿⣿⣿⣿⣿⣶⣾⠟⢃⣴⣿⠟⠀⠀⢠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣌⣉⠛⠛⠛⠛⠛⣉⣤⣶⣿⠟⠁⠀⠀⠀⠀⢀⣶⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣌⡙⠻⠿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⢠⣾⠟⠁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠃⠀⣠⡀⠀⠀⢀⣴⢷⣆⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠁⠀⠀⠈⠻⣦⡾⠛⠁⠀⠙⢿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣉⠀⠀⣀⣀⣀⡀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣉⠀⢸⣏⢈⣿⡇⠀⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⣽⡏⠉⠀⢠⣽⣯⡍⠁⣤⣽⣥⠀⢠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣬⡉⠀⣿⡇⠀⠀⢸⣯⣤⡄⠀⣿⣥⣤⠀⢸⣇⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⣹⡿⠀⣿⣧⣤⡀⢸⣯⣤⡄⠀⣿⣥⣤⠀⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠉⢱⡄⠉⠁⠀⠀⠈⠁⠉⠀⠀⠉⠉⠀⠀⠈⠁⠁⠀⢀⡁⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⡄⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⣸⠀⢰⢿⡇⣼⠀⠀⡀⣄⠀⠀⢠⣄⠀⠀⠀⣀⣰⢻⡇⠀⢸⡏⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡿⠀⣼⠘⣧⠇⠀⠀⠧⠟⠉⠁⠈⢿⡤⠊⠸⠵⠋⠈⠓⠃⠈⢧⡠⠂⠘⠋⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠇⠀⠉
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣙⣋⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⡏⠉⣿⣧⠀⢸⣿⠋⠛⠁⠀⢸⣿⠋⠙⣿⡆⠀⣿⡟⠉⠋⠀⠀⠀⢠⣿⢿⣆⠀⠀⠈⠛⢻⣿⠋⠛
⠀⠀⠀⠀⠀⠀⣿⣷⣶⡿⠃⠀⢸⣿⠿⠿⠇⠀⢸⣿⣶⣾⠿⠁⠀⣿⡿⠿⠿⠀⠀⢀⣿⣏⣘⣿⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⡏⢻⣷⡄⠀⢸⣿⣤⣤⡄⠀⢸⣿⠀⠀⠀⠀⠀⣿⣧⣤⣤⠀⠀⣾⡟⠛⠛⢻⣿⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠈⠉⠉⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⢀⠀⠀⠄⢀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠞⠀⢀⠚⡁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⡴
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠆⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⢠⠘⠁⠀⣀⠀⠀⠀⠀⢀⡴⠋⢃⠀⢱⠀⢀⡀
⠀⠀⠀⠀⠈⠤⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘⠀⠀⠀⡆⠸⠀⣠⠋⠀⠀⠀⠔⠋⠀⠀⢸⠀⠈⡆⢾⢋⡴⠒
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢾⠔⠁⠙⢦⠀⠀⠀⠀⠀⢰⢡⠃⠀⠀⠸⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢱⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⡃⠀⠀⢀⡦⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡍⡅
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠃⢀⠔⢛⢳⠀⠀⠀⣾⠁⠀⡘⣃⣼⠋⠂⢸⣻⠉⣀⠰⠅⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡆⠀⠀⠀⠇⠘⠀⢀⡼⠃⠀⠘⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠣⠀⠈⠂⠀⠠⠖⠉⠀⠀⠐⠁⢠⡄⠃⠀⠀⠀⠀⣀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠶⣶⣄⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⣸⠓⠒⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠇⢀⡴⠆⣠⡄⢠⡄⣴⢺⡇⠀⢠⠇⠀⠀⠀⢀⣔⡿⢄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⢼⣏⠴⡽⡧⣾⡼⠻⠛⡃⣼⣿⠀⠀⠀⠀⢦⡜⠷⠊⠄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢤⣾⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣴⠾⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠇⠀⠀⠘⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣀⣀⡴⠤⠤⠤⣇⡀⠠⣾⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠙⠣⠔⠋⠀⠀⠀⢠⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⢀⡠⢤⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡊⠀⠀⠀⠠⠀⠘⠀⠸⣦⣤⣤⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⢠⠀⣀⡄⠀⠀⢳⠖⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⣈⣃⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡴⠉⠀⠁⠀⠁⠳⠒⠄⢠⡀⠀⡤⠀⠀⠀⣀⣉⠉⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣄⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠑⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡖⠈⠀⠀⠀⠀⠉⠙⠒⠤⠤⢀⣀⡀⠀⢈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣄⠀⠀⠀⠀⣠⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣶⡞⠀⢀⣤⠞⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⣤⣴⣾⣯⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠄⠀⡜⢀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢃⠀⠀⠀⠀⠀⠀⢠⢤⡴⢠⠆⢀⠀⡴⠂⠀⢀⣠⢠⠆⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠱⠂⡀⠰⠄⢎⠄⠀⠀⠀⠀⠀⠙⠀⠀⠏⠐⠇⠘⠑⠠⠇⠈⠈⠎⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠐⠒⠒⠛⠃⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⣀⡀⠀⠀⠀⢀
⠀⠀⠀⢸⠠⠀⠠⠔⡄⠀⠤⠜⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠁⠘⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡘⢀⢦⠆⡠⠀⣠⠏⡠⢤⠋⣄⠀⠀⠀⠐⠈⠀⠀⠀⠀⠁⠒⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢠⢰⡲⠉⠀⠀⠀⠀⠀⠁⠀⠈⠘⠱⠀⢠⠄⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠘⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠰⡎⠄⢠⠂⠀⡴⡱⠀⠀⠀⠀⠀⢀⠎⢀⠐⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠈⠀⠃⠜
⠀⠀⠀⠀⠈⠉⡀⠁⡈⢈⠈⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠐⡀⠂⠈⠜⠄⠞⠈⠆
⠀⠀⠀⠀⠀⠔⠁⠴⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⢀⣀⠀⠜⠒⠀⠰⡖⠚⠰⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠔⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⢁⠀⠀⣤⠄⠀⠀⠀⠀⠀⣌⠠⠄⡄⢀⠀⡀⡤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⠠⠀⠄⠀⠀⢀⢈⠀⢰⣆⠀⠀⢀⡂⠄⠀⡁⠀⠀⣀⡀⣈⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢐⣻⠵⠀⠀⠁⠀⠈⠈⠀⠉⠀⠠⠁⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠂⠊⠠⠀⠐⡆⠀⠀⠄⠠⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠰⠄⠄⢀⡰⢠⠆⣀⢢⠄⠤⠀⠀⠀⢸⠀⠆⠀⡤⢢⠀⠠⠤⡜⠱⠄⡔⠡⠤⠞⠠⡄⠀⠰⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⠀⣿⡇⣿⣿⣿⣿⣿⢠⣶⡆⢀⣀⣴⣾⣿⣿⣯⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢸⣿⣾⣿⣶⣿⣶⣿⡇⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣼⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⢸⣿⡇⠻⠿⢿⣿⣿⣿⣿⣿⣿⣩⣩⣭⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠏⠀⠋⠉⠉⠉⠋⠀⠀⠀⠀⠀⢀⣍⣉⣉⣉⣉⣉⣉⣉⡙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⣉⣉⣉⣉⣉⣉⣉⣙⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣛⣙⣛⣿⣿⣿⣿⣿⣿⣷⣶⣦⢸⣿⡇⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡟⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⢸⣿⠿⣿⠿⣿⡿⣿⡇⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣻⣿⣿⡿⠟⠉⠁⠸⠿⠃⣿⣿⣿⣿⣿⢸⣿⠀⣿⠀⣿⡇⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣿⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠻⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⠃⠀⠀⠄⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣐⠒⠂⠀⠀⣀⠀⡀⢀⠜⡃⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣘⠿⢥⠿⠻⣿⡨⠷⠉⠊⣉⣀⠛⢀⣀⣊⢃
⠀⠀⠀⠀⠀⠀⢸⢮⠀⡧⠀⠀⡌⠈⣄⢃⡈⢸⠀⠁⢀⣨⠀⡇⢸⠘⠤⡁⣋⢁⢘⢘⡋⣙⢘⢀⣀⠖⠐⠀⠀⠤⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⣤⣠⡅⡠⣍⢌⣅⣈⣰⢡⠄⡸⢄⣅⣈⣈⡒⠁⢹⡿⡎⡼⢧⡟⣾⠸⡇⡀⠀⠸⠌⢽⢿⠐⠂⠐⠒⠐
⠀⠀⠀⠀⠀⠀⠁⠁⠉⠀⠋⢙⣁⡑⠋⣙⡙⡛⢙⣈⡀⠙⠊⠙⠀⠁⠀⠀⣉⢁⡐⣠⣦⡀⣀⠂⣈⡉⢁⡉⢈⠀⣉⣄⡀⣀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⡆⣆⠀⠰⡐⢰⡀⠀⠰⡄⢰⠐⡆⡆⠐⠀⡀⡐⣿⢾⡀⣿⠤⠀⠹⡾⠁⢿⣸⣷⣾⢸⡇⠘⡇⣿⣠⡇⣿⠀⣿
⠀⠀⠀⠀⠒⠒⠒⠀⠘⠙⠄⠃⠀⠠⠼⠘⣄⠀⡃⠳⠘⠙⠄⡣⠄⠀⡀⠐⠟⠈⠷⠻⠶⠆⠐⠇⠀⠸⠏⠘⠃⠘⠷⠾⠃⠟⠙⠦⠻⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⢧⢻⡌⢸⠈⡇⣇⡇⡅⢸⢘⠦⡀⠘⢬⢸⠀⡏⢸⠇⠀⠀⠀⢁⠘⣀⠀⠄⠀⡆⢈⠈⠠⡀⡇⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢈⠉⡀⠁⠁⡉⢩⠀⡍⡄⠨⠩⢸⣄⣵⡚⣷⠂⡖⣄⠈⠀⡀⠀⠁⠀⠁⠌⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠉⠀⠀⠀⠈⣀⣃⢈⢓⢈⡸⠙⠛⠦⠻⠄⠧⠋⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⡎⠃⠁⣀⡤⢄⢀⢠⡄


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣿⣽⣯⣭⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣭⣿⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠛⣆⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢻⡀⢸⡇⢸⡴⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⡇⠸⡇⠘⣇⠀⣷⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢷⠀⣷⠀⢿⠀⢻⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡁⠀⠰⡏⠳⣸⡀⠘⠀⠈⠀⠈⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄⠻⠃⠀⠀⢻⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠳⣌⢧⡀⠀⠀⠀⢳⡀⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠈⢧⡙⢦⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⠷⠖⠉⠀⠙⢲⣀⣀⣀⣤⠤⠤⠿⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⣼⠭⠤⠶⠒⠒⠛⣉⡉⡇
⠀⠀⠀⠀⠀⠀⠰⣇⣤⠞⠁⣠⠶⠀⠀⠀⠀⢀⡀⠀⡴⠳⢤⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠛⠃⢿
⠀⠀⠀⠀⠀⠀⢠⡞⢁⣴⠞⠁⣠⠞⠃⣠⢶⠏⢀⡞⠁⠀⠀⣸⢳⣄⡤⠶⠟⠶⠶⠤⠤⠤⣤⣄⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠈⡽⠋⢁⣴⠟⢁⡤⠚⢱⠇⣰⠋⠀⠀⠀⢰⢃⡞⠀⠀⠀⠀⠀⠰⠶⣤⣤⠤⠞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠳⠞⢿⣁⡴⢯⣀⡀⠈⠉⠁⠀⣀⡀⢀⡏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠓⠦⢤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⣛⠃⣼⣰⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠙⠲⠶⣤⣌⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠁⠈⠳⢤⣀⠀⠀⠀⠀⢀⡈⠙⠓⠶⣤⣄⣈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⡉⠛⠶⢦⣤⣈⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠴⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡌⢉⣙⢠⡄⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠘⠃⢘⠛⢈⠃⡙⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡖⣴⢶⡆⣲⣾⣧⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡐⡘⣉⠃⣹⣉⠋⣽⠉⣍⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⣿⣿⣿⣿⢿⡧⣿⣷⣾⡇⣿⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣼⣫⢽⣥⣤⣄⣠⣄⢰⢲⣦⡶⡶⣤⣦⡶⢶⣾⢲⡦
