Ice crystal Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠦⠀⡆⠀⠀⠀⠀⠳⣼⠄⠀⠀⢀⠀⠀⡄⠀⠏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠢⣤⡀⠀⠀⣨⠀⠀⠀⣸⡤⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⢲⠉⠀⠈⠲⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣀⠀⢀⡸⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠤⢻⠃⠀⠈⢑⠉⠀⠀⠹⠓⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡒⠀⠏⠀⠈⠀⠀⠀⢾⠦⡀⠀⠀⠀⠈⠇⠀⠖⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀
⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠈⠂⠱⣄⣱⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⣐⣠⠴⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠀⠀⡀⠀⡀⠀⠈⠢⣧⠞⠁⠀⠀⠀⢰⠀⠸⠥⠞⠁
⠀⠀⠀⠀⠐⠛⠃⢠⣄⠀⠀⠀⠇⠀⠀⢠⣄⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠄⣀⠀⠀⠀⣄⠀⠀⢀⣧⠴⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠈⢑⠊⠁⠀⠁⡖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠉⣶⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡨⣄⡀⠀⣀⢧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢄⡀⠀⣀⡿⠀⢀⣀
⠀⠀⠀⠀⠤⣤⡄⠘⠋⠀⠀⠙⡏⠀⠀⠘⠋⠠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠞⠿⠀⠀⠈⠋⠁⠀⠈⡟⠦⣤⠄
⠀⢀⠐⠰⠋⡙⠀⠀⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⠹⠙⠲⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⠀⠐⠁⠀⠁⠀⢀⠔⡟⢦⡀⠀⠀⠀⠸⠀⢠⡒⢦⡀
⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⠀⠀⠀⠀⠀⠁⢀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠢⣄⠘⠃⣠⠴⠀⠀⠀⠢⢀⢠⠀⠀⠀⠀⠀⠀⢴⣷⣙⣋⣾⡦⠀⠀⠀⠸⣿⣿⣷⣾⠇
⠀⠀⠀⠀⢠⡄⢹⠇⣄⠀⠀⠀⠈⢀⠀⠙⠃⠀⠀⠀⠀⠀⢴⣶⢛⡛⣶⣦⠀⠀⠀⠺⡿⣿⡿⢿⡆
⠀⠀⠀⠈⠁⠀⢸⡆⠀⠉⠀⠀⠀⠀⠂⠐⠀⠄⠀⠀⠀⠀⠀⠁⠻⠟⠈⠁⠀⠀⠀⠀⠀⠙⠃


⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠂⢠⣴⣦⡄⠒⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠙⠃⢠⡀⠸⠃⠀⠀⠀⠘⠃⢀⡆⠀⠛
⠀⠀⠀⠀⡀⠸⢿⡿⠂⣀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠴⠆⢈⡁⠰⠆⠀⠀⠀⠰⠆⠀⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠲⡆⢠⡀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⢀⣀⠸⡷⣤⣤
⠀⠀⠀⠀⠀⠀⢶⡖⠀⠀⠀⠀⠀⡚⠁⡰⠧⣈⣣⠀⠀⠀⠀⣹⣿⣿⣯⠀⠀⠀⠀⠀⣿⠸⡷⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣀⣄⠘⠃⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⢱⡷⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠳⢤⡄⣚⢠⡴⠛⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠈⠁⠀⢀⡀⠠⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⢀⣠⠌⠧⠡⣄⣀⠀⠀⠀⠀⠀⠳⠼⠀⠀⠀⠀⠀⠀⠀⠘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠋⠁⠀⣹⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢀⡀⠀⢿⡏⠀⣠⡀⠀⠀⠀⠱⡀⠀⡜⠀⠀⠀⢀⣤⠀⢈⣿⠀⢀⣄⠀⠀⣀⠀⠀⠇
⠀⠀⠀⠘⠐⡖⢩⡉⣿⠁⠁⠀⣀⣀⡀⣼⢲⡄⠀⡀⠀⠀⠉⠛⡂⠋⠞⠋⠉⠀⠀⠈⠁⣶⣷⡄⠈
⠀⠀⠀⢠⣤⠓⢬⡥⠛⢔⡆⠀⠀⠀⢀⠌⠙⢄⠀⠀⠀⠀⣶⠟⠡⡦⠙⠳⡖⠀⠀⠔⠈⠉⠋⠁⠢⠄
⠀⠀⠀⠀⠉⠀⠶⡷⠀⠀⠀⠀⠀⠀⠊⠀⠀⠈⠆⠀⠀⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠠⣰⠏⠀⠀⠀⠀⠀⠀⠀⢶⣄⡠⠀⣄⡑⢾⠂⣁⢀⡀⢠⡄⠀⠀⠀⢠⡀⠀⠀⠀⢸⣟⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣤⠒⢤⢍⠀⡀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠂⣼⣈⣿⣊⣹⠼⠿⠉⠁⠀⠀⠀⠀⠉⠿⣶⣐⠶⠧⢶⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠰⠦⠶⡦⢶⠰⣿⡧⢺⠰⡗⠗⠗⠒⠀⠀⠀⠀⠀⠶⣍⢸⡏⢾⢘⡋⢑⠶⠀⠀⠀⠀⠀⠀⠀⠈⣤⣓⢽⣾⣝⣣⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠖⢤⠜⣏⡁⠈⠀⠀⠀⠀⠀⠀⠀⢒⣦⠜⢋⢉⣾⡉⠙⢣⣄⡂⠀⠀⠀⠀⠀⠀⣬⣾⢵⣩⢩⣻⢷⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠂⠀⠀⠎⢷⡀⠀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠉⡡⣶⢌⠁⠈⠈⠙⠃⠀⠀⠀⠰⠋⠈⠈⠀⢔⣴⠂⠀⠈⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⢀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠑⠶⠔⠁⠀⡀⢀⢠⠀⠀⠀⠀⠀⠀⠀⢆⠈⡆⣿⢰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣆⠆⠀⡐⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡣⠧⢀⡀⢲⠂⢀⡄⠷⡙⠀⠀⠀⠀⠀⠀⠘⠳⢦⣕⡶⠼⢴⡊⠴⠞⣠⡀⣀⠀⠀⠀⠀⡐⠂⠙⠀⠄⠝⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢘⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⣤⠒⠉⠉⡁⢾⠀⠀⠀⣽⡣⠤⠤⠖⠋⠀⠀⢠⣴⠵⡦⠈⢰⣿⢈⠀⢦⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣠⠑⡆⠈⠀⢙⡁⠈⠃⡶⣊⠀⠀⠀⠀⠀⠈⠉⣥⡖⣪⢷⠲⠺⠓⠝⡓⠂⠀⠀⠀⠀⠀⠀⠈⡀⢨⡄⠆⢠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠄⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡐⠁⡘⢸⡇⠡⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠚⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡥⠒⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⡄⠐⠢⣿⠔⠂⣤⠀⣠⡄⠀⠀⠀⠀⠀⠠⠽⣎⠀⣤⠀⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢁⠦⣀⠀⢘⡃⢀⣂⣥⠧⠀⠀⠀⠀⠀⠈⠙⣷⣷⣀⠀⢿⠀⣀⣿⡞⠉⠀⠀⠀⠀⠀⠀⢠⣄⠙⣀⠍⣠⠋⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢱⣿⣿⡎⠓⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣃⣾⣞⡋⠀⠀⠁⠀⠀⠀⠀⠤⣦⢤⠤⢥⣽⣿⣯⡍⢡⣄⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢑⡲⡦⠙⠃⣹⡉⠈⠋⡶⣉⡁⠀⠀⠀⠀⠀⣁⣶⡖⠛⠁⣾⠈⠙⣶⣖⡀⠀⠀⠀⠀⠀⠀⣤⠖⠃⡼⡛⢅⠒⣤⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⢀⡠⢴⣌⠀⠀⠁⠈⠈⠀⠀⠀⠀⠘⠉⠀⠇⠀⡠⣽⣄⠀⠛⠈⠙⠂⠀⠀⠀⠀⠀⠀⢀⠾⠀⡇⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠉⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢦⣠⠀⢤⠀⢸⠆⡘⢀⡴⡇⠀⣤⠀⣀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣵⡀⣀⣤⠀⠐⢷⡀⢁⡿⠂⠀⣄⡀⢀⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡒⢤⡑⡀⣄⠓⠞⢠⢀⠊⡥⠐⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢻⠀⢽⡀⢤⠈⢇⡸⢀⡄⢀⡯⠀⠏⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⡛⠞⢌⡒⠿⢠⡇⠿⠗⡩⢳⢚⡰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠳⡄⣝⠺⢟⢸⡕⡿⢗⡯⣠⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠲⢖⠀⠬⣿⡆⢻⣳⠿⡶⣦⡛⢰⣷⠥⠀⣒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣄⡀⠒⣾⣆⣛⣤⠺⠖⣤⢛⣰⣳⠂⢀⣠⣦⠂