⠀⠀⠀⠀⠀⠀⠀⠤⠴⠤⠤⠤⠄⠸⢅⠟⠿⠓⠘⠃⠚⠘⠛⢯⡈⣘⠋⠀⠟⠉⠋⣉⣙⡉⡘⣃⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠶⠖⠲⠖⠳⠆⠀⠀⠀⠀⠀⠈⠉⠙⢊⡷⠗⡿⠿⡿⢻⢼⣵⣾⠷⢿⣽⡇⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠿⠚⠖⠻⠾⠳⠿⢛⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⣤⣶⣠⡏⣄⣴⣄⣴⣦⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣤⢤⡄⠀⠀⠀⣿⠹⣼⠿⣷⡏⠿⣯⣿⣋⠨⠭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⢉⡐⠋⢤⣤⣬⣤⠀⠒⢀⠛⡍⠘⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡡⢸⣷⣤⣦⢄⣶⢤⡄⡿⢤⢾⡧⣦⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣷⠘⠿⠙⢗⠛⠟⠻⢃⠛⠚⠳⠃⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⡅⣁⣴⣋⣽⢸⣧⣄⣁⣨⣏⣡⣾⡟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢹⣯⡿⡇⢸⣿⣧⣿⣿⣿⣻⣟⠃⠾⠲⠷⠶⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠲⠶⠾⢄⣁⡤⢀⣀⡆⢀⡀⢺⠿⢃⠲⠗⠒⠚⠳⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣛⣃⡘⣻⡛⣭⢛⣟⣋⣃⣀⣌⣰⣏⡀⣀⣿⠀⠐⣒⣂⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣬⣟⣿⣏⣸⣇⣸⣟⢉⣷⣘⣷⢸⡇⣇⡇⣿⣰⣶⡟⡟⢶⡖⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⢠⢉⣁⡈⣡⠍⠈⠉⠈⠁⠈⠁⠀⠀⠈⠁⠁⠈⠃⢡⣡⡈⠉⢉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠛⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠙⠚⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠟⠛⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠻⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠺⠏⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣤⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠤⠦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠶⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣤⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣩⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠞⠻⠖⠻⠖⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠒



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⠀⠀⡆⣔⠀⡇⠀⢳⣠⠀⠀⡀⢻⠀⠀⠀⡠⡀⡀⠀⠀⢰⣆⢠⡄⢰⠀⣶⢠⡤⢰⣦⡆⢔⡅⡼⠀⠀⢦⢴⡅⠀⠀⠀⠀⢀⠠⢀⠄⢠⠄⣶⠐⠂⢆⠀⡇
⠀⠀⢣⡶⣦⢹⠔⠸⠊⢈⠁⡄⣮⠀⠘⢇⠀⠀⢌⢒⡈⠀⠐⡏⠹⢸⠹⠆⠟⠻⠘⠁⠈⠉⠋⠙⠐⠃⠀⠀⠉⠛⠀⠀⢀⡀⢌⠎⠳⠣⣾⠘⠢⠉⡄⠃⠒⠀⠄
⠀⠀⠀⠁⣈⠀⡀⢰⠒⡾⡗⣼⠹⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠤⣄⡀⢀⣀⡀⢠⡄⢰⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀
⠀⠀⠀⠀⢹⣀⡜⠈⠓⠁⠀⠀⠁⣀⠀⢲⠀⠀⠀⠀⣠⠂⢰⣠⡇⣼⡄⣷⣤⠞⢸⠖⠁⣷⣃⠝⡿⣼⠇⠸⠀⠀⠀⡰⠉⠉⣧⡰⢀⡄⣀⡀⠀⠀⠀⠉⠸⠐⠂
⠀⠀⠀⠀⠀⠟⠀⠀⢠⣀⠀⢦⢠⡃⣤⠈⡇⠀⠀⠀⠧⠎⠘⠀⠋⠁⠃⠇⠉⠸⠘⠂⠀⠁⠉⠀⠃⠘⠀⠒⠀⠀⠀⠿⣤⣶⢫⡇⡼⣰⠃⢀⣟⠂⣶⠀⡄⢀⡀
⠀⢨⣗⣞⠀⢀⢠⠆⢳⣯⠓⢬⡆⠢⠻⡄⠰⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⡗⠀⢀⡾⠀⠀⠀⠀⠀⡠⠒⡠⠀⠀⠀⠈⠃⠉⠁⠛⠂⠼⠄⡼⢻⡼⢁⡞
⠀⠀⠋⠀⠀⠀⢻⡒⠠⠁⠀⠀⠉⠀⠀⠀⠀⠀⠐⣄⠲⣣⠀⠀⠀⠈⢟⠢⣠⠃⠸⡴⠋⡇⠀⠀⠀⠀⠚⣤⡻⠂⠀⠀⠀⡆⢠⠰⠂⠀⠀⠀⠀⠀⠘⠁⡘
⠀⠀⢶⠂⢤⠀⠀⠀⠀⠀⠀⢠⢤⣶⣎⠀⠀⠀⡀⠈⠲⠉⢧⠀⠀⠀⠘⡶⠶⢶⣖⣾⣿⡅⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠐⠒⠈⠐⠰⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⡵⠄⢳⡀⠀⠀⠀⣠⠀⣠⠈⢅⠂⣴⢢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣀⢀⠄⡤⠀⠀⡄⢠⠀⣄⠀⠂⠰
⠀⠀⠀⠙⠪⣧⡀⠀⠀⢸⠟⡎⣓⠀⠔⠃⠀⢈⠀⠀⠀⢀⡄⡄⠀⠀⣀⡀⠀⡀⠀⠀⢲⡸⠆⣰⠀⣖⡁⠸⠀⠀⠠⠇⠀⠉⢈⢀⡋⠈⠁⠉⠈⠀⠀⠀⠀⠂
⠀⠀⢀⢔⠀⠈⠙⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢸⡸⡤⢹⠖⢀⠈⣢⢣⡠⡗⠘⠃⡇⡧⠂⠀⠀⠀⠀⠀⠒⠉⠁⠚⠂⠉⠀⡀⢀⡀⡔⡄⣷
⠀⠀⠂⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡷⣴⠂⠀⠀⢸⠁⡇⠀⠃⠃⠼⠋⠁⠘⠁⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠀⣆⡇⣿⡀⡷⡜⣇⡿⠁⣿
⠀⠀⠀⣴⡸⠓⠿⢁⡠⣀⡀⠀⠀⠀⠀⢹⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠆⡆⣯⠇⠀⠀⠀⠀⠀⣰⡄⠀⠀⠰⣅⡄⢹⢹⠋⠁⠃⠀⠻⠘⠀⠴
⠀⠀⢀⢀⠀⠶⠶⠜⠉⠈⠀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠀⢠⡿⢀⠞⠈⡆⠀⠀⠀⠀⠃⠃⢁⣠⡐⡆⠀⠀⠙⣯⣽⠛
⠀⠀⠘⠋⠁⠀⠀⢀⡴⠂⡀⣏⠖⣸⣧⠈⡇⢶⡁⢸⠀⠀⠀⠘⠚⡆⢻⣀⡀⠀⠐⣯⣞⡎⡏⠀⡃⠀⠀⠈⠁⠈⠁⠀⣄⠀⡤⠀⢠⠀⠄⠀⣰⡀⢤⠆⡆⢸
⠀⠀⠀⠀⢄⣠⠀⢾⣠⢿⠀⡟⢦⡉⢸⠀⠃⠴⠋⠀⡄⠀⠀⠀⠴⠇⢈⠉⠇⠀⠀⠉⠀⠀⠀⠀⠁⡔⢒⠢⡀⠀⠀⠀⠩⠁⠑⠀⠸⠂⠂⠀⠀⠁⠈⠀⠁⠐
⠀⠀⠀⠰⢦⠷⠄⠀⠀⠉⠀⠀⠀⠉⠈⠁⠀⠀⠀⢀⣠⠄⠀⠀⠈⠈⠀⢀⣠⣄⠰⠂⣂⠞⠁⠀⠀⠱⠤⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠌⣃⠑⠀⠀⠀⠀⠀⠈⠉⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⢉⠁⠀⢠⠀⡆⡆⢠⠄⢴⠖⡠⣄⣞⣲⠞⢦⡟⠀⡇
⠀⠀⢀⣶⣼⣰⢗⡖⡆⠰⡐⢄⠆⡄⣶⠀⡇⠀⠀⠀⢰⡂⡖⢲⡀⣶⢲⣠⡼⠐⢱⣆⡖⠐⠶⡅⣊⡄⢸⠀⠀⠸⣾⠁⠗⡧⠆⢸⠸⡤⠏⡏⠳⣄⣸⠀⠀⠃
⠀⠀⠘⠃⠀⠃⠈⠁⠉⠀⠁⠀⠀⠁⠉⠀⠂⠀⠀⠀⠸⠊⠉⠚⠂⠈⠈⠘⠀⠀⠀⠈⠈⠂⠁⠁⠈⠁⠐⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠃⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣀
⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⢾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⣴⣿⣦⠀⠀⠀⠘⠛⠁⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠇
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⢀
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⢸
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠟
⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠿⣿⠟
⡷⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠀⠀⠀⠀⠘⠿⠛
⠀⠀⠀⢀⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠷⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⣤⣄⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⠘
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡄⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄
⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋
⠀⠀⠀⠻⠿⠏⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡗⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⡴⠋⠀⢸⢸⠀⣨⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡇⢸⢸⠀⡇⠀⠀⠀⡼⠁⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⢰⠃⠀⠀⢸⠈⣫⠴⠊⢹
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢠⢣⡄⠀⠀⡿⡄⢶⣄⠈⢇⠀⠀⡀⡇⠀⠘⣆⣤⡀⠘⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⠀⡇⡇⢸⢸⠀⡇⠀⠀⢸⢸⠁⠀⢸⣷⣟⢼⣎⣗⣾⡄⠀⡇⢸⠀⠀⢿⠀⣗⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠴⠧⠾⠼⠴⠷⠧⠼⠾⠤⠧⠄⠀⢸⢸⡀⢀⣇⣘⣠⠋⢧⣘⣀⣇⠀⡇⢸⠀⣴⣚⣈⣓⡍⠉⠁⠀⠀⠀⠀⢰⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢧⣸⣆⠀⢀⣐⣀⠀⢀⠿⡀⣇⡞⠀⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⡷⣄⠀⠀⠀⠀⠘⢮⡟⣨⡳⡤⣉⡡⡴⢋⣤⣱⡟⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⠓⣤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣀⡉⠙⡇⠀⠀⠀⠀⠀⠈⠁⣹⠇⠀⠀⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠯⠇⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⡠⠖⠒⠦⣼⠀⠶⠶⠆⠀⡇⠀⠀⣠⠖⠚⠻⣋⢷⠀⠀⠊⢱⢋⡻⠒⠲⠤⣀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⣀⣈⣉⣁⣀⡇⠀⡜⠁⠀⠀⠀⠈⠹⡖⠦⠶⡞⠉⠀⠀⠀⠀⠘⡆⠀⠀⢸⣉⣉⣉⣉⣉⣉⣿⣏⣹
⠀⠀⠀⠀⢀⡹⠀⠀⠀⡆⠀⠀⠈⣇⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢃⠀⢀⠃⠀⠀⠀⣤⠀⠀⢹⠀⠀⢸⠀⠀⠀⡴⠦⡄⠀⠀⢸
⠀⠀⠀⠀⡎⠀⠀⠈⠳⡷⠊⠀⠀⠈⢧⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠸⡄⡼⠀⠀⠀⠀⣇⠀⠀⠀⣇⠀⢸⠀⠀⠀⠳⠶⠧⠀⠀⢸
⠀⠀⠀⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⡠⠏⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⣿⠀⠀⠀⢹⡀⢸⠀⣒⣒⣒⣒⡒⠒⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠸⣤⣤⣤⣤⣤⣤⣤⣤⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠦⣾⠀⠀⠀⠀⠀⠷⠇⠀⠀⠀⠀⣯⡤⠤⠶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣲⣿⠭⢬⣣⣴⠃⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣼⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⣽⣷⡾⠋⠀⠀⠀⡵⣝⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠧⠤⠤⠴⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣤⣠⡀
⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢠⡄⢀⠄⢠⠀⠀⠀⠀⠰⠁⠥⠉⠰⠀⠀⠀⠀⡤⠉⢁⠆⠘⠀⠀⢰⠂⡄⣀⠔⣶⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⡄⠀⠉⠁⣀⠀⠀⠂⠐⣐⠂⡀⠐⠐⠀⢀⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠅⠀⢤⠀⠀⠀⠈⠁⢀⣀⡀⠁⠀⠀⠀⠀⠴⠠⠀⠀⠀⠀⠀⠀⡀⠂⠈
⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠂⠄⠂⠆⠀⠀⠀⠆⢡⠀⠀⠀⠀⠀⠀⠀⢁⢈⠁⠀⠀⠀⠀⠀⠀⣂⡀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠸⠆⠃⠐⠰⠂⠀⠀⠐⠒⠀⠀⠁⢈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⠁⠀⠀⠀⠀⠨⠀⠄⠀⠀⠀⠀⢀⡠⡤⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠋⠉⠉⠀⠀⠀⠀⠛⠀⠁⠃⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⢀⣠⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁⠀⠀⠀⠀⠀⠁⠀⡀⠈⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠐⢋⡀⢀⠘⠃⠀⠀⠀⢠⣲⣀⡒⣀
⠀⠀⠀⠈⣈⣉⣆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡈⠯⠁⡀⠀⠀⠀⠀⢱⡀⠁⠃⠀⠀⠀⢴⡇⠉⠉⠛⠇⠀⠀⠘⢿⣿⣿⣯⣵⡟⠀⠀⣼⣧⣼⣤⣿⡿⠂
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠙⠊⠀⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠉⠉⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⡤⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠂⢶⠂⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠈⠠
⠀⠀⢤⡄⠀⠘⠠⡤⠀⠀⠀⠀⡃⠙⠀⠀⠀⠀⠀⠉⠐⠀⠘⠉⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠁⠠⠄⠈⠀⠀⠀⠀⠀⢠⣭⣤⣄⠀⠀⠀⠀⠀⠀⠘⠠⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠩⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⡈

⢠⡄⠂⠀⠀⠤⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⢀⣼⡅⠀⠀⠀⠀⠀⢀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣮⣽⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣾⡇⣧⡄⠀⠀⠀⠀⠀⠀⡛⠛⠛⠒⠢
⢸⡇⢄⢸⡇⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠠⣿⠇⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠄


⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣰⡾⠛⠙⠻⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣽⠖⠲⡿⢦⠀⠀⠀⠀⠀⢀⣞⣉⡇⢹⠱
⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣟⣽⣿⣿⠅⠀⠀⠀⠀⢸⣸⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣲⢖⡃⡺⢄
⠘⢿⣶⣴⣾⠗⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⢯⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢩⣷⣻⠗