⠀⠀⠀⠀⠲⠖⡿⠤⢈⣹⠇⠐⠶⢞⡗⣻⡷⠸⣋⠶⠂⠐⣏⣁⠤⢾⠲⠖⠀⠀⠀⠰⣉⠶⠶⠄⢈⣉⡡⢚⠶⢸⠂⣾⣟⠰⡇⠶⡰⣍⣉⡁⠤⠶⠶⡹
⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⢀⢿⠇⣼⠿⢖⡷⠿⣧⡘⡟⢁⠀⠨⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⠋⠀⠤⠿⢎⣤⢻⢼⠦⡛⣬⠹⡿⠤⠀⠙⠏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⡥⢦⣊⠴⣶⠘⡇⣶⣦⢑⡬⢦⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠔⠋⣯⢶⣾⢸⡣⣷⡦⣏⠙⢦⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠄⠚⡱⠀⠂⡶⢧⠈⠈⠂⡑⠀⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣤⠄⣺⠀⠙⢀⡏⢹⠀⠃⠈⣗⠢⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠎⠙⠀⠚⠀⢸⠆⠡⠈⠱⡇⠀⠙⠀⠈⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠹⠀⠉⠙⠀⠠⣾⠅⡌⡷⠄⠀⠋⠁⠈⢏⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢘⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣠⠀⠘⢼⡗⠁⠠⣀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⣢⠀⠀⠀⠻⡀⠀⢜⣇⠀⢀⡟⠀⠀⠀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣆⡆⠀⢍⣫⡜⢠⢺⡑⡀⢧⣟⡡⠀⣀⡸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⡄⢈⣻⡀⢸⡇⢀⡸⡁⢠⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⢗⡢⠌⣧⠎⣼⣧⢱⣬⠡⢔⡺⡟⠓⠂
⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⢉⠹⣦⢨⠷⢮⡷⠾⡏⣴⠞⡉⢀⡀⣤⠄⠀⠀⠀⠀⠀⠀⠸⠓⢸⣄⣣⠘⡈⣳⣶⢌⣦⢋⡱⣼⡡⣖⡏⢱⢁⣎⣴⡄⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠺⢦⡟⠻⡦⢽⢣⢷⢟⠳⡴⠧⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠒⣉⠱⠟⠤⣧⣰⣺⠮⠷⣷⣆⣮⠔⠿⢌⡙⠒⠈⣀
⠀⠀⠀⠀⢶⠦⠰⠶⠱⠶⠶⢎⡷⠿⣓⣎⣹⣎⠾⢾⡱⠶⠶⢮⠴⠆⠴⡶⠄⠀⠀⠀⡶⢾⡶⣏⠰⠶⣿⣎⠱⣿⡇⣏⡱⢸⡳⢌⣱⣷⠶⠆⣽⢾⠷⢖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠾⡧⣽⢗⣪⡝⡺⣮⢴⠳⡶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⣉⣐⣦⠐⡟⠹⢽⣖⡶⡯⠏⢟⠢⣴⣊⣉⠤⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠟⠉⠁⣈⣰⠟⢚⡦⢞⡷⢶⡇⠻⢆⣁⠈⠁⠻⠂⠀⠀⠀⠀⠀⠀⢠⣤⢹⠟⡹⢡⢃⡸⠷⠂⠟⣌⡱⢻⠐⡿⣇⡰⡈⢏⠺⠯⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠃⢈⣽⠁⢸⡇⠘⢫⡁⠘⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣶⡎⠥⢒⡟⠆⢻⡟⡸⢓⠒⠬⡱⣧⣀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠝⠀⠀⢀⣬⠋⠀⢪⡗⠀⠘⣧⡀⠀⠀⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠎⠏⠀⢊⣝⢣⠘⣸⣡⠁⡜⣏⡒⠀⠉⠳⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢈⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠙⠀⢠⢾⡷⡀⠐⢙⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠊⠃⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣨⣇⠀⠀⢀⡄
⠀⠀⣠⢀⠐⡦⣄⡉⣠⢴⠂⠀⣀⠀⠀⠀⠀⣶⣴⡀⠀⠙⡏⠀⢠⣾⣴⠀⠀⠀⠀⠀⠘⠻⣦⣞⣾⣆⣷⠿⠟⠀⠀⠀⠀⠀⠀⠀⠙⣶⡆⢹⡏⢰⣷⠃
⠀⠨⢟⠿⠤⣹⣾⠷⣵⣞⠠⠷⡛⠇⠀⠀⠀⠉⠋⠉⢲⠚⠳⠖⠉⠙⠉⠀⠀⠀⠀⣤⣤⣾⣭⣿⣿⣿⣯⣽⣦⣤⡄⠀⠀⠀⣀⣄⣤⣀⢙⣾⣷⢋⣀⣴⣀⣠
⠀⠀⠀⢠⣞⣹⣿⣶⣿⣯⡱⠦⠀⠀⠀⠀⠀⢤⣶⡴⠊⠳⡎⠑⢦⣴⡤⠀⠀⠀⠀⠉⠉⠺⣽⣿⣿⡿⣿⡭⠊⠉⠁⠀⠀⠀⠀⠀⢉⣀⡴⢙⡏⢦⣀⡉
⠀⠀⠀⢀⣠⡔⠙⣭⠇⢳⣄⢄⠀⠀⠀⠀⠈⠋⠙⠁⠀⣼⣧⠀⠈⠻⠙⠀⠀⠀⠀⠀⢰⣾⠃⠓⣽⡕⠋⢿⡶⠀⠀⠀⠀⠀⠀⢀⡼⠛⠃⢼⡧⠘⠛⢦⡀
⠀⠀⠀⠀⠛⠜⠀⠉⠀⠂⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇

⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠏⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⣀⠑⢿⠒⣀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⢰⣬⣧⡆⡄⢀⣀⠀⠀⠀⠀⠀⠛⠆⠀⠀⣀⡠⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⢶⣆⣴⣼⣧⣦⣰⡾⠁
⠀⢀⣿⣮⣆⢹⣷⣶⣾⡟⢠⡵⣿⡆⠀⠀⠀⠈⣩⡾⣯⣹⣏⣿⣷⣍⠁⠀⠀⠀⢀⣀⠀⠠⢰⢋⣯⣟⢷⡠⠀⠀⢀⠀⠀⠀⠀⣀⢰⣿⠿⣽⣯⢿⣿⡆⣀
⠀⠀⠁⠊⣠⣿⣿⣿⣿⣿⣤⡉⠂⠀⠀⠀⠀⠀⠲⣿⡶⢻⡟⣶⣿⠖⠀⠀⠀⠀⠘⠛⠀⠀⢻⡜⡿⡟⣼⠃⠀⠘⠓⠁⠀⠀⠘⠛⢻⣿⣯⢿⡿⣽⣿⡟⠛⠁
⠀⠀⠀⠀⡉⣭⠛⣿⠟⣥⡀⠀⠀⠀⠀⠀⠀⠞⠋⠹⢹⣿⣿⡏⠏⠙⠷⠀⠀⠀⠀⠀⢀⡀⠀⠉⠓⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⡟⢿⣿⣿⡿⢻⣤
⠀⠀⠀⠘⡿⡋⠄⠉⠀⢋⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⡠⡄⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⢾⡧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠸⣿⡄⠀⠰⣽⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣸⣇⡄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣼⣿⣿⣤⡀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣸⣇⠀⣀⣤
⠀⠀⠀⠀⠀⠈⢣⣀⡰⠉⠀⢀⠀⠀⠀⠀⠀⠙⢷⣿⣿⢿⡿⣷⣧⡶⠋⠀⠀⠀⠀⠸⢿⣿⠋⢻⠀⡸⠋⢻⣿⠿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣾⡿⠁
⠀⠠⠿⢾⠆⠀⢎⡀⡱⠆⠰⢷⢿⠆⠀⠀⠀⠀⣭⣿⣯⢿⣿⣽⣿⣏⠀⠀⠀⠀⠀⠀⢸⡷⠶⠒⣁⡱⠲⠶⣿⠀⠀⠀⠀⠀⠰⠶⠾⣿⣿⣿⣿⣿⣿⡷⠶⠆
⠀⠀⠀⠀⠀⢀⡞⠁⠱⣀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣿⢿⣾⣷⡿⡿⠷⣆⠀⠀⠀⠀⢨⣿⣿⣦⣾⠁⢹⣦⣼⣿⣮⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⢿⣷⡀
⠀⠀⠀⠀⢬⣿⠃⠀⠐⣿⣥⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢹⡏⠃⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⢻⣿⣿⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⢹⡏⠀⠈⠙
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⡿⢆⣀⣠⢾⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣨⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣄⡀⠐⣿⡇⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠸⡇⠀⠀⣤⡄
⠀⠠⣤⡤⣰⣾⣀⣿⣇⣼⣦⣤⣤⠄⠀⠀⠀⠀⠘⢶⡄⠘⡇⢠⣷⠃⠀⠀⠀⠀⠀⠀⠘⢿⣦⡏⢾⠎⣧⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⣶⣆⣿⣯⣦⣶⠋
⠀⠀⠀⣹⣦⣼⣿⣿⣿⣯⣤⣎⠁⠀⠀⠀⣀⣠⣤⣄⣈⣶⣷⣁⣠⣴⣄⣀⠀⠀⢀⣤⣦⣝⣬⣹⣾⣾⣩⣔⣥⣶⣄⠀⠀⢠⣤⣄⣤⣯⣿⣿⣿⣿⣵⣤⣠⣤⡄