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣤⣤⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣼⡆⢀⢈⣿⢀⠄⠀⠀⠀⠀⣠⡀⢁⢂⣠⣶⡤⠢⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢
⣿⣿⣧⣤⣾⣿⡇⠀⠀⠀⠀⠀⢻⡇⠈⠘⡿⢀⠀⠀⠀⠀⠀⠸⠱⣦⡦⢫⢔⠔⠳⠄⠀⠀⠀⣯⣱⣾⣿⣶⣶
⠛⠛⠛⠻⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠛


⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⡇⣠⠿⢿⡃⠀⠀⠀⠀⢨⣭⢨⣭⠈⠉⠁⠀⠀⠀⠀⠀⢀⡀⣴⢰⣿⢸
⢿⣿⣯⣽⣿⣿⠇⠀⠀⠀⠀⠀⡿⠛⢾⣿⣦⣾⡇⠀⠀⠀⠀⠰⠶⠰⠶⠰⠶⠲⠶⠆⠀⠀⠀⢸⡇⣿⠨⣿⢸
⠀⠏⢀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠿⠶⠿⠿⠿⠿⠃⠀⠀⠀⠀⠘⠛⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠙⠀⠋⠘
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠐⠲⠄⠀⠐⢂⣤⡄
⠀⠀⠀⠀⠭⠭⠽⠮⠄⠈⠛⢑⢒⣟⡻⣛⢆⡒⡒⣒⢚⣓⡂⣀⣀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀
⠀⠀⠀⠈⣉⢩⣙⣛⡛⣙⡟⡿⠧⠥⠁⣿⠛⠛⠛⡟⣻⠙⠋⠤⢽⠭⠤⠤⠬⠥⠤⠤⠴⠤⢒⡀⢷⢶⢶⠈⣉
⠀⠀⠀⢈⣂⣈⠙⡍⢘⣿⣧⡁⣞⢚⡓⣃⠸⠛⠛⣛⣛⡛⣓⣒⢃⡒⢒⠒⠒⠂⠐⡖⣺⢳⢓⣀⣀⣀⡄⣢⢤⢀⡀
⠀⠀⠀⣀⣀⣟⡒⠧⡾⢿⣿⣟⣿⡻⠿⢏⣌⣩⣉⣿⢹⡇⣿⢿⠸⣧⣿⣾⠩⢭⣽⠇⡘⢻⣿⠛⢻⠛⢃⢿⠻⠛⠛
⢀⣀⣀⣀⣉⣥⣀⣛⣉⣩⡈⣽⣽⣧⡿⣧⢼⣴⣤⣯⣜⡡⠍⠉⠤⠿⠬⡭⠴⠮⢘⣛⣱⡸⣿⡏⣹⣿⣿⣿⠿⠇
⠘⠛⠛⠻⠟⡿⢛⣟⠟⣸⠂⣨⣼⣷⡶⢾⠤⠎⠤⠅⣯⣶⣶⣶⡗⣿⡆⠤⡼⢶⠷⠶⠀⠒⣒⣀⢭⣭⣭⠈⠤⠄
⠀⠀⠀⢀⣛⣛⣋⣻⣀⣡⡛⣙⣟⢉⣃⡈⡖⣛⣍⢋⣀⢸⠿⣴⣴⢶⢦⡄⣉⣭⣭⡭⠭⢱⠒⣒⣒⢒⣒⡂⠆
⠀⠀⠀⠀⠤⠤⣿⣸⢿⣟⡏⣿⣿⢸⣿⡿⡿⣿⣻⠉⣧⣤⡴⠋⣷⠦⠬⣅⠉⠞⠁⣐⣒⠠⠤⠬⠅⠉⠀⣉⣉⡀
⠀⠀⠀⠈⡉⢁⣛⣴⡆⢰⣒⣲⢲⣘⣃⡐⠴⠶⠶⠶⢶⠀⠀⠋⠉⠉⠀⠉⠁⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠂⠒⠂⠉⠉⠃⠀⠈⠉⠁

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⡤⠤⠤⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣠⣶⣶⣦⡀⠊
⠀⠀⠀⠀⠀⠀⣀⣀⢠⡏⠀⠀⠀⠈⡆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣼⣿⣿⣿⣿⣿⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠼⢧⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠹⣿⣿⣿⣿⡿⠡⣄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢳⣀⣸⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡠⠂⠘⣿⣿⡟⠀⠲⡌⢳⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⣶⡖⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢒⣒⠂⠀⠀⠀⠀⢷
⠀⠀⠀⢀⠖⠛⠓⢆⠀⢀⡤⠤⠤⡀⠀⣰⠋⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⡀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣶⣦
⠀⠀⠀⢸⡀⠀⠀⣸⠀⡟⠀⠀⠀⢸⠀⣳⣀⠀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠀⠀⣼⣿⣿⣿⡄⠀⠸⣿⣿⣿⠃
⠀⠀⡴⠋⠉⠛⠋⠉⣳⠿⢤⣀⡠⠾⢏⠀⠈⠉⠁⠀⢳⠀⠀⠀⠀⠀⠀⣠⣦⣭⣯⣵⣦⠀⡻⣿⣿⠿⡃⢰⣾⣶⣿⣶⣷⡄
⠀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣⣾⣿⣷⣶⣾⣿⣦⢻⣿⣿⣿⣿⣿
⠀⠀⠧⣤⣀⣀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠼⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣺⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⣀⣀⣀⣠⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣤⣼⣇⡀⣼⠈⣿⠃⠀⠀⠀⠂⡠⢰⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠠⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⡠⠔⠀⠀⠀⠒⠤⠤⠀⠀⠀⠀⠀⠀⡐⠈⠈⠁⠀⠋⠙⠀⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠉⠀⠐⠀⠺⠁⠀⠘⠃⠾⠁⣀
⠀⠈⠀⠀⡰⠀⠐⠀⢄⠀⠀⠀⡀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠁⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠂⠀⠀⢀⠄⠀⠠⠀⠔⠢⠃⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠄⡀⠀⢸⠀⠀⠠⠞⢹⣿⠧⢤⡆⠀⠀⢀⢤⠶⠒⠲⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠈⠀⠀⠀⠀⠉⠻⠄⣜⣀⢀⡄⠛⠁⠀⠀⢀⡇⠀⠀⡏⠀⠀⢠⠞⡰⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠸⠋⠀⠀⠀⠀⠀⡜⠃⠀⠀⠿⠚⣦⠏⣰⢷⠄⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢃⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣺⠃⠀⠀⠀⠀⠀⠈⠐⠁⡜⠸⡉⠛⡼⠛⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠀⣀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢿⡄⠻⣷⣤⣸⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠙⠁⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠁
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠈⣿⣀⣀⣼⣿⠀⠈⠙⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣴⠀⠀⠀⠀⡀⠀⢳⡾⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠘⣿⠀⢸⣿⠏⠉⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⡀⠈⣿⡀⣤⡀⣿⠀⢸⠀⣠⡇⠀⠀⣷
⠀⢀⣀⠀⠀⠙⢻⣄⠀⣿⣷⣤⣿⠀⠈⣿⡆⠀⠈⠿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⣿⠏⢳⣿⠀⠸⡃⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡟⠈⠻⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠟⠞⠀⠘⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠶⠀⢀
⠀⢀⣰⣶⠀⠀⠀⠂⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡤⠀⡄
⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⡀⣀⣠⠀⠱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⣀⡀⠀⠀⠀⠠⡀⠤⠂⠉⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⡄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣰⠆⣴
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠐⠠⠦⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠒⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⠀⠀⠈⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠄⠃⠀⠀⠙⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠇⠀⠀⠀⠀⠠⢔
⠀⠀⠀⠀⡀⡀⠀⢀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠠⡀⠈⠃⠀⠀⠁⠀⠀⠀⠀⡀⡆⠐⠈⠒⣄⣄⠀⠀⠀⠀⣰⣦⠀⣤⣿⠏⠻⣆
⠀⠀⠀⢀⡌⠓⠚⠈⢄⡸⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢠⢀⡂⠀⢀⠀⠰⠄⢀⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⢞⠀⠁⠀⠀⠀⠙⣿⣆⢸⣧⢀⡿⢻⣤⣏⣿⡄⢠⡿
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠿⠁⠎⠁⠘⠒⠇⠀⠀⠈⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠏⠀⠀⣀⣀⠀⠀⠘⢿⡿⠙⣿⠇⠘⠂⠘⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠤⠀⠀⠰⠄⠄⠤⠤⠀⠀⠠⠀⠠⠀⠄⠄⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠐

⠀⠀⠀⠀⢀⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⣿⣿⣏⢸⣿⣿⡇⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣛⣩⣥⣭⣝⣫⣭⣬⣭⣛⣭⣥⣭⣝⣫⣭⣬⣭⣛⣭⣥⣭⣝⣫⣭⣬⣭⠀⠀⠀⣛⣛⣓⢐⣛⣛⡃⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⢏⠻⣿⣿⡿⡙⢿⣿⣿⢋⠻⣿⣿⡟⡙⢿⣿⡿⢋⢻⣿⣿⠟⡹⣿⠀⠀⠐⣖⣒⣖⢐⣖⣒⡂⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⡛⣡⣿⣷⣜⢋⣼⣿⣮⠛⣱⣿⣷⡝⢋⣾⣿⣎⠛⣱⣿⣷⡙⢫⣾⣿⣤⠀⠀⠀⠉⠉⠁⠀⠉⠉⠁⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⢿⠟⠋⠙⠿⡿⠋⠉⠻⢿⠟⠉⠙⠿⡿⠋⠉⠻⡿⠟⠉⠙⢿⠿⠋⠉⠻⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣄⣴⣾⣷⣤⣠⣶⣿⣦⣀⣴⣿⣷⣄⣠⣾⣿⣦⣀⣴⣿⣷⣄⣠⣾⣷⣦⠀⠀⠀⠀⣨⡘⢿⣶⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠿⢟⣛⣛⠻⠿⣛⣛⡛⠿⢟⣛⣛⠻⠿⣛⣛⡻⠿⢟⣛⣛⠿⠟⣛⣛⡻⠀⠀⠀⠀⠹⢿⣦⠙⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⢿⣿⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠿⢋⣴⣦⠻⠟⣡⣶⡝⠿⢋⣴⣮⠻⠟⣱⣶⡙⠿⢋⣶⣎⠻⠟⣵⣦⡙⠀⠀⠀⣀⣀⡀⢀⣀⣀⡀⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⣶⡿⠟⠻⣷⣾⠿⠛⢿⣶⡿⠟⠻⣷⣾⠿⠻⢿⣶⡿⠟⠿⣷⣾⠟⠻⢿⠀⠀⠠⠿⠿⠯⠨⠿⠿⠇⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠉⣀⣴⣦⡈⢁⣠⣦⣄⠉⣀⣴⣤⡈⢁⣤⣦⣄⠉⣠⣴⣤⡈⢁⣤⣦⣀⠀⠀⠠⣭⣭⡯⠨⣭⣭⡅⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⣿⣿⣏⢸⣿⣿⡇⠀⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠂⠂⠂⠋⠘⠀⠘⠀⠀⢃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠔⠉⠀⡀⠀⠀⠋⠀⢠⠚⠉⠁⠀⠀⢀
⠀⠀⢠⠁⠀⡰⠃⢀⡤⠀⢀⠀⣴⠰⣈⠂⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⡀⠀⣤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡆⡠⠲⡄⠀⠀⠀⡄⡏⠀⣸⣴⠁⢀⠀⠀⠀⠈⠂⡁⠀⠀⠂⠊⠁⠈⣉⡀⠀⠉⠉⠁⠀⡀⠀⠀⡠⠐⠂⠈⠁⠀⠀⡆⢠⠀⠀⢰⠈⠁⠐⠂
⠀⠀⢡⠈⠀⠙⠀⠠⠴⠁⠸⠄⠇⠙⠤⠜⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠂⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⡀⠁⠘⠀⡀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠐⢲⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡠⠖⡦⠀⢨⡇⡔⠀⠲⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠁⠐⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⣠⠁⡀⣀⢰⠁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠘⣧⠈⠀⡇⠳⠄⠨
⠀⠀⠀⠀⠀⠀⠀⢀⣹⠈⠂⠀⠐⠁⠔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠈⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⢠⠏⠐⡠⠇⠀⠀⠈⡄⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠁⣔⣀⠔⢠⠊⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⢒⡴⢁⢆⢾⢠⡎⠑⠂⠀⠀⠀⠀⠀⠀⠀⢸⠘⠃⠉⠉⢀⠀⠀⠀⠐⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡉⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠚⢯⠀⣸⢃⠘⡞⣇⠀⡘⠄⠄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠉⠁⠈⠚⠃⠈⠉⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠀⠒⠠
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡷⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣿⣿⣿⠆⠀⢀⣾⣿⣿⣇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⢼⣿⣿⡿⠃⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣏⡇⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠁⠀⢿⠀⠾⢿⢿⣇⡀
⠀⠀⠀⢀⡀⣠⡀⠀⠐⠚⠛⠉⠁⠀⠉⢓⡠⠀⠀⠀⠀⠀⠹⠟⠛⠃⠀⠀⠠⣄⠻⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠳⠔⠂⠈⠉⠉⢳⡀
⠀⠀⢦⣽⣿⡿⠟⠀⠀⠀⠀⢠⡤⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⢿⡇⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠇⠀⠀⠀⠀⢴⣶⠆⣀
⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠘⣿⠀⠀⠀⢶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⠾⢛⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡄⠀⠙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣊⣉⣛
⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠛⠛⢻⣿⠟⠀⠛⠀⠀⠀⠀⠘⡿⠋
⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢲⠀⠀⠀⠀⠀⣴⢢⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠖⡆⠀⠀⣿⠀⠀⢲⡆⠀⠈⠁⠀⠀⢴⣦
⠀⠸⣷⣄⠙⠿⠄⠀⠀⠀⠀⠀⣰⡆⠀⠙⠚⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠚⠂⠀⠀⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⣀⣤⣤⣶
⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⢀⣼⣿⠃⡀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⣰⣦⡄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠘⠂⠀⠀⠀⢀⣾⡿⠃⠘⢁⣤⣾⣿⣿⣷⣄⡀⠀⠀⠀⣿⣿⣿⣦⡀⠀⠈⠻⣿⡟⠁⠀⠀⣴⡿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⢀
⠀⢠⣄⠀⠀⠀⠀⠀⠀⠞⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠰⣿⣿⣿⣿⣿⣄⠀⠀⣼⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢸⠿⠟⠋⠁⢠⣤⡄⠀⠀⠀⠐⠛⠛
⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⡀
⠀⠘⣿⣿⣷⠀⢠⣶⣆⠀⠀⠀⠀⠈⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠛⠀⠄⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣷⡀⠀⠀⠠⣦⠀⠀⠀⢀⣾⠇
⠀⠀⠘⢿⣿⡇⣨⢻⣿⡄⠀⠀⠀⠀⠈⠁⠀⠀⠠⠴⠶⠾⠿⠿⠿⠿⠷⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠹⣷⡀⠀⠀⡏⠀⠀⠀⣼⠟
⠀⠀⠀⠀⠉⠃⣿⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⢀⣧⠀⠀⠰⠋
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠈⠻⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⡿⠛⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠿⠿⠿⠿⠷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣩⣤⣶⠾⠿⠿⠷⢶⣦⣌⡙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⣴⡿⢋⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⠻⣷⡀
⠀⠀⠀⠀⠀⣼⡟⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠙⣿⡄
⠀⠀⠀⠀⢸⡿⢠⣿⠁⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢻⣧⢹⣷
⠀⠀⠀⠀⣿⡇⣾⡇⠀⠀⠹⣷⡀⠀⠀⣴⣶⡀⠀⠀⣰⡿⠀⠀⠘⣿⠀⣿⡄
⠀⠀⠀⠀⣿⡇⢿⡇⠀⠀⠀⢻⣧⢀⣼⡟⠙⣷⡄⣰⡿⠁⠀⠀⠀⠉⠀⣿⠇
⠀⠀⠀⠀⢹⣧⠸⣷⠀⠀⠀⠀⢻⣿⠏⠀⠀⠘⣿⣿⠁⠀⠀⠀⣸⡟⢰⣿
⠀⠀⠀⠀⠈⢿⣆⠹⣷⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⡿⢡⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣦⡙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣍⠛⠿⣶⣶⣤⣤⣴⣶⠾⠟⣋⣴⡾⢿⣷⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣤⣤⣴⣶⠿⠛⠉⠀⠺⣿⡀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣷⣄⠀⠀⣼⣿⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⢿⣷
⠀⠀⠀⣿⡏⠀⠀⠀⠀⣀⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿⡏⠉⣿⣿⣿⣶⣄⠀⢸⣿
⠀⠀⠀⣿⡇⠀⢀⣴⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠙⣿⡇⠀⣿⣿⠀⣿⣿⣤⣼⣿
⠀⠀⠀⣿⡇⠀⢸⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣏⠀⣿⣿⠛⢿⣿
⠀⠀⠀⣿⡇⠀⠀⠙⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢠⣾⡿⠿⣿⣿⠀⠀⠀⠀⣀⡀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣩⣽⣿⡿⠟⠀⠀⠀⠀⣠⣾⡿⠁⠀⣿⣿⠀⠀⢰⣿⡿⢿⣷⣸⣿⡇⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⢁⣀⣤⣤⣶⣾⣿⠿⠛⠁⠀⠀⠘⢿⣿⣾⣿⣿⡆⠈⢿⣿⣿⡇⠀⠉⠁⠀⠉⠁⠀⠈⠁⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟
⠀⠀⠀⠀⣠⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⢀⡀⠀⠀⡀⠀⠀⡀⠀⢸⣿⣿⣷⡀⠸⣿⣿⡿⣿⣷⣄⠀⠀⠀⣠⣶⣿⡿⠿⠛⠛⠉⢁⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣾⣿⠀⢸⣿⠀⢸⣿⡏⢿⣷⣶⣿⠇⠀⠀⣿⣿⠀⢀⣾⡿⠋⠀⠀⠀⠀⣴⣾⣿⣟⣋⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣿⣿⠀⢸⣿⠀⢸⣿⡇⠀⠉⠉⠁⠀⠀⠀⣿⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⣽⣿⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣷⣄⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣷⣤⣿⣿⠀⢾⣿⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣿⡇⠀⢸⣿
⠀⠀⠀⠀⣿⡿⠛⣿⣿⠀⣹⣿⠀⢸⣿⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠹⢿⣿⣿⣿⡀⣸⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠋⠁⠀⠀⠀⣸⣿
⠀⠀⠀⠀⢿⣷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⡟⠀⠀⠹⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣿⠟
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠐⢒⡒⠒⠒⠒⠆⠀⠀⠀⢠⠒⠒⠒⠒⠒⢦⠀⠀⠀⠀⠀⡴⠲⠿⠖⢢⠀⠀⠀⠀⠀⢠⣶⣿⡷⠐⠄
⠀⠀⠀⠻⠷⠀⠀⠀⡆⠀⠀⠀⢸⠀⠤⠤⢾⠉⣛⠀⠀⠀⠀⠀⡟⠿⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣣⣄⣈
⠀⠀⠼⠿⠿⠽⠿⠿⠧⠀⠀⠀⠈⠉⠩⠿⠏⠉⠙⠂⠀⠀⠀⠀⣧⣤⣤⣶⣸⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⠶⡶⢦⡀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠆
⠀⠀⡇⠀⣄⢀⣄⡀⣿⠀⠀⠀⠀⣿⠒⣿⢚⡇⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⣿⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤
⠀⠀⣇⣺⣛⣟⣟⣇⡿⠀⠀⠀⠀⠈⠓⠛⠛⢧⡀⠀⠀⠀⠀⠀⢸⣿⣿⡃⠋⠀⠀⠀⠀⠀⠀⠺⠛⠒⠛⠻
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣤⣀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣠⡀
⠀⠀⣀⣰⣋⡠⠿⣶⡶⠀⠀⠀⠀⣰⠏⠁⠀⢛⢳⡄⠀⠀⠀⠀⢘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠴⢒⣄
⠀⠀⠉⠉⠻⠥⠴⢇⠀⠀⠀⠀⠀⢿⡠⠶⠴⠿⣸⠇⠀⠀⠀⠀⠸⠴⢤⡤⠦⠄⠀⠀⠀⠀⠀⡟⢖⣛⣜
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠰⠾⠷⠀⠀⠀⠀⠀⠀⠀⠳⠶⠴⠶⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡿⠿⠿⠿⠿⠿⣟⠀⠀⠀⠀⡞⠉⣩⡿⡆⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⠀⠀⠀⠀⠀⡠⡼⠩⠍⢧⢄
⠀⠀⡤⣤⣤⣔⣩⣕⣾⠀⠀⠀⠀⢷⣛⣛⣳⡃⠀⠀⠀⠀⠀⠀⣿⣁⣉⣀⣿⠀⠀⠀⠀⠀⠂⡇⠐⡂⡰⠐
⠀⠀⠦⠤⠤⠬⠵⠭⠮⠀⠀⠀⠀⠀⠈⠉⠀⠹⣦⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠭⣈⣣⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⢲⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢠⠈⡌⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣖⣒⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⢔⡳⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⣄⠀⢘⡙⠛⡛⡋⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⢍⠉⣡⢠⠄⡄
⠀⠀⠀⠀⠀⡯⢸⠇⠣⠅⠹⠻⠃⢱⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠟⠡⡘⠄⠏⠀⡇⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣄⣤⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⡿⣿⢻⡿⣿⢻⡿⣿⣻⣿⢿⡟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣽⣽⣷⣿⣸⣿⣶⣾⣷⣿⣾⣷⣽⣾⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠟⠛⠻⠿⠿⠟⠋⠈⠉⠉
⠀⠀⠀⠀⠀⣿⣿⣿⣥⣽⣿⡇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣯⣷
⠀⠀⠀⠀⠀⣀⠈⠀⡀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢿⣷⣿⣾⣭⠟
⠀⠀⠀⠀⠀⠎⠰⠴⠳⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢶⠖⠓⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣀⣶⣙⠀⠀⠀⠀⠀⢸⡎⣿⡀⣼⣀⢺⢣⠹⡄⢹⢔⡦⣿⡀⣼⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡍⠿⠉⠀⠀⠀⠀⠀⠘⠁⠁⠉⠀⠉⠈⠈⠀⠁⠈⠀⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⢰⡄⣀⢠⡔⠐⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠢⠻⠃⠸⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣾⡆⠀⣿⠀⠀⠀⠀⣠⣾⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣠⣾⠟⣳⠀⠀⣰⡾⣛⣭⣽⡻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡄⠀⣿⡇⠀⣿⠀⠀⠀⣸⣿⣿⣿⢟⣭⡻⣿⣿⡄⠀⠀⠀⣿⡿⠿⠿⠿⣿⣫⣾⠟⠁⠚⠁⠀⢰⣿⣸⣿⣿⣿⣿⡞⣿
⠀⠀⠀⢰⡆⠀⣿⠀⢸⡇⠀⣿⡇⠀⣿⠀⠀⠀⢻⣿⣿⣿⠻⠿⢇⣼⣿⣶⠀⠀⠀⣿⡿⠿⠿⣿⣣⣬⣷⠀⠀⠀⠀⠀⠘⣿⡜⣿⣿⣿⡿⣳⡿
⠀⠀⠀⢸⠇⠀⢿⠀⠸⡇⠀⢿⠇⠀⠿⠀⠀⠀⠈⢿⢟⣵⣿⣿⣿⢟⣱⠏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣷⠾⢛⣵⣤⡀
⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠙⠓⠲⠚⠋⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣴⣶⣦⠀⠀⠀⠀⠀⠀⣴⣿⣅⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⠉⠁⠀⢀⣠⣀⠀⠀⠉⢉⡹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢠⣤⠏⠉⠉⣷⣄⠾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⠛⣧⠀⢰⡟⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠛⡆⢀⡀⢿⣦⠿⣶⢀⠀⠘⠛⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⢼⡇⠁⠁⠀⠀⠀⠀⠈⢐⣀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠶⠿⠿⠇⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢠⡇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣾⣷⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⠛⠛⠛⠛⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢉⠀⠀⠈⠀⠉⠓⠠⠄⠀⠀⠀⠀⣄
⣀⡀⢠⣄⣀⡄⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⢰⢠⡶⠆⠀⠀⠀⠀⢶⠆⠀⠀⡀⠈⠑⢄
⠛⠛⠿⢿⣿⣷⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠸⠈⠳⠂⠀⠀⢠⣠⠀⢀⡀⣾⣿⣷⣤⣄⣤
⠀⠀⠀⠀⠈⢿⣿⣿⣟⠀⠰⣶⠈⠂⠠⢤⠈⢳⠀⢰⣶⡄⢠⠀⣶⡶⠀⠀⢠⣤⡄⠀⠀⠀⠀⠑⢿⣿⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡶⠆⠀⠘⠛⠃⠈⠀⠛⠛⠀⠀⠸⠏⠀⠀⠀⠀⢄⡄⠀⠀⠁⠀⠀⠈⠙⠿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠀⠚⣥⣭⠝⡏⠁⣤⠀⠘⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠃⠀⠿⠹⠂⠃⠀⠿⠀⠀⠐⠿⠃⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⣤⡤⠁⠈⢠⡀⠀⠈⣉⢉⡉⠊⢩⣈⡅⠘⢡⠤⡄⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠧⠀⠀⢸⣥⠀⠀⡿⢿⡇⠀⠸⠝⠇⠀⠘⠶⠃⠀⠻⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⠀⠈⠉⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢰⣾⣧⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⣉⣤⣤⣤⣤⣄⣉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⠟⠋⠁⠀⠀⠀⠉⠙⠿⣦⡈⢻⣆
⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⠿⠷⠶⠶⠶⠶⠶⠶⠶⢶⡆⠈⢿⡄⠹⣇
⠀⢸⡇⠐⢯⡁⣠⣦⡀⣶⡄⣤⠄⡴⠆⣿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⠀⣿⡄
⠀⢸⣇⣐⣒⣋⣙⣛⣘⣓⣃⣛⣀⣓⣂⣛⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠛⠁⣸⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⠙⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢠⡿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠛⢶⣤⣀⣀⣀⣀⣠⣴⠾⠋⣠⣾⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣌⣉⣙⣛⣉⣉⣠⣴⠾⠋⣽⡟⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠈⠻⣦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠑⠦⠞⠁⠀⢸⣷⡤⠚⠉⢉⣵⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢽⡀⠀⣄⡀⢠⣶⣄⡁⣠⠂⣰⣿⠟⠁⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⢦⡀⣷⠀⠀⢸⡇⠀⢻⣟⠻⡟⠈⠙⡇⣼⡿⠃⢠⠞⠉⠀⠀⣀⠈⠳⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⣿⠇⠀⠀⣾⣿⣶⣴⡾⠉⠉⠑⢦⣙⣿⡃⡰⠃⠀⠀⣠⣾⣿⠀⠀⣿⡆