⠀⢀⣤⣞⣁⣽⡿⣿⡿⣯⣉⣓⣄⡀⠀⠀⠀⠀⢉⣠⡔⠉⠟⢢⣀⡁⠀⠀⠀⠀⠀⠉⠉⠾⣤⡞⢻⡛⣦⣜⠂⠉⠀⠀⠀⠀⠀⠀⠈⣮⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠈⣏⡰⠿⢆⣹⠁⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢸⡧⠀⠛⢢⡀⠀⠀⠀⠀⠀⢸⡿⠇⠒⣽⡕⠋⢿⡿⠀⠀⠀⠀⠀⠀⢠⡶⠉⠉⠻⡗⠁⠉⣶⡆
⠀⠀⠀⠀⠀⠟⠁⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇

⠀⠂⣠⣄⠠⡁⠺⠀⠀⠀⠒⠁⠀⠒⠂⠢⠤⠤⠀⠀⠀⠐⢋⡈⠀⠀⠀⠀⠀⠀⠀⣀⠆
⡔⢠⣿⣯⣂⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⡀⢀⠀⡀⠀⠀⠀⠅⡦⠀⠀⠀⢀⡴⠞⠁
⠒⢠⢾⣶⣾⡽⢋⠁⡀⠂⠀⠀⢀⠀⠔⡟⠋⠡⠊⠁⠀⠀⠀⠀⠀⠁⠀⠃⠊
⣠⡴⣯⣿⣯⢔⡀⠉⠀⠀⠀⠂⠉⠐⠋⠟⣠⡄⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⣶⢤⣤⠤⠄
⢔⣳⡟⠛⠛⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢭⡂⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⢰⡶⢶⢆⡀⠠⠄
⠸⠟⠋⠁⠀⠀⢀⠀⢒⣖⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡷⢸⣹⣼⠀⠙⠂⡀⠨⠔
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠙⠀⠀⠀⢀⠀⠀⠀⠀⢤⠀⠁⠀⠲⠀⠀⠀⠀⠀⢀⡒⠐⣛⣷⠀⣠⣤⡶⠊⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣶⠟⡀⠀⠀⠀⢀⠂⠀⠌⢀⡀⠀⠀⠀⠀⡛⣷⢄⠀⠑⠖⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠚⠀⠀⠀⠀⠘⠀⠀⠀⠂⠰⣦⠄⠀⠈⠀⣾⠂⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⢋⣿⡞⢀⠀⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠗⠋⢰⢟⣎⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡓⠍⢁⠇⣾⡟⠠⣯⡄⠀⠐⠪⣌⠠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⡟⣡⣽⠯⠖⠄⢠⠀⠀⢀⢠⠀⠈
⠀⠀⠀⠀⠀⠉⠀⢀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠟⣠⣏⣃⠁⠀⠀⠀⠀⡠⡄⢘⡔⠈
⠀⠀⠀⠀⠈⠚⠂⠁⠡⠂⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢡⠀⢀⣤⠖⠂⠀⠰⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢀⠈⠨⠀⠀⠀⠀⣠⣄⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠙⢷⡄⣶⡾⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠸⣿⠉⠛⢦⣼⡇⢹⣶⡿⠛⣿⠆⠀⠀⠀⠀⠀⣠⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠛⢿⡆⠀⠀⠀⠀⠙⢶⣄⡀⠉⠁⠈⠁⣠⡴⠟⠀⠀⠀⠀⠀⣰⡟⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢻⣆⠀⠀⠀⠀⠀⠈⠛⣦⠀⣴⡞⠉⠀⠀⠀⠀⠀⠀⣴⠏⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢻⣆⠀⠀⣴⡶⣦⣀⣿⠀⣿⣇⣴⢶⣄⠀⠀⠀⣼⠏⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⣰⣶⡿⢷⣦⣄⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠹⣆⠀⢻⣇⡀⠙⠿⠀⣿⠟⠁⢀⣿⠀⠀⣼⠏⢀⣾⠃⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣠⣶⠿⠛⢿⣿
⢿⣇⠀⠀⠀⠙⣿⡀⢾⡇⠉⢿⡄⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣆⠀⠉⠻⣦⡀⠀⠀⣠⡴⠛⠁⠀⣼⠋⢀⡾⠃⠀⠀⠀⠀⠀⣾⠟⠻⣦⠀⣸⡏⠀⠀⢀⣼⣿
⠈⠻⣶⣄⣠⣤⣌⡛⠿⡧⠀⢸⡇⠀⢰⡾⠷⣄⠀⠘⣧⠀⠀⠹⣦⠀⠀⠈⣿⡆⣴⡏⠀⠀⠀⣼⠃⢀⡾⠁⣠⡾⠻⣦⡀⠀⣿⠀⠠⣿⠟⢋⣡⣴⣶⡿⠟⠃
⠀⠀⠀⠛⠛⣉⣽⡿⠶⠀⠀⠈⣿⣄⣘⣧⠀⢸⡇⠀⠘⣷⡀⠀⢿⡀⠀⠀⢸⡇⢸⡇⠀⠀⢨⡇⣠⡿⠀⠀⣿⠁⠀⣾⣁⣴⠟⠀⠀⢠⣶⣟⣉
⠀⠀⠀⠀⣼⣏⠀⠀⣀⣤⡶⠶⣤⣍⠛⠛⠀⠈⣿⠀⠀⠈⠙⠻⣎⢷⡀⠀⢸⡇⢸⡇⠀⢠⡟⣴⠋⠀⠀⢠⣿⠀⠀⠟⠋⣡⣴⠶⢦⣄⣀⣉⣿⣷
⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⢀⣠⣤⠿⠛⠀⠀⠀⠙⢦⣄⡀⠀⠀⠹⣎⢷⡀⢸⡇⢸⡇⢠⢟⡼⠃⠀⢀⣠⡾⠋⠀⠀⠀⠿⣯⣤⡀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣤⣴⠾⠛⠳⢦⣌⡛⠷⣤⣀⠹⣆⢷⣼⡇⢻⣦⣿⣿⣁⣤⠾⢛⣡⡴⠞⠳⠶⢦⣄⣀⣸⣧
⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⠷⣦⣝⠻⣿⣆⣿⡇⢿⢋⡾⠟⢋⣤⠶⠛⠉⠀⠀⠀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢰⣿⡋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠛⠛⠷⠶⠶⠶⣶⣶⡿⠷⠦⠈⠉⠁⠀⠈⠰⠾⢿⡷⠶⠒⣒⣒⣿⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣻
⠀⠀⠙⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠉⠉⠉⣉⡿⠟⣃⡀⠀⠀⠀⠚⢿⣯⣉⠉⠉⠉⠉⠉⠙⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⡴⢛⣩⡴⠞⡿⢣⡆⢰⡘⣿⠶⣬⣙⠻⣦⣄⣀⠀⣀⣠⡶⠟⠛⠒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⠀⠙⠻⣦⣄⣠⣴⠾⣛⣥⠶⠛⠁⠀⡼⣡⢿⡇⢸⣷⡘⣦⠈⠙⠷⢦⣉⠉⠛⠋⠁⠀⢀⣀⣴⠿⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠰⣿⠟⠿⢶⣄⡀⠉⢛⣦⡄⠀⠉⣉⣴⠞⠋⠀⠀⠀⢀⡾⣱⠏⢸⡇⢸⡇⢻⡜⣧⠀⠀⠀⠹⣧⠀⠀⠐⢾⣿⣉⣀⣤⠶⠟⠋⠉⣹⡟
⠀⠀⠀⠀⠀⠛⠲⢦⣀⠈⠙⠛⠛⢉⣤⡄⠀⣿⠀⠀⠀⠀⠀⣠⡾⣵⠋⠀⢸⡇⢸⡇⠀⢻⡜⣧⠀⠀⠀⢻⡄⠀⣿⡿⣷⡍⠉⠀⠀⣠⣤⠴⠛
⠀⠀⠀⣠⣄⡀⣀⣴⠿⠀⠀⢀⣾⠋⢹⡇⠀⣿⠀⠀⠀⠀⣼⠋⢸⡯⠀⠀⢸⡇⣼⡇⠀⠀⢻⠎⠻⣦⠀⠸⣧⠀⢹⡇⠈⣷⠀⢠⣦⣝⣿⣦⣤⣦⣄⡀
⠀⣴⠿⠛⠉⠛⢉⣠⣶⣦⠀⢸⣿⠀⠸⣧⣄⣿⠀⠀⢀⡾⠃⢀⡾⠁⠀⣠⡾⠃⢸⣧⠀⠀⠻⣧⠀⠘⣧⠀⠻⣄⣠⡧⠀⢸⡆⠀⢿⡉⠻⣾⡁⠀⠙⠻⣶⡄
⢰⡿⠀⠀⠀⢀⣿⠁⢀⡟⠀⢸⣿⠀⠀⠈⠙⠁⠀⢀⡾⠁⢠⡟⢁⣴⠟⠉⠀⠀⠀⠉⠻⢦⣀⠈⢷⡀⠘⣧⡀⠈⠋⠀⠀⠸⣿⡀⣼⠇⠀⠉⠻⣦⣄⣀⣽⣿
⠻⠿⠷⣶⡾⠛⠉⠀⠈⠻⣶⡿⠁⠀⠀⠀⠀⠀⢠⡿⠁⢠⡟⣼⠋⠀⢀⣴⣶⡄⣴⣶⣄⠀⠉⣷⠈⢷⡀⠘⣷⡀⠀⠀⠀⠀⠈⠛⠟⠀⠀⠀⠀⠈⠛⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⡟⠁⣰⠏⠐⠿⢶⡶⠟⢁⣼⠇⢻⣆⠙⢷⣶⢿⡆⠈⢿⡀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣰⠏⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢿⡄⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⣠⡾⠋⠀⢀⣠⡀⣶⣤⡀⠙⠳⣦⡀⠀⠀⠈⠿⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡴⠟⣹⡇⣿⠉⠻⣦⣤⣿⡇⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡟⠁⠘⣷⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣾⠿⠃
⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣟⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⢸⣿⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣴⡄⠀⠀⠈⢻⣷⣼⣿⣰⣿⠋⠀⠀⠀⣴⡄⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⢹⣿⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⢸⣿⢃⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣙⣿⣿⣿⡆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⣿⣿⣟⣡⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⣸⣿⡀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠙⣿⣿⠟⠛⢿⣿⡟⠁⠀⠀⠀⠀⠀⣀⣴⣾⠟⠃