⠀⠀⠀⢀⡜⠁⠀⢠⠀⠀⢀⣿⠋⠀⣠⣾⣟⠉⠀⣸⣷⣴⠂⠀⠘⠉⠀⡽⠁⠀⠀⣼⣿⠋⣏⠀⢀⣽⣿⠆⠀⡠⢦⡀
⠀⠀⠀⡼⠀⠀⢠⡿⠀⠀⠼⠁⠀⠞⠋⠉⠉⠀⠀⣾⡯⠟⠀⠀⣴⠃⢰⠇⠀⠀⠘⠛⠳⠤⠬⣿⡻⠟⠁⣠⠞⠁⣸⣿
⠀⠀⠀⡇⠀⢠⣿⡇⠀⠀⠀⣀⣤⡶⠀⠀⢠⣤⣀⣠⣴⣇⣀⣼⡿⢇⣀⠀⠀⠀⣄⠀⠻⡖⠀⠨⡷⠴⠚⠁⢀⣴⡿⠃
⠀⠀⠀⠹⣀⣿⡟⡇⠀⠀⢸⣿⣻⠁⠀⠀⢋⡽⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣿⣷⣶⠀⠀⣠⣤⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠙⠿⠀⢷⠀⠀⠀⢿⣧⣀⣠⣴⠏⠀⠀⣀⣠⣤⡴⣶⣾⣿⣿⢧⠀⠀⣿⠿⠃⠀⢠⣿⠏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⣿⡙⠛⣯⣴⣾⣿⢟⣫⣵⣾⠿⠛⠋⠁⠈⠳⣄⡀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃⠀⠈⠉⠈⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡟⢷⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡟⢿⡇⢹⡇⢸⠆⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣿⣭⣭⣭⣭⣭⣭⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⠻⠃⠘⠁⠘⠁⢸⡏⠉⣉⠉⠉⠉⠉⠉⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⠟⠛⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠉⠁⢀⡾⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⣤⣤⣤⣤⣤⣤⣾⣦⣄⡀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣄⠀⠙⢷⡄⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠉⠻⠶⡾⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡶⠶⣦⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣤⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢷⣄⠀⠙⠷⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⠃⠀⠀⠈⠛⠻⡿⠛⠛⠛⠛⠛⠛⢛⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿
⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⣠⡾⠁⢀⣀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣄⣴⠿⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣀⣀⣀⣀⣉⣀⣸⡇⢠⡄⢀⡄⢰⣦⢸⣧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣛⣛⣛⣛⣛⣛⣿⡟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡇⢸⡇⢸⣇⢸⣷⣼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠾⢷⣼⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣠⣤⠀⠀⡀⠀⣤⡄⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣿⣿⡇⣰⣿⣿⠀⣿⡇⢀⣿⡇⠀⠀⠀⢰⡟⣵⣿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣏⡇⠀⠀⢸⡟⣿⣷⡿⢹⣿⠀⠙⠷⠞⣿⣧⠤⡄⠀⢸⣧⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⣼⠇⣿⣿⡇⢸⣿⠀⢠⠔⠋⣿⠃⠀⠀⠀⠘⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠀⣀⡀⠛⠀⠘⠛⠁⠘⠛⠀⢿⣤⡼⢋⣀⠀⣠⡄⠀⠻⠟⠉⠀⠀⠀⢀⡀⢀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣰⣿⣧⡤⠴⠖⠒⠛⠉⠉⠉⠉⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⢴⣦⠀⣠⠟⣲⣦⠀⢀⣴⣦⠀⣠⣤⣤⣴⡄⢠⣿⡏⠀⢠⣴⣦⠀⢀⣤⣄⠀⢰⣿⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢋⡴⢿⣿⠞⠁⣰⣿⠇⠀⣿⣿⠞⢰⣿⢋⣾⡿⠁⢸⣿⠀⢠⣿⡿⠃⣠⣾⣿⣈⠔⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠴⣿⠇⠀⠀⣿⡏⢀⡴⣿⣇⡴⠻⠿⠋⣿⠃⢀⣿⣇⡴⠻⣿⣠⡴⢋⣼⣿⡇⠀⣿⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⡟⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⢿⣠⠟⠀⠀⠀⠀⠀⠀⢀⡎⢀⣿⠃⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠴⢫⣾⢿⡆⠀⢀⣶⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣸⠃⢀⣾⡏⢰⠇⠀⠀⠀⢀⣀⠀⢰⣾⠛⠆⠀⠾⠂⠀⠀⠀⠀⠀⠀⢀⠀⣤⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡴⠃⠀⢸⣿⣡⠋⣰⡿⡷⠀⣿⡏⠃⢸⣿⡀⠀⣾⡗⢰⣿⣠⣶⡄⢀⣾⡟⢻⣿⡇⣰⣿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣿⣿⡤⣄⣀⣼⡟⠁⢀⣿⠗⢁⡔⣿⣧⠒⠈⣿⡷⢺⣿⠁⣼⣿⢃⣿⠇⢸⣟⡰⢋⣿⠟⢉⣿⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣠⣿⡏⠸⣧⡴⠋⠿⠴⠋⡴⢻⣿⠀⡴⢻⣷⠈⠿⠞⠘⠟⢸⡿⢠⠇⢨⠔⣻⡿⢠⡏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣿⠃⠀⠀⠀⠀⠀⠀⠘⠧⠼⠃⢰⡇⢸⡟⠀⠀⠀⠀⠀⠘⠛⠁⢰⡇⣠⡿⠁⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⣀⣀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⣙⠋⠀⠀⠀⢀⡀⠀⠀⢀⡀⢈⣉⣁⣄⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⢀⣾⠛⢻⣷⠀⣾⠟⣿⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⡀⢀⣿⣿⢸⡏⠉⠉⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡉⢸⣿⠀⠀⠛⢸⣟⣀⣿⢀⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⡿⣷⣾⢻⣿⢸⣧⣤⡄⠀⠉⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⡤⠸⣿⠀⢠⣷⢾⡟⠛⣿⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠙⠋⢸⣿⢸⡏⠉⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠻⢷⡾⠃⢸⠇⠀⠿⠘⠿⣶⡶⠸⠿⣶⣶⠄⠀⢿⠃⠀⠀⠸⠿⠸⠷⠶⠶⠆⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢤⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡼⣿⡆⣠⣤⡀⠹⣧⣤⠈⢣⠀⣿⣿⣰⣶⣆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢀⣿⣿⢫⣿⡇⢠⣿⡟⠉⡻⠉⣿⣿⡇⣿⣿⠎⣼⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇⢸⣿⠁⣼⣿⠇⣠⠇⠀⣿⣿⠀⣿⡟⠀⣿⡇⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠛⠀⣿⡏⣼⠃⠙⠛⠁⠀⠀⠉⠁⠀⠙⠁⠈⣿⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⣿⡟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠻⢿⣿⣿⣿⠀⠀⠀⠋⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣌⣉⣉⣀⣤⡴⠟⠉⢳⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣤⣤⣉⣉⡁⠀⢠⣾⣦⡙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣦⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠘⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡖⠒⢲⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⠂⢐⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⢰⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⢁⠞⠁⡠⠄⠈⠢⠑⡄⠀⠀⠀⠀⠀⡀⠤⡀⡀⠿⠸⠸⢂⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠠⢤
⠀⠀⠀⠀⠀⡂⡯⠭⢽⠀⠒⠒⡆⠀⠀⠀⠀⢘⠁⡆⠀⡠⠄⡇⠀⠀⠀⠀⠀⡼⠤⠂⠘⡈⠖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠠⠠⠤⠠⠤
⠀⠀⠀⠀⠀⠄⣏⠉⣿⢰⣄⣠⡇⠀⠀⠐⡈⢮⡀⠅⠀⣇⡴⢠⠂⠀⠀⠀⠀⠈⣄⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠑⠂⠠⣄⠔⡱
⠀⠀⢸⠈⢹⠅⠏⠉⡿⠸⡏⢀⠇⠀⠀⠀⠈⠢⠍⣁⡉⠡⠴⡣⠑⠄⠀⠀⡔⠁⠀⠎⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠗⠠⠀⣈⣀⠠⠊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠈⠀⠈⠈
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠔⢹⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⡒⠀⠀⠀⠠⠂⠀⠀⠀⡠⡀⠈⠆⠀⠀⠀⠀⠀⠀⢀⠄⣒⣂⠠⣀⠆⠸
⠀⠀⠀⠋⠀⠊⠀⡄⡂⣀⢇⠀⠀⠀⠀⠀⠀⢀⠔⣉⠢⠔⡠⠲⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⣇⣠⠃⠀⠀⠀⠀⠀⡐⡐⢁⢄⢀⠐⡌⠎⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡆⠆⠀⠀⠀⠀⠴⡡⠊⠀⠑⠊⠀⡇⠀⠀⠀⠀⠀⠀⠀⠜⢌⠀⠃⠁⠗⠀⠀⠀⠀⠀⡁⢇⠔⠢⡥⠊⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠊⠤⠌⣜⢀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⢄⠙⠪⣂⠀⠀⣊⡔⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠤⠤⠧⠠⠤⠸⠤⠤⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠁

⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢩⢩⡍⣭⠉⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠐⠂⠐⠒⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣔⡄⢀⡢⠈⠀⠀⠀⠀⠰⠒⠒⠒⠒⠖⠶⠲⠖⠲⡁⠀⠀⠀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠰⠳⠣⠇⠶⢰⠐⠞⢆
⠀⠀⠀⠀⠀⠙⠀⠘⠝⠀⢀⠀⠀⠀⠀⢀⣘⣈⣃⣛⠄⠀⠠⡐⣄⠇⠀⠀⠀⢀⣀⣀⡀⠁⣀⣀⣀⠀⠀⠀⠀⠆⠤⠴⠤⢤⢔⠢⢑⠾
⠀⠀⠀⢆⣀⣀⣀⣄⣀⣄⣀⠲⠀⠀⠀⠀⢤⠠⠄⠈⠀⡀⠀⠐⡈⡆⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠡⡴⡤⡄⣼⢀⠀⠀⡁⠁
⠀⠀⢘⠘⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠈⠀⠀⠀⠓⠉⠒⠐⠚⢝⠇⠀⠀⡏⠉⠈⢰⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⠈⠳⠥⠬⠶⠥⠄⠪⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠁⠁⠈⠁⠈
⠀⠀⠀⢀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠈⠔⠈⠉⠁⢢⠀⠀⠀⠀⠀⠀⠱⠆⠒⠀⠂⠒⠀⠐⠂⠶⠃⠀⠀⠈⡤⠤⠄⠠⠤⠤⢬⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠀⢀
⠀⠀⢠⠤⠥⠔⠠⡀⢰⠠⠖⢄⡀⠀⠀⠀⠀⣀⣀⠉⠀⠀⠔⡄⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⡰⡀⠀⠀⠀⠀⠀⠀⠀⣽⢛⣙⣫
⠀⠀⠘⠒⠒⠢⠐⠁⢠⠒⠦⠊⠁⠀⠀⠀⠀⣃⣸⣀⣖⣲⣀⡇⠀⠀⠀⠀⠀⠔⡆⡇⠀⣄⡀⢌⠘⠀⠀⠀⠀⡄⠀⠀⢤⠀⠀⠠⠠⠀⠠
⠀⠀⠀⠀⠢⠠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠤⠤⠤⠤⠎⠀⠀⠀⠀⠈⠁⠁⠘⠝⠛⠫⡞⢄⠀⠀⠀⣇⣋⣀⣸⠈⠁⢃⣉⣀⣀
⠀⠀⠀⠠⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠤⠈⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠎⠁⠉⠱⠀⠀⠰⠉⠈⠱

⡿⢿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣿⣹⣾⣾⣧⣯⣿⣿⣿⣿⣷⣛⣻⣟⣿⣟⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⣿⣿⣿⢭⣭⣭⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣏⣿⣹⣽⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⡿⣝⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡌⣿⣿⢸⢇⣿⣾⡆⣷⣿⣿⠶⠶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣾⣿⣘⣿⣸⣧⣻⣿⣇⣿⣿⣿⣯⣿⣿⣿⣿⢛⣿⣷⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⡿⣿⢿⢻⢿⣿⣿⢿⣿⣹⣿⣿⣟⣿⣟⣿⣿⣟⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣷⣿⣾⣽⣿⣿⣿⣽⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣽⣽⣯⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡟⢡⣾⣿⣦⣹⣿⡆⣾⣿⠙⣿⣿⡆⣾⣷⣦⣿⣿⣿⢯⡄⢿⣿⣴⣾⡆⢰⣷⣼⣿⡆⣾⣿⣆⠸⣿⣿⢆⣾⣿⡆⣾⣿⣦⣧
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⣽⡉⢾⣿⣿⡇⣽⣯⣿⣿⣿⢏⣿⣳⡘⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⡆⢻⣏⣾⣿⣿⡆⣼⣥⣿⣿
⠀⠀⠀⠀⠀⠈⣷⣌⣻⣿⣻⣿⣿⣃⣻⣿⣌⣻⣟⣃⣛⣛⣛⣿⣋⣺⣿⣿⣇⣘⣿⣿⣃⣘⣿⣿⣟⣃⣛⣿⣿⣿⣀⣿⣿⣿⣿⣂⣛⡛⣛⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣯⣭⣛⣻⣿⣿⣿⣿⠲⠶⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⡭⣿⣿⣿⣮⣭⣿⢋⣽⣿⣿⣿⣭⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣛⣏⣿⣿⢿⣷⣭⣽⣼⢟⣿⣿⣿⢦⡍⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⣾⢷⣿⣿⣿⣧⣮⣭⣽⣿⣿⣿⣿⣻⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣵⢏⣴⢽⣿⣿⣿⣿⣦⣴⡿⡿⣿⣯⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⣿⣿⣿⣫⣻⣿⣿⣿⣿⡿⠿⢦⣭⣿⣿⣿⣟⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⢿⣷⣭⣩⣼⣿⣿⣿⣷⡲⢶⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣽⣿⣿⣿⣷⣷⣲⣦⣍⣽⣿⣿⣿⣿⣿⣻⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠷⠦⠭⠾⠿⠿⠟⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠆⠀⠀⠰⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠷⣤⡤⠞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠤⠤⠀⠀⠤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⣄⠀⠀⠀⢠⠀⠀⠀⢀⡴⠖⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣹⠀⠀⢀⣼⣄⠀⠀⢸⡁⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠶⠶⠞⠛⠳⣄⠉⠀⠈⢁⡴⠛⠛⠶⠶⠞⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣦⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣯⣿⣿⣿⣿⣶⣲⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⡿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⢻⡿⣿⣟⣻⣿⣿⣓⣿⣿⣯⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣽⡎⣿⣸⣜⣿⣿⣺⣿⣿⣺⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⡿⣿⡿⣿⡿⠿⣿⢷⣿⡿⠾⡿⠿⣿⣿⣿⠿⣿⣽⠽⡯⠯⡿⢿⡿⠿⣿⠿⢿⣿⡿⢿⣿⠿⣿⠿⡇
⠀⠀⠀⠀⢰⡏⣾⣿⣿⣾⣿⠸⡿⢂⣿⣿⠸⠿⣷⣿⣿⢏⣦⢹⣿⣾⣿⢸⣿⣾⣿⢸⣿⣧⠹⣿⢧⣿⣿⠀⡿⣷⣿
⠀⠀⠀⠀⠸⣇⠻⣿⣿⣿⣿⠰⣷⡘⣿⡿⠸⣿⡿⣿⠟⣾⣿⡆⢿⣿⡿⢸⣿⣿⡿⢸⣿⣿⣆⢛⣾⣿⣿⠀⣿⡿⢟
⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣶⣿⣿⣾⣷⣷⣿⣿⣿⣾⣿⣟⣛⡾⣿⣷⣷⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣾⣷⣾⡇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣯⣽⣛⣿⣿⣿⣿⠲⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣹⣿⣿⣿⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠷⣮⣽⣿⣿⣓⣺⣿⣿⣽⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣛⣿⣿⣿⣷⣚⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⢶⣿⣿⣟⣺⣿⣿⣿⡿⢯⣭⣻⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣭⣭⣿⣿⣿⣷⡶⣸⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⠶⡦⢿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠚⠛⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡏⠩⢹⡟⣻⢻⣿⣛⣿⣟⣟⣿⣻⣿⣻⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣠⡤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⠟⠇⠛⠑⠚⠙⠃⡇⠠⠤⠤⠀⠀⠆⠡⠶⠶⠺⠆⠀⠀⠀⡇⢥⠁⣉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠰⠴⠈⠙⠉⢉⣈⣉⡁⢡⢤⡤⠄⣤⠀⠿⠀⠀⠘⠛⠳⠛⠙⠀⠃⠿⠀⠄⡀⣀⣀⢀⣠⣀⡀
⠀⠀⠠⠤⠤⠤⠤⠐⠂⠀⠒⠀⠒⠰⣶⣶⣾⠀⢂⣀⣠⣤⡄⢠⠀⡿⠐⡖⣶⣰⡖⣶⣚⣐⣦⡶⢈⡇⣁⡁⣈⡈⠉⠉
⠀⠀⠀⠀⢀⠀⡌⠉⠈⠀⠒⠂⠒⠖⢸⣿⡇⠀⡄⠀⢠⣤⣤⡀⢠⣤⣤⢠⣤⣤⡄⣠⣤⣤⡀⡀⣄⣀⣀⣀⠀⡤⠀⡀⡀
⠀⠀⠀⠀⠹⢸⡵⡗⡯⡇⡇⡗⢰⠄⢸⣿⡇⠀⠇⢀⣿⡏⢹⣿⠈⢿⡏⠀⣿⡏⢰⣿⠁⢹⣧⢠⡀⢀⣄⣠⣰⢠⣄
⠀⠀⠀⠆⠆⠐⠐⠂⡂⠤⢠⡄⢸⠂⢸⣿⡇⢸⣿⢸⣿⡇⢸⣿⠀⢸⣿⢠⣿⠁⢸⣿⠶⠿⠿⢨⡅⠐⠆⢰⢠⣠⣄⣤⣦⡤⣤⡤
⠀⠀⠀⡄⠀⠀⠐⠒⠐⠒⠒⠂⢨⠀⣸⣿⣇⣸⣿⠈⣿⡇⢸⣿⢀⠀⣿⣿⡏⢠⠸⣿⡀⣠⡤⢸⡇⠀⠥⠘⠙⠉⠋⢟⠋⠑⠃⠃
⠀⠀⠀⣿⣹⣻⣝⡵⡟⣻⠀⡇⢀⠘⠿⡿⠿⠿⠿⠀⠙⠿⠟⠃⠸⠃⠸⠿⠁⠸⠀⠛⠿⠟⠁⢸⠃⣆⣠⣬⣩⣡⢩⠉⠉
⠀⠀⠀⠀⠀⠠⠠⠤⠄⠤⠀⠃⠘⠿⠟⠁⣈⠋⡉⣘⢙⢃⢀⡀⣐⠂⠐⠂⠒⠒⠒⠀⠀⡆⢠⡌⣀⣋⠃⢃⣓⡀⢘⣀
⠀⠀⠀⠀⠀⠀⡀⣀⡘⣛⡚⢂⢉⠛⢙⠀⣯⠷⠯⠽⠽⠼⠺⠿⠿⠀⠘⠘⡃⠁⠃⠟⠀⠇⢸⡁⣤⢄⡄⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢸⠘⠛⠈⣃⡁⡐⢒⢒⡂⢰⠀⠀⠀⠀⠠⠐⠇⠈⣁⣈⣉⣉⠐⡇⠴⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠈⢰⠐⠒⠒⠒⠒⠀⠃⠀⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄
⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣆⠀⠀⣿⣿⣿⡇⠀⠀⣠⣾⣶⡄
⠀⠀⠀⣿⣿⢿⣧⢰⣿⠏⣿⣷⢀⣴⣿⣿⣿
⠀⠀⠀⢹⣿⠈⢻⣿⣿⠀⢿⣿⣾⠟⣿⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠙⠃⠀⠈⠛⠋⢠⣿⡿
⠀⠀⠀⠀⣿⣧⢀⣠⣤⣤⣤⣄⡀⣸⣿⠇
⠀⠀⠀⠀⠙⠛⠻⢛⣛⣛⣛⠻⠿⣿⡍
⠀⠀⠀⠀⠀⡤⢞⣭⣿⡿⠿⣷⣄⠈⠛
⠀⠀⠀⢠⢞⣴⣿⠟⠁⠀⢰⢿⣿⣷⡄
⠀⠀⣰⢫⣾⡿⠃⠀⠀⢀⡞⣸⣿⣿⡇
⠀⢰⣯⣿⣿⠃⠀⠀⣠⣟⣴⣿⣿⣿⡇
⢀⣿⣿⣿⠇⠀⠀⠀⠹⢿⡿⣿⣿⣿
⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⢧⣄⠀⠀⠀⢀⡀⠀⠀⠀⢀⡠⢤⣤⣀⠀⠀⠀⣀⠤⣤⣄⠀⠀⠀⠀⠀⢀⣤⣄
⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⣿⣿⡟⣸⢻⣷⡄⠀⡿⣿⣦⠀⢠⢎⣾⣿⠟⣻⣧⢀⠞⣵⣾⡿⢿⣷⢀⣿⣦⣰⣿⢻⣿⣷⡄
⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⡿⢠⡟⣸⣿⠃⢸⠇⣿⣿⢀⣏⣾⣿⣃⣴⣿⣿⣿⣾⣿⠟⣠⣿⡿⣸⢸⣿⡿⢁⡞⣼⣿⠇
⢿⣿⣿⣧⠀⠘⢿⣿⣿⣿⣿⠁⣼⣧⣿⡟⢀⣿⣼⣿⡇⢸⣿⣿⡟⠛⠛⢋⣼⣿⣿⡿⣾⡿⠟⣠⣿⣿⣿⠃⡾⣰⣿⡟
⠸⣿⣿⣿⡄⠀⣸⣿⡜⣿⣷⡀⢹⣿⣿⢃⣾⢿⣿⣿⡇⠘⣿⣿⡇⠀⣠⣾⠻⣿⣿⡇⠀⣠⣾⠿⣿⣿⠇⣸⢣⣿⡟⠀⣶
⠀⠙⢿⣿⣿⣾⣿⣿⣷⢹⣿⣷⠀⠙⠿⠿⠋⠀⢿⣿⣄⣼⠛⢿⣿⣾⠿⠁⠀⠙⠿⣿⣿⠿⠃⠀⠙⠋⠀⣿⣾⡿⠁⢰⣿
⠀⠀⠀⠙⠻⠿⠟⠋⢻⣧⣻⣿⡄⠀⠀⠀⠀⠀⠀⠉⠋⠁⢀⣀⣠⡤⠴⠶⢒⣚⣛⣻⣿⣿⣿⣷⣦⡀⠘⣿⣿⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣶⡤⠀⠀⣀⣠⡴⢖⣛⣭⣭⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠹⢿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣠⣶⣿⣿⣷⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠉⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⣠⡖⠉⢉⠇⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⣿⡀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⣾⠟⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠈⠛⠓⠛⠉⠀⠀⠀⠀⠀⡠⠲⣶⡄⠀⣀⠁⠀⢠⣿⡯⠔⠁⢀⣤⡾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⣴⠄⡠⢒⡖⡠⠊⢀⣾⡿⠀⣾⡟⠀⢀⣿⡏⠀⠀⢠⣾⣏⠤⠞⠁⣠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣿⣿⠀⣼⡏⡜⢁⣿⡟⠀⢠⣿⠏⠀⣸⡿⠀⢀⣾⡿⠀⠀⢀⣿⡏⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⠀⣿⡟⢀⣿⠏⠀⣾⠏⠀⢠⣿⠋⠀⡰⠻⣧⠔⠁⣿⡇⠀⣠⠊⠙⠷⠴⠚⠁⠀⣠⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⣰⠟⠀⠈⠛⠀⠀⠈⠀⠀⠸⣿⣀⠜⢀⡴⢒⠀⠀⠹⠿⠞⠁⠴⠚⠛⠛⠒⠦⣴⣿⠃⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠉⢋⡉⣀⣀⠀⢤⡤⣤⠀⡄⣠⢤⠀⠀⠀⣠⡟⡰⠃⠀⠀⠀⢀⣀⣀⢀⣤⠖⠂⡂⣰⡿⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢧⡁⠀⡞⢰⠟⣾⡟⠓⣚⠀⠀⢰⡿⢋⠴⠶⣦⠀⣴⡟⠡⠀⢸⣿⡀⠈⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠑⠉⠀⡈⠁⠈⠀⠁⠙⢚⣁⠤⠖⣿⡗⢁⠀⠀⡿⢹⡏⠀⢀⠀⠀⢹⣿⠀⣼⡇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⡴⢋⣿⠇⢀⡴⢚⣷⠄⠀⠀⠘⡿⠀⠫⣤⣊⠀⠘⠷⠤⠋⠐⠤⠾⠋⠀⠙⠷⠊⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⢇⠎⠀⣼⡟⡴⠃⢠⣾⢏⠴⠖⠶⠤⢄⣠⡞⠥⠊⠀⠀⢀⣀⠀⠀⣠⡶⠀⢠⡖⣠⡿⠊⠁⢸⡇
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣼⣿⠞⠀⣰⣿⢋⣤⠖⠲⣤⠀⣼⣏⠴⠲⡆⣠⡾⠋⡨⢀⣼⠏⠀⢠⡟⢠⡟⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⢰⣿⠇⠀⣸⣿⠋⠀⣰⣿⢣⡞⠁⠀⣼⠏⣸⣟⣁⠤⠚⢹⡿⠐⠊⡀⣸⠇⠀⢠⣿⢁⡿⢥⣤⠾⠋
⠀⠀⠀⠀⠀⣼⡏⠀⢠⣿⠏⠀⢰⣿⠇⣿⠀⠀⣼⠏⢠⣿⠉⠹⣷⣄⠘⠳⠖⠊⡀⢿⠀⡰⠁⠇⢸⣇⠠⣄⡀
⠀⠀⠀⠀⠀⠿⠀⠀⠘⠟⠀⠀⢸⣿⠀⠛⠒⠉⠻⠖⢹⡏⠀⠀⠈⠻⠷⠶⠶⠚⠀⣀⣩⠴⠒⠊⠙⢧⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠤⠀⠰⣄⠀⠀⠁⠀⠀⠀⣀⣀⣤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⡀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⢰⠀⠐⠂⢀⢀⣀⠀⣀⣀⡀⠀⡃⠀⢀⡀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⣀⣀⣀⠀⡁⡀⡀⠐⡐⠀⠠⢐⠀⠂⠀⠸⠀⠰⠆⠤⠄⢤⠦⡄⠀⠀⠂⠀⠠⢀⣤⡀⣀⣀⣠⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠈⢀⠀⠁⠀⠁⡀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⣹⡿⠛⠛⠿⡷
⠀⠀⠀⠀⠀⣤⠀⠐⠰⠇⠀⠢⠀⠘⠥⠁⠀⠀⠈⠀⠀⠀⠋⢩⠈⠁⢨⡈⢁⣭⡉⠀⠀⠀⠠⢠⠐⠛
⠀⠀⠀⠀⠀⣿⠋⠙⣶⢰⣞⣉⣳⡄⠚⣋⣹⡆⢸⠃⠀⢸⠉⢻⠋⠉⢰⠠⣾⠶⠄⡿⠁⠀⣿⢸⠀⠀⠄⠠⣏⣹⢿
⠀⠀⠀⠀⠀⣿⣀⣀⡾⠸⣏⣉⣩⠁⣏⣉⣉⣧⢸⣆⣀⣼⠀⢸⣀⡀⢸⡀⣿⠺⠂⢿⣀⣠⣿⢸⡅⠀⠁⢠⡖⠓⠂
⠀⠀⠀⠀⠀⠤⠬⠥⢤⠀⠈⡉⢡⠄⠈⡉⡁⠀⠀⠀⠀⢀⠀⢀⣉⡀⠀⡄⠀⠀⠀⠂⠈⣤⢀⠀⣄⡤⢄⢀⣳⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢸⠀⡏⠀⠈⡆⣾⠀⠄⣸⠀⡡⠤⢹⠀⡇⠀⠀⠀⠰⠂⠓⠈⠀⠛⠃⠘⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠂⠤⠰⠆⠠⠂⠀⠸⠄⠳⠄⠴⠃⢈⡒⠒⡟⠘⢦⡤⠸⠀⠇⠀⠈⠑⠃⠚⠛⠙⠀⠂⠀⠀⠅⠔⡖⡆
⠀⠀⠀⠀⠀⣠⣄⡀⣤⢘⣐⠀⢀⣈⠁⠐⠃⠒⡀⠉⣉⡀⠀⡄⢀⠀⢁⣄⡀⢁⡬⡅⡀⠉⢁⢠⡄⠀⠀⠆⡁⠙⡃
⠀⠀⠀⠀⠀⢸⡏⠁⢹⠁⢹⡆⡏⠈⢻⢸⠁⠀⡇⣾⠁⢹⡇⡟⠋⢻⠈⡏⣅⢸⡗⠀⡇⢸⢸⠁⡇⠀⠀⠈⠣⠤⠇
⠀⠀⠀⠀⠀⠈⠳⠂⠘⠀⠘⠃⠓⠖⠋⠘⠳⠞⠃⢨⣛⣻⠃⠇⠈⠚⠀⠳⠖⠘⠃⠀⢙⠒⠚⠀⠃⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⡤⠀⠐⠐⠈⠀⠈⠀⠃⠀⠀⡀⢠⡤⡶⠲⢖⡶⠄⡏⢀⠴⠀⣩⠀⡦⠒⠲⡄⢀⠖⠒⢼⡇
⠀⠀⠀⠀⠀⢶⡂⣠⠤⡄⡠⢤⢠⠤⡄⣠⢤⡀⡤⠀⡁⢄⢠⠀⣄⣠⠦⠀⡗⠫⡀⠀⢸⠀⡇⠀⠀⡇⢸⡀⠀⢸⡇
⠀⠀⠀⠀⠀⡰⡇⠙⣒⡏⠯⠭⠸⠀⠘⠻⡬⠁⠇⠀⠦⠜⠘⠤⠟⠬⠸⠂⡉⡀⢈⣀⠈⠀⠃⠀⠀⡁⠠⠉⠋⠉⡁
⠀⠀⠀⠀⠀⠌⠁⠀⠀⠂⠈⠀⠀⠀⠀⡀⢠⡶⠛⠛⠶⠀⠀⣀⣤⣄⡀⠈⣩⣉⣬⣅⠀⣍⣡⣬⡁⠁⣠⡴⣤⣄
⠀⠀⠀⠀⠀⢺⠇⠠⣤⠄⠀⠤⠄⠄⠄⠁⠘⠷⢬⣤⣀⠀⣼⣋⣀⣬⣿⡆⢸⡃⠀⠀⠀⡿⠀⠀⠀⢈⣁⣤⣄⣹⡆
⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠉⠁⢠⡄⠀⠆⢀⣀⠀⠀⣹⡆⢻⡄⠀⠂⣀⠀⢸⡇⠇⠀⠀⣷⢰⠀⠀⣾⡁⠄⢄⣹⡇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠉⠛⠛⠁⠀⠘⠃⠀⠀⠀⠛⠈⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠶⣶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⠆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⣿⠀⠈⢻⡀⠀⠀⠀⣤⠀⠀⠀⠉⠙⢧⡀⠀⠀⠀⣸⣏⣹⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⣴⠟⠳⢦⣼⠇⠀⠀⠀⣿⠀⣤⣤⣤⠀⢨⡟⢳⡶⠛⠉⠈⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⢾⣅⣀⣠⡴⠋⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⢀⣛⡛⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⣿⠀⡿⠀⣿⠀⣿⠀⣿⠀⣾⠛⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⣤⣤⣤⡤⠠⣤⣤⣤⡄⠀⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡽⠋⠉⠉⠉⠉⠉⠉⢿⡍⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⣭⣭⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⠴⣶⠤⣄⣠⠞⠛⠛⠛⠨⠛⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡞⠁⠀⣿⠀⠞⢳⡀⠀⠀⠀⠈⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠛⠒⠒⢺⠇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⣄⡈⠳⣄⣠⠞⠀⠀⠀⣶⣶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠛⠚⠛⠛⠂⣦⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣽⡉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠶⢾⣿⠟⠛⠟⣿⡟⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠶⢾⣿⠀⠿⠂⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡛⢿⣿⠂⣶⣿⣿⠉⣈⣽⣿⠉⣬⣽⣿⠉⣭⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣉⡛⠻⣿⠀⣿⣿⣿⠀⣭⣽⣿⠀⣤⣼⣿⠀⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣦⣙⣋⣴⣿⣤⣭⣽⣿⣤⣤⣼⣿⣤⣤⣼⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣵⣿⣿⣿⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⣿⢸⣿⡟⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⢸⣿⢡⢻⣇⣿⣿⡿⢿⣿⣿⠿⣿⣿⡿⠿⢡⢸⣿⣏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡏⣾⡏⣾⠸⣸⣿⣧⣫⣾⣿⣿⣆⣫⣾⣧⣵⣿⣮⣿⣿⣸⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⢱⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠻⠿⣿⣿⠿⠴⠛⢻⣿⡟⠛⠛⠛⢿⣿⡋⠉⠉⢙⣿⣿⣿⡟⠙⢿⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢰⣶⠀⢹⣿⠀⢰⡶⢾⣿⡇⠀⣿⠇⢈⣿⡇⠘⠛⠻⣿⣿⡟⢀⣆⠘⣿⣿⣿⣿⠀⢸⣷⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢀⠀⢠⣾⣿⠀⢠⣤⣼⣿⡇⠀⣤⣴⣿⣿⡇⠰⠶⢾⣿⡿⠁⣈⣉⡀⠸⣿⣿⣿⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣿⣿⣇⣸⣧⣀⣹⣿⣀⣈⣉⣸⣿⣧⣤⣿⣿⣿⣿⣧⣤⣤⣴⣿⣧⣴⣿⣿⣿⣤⣽⣿⣿⣤⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣇⢸⣿⣇⣴⣶⣄⣼⣿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣹⣿⣼⡿⣿⠿⣿⣿⣏⣿⣿⡟⢻⣿⢹⣷⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⣶⣶⣔⢻⣿⢻⣧⢻⡿⣁⣿⣷⡿⢸⣿⠇⣿⣇⣿⢿⣿⣿⣿⢟⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣻⢿⣷⠸⣏⣿⡎⠿⢿⣛⠪⠅⣉⠀⡉⢤⡅⢩⣘⡿⣿⡿⣾⣟⣿⢏⣾⠿⣫⣬⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣶⣮⣙⣯⣿⣇⠹⣟⣁⣤⠣⡖⢿⡃⢞⠃⣷⢭⣍⣿⢸⡦⣭⡜⢛⣹⢋⣾⣿⢶⣿⣯⣿⡏