⠀⠀⠀⠀⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⠁⠀⠀⠀⢹⣿⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⢈⣿⣷⣤⣀⣴⣿⣏⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⢻⣿⠋⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣿⠟⠁⠀⠀⢸⣿⠀⠀⠀⠙⢿⣷⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⢛⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣟⠻⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢹⣿⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⢸⣿⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠿⠇⠀⠀⠀⣰⣿⢻⣿⢿⣷⡀⠀⠀⠈⠿⠇⠀⠙⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⢸⣿⠀⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣿⡇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⢹⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣷⣿⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣧⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣷⡀⢸⡇⠀⠀⢰⡆⠀⢠⡄⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⣇⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣻⣿⡇⠀⠀⢸⡇⠀⠀⠙⢦⠀⠀⡇⠀⠀⢀⣾⠇⠀⢸⡇⠀⠀⢸⡇⠀⢀⣿⣿⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⣦⡀⣸⠃⠀⠀⠀⠈⠳⣀⣇⣠⠖⠋⠀⠀⠀⢸⡇⠀⠀⢸⣇⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣷⣾⠀⠀⠀⠀⠀⠀⠹⡟⠁⠀⠀⠀⠀⠀⢸⡇⠀⢀⡼⠿⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⢳⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣾⣧⣾⣋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⠿⠿⢿
⠀⠀⠀⠀⠀⢠⣄⠀⠀⢤⡄⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⢸⡇⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢀⣤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠙⣦⡀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠇⣠⡴⠟⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣰⡿⠋⠀⠀⢀⣴⠞⠋
⠀⠀⠰⠿⠿⠿⢛⣿⡿⠛⠛⣻⡿⠛⠛⢻⣿⠟⠛⠻⠿⠿⠿⠿⠿⠿⢛⣿⣿⣟⠛⠛⠛⠛⠒⠒⠶⠿⣿⡛⠖⠖⠲⣿⡿⠷⠶⠖⢶⣿⠷⠲⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠰⠿⠋⠀⣀⣼⠏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⠇⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠙⢦⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠙⢷⠄⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢤⣤⣤⣤⣤⣶⣶⣶⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞⢹⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢹⣿⡉⠉⠙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢛⣹⢿⡏⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠙⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠋⠁⣼⠀⠀⢸⡇⠀⠀⠀⢀⣴⣾⡷⣄⡀⠀⠀⠀⠀⢸⡇⠀⠈⣻⣯⡉⠙⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⡿⣿⠁⠀⠀⣿⠀⠀⠈⠃⠀⢀⣴⠟⠁⢸⡇⠈⠙⠲⣄⡀⠀⠸⠇⠀⠀⣿⠈⠻⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⣿⠀⠀⠀⠏⠀⠀⠀⠀⠀⠙⠁⠀⣠⠾⣷⣤⠀⠀⠈⠉⠀⠀⠀⠀⠀⡿⠀⠀⢹⣿⣍⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⢀⡏⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣧⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣿⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣲⡠
⠀⠀⠀⠀⠀⡄⡀⠡⢀⢃⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣄⡠⠂⠀⠀⠀⠀⠀⠀⠀⢃⡉⠥⠉
⠀⠀⠀⠀⠀⠀⣀⠵⠿⡃⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢺⢿⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠋⠀⡘⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⠿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠶⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣠⠀⢀⡀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄⠀⢠⡀⠀⠀⠀⠀⠭⣳⡞⠀⣀⠀⢳⡯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⢶⣄⢸⡃⣠⠖⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣹⡼⠉⣧⣏⣠⡀
⠀⠀⠀⠀⠀⣀⣤⡬⡳⠎⢧⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣠⣐⣦⣀⣳⣄⣘⣴⣃⣠⣞⣀⣴⣣⣤
⠀⠀⠀⠀⠀⠀⠀⣰⠇⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠋⢀⣞⣁⣰⠋⢦⣈⣳⡀⠙⠂⠉⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠹⣤⠏⢧⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⣿⡟⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢈⣽⠳⠀⠀⠀⠼⢻⣭⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡄⡦⣿⣿⠔⣧⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣷⣟⣿⣿⣿⠿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⣹⣮⣷⢿⣿⡿⣿⣿⣿⣾⣷⣆⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠱⠀⢀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⣿⣫⣿⣿⢿⣿⡼⠆⠙⠿⡿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠠⣦⡆⠄⠒⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣾⣿⠳⠏⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠄⠂⢁⠋⠄⠑⠠⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠀⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠐⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠿⠿⠟⠋⠀⠀⠁⠀⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣅⡋⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢸⠗⠀⠀⠀⣀⠤⠶⡾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⣿⣿⡟⠉⠉⠓⠒⠒⠢⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⢙⣿⡿⠁⡀⠁⠀⠀⠀⠀⣠⣴⣿⣿⣦⣄⠀⠀⠀⠀⠌⠀⠀⠀⢸⡇⢀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣴⡿⠁⡀⠀⠀⠀⠀⣠⣾⡿⢻⣿⣿⣿⣿⣿⣦⣀⡼⠀⠀⠀⠄⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠟⠉⠉⠉⠉⠉⠉⠙⠛⠻⣿⣿⠃⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠐⠀⠀⠀⠀⢀⠀⠰⢁⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⢶⣄⣀⠀⠋⣠⠂⢁⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡈⣷⣻⣀⠈⡅⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⣿⣶⣆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠈⠁⢀⠶⠂⠀⠀⠀⠀⠀⠀⠀⢸⣫⡆⢐⢮⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠺⠂⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣤⣄⠁⠀⣠⡄⠀⠀⠀⠀⠀⣀⣤⣠⡋⠈⢩⣤⣶⣦⠄⠀⠀⠀⠀⠀⠐⠛⠢⣤⡤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠚⢈⡶⠭⢶⣁⠉⠀⠀⠀⠀⠀⠀⠀⣔⡶⠊⠉⠈⠐⡶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣠⡄⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠂⠙⠾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⡃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣠⢀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⠁⡀⠀⣤⠀⠀⠀⠀⠀⠀⠰⣖⡴⠈⠪⠞⢱⢰⣲⠂
⠀⠀⠀⠀⠀⠀⠐⠷⡵⠄⡦⢱⡎⣥⢀⡴⣠⡀⠀⠀⠀⠀⠀⠀⠬⣖⣭⡲⠅⠀⠀⠀⠀⠀⠀⠀⠀⣓⠊⢑⡊⢰⠉⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠇⠻⡂⠀⠘⠈⠀⠀⠀⠀⠀⡀⠶⠀⠔⠙⠂⠀⠶⠀⠀⠀⠀⠀⠀⣠⣖⢭⠃⣨⡁⢹⣱⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠑⠀⠠⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢔⡮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠇⡰⠲⠔⢦⢸⣷⠂⠀⠀⠀⠀⠀⠛⣨⣄⠀⠭⢀⣸⡀⠓⠀⠀⠀⠀⠀⠘⣂⣅⡀⠸⠇⣀⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⣁⠀⠀⣁⡶⠈⠁⠀⠀⠀⠀⠀⢈⡀⢈⡹⣿⢎⠀⣀⡁⠀⠀⠀⠀⠀⠀⡀⢈⣉⠾⠦⣉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⢿⡇⠳⢞⠦⠆⢰⠯⡄⠀⠀⠀⠀⠀⡤⢘⠇⢀⣖⠀⢸⠑⡴⠀⠀⠀⠀⠀⠠⠌⠋⠁⢸⡆⠉⠏⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠓⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⡀⠀⣀⣀⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣍⠛⣛⣭⣶⣾⣿⣿⣷⣶⣭⣛⠛⣩⣾⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢸⣿⣿⡿⣋⣴⢰⣮⡻⢿⣿⣿⣿⣿⡿⢟⣵⡆⣦⣙⢿⣿⣿⡇⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠸⢟⣡⣾⣿⣿⢸⣿⣿⣦⣙⢿⡿⣋⣴⣿⣿⡇⣿⣿⣷⣌⡻⠇⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⡄⢴⣶⣶⣶⣦⠰⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⠆⣴⣶⣶⣶⡆⢠⣶⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠙⣿⣿⣿⣇⢿⣿⣿⣿⠇⠸⣿⣿⣿⡿⣸⣿⣿⣿⠋⢠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡜⣎⢻⣿⣿⡘⣿⣿⣿⢸⡇⣿⣿⣿⢣⣿⣿⡟⣱⢣⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡜⣷⡙⣿⣧⢹⣿⡟⣸⣇⢸⣿⡏⣾⣿⢋⣾⢣⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠘⣿⣎⢻⡆⢿⡇⣿⣿⢸⡿⢰⡟⣱⣿⠃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡙⠸⢡⣿⣿⡌⠃⢋⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢸⣿⣿⡇⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡎⣿⣿⢱⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠸⠇⠞⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⡯⠴⠒⠋⠉⠈⠓⢄⣀⣀⡤⠶⠚⠉⠁⠀⠉⠙⠒⠦⣤⣀⣀⠴⠋⠈⠉⠓⠲⠬⣷⣤⡀
⠀⠀⠀⠀⢀⣠⠞⣯⠀⠀⠀⠀⠀⢀⣠⠴⢺⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢻⡒⢤⣀⠀⠀⠀⠀⠀⢈⡟⢦⣄
⠀⠀⣀⢴⡿⠃⠀⢻⠀⢀⣠⠴⠚⠉⠀⢠⠏⠀⠀⠈⠙⠦⣀⠀⠀⢀⡠⠞⠉⠀⠀⠀⢧⠀⠈⠙⠲⢤⣀⠀⢸⠃⠀⠹⣷⢄⡀
⠀⢾⡷⣿⠶⠶⠶⢾⣾⠿⠶⠦⠴⠶⢶⣿⡶⠶⠶⠦⠶⠶⠾⣷⣶⡿⠶⠶⠶⠶⠶⠶⣾⣷⠶⠶⠤⠶⠾⢿⣾⠶⠶⠶⢾⡷⣿⠆
⠀⠀⠙⢮⡳⣄⠀⠀⠈⢷⣄⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⡴⣫⠞⠁
⠀⠀⠀⠀⠉⠢⣕⢦⡀⠀⠹⣷⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣰⡿⠃⠀⣀⢔⡫⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠈⢯⡳⡄⠀⠀⠘⡆⠀⠀⠀⠀⡾⠸⡆⠀⠀⠀⠀⡼⠁⠀⠀⡠⢪⠟⠀⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡢⣄⠱⣌⠢⡀⠀⠹⡄⠀⠀⠀⡇⠀⣇⠀⠀⠀⡼⠁⠀⣠⠞⡴⢃⡠⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣷⣌⢦⡙⢦⡀⠹⡄⠀⢸⠃⠀⢹⠀⠀⣸⠃⣠⠞⢡⢞⣴⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣷⣄⠙⢦⣳⡀⣼⠀⠀⠸⡆⣰⣣⠞⠁⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠙⢷⡇⠀⠀⠀⣷⠟⠁⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⢧⠀⠀⢠⠏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣧⢠⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠰⣦⠀⠀⢺⣇⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⣤⢘⣇⡤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣆⠀⡐⡿⠁
⠀⠀⠀⠀⠰⠾⠾⠒⡒⣇⣪⡓⠓⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣟⢆⢸⢃⣤⡼⠞⠃
⠀⠀⠀⠀⠀⠀⣐⡶⠋⢐⣇⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣈⣨⡭⠝⡿⡗⠤⣶⣴⡄
⠀⠀⠀⠀⠀⠐⠋⠂⠀⢐⡗⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠉⠁⣺⡇⠈⢶⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠈⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠜⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠
⠀⠀⠀⠀⠀⠀⢬⢵⠷⣛⠀⠀⠀⠀⠀⠀⠀⠠⡄⣆⡄⠀⠀⠀⠀⠀⠀⣀⡇⠀⢠⡥⠀⣀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⡺⡿⡖⠀⠀⠀⠀⢀⠀⠀⡘⠣⣀⣀⡔⠓⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠼⠉⠉⠉⢉⡽⠯⣉⠉⠋⠉⠙
⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠋⢀⡆⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣥⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠑⠀⢨⣇⠀⠈