⠀⠀⠀⠀⠀⠀⢀⠄⠾⠿⠿⠟⠛⡛⣟⡛⣯⣸⣭⣹⣇⣧⡗⣾⠃⣿⣿⣿⣮⡏⣿⡾⣷⡏⠷⡟⣷⣨⡩⣅⢞⣩⣍⣦⡧
⠀⠀⠀⠀⠀⠀⠘⣷⢏⣿⣹⠿⠳⢙⣭⡴⠺⢹⡾⣿⣿⣾⣥⡾⠟⣽⡁⣟⣵⡶⣿⢹⢸⡟⡃⣿⢈⡿⢙⡛⣌⡛⣏⣠⣿⣷⣦⡂
⠀⠀⠀⠀⠀⠀⠀⢽⡓⢥⢧⡶⢻⡼⢿⠷⣿⢾⣇⡛⣧⠿⠉⠿⣛⢯⠓⠏⢻⠶⣿⠸⣿⣿⣿⣻⡉⠃⠬⢹⣸⡉⣿⣯⢻⣿⣿⠥⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡛⠲⡖⢂⡓⢺⠦⣦⡶⢾⣏⣧⠀⠒⠉⠀⠈⠸⠳⠐⠘⠉⠓⢆⡉⠻⢺⣟⡁⡃⢠⠉⠸⢅⣿⢨⠶⡀⠐⣀⣐
⠀⠀⠀⠀⠀⠀⢀⡜⠷⠜⢾⠸⠱⢷⣰⣴⢰⣆⣹⣡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠶⢽⠄⠉⢛⠈⠂⠘⠈⠀⠀⣀⡨⢀⡍
⠀⠀⠀⠀⠀⠀⢘⡤⢵⡎⢩⢠⣖⠄⢆⢀⠈⢈⡸⢃⡴⠓⠶⠶⠆⠴⠤⠀⠴⢠⡿⠈⠛⠓⡞⣷⣶⣦⡄⢠⢠⣴⢷⢺⡇⣏⢿⡸⡇⣶
⠀⠀⠀⠀⢀⣴⠻⣷⣖⠱⢻⢸⣄⡇⢢⡴⢛⢻⡄⠀⠀⣀⣀⡤⠿⠋⠀⠀⠀⠄⢠⢤⠴⠀⡟⣧⢸⣧⣸⣽⢿⣽⣼⣼⣇⣯⣾⢿⢣⡿
⠀⠀⠀⠀⠻⣌⠳⣱⢯⡟⣸⣼⡐⡗⣿⣅⢹⢸⣇⠟⠋⠈⠁⠁⠀⠀⠀⠀⠀⢰⡄⠈⠛⠓⢧⣻⡟⣷⢫⢻⢹⣧⣹⣿⢸⡷⠿⠾⢰⡇
⠀⠀⠀⠀⠀⠈⠳⢨⡗⣸⣭⠇⡍⡍⢃⣜⣺⡧⣶⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣆⠁⠀⠀⠀⠀⢘⠋⣼⣤⡭⣿⡬⠁⢥⣜⣷⡶⣆⣨⡅
⠀⠀⠀⠀⠀⠀⠛⡿⢙⣻⢿⣋⣹⠀⣶⣮⠽⡝⢷⡄⠀⠀⠀⠀⠀⠓⠀⠀⠘⠣⠝⡦⠀⢰⠴⢿⣯⡆⠉⣻⠾⠞⣴⣈⣫⣷⣇⣿⣭⡅
⠀⠀⠀⠀⠀⠀⠐⢯⡼⢹⣟⣭⣥⡠⣙⣛⠚⣡⣖⢳⠀⠀⠀⢀⡤⠀⢀⠀⡤⡖⢶⢸⣧⡺⠺⣧⢸⣙⡳⡶⠿⠯⣿⡷⢺⡟⡗⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣂⡛⣯⢹⠃⢯⣸⠌⣿⣈⠀⠀⠀⣾⠶⠑⠛⠐⠗⠇⢾⣴⡇⠀⡶⣩⣻⡝⣇⣤⢗⣠⡶⢝⡗⢂⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠞⣥⢸⣿⢩⡿⣹⣆⣀⣀⣧⡀⠸⠆⣠⡤⣴⠚⠓⡇⣼⣰⠆⡀⣹⠞⣽⠤⡸⡝⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠸⣴⢣⡄⡈⠳⣍⢟⡙⠓⠚⠉⠀⠚⠮⠨⢗⡿⠿⢹⣾⠏⠛⢆⢏⡃⢿⣨⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡬⢷⢉⣀⡋⣏⢸⣷⣤⣶⡀⠤⢀⣶⠣⣼⠉⢉⡡⢭⣿⣸⡛⠟⠙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣿⣷⠃⣬⠙⠗⣧⢸⣍⠂⠉⡄⠐⢈⠉⡿⢛⡀⠂⡀⣋⣽⣿⡷⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣷⠏⣰⣶⢿⠁⠀⠀⠀⠀⠛⢧⣆⠧⣤⠆⣼⠀⡂⡀⡇⢸⡇⢻⠣⣼⣿⡽⣶⡗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠾⣧⣧⣌⠀⠚⠅⠀⠀⠀⠀⠀⠀⠀⠈⢠⡉⡀⡀⢠⠥⡄⢠⠠⠄⠀⣤⠤⢀⡷⢞⣫⡴⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡿⢼⠦⢌⣓⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⣸⡜⠤⢰⣁⢸⡿⣶⣿⢷⣾⠋⢿⣿⣟⣻⣯⠗⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠿⢘⣿⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢿⢣⠀⣸⠻⣜⣧⣿⣷⣿⣿⢩⣿⣛⡿⢿⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣅⣱⣬⡷⢧⣄⠀⠀⠀⠀⢀⡠⣶⢆⣶⣘⠖⣤⡖⢭⣿⡟⡷⢾⣇⢻⡼⡇⢹⣿⡿⠻⣑⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣗⢾⠀⠀⠀⠀⠸⣿⣹⡾⢦⡿⣇⣹⣟⢐⣅⣦⣿⢸⠟⠇⠀⠀⠸⣷⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠫⣶⡇⣾⣭⣇⣿⣟⣙⠠⠁⠈⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣾⣘⠿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢋⡑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢚⡙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⣴⣶⣿⢟⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡻⣿⣷⣦⣻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⣡⣾⣿⣿⡿⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⢟⣴⣿⣿⣿⢋⣾⣿⣿⡟⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢣⣾⣿⣿⣿⡇⣾⣿⣿⢏⣼⣿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣷⣌⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⣝⣋⣵⣾⣿⣿⣿⣿⣿⣦⡙⠿⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣥⣬⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠳⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢟⣤⣭⡻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⣙⠻⣿⣿⣿⣯⣴⣿⣯⡙⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣣⣾⣿⣿⡌⢿⣿⣯⡻⣿⣿⣿⣦⡙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢩⣾⣿⣿⡿⢋⣴⣷⡎⣿⣿⣮⡻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⣴⣿⣿⢟⣅⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠿⠿







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠰⠊⡼⠑⣇⣈⢠⢴⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣾⠁⢀⣤⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠈⠃⠀⢻⠳⠎⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸⠄⠀⠀⠀⡀⠤⡀⠀⠄⠀⠀⠀⠀⠑⡄⡇⠀⠏⢛⠸⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠇⠂⠆⠀⢦⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⣹⠀⡾⡇⢸⡇⠀⠸⡎⠀⠀⠀⠀⢀⠀⠊⠰⠄⠀⠈⠂⠀⡄⠀⡅
⠀⠀⠀⠀⢀⣠⡇⣀⠀⢊⣄⠠⡄⠀⢠⢀⠀⡠⢦⠀⠀⠀⠀⠀⠀⢰⢿⠀⠀⠃⡠⠀⠀⠀⡇⠀⠀⠀⠀⢼⠀⠀⠀⣴⢰⡄⣟⠀⣇⠐⠁
⠀⠀⠀⢰⢹⢹⡧⢸⣀⡷⡇⠼⢤⣾⢸⠀⢼⡇⠄⡗⠀⠀⠀⠀⠀⡁⠸⡄⢀⠀⢃⡂⠀⣠⠂⠀⠀⠀⠀⢸⠀⢸⡇⠛⠰⡇⡏⠀⣷⠀⠄
⠀⠀⠀⠈⠸⡌⠇⠈⠉⠀⠑⠁⠌⢿⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⡞⢠⡆⡆⢰⢀⡆⠃⠈⠁⠀⠀⠀⠀⠀⠸⡄⠌⠃⠀⠀⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠣⠀⠃⢇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⡆⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣤⣰
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡾⡀⣇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠤⡄⡀⢠⡄⡇⡏⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠀⠀⢠⠧⡖⠀⠀⠀⠀⠀⠀⠀⣇⠼⢸⡐⠇⠃⠇⡇⠿⠈⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⡏⠀⢸⠠⢄⡀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⢠⠀⢑⠀⠀⣀⠀⢸⠀⠀⠈⡀⠀⠀⣄⠀⠀⠁⣴⠐⠢⡀
⠀⠀⠀⠀⠀⠀⢀⢡⡀⢧⠀⢿⠀⠸⡁⠈⢻⠇⠀⠀⠀⣿⠀⠀⠨⢅⠀⡇⣿⠀⢸⠉⢠⡏⠀⣼⠀⠀⢀⡷⠤⠀⣸⢰⣻⠀⠛⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠈⠟⣃⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢹⡀⠰⠁⣿⠀⠁⢻⠀⢸⠀⠈⠧⠀⠃⠀⠀⠀⡗⠀⠀⠻⠀⠘⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢠⠎⠀⢳⢀⣨⣆⢠⡴⢹⠃⠀⠀⠀⠀⠀⠁⠠⠀⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⢀⡀⢆⡀⡗⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡿⠄⠳⠂⠓⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⠀⠈⡇⢇
⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣡⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣦⡙⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠛⠿⡿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣂⡀⣴⣮⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠇⣿⡇⣾⣿⢘⣛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣋⡻⡏⣼⣿⢸⣿⠃⣿⡇⣾⣿⢸⣿⠟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣿⣇⠁⣿⣿⣼⣿⣸⣿⣃⣿⡇⠚⠁⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣭⣭⣍⣙⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⠀⣠⢤⡀⢰⠀⠀⠠⠤⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⢤⠤⠤⠂⢸⢨⣤⣦⣆⣅⣤⣈⣤⣤⣜⣭⣼⣠⣏⣩⣁⡍⣍⠭⠤⠤⠤⠀⠀⡀
⠀⠀⠀⠀⢐⡂⢃⠀⠋⠳⠻⠻⣿⣻⡛⢚⣈⠅⣤⣡⢥⣤⣅⢹⡇⣚⣚⢠⣤⣬⣴⣶⣴⣤⣯⣍⠉⠃⠉⠁⢳⠤⠤
⠀⠀⠀⡄⠤⡶⠠⠦⠴⠆⠁⠀⣿⢹⣷⣿⢽⣿⣿⣿⢸⡏⣿⢿⣿⡿⢿⢨⣭⣥⣭⡥⡍⢛⣊⣈⣄⣩⣍⣅⣾⠆⢰⠸
⠀⠀⢒⡇⡂⣀⣘⣛⣛⣛⣙⡀⢿⢛⠥⡹⢟⣥⣙⢋⢸⠟⠫⠽⠯⡝⠯⠴⠶⠾⠶⠶⠶⠸⣛⠛⡛⣛⠛⠛⣿⣍⢸⢰⢀
⠀⡆⣀⣇⣇⣄⣬⣩⢭⣭⣥⠉⣿⣿⢸⣹⡟⣷⡏⣿⢿⣾⢙⢺⣿⣷⣿⣿⣿⣾⢿⣻⡟⡏⣿⠁⡎⣭⣉⣩⣛⣉⣉⢘⣀
⠀⠇⠉⠉⢉⣉⣩⢸⣶⢶⣾⣀⡯⣿⠨⠭⣁⡍⠡⢭⠩⠬⠬⠬⠭⠥⠡⠭⠭⣎⣉⣬⣡⣡⡉⣠⢱⣩⣡⣉⣭⡏⠩⢤⠄
⠈⠩⠭⠭⢸⠈⣧⣼⢹⢿⣿⡏⣷⢿⡇⠀⣹⢵⣿⢾⣿⣾⣷⣿⣾⣿⣾⡗⠄⡇⢈⢩⡍⣩⣭⣭⡌⠹⠟⠿⠿⠷⠉⠉⠁
⠀⠀⠀⠀⠸⠄⣿⠐⠂⠐⢰⠆⠛⠛⡿⠃⡿⠷⠈⠒⣲⣓⡒⠀⡬⠯⠤⠄⠀⡇⠸⢰⡇⠐⢲⢾⣶⣨⣏⣙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍⢸⢆⡉⠁⠗⣀⣆⣒⣨⠀⠰⠶⠀⠀⡧⠛⡟⢓⡀⠅⡏⠉⠉⢉⠈⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠯⠀⠁⠀⠀⠃⠁

⣷⣿⠿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⢸⡿⡿⠿⠿⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠒⠂⠐⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⢉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⣀⣀⣰⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣛⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠋⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠛⠛⢛⡛⠉⠋⠙⠋⠙⠛⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣟⣿⣻⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⢿⣿⣿⡿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⢿⡿⢿⢿⣿⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠻⠛⠻⠟⠟⠛⠻⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⠛⠿⠿⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⣼⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠿⠿⠭⠷⠧⠽⠧⠿⠾⠧⠿⠿⠾⠾⠿⠿⠮⠿
⠀⢀⡰⢢⣠⠄⠀⠀⢠⠶⠶⡄⢀⣀⡠⠀⠀⠀⠀⠀⠂⣐⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⣴⣶⣿⣦
⠀⠀⡅⣇⣆⡇⠀⠀⠻⣄⣠⣏⠘⠿⠳⣅⠀⠀⠀⠈⠸⠤⠇⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠘⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢀⡐⠆⠐⠇⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⢴⣷⠀⠀⠀⠀⠀⢠⣾⠿⣷⣄⠀⠀⠀⠀⠀⣠⡄⣿⡇
⠀⠈⢁⠻⠿⡀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠷⢠⣤⠾⠆⠀⠀⠀⢹⣧⣀⣼⡿⠀⠀⠀⣿⡇⣿⡇⣿⡇
⠀⠀⠙⠀⠀⠉⠀⠀⠀⠀⠃⠈⠃⠘⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢠⠤⠤⡄⠀⠀⠀⠀⢰⣶⢀⣀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⣠⣲⣂⠄
⠀⠀⢉⡏⢥⡄⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⣿⢸⣿⢸⣷⠀⠀⠀⠸⠿⣿⠿⠇⠀⠀⠀⠈⣹⣿⣿⣮
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠚⠛⠚⠛⠚⠛⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠚⠂⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠘⠛⠛⡷⠤⠀⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⠀⢠⣋⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠖⢂⡐⠶
⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠣⠤⠴⣅⠀⠀⠀⠀⠀⣐⣖⣯⡇⠀⠀⠀⠀⣆⡘⢃⣤
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡷⡧⠘⡆⠀⠀⠀⠀⢀⡄⠀⠠⠆⠀⠀⠀⠀⡔⢉⡙⢆⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⡐⢈⡐⠂
⠀⠀⣇⣄⣼⡃⠀⠀⠀⠘⠃⠁⠶⠀⠀⠀⠀⠀⠀⠣⣄⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⠡⢈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠁⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠑⠂⠃⠐⠚⠂⡄⡠⣀⣀⡠⢄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣶⢄⢈⠀⡀⠠⠀⢀⡄⢀⠀⢀⡀⣥⠌⡀⠈⡉⡁⣂
⠀⠀⠀⠀⠀⠀⠀⢚⠁⠛⣛⢈⠑⢖⣛⣀⣀⢈⠳⠚⠂⠸⠃⡷⠂⠿⠛⠧⠛⠷⠴⢦
⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠈⠀⠉⠀⠀⠀⠈⠀⠈⠀⠀⠀⠵⠉⠀⠀⠈⠈⠁⠈⠍⠡