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⠉⡴⢰⡈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲

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

⣰⣷⡟⠆⠀⡼⠛⣧⣠⣿⣿⠆⠀⠈⣸⢃⠛⡄⠛⠃⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡴⠋⠠⠆⠀⠀⠈⠀⠜⠋⠁⢀⣶⣀⣥⣤⡶⢿⣿
⠿⣿⠠⣀⠀⠏⠀⢹⣿⡿⠃⢀⠀⢀⣿⡿⠀⠀⠀⠀⡼⡋⠀⣠⠘⠘⠃⠀⠀⠀⠀⠄⠀⠠⢠⠮⠃⠈⠏⠇⠀⠀⠀⠀⠀⠘⡇⠀⠘⢿⠿⠿⣳⣶⠿
⠀⢿⣿⣿⢷⣦⣤⣾⡟⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⡸⠁⠉⠃⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⠀⠀⠈⠓⡀⠀⠀⠀⢁⣠⣤⡀⠀⢀⣾⣿⡦⢰
⣀⠈⢿⣿⣷⣤⣭⣿⡇⠀⠀⡀⢴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠐⠀⠀⠀⠀⢀⡄⠘⠂⠀⠀⢀⠀⠀⠈⢠⣗⣄⣰⡴⢾⣿⣿⣧⠀⠘⠟⢿⣷⣿
⣿⣿⣥⣿⡿⡿⣿⣿⠧⣤⡾⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠈⠀⠤⠄⠀⠀⠠⣿⠿⠿⠿⠿⣿⣇⠀⠘⢦⡙⣝
⣯⣿⣿⣿⣿⣿⣾⣄⡀⠻⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀⣦⠀⠀⠀⠉⠀⠀⠀⠙⢮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⠧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⢿⢿⣿⡀
⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢏⣅⠀⠈⠻⢎⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠟⡉⡞⠹⣿⣯⡛⠛⣿⠃⠀⠀⠁⠀⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐
⢈⠛⢀⣶⣬⣿⡟⢦⣍⠣⣔⠆⠀⠀⠾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⠁⠀⠀⠀⠀⠀⠀⢠⡆
⢸⡟⣾⣿⣿⣿⣿⣾⣝⣆⠈⣓⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣴⡇⠀⠀⢀⡠⠋⠁⠀⠀⠙⠦
⣻⣸⣿⣿⣿⡿⠛⠛⠻⠿⢻⣿⡃⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⣄⠀⠀⠀⠀⠀⡀⢀⣄
⣿⣿⠛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⣿⡟⠑⡷⣬⡀⣿⣿⣿⣿⢿⡈⢤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⢰⠀⠀⠀⣀⣬⡿⠀⠀⢀⣠⠐⢀⠀⡀⠈⠉
⢸⣤⣠⣻⣾⣿⣹⡿⢿⣛⠛⠉⣁⠾⠉⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⠀⢀⠆⡀⡉⠉⠻⣿⠃⠀⢀⡜⡧⢡⡈⢇⠀⣤⣄
⠹⣷⣿⣿⠻⣿⣟⠧⡄⠹⠷⣷⢿⣦⣤⡀⣀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⢀⣿⡯⠀⡘⢠⣸⣇⠀⠀⡟⠀⢀⣴⣿⡇⢻⣷⡈⢻⡄⣛
⡟⣿⣿⣿⢢⡄⢻⡄⣌⠐⠿⣿⣿⣭⣉⡉⣉⠀⠀⡀⠀⢦⡄⠁⠀⠀⠈⠁⠀⠙⡈⠀⠡⠃⠠⣦⣶⣿⠋⠈⠹⣿⣿⠁⢀⣰⡈⠛⢜⢨⣿⡇⣺⣿⠏
⣿⡀⠻⢿⣿⣿⡾⣧⣈⣵⡾⠿⣿⣿⣏⣯⡍⠙⠓⠀⠀⢨⠀⠀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⢀⣹⣿⠏⢀⠀⠀⢹⣿⡠⢠⣎⢻⣿⣮⡉⢿⣿⠏⢘⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠌⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣦⣄⠀⣿⠀⣠⣴⠞⠃⠀⠀⠀⣰⢤⡹⣽⢃⣤⡆⠈⠀⠀⠀⠀⠀⠀⠶⠀⠰⠇
⠀⠀⠀⠀⠀⠰⣶⠆⠀⠀⠀⠀⠀⠀⠂⠀⢉⣓⢾⣞⡉⠀⢐⠀⠀⠀⠀⢈⣛⣻⣿⣟⣋⡁⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠠⡷
⠀⠀⢂⠨⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣤⠾⠋⠁⣾⠀⠙⠻⢦⡀⠀⠀⠀⠻⠞⢱⣻⡜⠾⠇⠀⠀⠀⠀⠀⠀⢐⡴⠀⠰⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠤⣤⢠⣬⣼⣥⡤⢤⡤⠀⠀⠀⠀⠠⠄⠈⠀⠉⠀⠄⠠⠀⠀⠀⢀⡀⢀⢀⠀⠄⠀⢀⠀⠀⠀⠀⢀⠀⠀⠻⡦⠀⣴⠦⠄
⠀⠀⠘⢣⣿⣯⣝⣿⣿⡜⠁⠀⠀⠀⠀⠂⠀⠀⣤⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡉⠀⢉⡤⠀⠀⠀⠀⠀⠘⠶⠖⠀⠀⠀⠉
⠀⠀⢰⣮⢟⣿⣽⣿⡿⢴⡆⠀⠀⠀⠀⠂⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⡄⠡⢔⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⣰⠄⢀⡀⠘⠛⢧
⠀⠀⠉⠉⠀⠡⣭⡍⠀⠉⠉⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠃⠭⠘⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⢓⣿⢿⢠⡄⣠⡄
⠀⠀⠀⠀⠠⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠑⢣⣄⣻⣠⡄⠪⡥⠀⠀⠀⠀⠀⠠⠠⠡⠀⠀⠀⠀⠀⠀⠀⢩⢻⡶⣍⣹⣩⡶⣟⣯⠁
⠀⠀⠀⠀⠠⠘⠛⠣⠀⠀⠀⠀⠀⠀⠴⢄⡠⠜⢻⠳⢆⡠⠦⠀⠀⠀⠀⠀⠀⠡⠡⠌⠀⠀⠀⠀⠀⠀⠰⣰⣥⠞⣿⠳⣮⣇⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠆⡀⢭⢀⠰⠮⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠫⠆⡹⣿⢾⠱⠏⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠍
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳
⠀⠰⣶⢫⠧⣩⠉⣏⠴⡜⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠢⣤⣾⢾⣆⣤⠴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢙⡛⢴⢽⣿⡯⡦⢚⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⣽⣻⣯⣿⠋⠀⠀⠀⠀⠀⡀
⠀⢀⣮⣱⡄⠾⠭⠗⣀⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⠷⢾⣹⡷⢿⣑⣄
⠀⠀⠉⠉⠁⢏⣒⡟⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣶⡶⣶⡶⠶⠶⠶⠶⠶⣶⣶⡶⢶⣶⣶⠶⠶⠶⠶⠶⢶⣶⢶⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠉⠁⠀⠈⠙⢦⣠⡴⠖⠛⠉⠀⠀⠀⠀⠉⠛⠲⢦⣄⡴⠋⠁⠀⠈⠉⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣿⠀⠀⠀⠀⣠⡴⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡟⢦⣄⠀⠀⠀⠀⣯⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣿⠀⢀⣤⠞⠁⠀⢸⡇⠀⠈⠳⣤⡀⠀⠀⢀⣠⠞⠁⠀⢸⡇⠀⠈⠳⣤⡀⠀⣟⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣏⣀⣀⣀⣽⣶⣏⣀⣀⣀⣀⣼⣄⣀⣀⣀⣈⣹⣦⣴⣏⣁⣀⣀⣀⣠⣧⣀⣀⣀⣀⣹⣶⣧⣀⣀⣀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢠⣾⠁⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⣿⣦⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣴⣿⠃⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⣯⠳⣄⠀⠀⠈⣧⠀⠀⠀⢀⡇⢸⡀⠀⠀⠀⣼⠁⠀⠀⣠⠞⣽⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠘⣇⠙⢦⡀⠀⠸⡆⠀⠀⢸⠃⠘⡇⠀⠀⢰⠇⠀⢀⡴⠋⣸⠃⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⣆⠈⠳⣄⠀⢻⡀⠀⣾⠀⠀⣷⠀⢀⡟⠀⣠⠞⠁⣰⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣆⠀⠙⢦⡘⣧⠀⡟⠀⠀⢻⠀⣼⢃⡴⠋⠀⣰⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠈⠳⣽⣼⡇⠀⠀⢸⣧⣧⠞⠁⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⢿⠀⠀⠀⠀⡿⠃⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠘⣇⠀⠀⣸⠃⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢹⡄⢠⡏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣷⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠄⢐⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠠⠠⠸⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⣀⠠⠀⠀⠀⠀⠀⡠⠂⠐
⠀⠀⠀⠀⠀⠁⢀⡐⠀⠀⢄⢤⡀⠀⡆⡌⠄⠐⠈⠠⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠀⢈⠊⠀⠀⢄⠀⠐⠀⠂⠈⠄⣀⠠⢀⠌⠁⠂
⠀⠀⠀⠀⢀⢀⠀⠁⡀⠀⢈⡓⠈⠈⠁⢂⡀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⢐⠀⠀⠀⢀⠆⠂⢆⠀⠈⠄⠀⠀⠐⠀⡂⠈
⠀⠀⠀⠀⠀⠀⠆⢀⡂⠀⠂⠄⠀⠀⠈⡀⠎⠁⠂⠑⠈⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢈⠔⠁⠀⠠⠀⠀⠰⠀⠀⠀⠠⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⡥⠖⠆⠍⠢⠀⠀⠁⠄⡀⠠⡀⠀⠀⠀⠒⠁⢈⠄⠀⠀⡀⠀⠀⠁⠈⠀⠀⠂⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠂⢀⠉⡄⠀⠀⠄⠀⠀⠀⠄⠂⠃⠀⠈⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠠⠈⠀⠄⢀⠀⠑⡠⠂⡄⠤⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠂⠢⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⢀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠠⢀⠈⠀⠰⠐⠴⠈⠆⠎⡄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⢀⡠⠀⡀⠀⠈⢀⠘⠁⠀⠀⠀⠀⠘⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠀⠂⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠾⠂⠀⠀⠀⠀⠸⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⠀⡈⠀⠃⠀⠀⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⢠⠸⡳⠁⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠠⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣴⡿⠟⠉⠀⠀⠀⢀⣀⣤⡤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⠟⠉⠀⠀⢀⣠⣴⡾⠟⠋⠁
⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⠟⢡⡾⠋⠁⠀⣀⡴⠞⠛⠉
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⠏⣴⠏⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⢃⡾⠁⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⢇⡞⠀⠀⠀⢀⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣷⣶
⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡿⣼⠁⠀⢀⡴⠋⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻
⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⡇⡇⠀⢠⠏⠀⠀⠀⢉⣀⣀⡀⠀⠀⠉⠙⠲⢤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⣿⣿⡇⡇⠀⡞⠀⠀⣰⣾⣿⡿⠿⣿⣿⡦⣄⠀⠀⠀⠉⠳⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣷⣳⠀⢣⠀⢸⣿⣿⣿⣷⣖⣶⣝⣿⣮⢷⡀⠀⠀⠀⠀⠙⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣧⡈⢦⡈⠻⣭⣥⣹⣿⣿⣿⡞⣿⣧⢿⡀⠘⣆⠀⠀⠈⠻⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣿⣶⣿⣷⣶⣿⢿⣿⣿⣿⣿⣿⣿⠸⣧⠀⠸⣇⠀⠀⠀⠘⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣿⣿⣭⣷⣿⡿⣻⣿⡏⣿⣿⠇⣿⠀⠀⢿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣼⣿⡿⣹⣿⣿⢀⣿⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣛⠛⠛⠛⠛⣛⣋⣭⣴⣾⣿⣿⡿⣱⣿⣿⡏⢸⣿⠀⠀⢸⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⣿⡿⢀⣿⡟⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⡿⠁⣼⣿⠃⠀⠀⢸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣵⣾⣿⣿⣿⡿⠁⣼⣿⡏⠀⠀⠀⣼⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣥⣾⣿⣿⣿⣿⣿⠟⠀⣼⣿⡟⠀⠀⠀⢀⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⣩⣴⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⡿⠁⠀⠀⠀⣼⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢹⣿⠁⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣶⣄⢸⣿⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⣀⠀⠀⠀⠀⠰⣿⡀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⢸⣿⠀⠀⠀⢴⡆⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣿⡇⠀⣸⣿⠁⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣨⣿⣆⡀⠀⣿⡇⠀⠀⠀⢠⣤⠀⠀⠀⢸⣿⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⣸⣿⣴⡾⠟⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠙⠿⣷⣿⣧⠀⠀⠀⠀⠀⣤⡀⠀⢸⣿⠀⠀⣰⡶⠀⠀⠀⢀⣠⣶⡿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⢿⣦⣄⡀⠀⠙⣿⣄⢸⣿⠀⣰⡿⠁⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠉⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣜⣿⣾⣿⣴⣿⣷⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⢀⣀⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠶⠀⠰⠆⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠃⠈⠉⠉⢉⣩⣿⢿⣿⣿⣿⡿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⢁⣾⠟⣿⡿⣿⡄⠉⠛⢿⣶⣄⡀⠀⠀⠀⠀⢀⣠⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣶⣶⣶⡿⠟⠉⠀⠀⢠⣾⠏⠀⣿⡇⠘⢿⣆⠀⠀⠈⠙⠻⢷⣶⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣴⣾⠟⣿⡿⠁⠀⠀⠀⠀⠘⠋⠀⠀⣿⡇⠀⠈⠉⣀⠀⠀⠀⠀⠀⢹⣿⠿⣷⣦⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⣿⡏⠀⢠⣿⠃⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⡇⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⣿⡄⠀⠉⢿⣏⠉⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⡾⠟⠀⠀⢸⣿⠀⠀⠀⠀⠰⠆⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠺⠇⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⣿⡇⠈⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣿⣇⡀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠆⡀
⠉⠈⠀⠀⣤⣤⠤⠤⠤⠤⠠⠠⢄⣄⣀⡀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⢴⢦⡈