⠀⠀⠀⠀⠀⠞⠂⠒⠀⠐⠛⠓⠐⠿⠐⠃⠒⠒⠒⠐⠐⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠸⠤⠰⠐⠀⠖⠰⠦⠦⠶⠀⢶⠶⡾⣿⢷⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠰⠆⢢⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠂⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡌⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⡗⢒⡞⢹
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠲⢽⢿⣫⣿⣇⠀⠉⠏⢉⡀⢠⡥⠃
⠀⠀⠀⠀⠀⠀⢹⣿⠟⠠⡌⠳⢿⡏⠐⡄⠀⠀⠀⢈⣶⠶⠟⡆⠴⢤⢬⠰⠂⠀⠉⠀⠂⣛⠀⡈
⠀⠀⠀⠀⠀⠀⣄⣻⣿⠾⣵⡖⠴⠊⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⢉⠈
⠀⠀⠀⠀⠀⠀⢘⢻⡁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠈⠢⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣥⣌⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠐⠆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⢀⠀⣠⢴⡀⣸⠗⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⠁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠞⠑⢒⠻⡀⣀⡿⡖⣆⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠸⠓⠚⠒⠛⠸⠆⠖⠇⠦⢬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠁⠀⠠⠄⠁⠁⠁⠨⠀⠌⠉⢉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠐⠃⠀⠀⠐⠂⠐⠂⠋⡅⠀⠀⠤⠀⠤⢠⠠⠄⠀⡄⣀⢤⡄⢠⠄
⠀⠀⠀⣰⡛⠩⡛⢂⠹⠋⠁⠀⠀⠀⠀⠀⠐⠀⠒⡒⡆⢠⠤⠀⠀⠄⠠⠀⠀⠀⠀⠀⡤⡄⠀⡠
⠀⠀⡤⠤⡧⠴⠠⠄⠰⠀⡻⠚⠚⠐⠘⠶⠧⠠⠨⠀⠘⠳⠰⠾⠦⠤⠴⠵⠞⠦⠼⠠⠤⠼⠶⠦⠵⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⠀⣰⣿⣿⣿⣷⡘⢿⣿⢃⣼⣿⣿⣿⣆⠀⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣿⣿⠁⢰⣿⣿⣿⣿⣿⣷⡌⢁⣾⣿⣿⣿⣿⣿⡆⠀⢿⣿⡟⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢻⡏⠀⣸⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣇⠀⠘⡟⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣿⡦⠤⣤
⠀⠀⠀⣿⢻⢻⠡⢴⠶⣒⣶⠶⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂
⠀⠀⠀⡇⢸⢸⣿⣿⣶⣿⢲⡆⠀⠀⠀⠀⢠⡞⡇⣀⢠⠄⣠⠤⣶⡁⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⡗⣻⣸⣻⢿⣿⣿⣸⡃⠀⠀⠀⠀⢈⡷⢧⣀⣹⡗⣮⠿⣖⣥⠀⠀⠈⠿⠯⠃⠀⢷⠀⠻⠿⠝
⠀⠀⠀⠈⠈⠙⠛⠸⠿⣿⣿⡃⠀⠀⠀⠀⠈⠑⠲⢤⣉⡿⢒⣫⡽⠗⠀⠀⠀⠀⠀⣠⣴⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠉⠉⠉⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢤⣶⣿⣽⣿⣯⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⡇⠀⠀⠀⢲⠀⠀⠀⠘⡟⢻⠛⡟⢿⠻⡟⡇
⠀⠀⠀⠀⠂⠲⠖⢀⣿⡀⠖⡶⠆⠀⠀⢀⣧⣤⣴⣶⣶⣷⣶⣶⣤⣘⡆⠀⠀⠀⡇⣿⠀⡇⢿⢸⡇⡇
⠀⠀⠀⠀⠀⠠⣶⣶⣾⣿⠦⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠓⠛⠚⠓⠻⠾⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⢈⠠⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠈⠁⡐⠀⠄⠀⢀⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⣀⣀⡈⠀⢠⠂⠀⡀⠈⠤⠀⠀⠀⠎⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠀⢸⡆⠚⠒⠓⠂⠀⠈⠀⠂⠘⡀⡀⠂⠀⠠⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠸⠆⠭⠭⠅⠀⠀⠐⠀⠁⠈⠂⡀⠁⠈⠀⠆⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠊⠀⠀⠴⠄⠠⠤
⠀⠀⠀⠀⠀⠀⡄⠀⠨⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠉⠉⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⡇⢈⣉⠀⢘⡁⣉⡁⠀⠐⠀⣀⢠⣄⠁⠀⠀⠀⠀⠣⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠰⠀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢈⠑⠀⠀⠀⠀⠀⠀⠀⢠⠍⠈⢅⠀⠀⠀⠀⠀⠀⠄⢄⣀⠂⡀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠌⠀⠠⠀⠆⠰⠀⠀⠰⠀⠀⠦⠆⠆⠆⠀⠠⠀⠐⠀⠈⠂⠠⠊⠊⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡆⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠆⠐⠀⠀⡀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠄⠀⠉⠈⢀⣄⠀⣀⠀⢀⡀⠀⣀⡀⠠⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⢰⠀⠀⡆⠀⣶⠀⢸⢣⣞⢆⢲⠀⡶⠀⠀⠀⠀⢀⢀⠀⢀⠀⢀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠖⠀⠀⠀⠀⠀⠀⢸⠖⠒⡇⢰⠧⣇⢸⠎⢸⠎⠈⡿⠁⠀⠀⠀⠠⠁⠀⠙⠁⠀⠀⠃⠁
⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⣸⠀⠸⣸⡄⢸⠀⢰⠃⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠉⠁⠈⠀⠉⠀⠀⠀⠀⠀⠐⠈⠑⠄⢀⠔⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠏⡡⢈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡤⠀⠀⠀⢠⠀⢠⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠄⡇⢀⡀⠀⢸⠀⠈⡇⠀⣀⣀⠀⠀⠀⣇⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣸⠀⠀⡇⠸⡇⠀⢾⠀⠨⣧⠀⢧⣠⠂⠀⠀⢹⡀⢰⠆⢠⠇
⠀⠂⠀⡀⠀⠠⢀⠀⠀⠀⠀⢠⡙⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠰⢮⣙⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠳⢤⡍⢀⠀⠃⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⢄⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠰⢈⠀⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠄⡀⠀⠀⠀⠀⠀⠈⠒⠈⠉⠀⠁⠈⠛
⠀⠀⢠⠄⠀⠒⠲⠒⠒⠒⠐⠂⠀⡸⠃⠀⠤⡈⢃⣀⢠⠤⠄⠒⠒⠒⠂⠀⠀⠒⠲⠤⢄⣠⠃⠔⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠨⠀⠀⠰⠂⢠⣄⢤⠆⠀⠘⠢⣀⠀⢠⠌⠈⠍⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠂⠤⠀⣃⠀⠀⠀⠀⢀⠔
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡤⡀⣤⠄⣤⡄⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣂⠒⠀⢠⠀⠀⠀⠀⠀⠀⢸⡗⢸⢿⣹⡧⢸⡧⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁⡀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠃⠘⠈⠛⠓⠘⠗
⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⢀⠄⠠⡀⠂⠈⠐⠄⠀⠈⠢⡀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⡟⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠘⡇⣰
⠀⠀⠀⠀⢸⡇⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠸⠠⠤⠶⠀⠀⠖⠆⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⢃⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠀⢀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣀⠄⠂⠄⠄⠁⠀⠀⡀⠐⠈⠁⠛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢚⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⠐⣈⡙⢳⡄⢸⡇⢠⣄⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢲⡈⠷⠁⣼⡇⠘⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠠⠀⠀⠀⢀⠀⠀⠀⢠⣠⡄⣠⣠⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣐⣂⠐⢶⠂⣄⢸⣀⣉⣉⢀⠒⣒⣘⢸⠉⣧⣴⣦⢠⣴⡴⣦⣴⢦⣠⡶⡤⣤⢦⢤⢶⡤⡷⢤⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣒⡀⣤⢀⡌⡀⢠⣮⣭⢁⠇⢸⠀⣟⠲⠶⠆⡄⢸⡄⠇⠂⠸⠶⠟⠿⠼⠸⠟⠇⠇⠻⠼⣛⣷⣗⣿⣀⣻⠿⠇⠷⠸⠽⠃
⠀⠀⠀⠀⠀⠀⠶⡆⣺⣀⡆⢹⣿⡞⠿⠻⠟⠿⠻⠿⠋⠻⠇⢸⠀⠿⠟⠓⢿⠷⠺⠰⠶⠿⠿⠿⠿⠆⠷⠒⠶⠶⡆⣆⡘⠟⠛⠛⠛⠛⢻⡃⠤
⠀⠀⣀⢒⢒⣒⡀⠰⡔⡦⡄⢸⣉⡹⣿⠿⠟⠷⠻⠿⠏⠻⠿⠿⠿⠿⠿⠿⠿⠙⠸⠾⠲⠒⠺⠛⠚⠶⠰⣿⠷⠿⠿⠿⠷⡷⢰⡿⢿⠿⢿⡓⣒⢒⢀⢰
⠠⠬⠭⠍⠹⠯⠛⡉⠉⠓⠁⢸⣼⡆⡀⢲⠀⢻⢿⠛⢺⠀⠽⠿⠟⠿⠷⠸⡘⠛⠻⠟⠟⠛⠛⠙⠀⠛⠓⢰⣶⡆⣟⠛⠁⣶⠘⠿⠸⣿⡿⠃⠠⠼⠮⠔
⠀⠀⠀⠹⠛⠎⣟⠟⠿⠛⠛⢸⣿⠆⣷⣿⣶⣟⣲⣿⣾⡿⣾⣷⣷⣾⣶⣿⢡⣶⣶⣶⣷⣶⠘⣟⣛⣛⣂⣩⣿⡇⣿⢠⠀⣿⢲⡿⠇⠛⠛⠿⠛⠻⠏⠟
⠀⠀⠀⣷⣦⣤⣶⣬⣭⣭⣭⣸⣿⡇⢱⢘⡐⢩⡔⠋⠈⡖⣲⢰⡶⣶⣴⣖⣦⢴⢶⡆⣶⢶⡆⣿⣴⣶⣆⣲⣾⡂⢉⢸⠀⣮⠸⠿⠿⠿⠿⠇⢩⣭⣭⠭⠉
⠀⠀⠀⠇⢡⢡⣄⣈⣶⣁⡁⢸⣿⡅⢸⣼⠖⢹⠁⣿⣇⣷⡟⢻⣷⠿⠻⠧⠆⠸⠤⠇⣿⠼⠗⠿⠻⠷⠆⢸⣧⠄⠄⠨⠀⠽⢰⡿⢿⠰⢿⡄⠒⣶⢖
⠀⠀⠀⠒⣒⣘⣉⢩⣭⣭⣩⡾⠿⡅⠸⢼⡇⠐⢠⠤⠤⠤⠠⠬⠧⠸⠼⠇⠷⠠⣭⡥⣭⠤⣭⠁⢸⡆⡇⠿⠯⠏⠛⠛⠉⢻⠸⣷⣾⣷⣾⠇⣬⡭⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⡉⠭⠧⠤⢸⡇⢸⢸⠠⠭⠭⠭⢭⠄⠰⠖⠶⠚⠆⠄⠜⠛⠛⣛⠃⠈⠀⡇⢒⣀⢛⣋⣙⠙⡛⢰⣶⣶⣶⣶⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢠⠸⢠⠀⣒⡒⣙⡃⡇⠈⠛⠛⠌⠩⠴⠖⠀⡇⠀⠉⠉⠉⠉⠉⠉⠉⡘⢡⣶⣾⣷⣶⣶⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⡇⠉⠉⠉⠀⠉⢹⠁⠂⠀⠈⠉⠉⠈⠉⠩⠭⠭⢠⣦⢠⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠽⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣧⣻⣶⠀⢀⣀⡀⠀⠀⠀⠔⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠐⠐⠒⡂⠿⠺⠛⠁⠈⠀⠀⠀⠈⠁⠸⠘⢟⣫⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⢰⣼⣻⡃⠀⠀⡴⢏⡯⠆⠀⠀⠀⡀⣴⡆⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠰⢷⡄⠀⠀⠐⣾⣛⣴⠀⠀⠻⠿⠃⠀⠀⠀⠀⠹⣿⣏⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣄⠀⢠⢻⣭⣧⣱⢄⣀⡀⠀⣀⣠⣀⠀⠀⠈⠁⠀⢀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⡽⠘⡥⢼⠭⣿⣠⡿⠪⢿⡶⢄⣤⢈⡀⢀⠰⣦⡖⣺⣾⡏⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⣜⣿⢟⣻⣯⣿⣯⠋⢯⣯⢸⣶⣴⠶⢬⠃⣾⣹⢇⣲⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢾⡎⢿⠟⠋⢿⣻⢗⡃⡿⣿⣹⢧⠀⢈⣏⣭⣝⢋⣽⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢿⢻⠆⠈⢹⢛⣿⡇⣶⣥⡮⠀⠀⣾⣿⠮⢽⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡇⢟⣿⣾⡀⠘⢽⡯⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⣀⣼⣏⠁⠀⠀⡀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣷⣫⣿⣿⡏⢻⣿⢟⣯⠯⠝⡟⡿⠋⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣋⣿⡏⢿⢷⡿⣟⡧⠛⠟⠛⠛⠙⠓⠳⡟⡽⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠙⠿⡿⡿⣻⢻⣿⣼⢏⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠼⠿⠿⠿⡿⠿⠿⠿⠟⠺⠃⠀⠀⠀⠤⠤⣄⡀⠀⠀⠀⠀⠈⢺⣶⣣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⠭⠃⢀⣀⡉⣠⣙⣷⡓⡐⣠⠒⠁⠀⠀⠐⢦⣀⣰⡷⠀⠀⠀⠀⠀⢸⣷⢶⣿⠋
⠀⠀⠀⠀⠀⠀⢀⡰⠚⣕⣿⠞⣛⣯⢩⣿⣛⣽⡁⢯⠙⠀⠀⠀⠀⠀⠉⠃⠈⠀⠀⠀⢿⠿⢷⡄⣿⣶⢯⡄
⠀⠀⠀⠀⠀⡠⣏⠀⡆⣯⢹⡟⣷⣾⠿⣽⠭⠭⠾⢉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⣷⣿⣏⣫⡀
⠀⠀⠀⠀⠠⣕⣭⢡⠴⢢⣾⣧⢻⡿⢿⠀⠠⡊⣓⡛⠀⠀⠀⠀⣀⡀⠀⠠⠬⣿⣷⣦⠀⠀⠈⢀⡳⣿⣽⣮⠇
⠀⠀⠀⠀⡚⣯⣥⡜⣧⢺⣟⣮⣷⣥⣾⣟⣾⣩⢯⡏⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡉⠛⠀⠀⠀⢈⣯⣽⠛⡷⣤
⠀⠀⠀⠠⠿⢼⠿⠶⠶⠡⣟⡾⣻⣶⣾⣿⣍⡹⢾⡅⠀⠀⠀⠀⠀⠀⠀⠲⢤⠀⠘⠂⠀⢠⣠⡮⡟⠮⠬⠿⣚
⠀⠀⠀⢸⣦⡤⢟⡘⣟⠗⠸⠛⣿⣿⣿⣶⡹⡟⣽⣷⡄⠀⠀⠀⠀⠀⣽⣦⣤⣤⡦⢸⣷⣝⣿⣿⡾⡟⠿⠒⠯
⠀⠀⠀⣾⣟⣀⡋⢉⡁⢛⢁⢠⡸⣏⣭⣽⡦⢌⡦⣾⣿⣷⢢⣠⣄⣀⡈⠙⠚⠁⢠⣿⣿⣯⣳⣧⣛⣛⣛⣫⡵
⠀⠀⢀⢡⣧⠈⢰⡆⣦⣰⣶⣮⣫⣭⣹⡿⣧⢸⣷⡙⣾⢛⡟⣿⣿⣿⡷⣦⣠⣤⣿⣟⣮⣖⡇⢡⠝⣺⢯⢜⠃
⠀⠀⡈⢸⣟⣰⣸⣧⣷⣿⣿⢺⣹⠿⣏⣷⣞⡘⢯⣿⣿⣿⣹⡽⡿⣿⣿⣾⣧⠐⣿⣧⢹⣿⡎⡱⠞⢙⣿⣻
⠀⢀⣁⣺⣼⡞⢟⣟⣽⣋⡫⣉⢷⣾⣷⢿⣿⡛⣎⢫⣿⣿⣿⢿⣾⠾⣽⡿⢳⣬⣿⣟⣘⢮⡏⢻⡾⣿⣿⢹⡀
⠀⠀⠖⣬⡿⣿⢼⡿⣧⢹⣟⣯⣼⣻⠾⣯⢿⣿⡾⣅⢻⣹⣷⣿⠟⢋⣤⠶⢃⣾⡿⣻⣿⣿⣆⣟⡄⣥⢹⠿⡫⠄
⠀⠀⣭⣞⠿⢼⢽⡤⢯⣞⡏⠳⣇⠿⡿⣿⡷⢞⣿⠫⡄⢛⣬⡱⠒⠋⠁⢀⣾⣿⣮⣽⣿⣿⢾⢿⣧⢹⣿⡅⠾⠄
⠀⠀⣿⣉⣓⢃⡂⠲⢎⠛⢗⣙⣛⣣⣡⡿⢿⡿⣷⢧⢿⠿⠂⠀⠀⠀⡰⢿⠿⣿⣾⣝⡷⣿⣿⢿⣿⣟⡿⣇⠶⡂
⠀⠀⢻⡼⠷⣋⣁⠤⢄⢀⣘⠋⣟⣟⣛⡁⠀⢳⣹⣿⡟⠀⠀⠀⣀⣾⣿⡿⣱⣤⣿⣿⢗⣼⠍⠈⣽⡎⢁⠻⡆⢻⡄
⠀⠀⢨⣿⣾⣿⣟⠿⣏⡿⣿⣿⣿⣿⣿⣧⠀⠀⢻⡿⠁⠀⠀⣴⣯⣽⣿⠹⠍⣼⣟⣧⣾⡶⠀⠀⢸⡗⠈⡇⠩⣄⢻⡄
⠀⠀⠀⢿⣷⣾⢒⣎⢪⣿⣿⣿⣿⡟⣑⠀⠀⠀⠀⠁⠀⠀⣰⢟⣿⡛⠃⣿⠴⡿⣿⢛⣻⡏⠀⠀⠀⣵⠀⠹⠆⠙⡀⠠
⠀⠀⠀⠘⡴⢯⣶⣶⠟⣿⣻⣶⣯⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟⣸⠛⠀⢀⣿⠘⡿⠺⢿⣿⣇⠀⠀⠀⠹⠀⠀⢹⡄⢥⠐⠆
⠀⠀⠀⠀⡇⠀⢰⠀⢆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣛⠀⠀⢨⠎⠀⠃⠀⠀⣧⠈⢣⣀⠀⠀⠀⠀⠀⠅⠈⣆
⠀⠀⠀⠀⢾⡄⠀⠃⠈⢂⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣬⠃⠀⠀⣿⠃⠀⠀⠀⠀⠹⣆⠀⠘⠷⣀⠀⠀⠀⢾⠀⣱
⠀⠀⠀⠀⢸⠁⠀⠰⡄⠀⢣⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠉⠲⡄⠀⢸⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