⠀⠀⠀⠀⡟⡌⠑⠢⢄⡀⠀⠀⢀⡴⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⢟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⣀⢏⣀⠽⣦⡀
⠀⠀⠀⠀⡇⠘⡄⠀⠀⠈⢑⣶⣏⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢟⡺⢗⡺⣗⡟⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⢸⠀⢠⠟⢧⡀⢰⠁⣙⣆
⣖⣲⠀⠀⡇⠀⠘⡄⢀⡴⠋⠈⡆⠈⠑⢺⠅⢐⠊⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⢠⡀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⢸⢠⠏⠀⣀⡽⢿⡋⠁⡆
⠈⠁⠀⠀⡇⠀⢀⡼⡯⠤⢄⣀⢸⣀⠔⠁⠐⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣖⣋⣁⣀⣀⣙⣦⠃
⠀⠀⠀⠀⣇⡴⠋⠀⠘⡄⠀⢀⠝⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠒⠒⠒⠤⠾⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⢀⠴⠦⡀⠀⠀⠀⠀⠀⢠⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⣯⠟⠗⠪⣦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢁⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢧⡟⣟⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡏⠳⢄⡀
⠀⠀⡀⢆⡀⠀⠀⠀⠀⠀⡰⠛⡆⡸⠙⡄⡸⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⡇⠀⢀⣉⣦⠀⠀⠀⡴
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⡗⠒⢺⠓⠒⢺⠗⠒⡺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣀⡠⠴⡷⢍⡁⠀⠰⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢇⠀⡎⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⣴⡟⠒⠋⠉⠀⠀⠀⡇⠀⠉⠓⣴
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠈⠺⣶⠞⠁⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠓⠲⠤⢄⣀⣇⡤⠖⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡠⠚⢏⠉⠒⠒⠒⠤⣤⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⡏⠐⠲⠤⣬⠄⡐⠂
⠀⢰⡶⣒⢒⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠈⢦⠀⠀⣠⠞⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡇⢀⡠⠞⠁⢠⡉⠁
⠀⢸⢱⣴⢻⣲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⡠⠊⢻⠉⠙⠒⠲⠬⣧⠞⠁⠀⠀⡇⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠙⠗⠉⠀⠀⠀⠀⠁
⠀⠸⠯⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⠀⢠⣎⠀⠀⠈⡇⠀⠀⣠⠞⠉⢆⠀⠀⢀⡇⠀⠀⠀⠙⠊
⠀⠀⠀⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡀⠉⠒⢤⣸⣠⠞⠁⠀⠀⠈⢧⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠞⠉⠒⠤⣀⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠔⠀⠀⠀⠀⢰⡷⠾⣑⡷⡆
⢠⠶⡄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢛⣠⠞⠁⠀⠀⠀⠀⠈⠉⠒⠤⣈⢦⡇⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢸⣏⣶⣛⣯⠇
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠒⠒⠒⠒⠒⠚⠛⠃⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠛⠸⠞⢁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣖⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠔⡹⠙⡝⢦⡀⠀⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⢠⡏⢦⣀⣠⠴⠚⡽⡇⠀⠀⠀⠈⠁⠀⠀⠀⢤⠦⠆⠀⠀⠀⠀⠀⠈⠠⠈⠀⠀⠀⢀⠔⠁⢠⠇⠀⢱⠀⠙⢦⡀
⠀⣤⠀⢸⡤⠒⡟⢢⡀⡼⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣯⠟⣽⠳⡀⠀⠀⠀⠀⠀⠀⠰⡇⠤⠤⣾⠠⠤⢰⣷⠠⠄⣿
⠀⠐⢣⠀⠙⢾⡤⠒⡿⢧⡀⡇⠀⠀⢈⡁⡋⠀⠀⠀⠈⢧⡹⡁⣏⡽⠃⠀⠀⠀⠀⠀⠀⠀⠙⢆⡸⠀⢣⣀⠎⠘⣄⡔⠁⠀⠀⠀⢰⢱⠄
⠀⠀⠀⠀⠀⠀⠙⠾⠥⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣼⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣻⡶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣶⣬⣙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⣉⣤⣴⣶⣾⠿⠿⠿⠿⠿⠿⢶⣶⣤⣄⡉⠛⠿⣿⣦⡈⠛⢦⡀
⠀⠀⠀⠀⠀⣠⣾⡿⢟⣡⣶⡿⠟⠋⠉⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠙⠻⢷⣦⣈⠛⢿⣦⡀⠙⢦⡀
⠀⠀⠀⢀⣾⣿⠟⣵⣿⡿⠋⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠻⣷⣄⠙⢿⣦⠀⠹⣆
⠀⠀⢠⣿⡿⢣⣾⣿⠋⣠⣴⣿⣿⣿⣿⣿⠿⠟⢛⣛⣛⣛⣛⡛⠿⢿⣿⣿⣷⣄⠀⠈⠻⣧⡈⢻⣧⡀⠘⣧
⠀⢠⣿⡿⢡⣿⣿⣷⣾⠟⣫⣿⡿⠛⣉⣴⣶⡿⠟⠛⠉⠉⠉⠛⠛⠶⣬⡙⢿⣿⣷⣄⠀⠙⣿⡄⠹⣷⡀⠘⣧
⢀⣿⣿⢡⣿⣿⣿⠟⢁⣾⡿⠋⣠⣾⡿⠛⠁⢀⣠⣴⣶⣶⣶⣶⣤⣀⠀⠙⢦⡙⣿⣿⣆⠀⠘⣿⡀⢻⣧⠀⢹
⣸⣿⣏⣾⣿⡿⠁⣰⡿⠋⣠⣾⣿⠏⠀⢀⣴⣿⡿⢟⣻⡭⠭⣝⣻⢿⣷⣆⠀⠻⡜⣿⣿⡆⠀⢹⣇⠘⣿⡄
⣿⣿⣿⣿⡟⠀⣼⡿⠁⣰⣿⣿⠃⠀⣰⣿⣿⢋⡔⢋⣠⣶⣶⣦⣌⠳⡝⣿⣧⠀⢻⢹⣿⣧⠀⠘⣿⠀⣿⡇
⣿⣿⣿⣿⠁⣸⡿⠁⣰⣿⣿⡏⠀⢰⣿⣿⢣⠏⢠⡿⣿⡿⢋⡙⢿⣧⢸⢸⣿⡇⢸⣿⣿⣿⠀⢀⣿⠀⣿⡇
⣿⣿⣿⡇⢠⣿⠃⠀⣿⣿⣿⠁⠀⣼⣿⣿⢸⠀⣿⡇⣿⣇⢇⠶⠿⢃⢞⣾⣿⠃⣼⣿⣿⠇⠀⣸⡇⢸⣿⡇⢸
⢿⣿⣿⠀⢸⣿⠀⢸⣿⣿⣿⠀⠀⢻⣿⣿⢸⡀⢹⣿⣝⢿⣷⣭⣭⣷⣿⡿⢃⣼⣿⣿⠏⠀⢠⡟⢠⣿⣿⣡⣿
⠸⣿⣿⠀⣿⡇⠀⢸⣿⣿⣿⡇⠀⠸⣿⣿⣆⢷⡀⠹⣿⣷⣯⣽⣿⣭⣥⣶⣿⣿⠟⠁⢀⣴⠟⣠⣿⣿⣿⣿⠃
⠀⢿⣿⠀⢿⡇⠀⠸⣿⣿⣿⣷⠀⠀⢻⣿⣿⣦⡙⢤⡀⠙⠛⠿⠿⠿⠿⠛⠋⠁⣀⣴⠟⣡⣾⣿⣿⣿⡿⠃
⠀⠈⣿⡆⢸⣿⠀⠀⢿⣿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣦⣝⡓⠦⢤⣤⣤⣤⠴⠶⢛⣉⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠘⣷⠀⢿⡄⠀⠘⣿⣿⣿⣿⣷⣄⠀⠈⠻⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢀⡴⠂
⠀⠀⠀⠈⢧⠈⢷⡀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⢀⣠⣶⠏
⠀⠀⠀⠀⠀⠁⠈⢷⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠓⠒⠒⠦⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡤⠴⠖⠒⠚⠉⠉⠙⢦⡀
⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠻⡗⠲⠦⠤⣤⣀⣀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⣀⣀⣠⠤⠴⠖⢺
⠀⠙⣆⠀⠀⠀⠀⠈⠉⠉⠓⢿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡿⠚⠉⠉⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠸⡄⠀⠀⠀⠀⢠⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢳⠀⠀⠀⠀⡞⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣇⠀⠀⣸⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡄⢠⣇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠴⠶⠒⠚⢻⡿⢍⠉⠉⠉⠉⠷⣄⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠉⡠⢺⠳⠀⠀⠀⠀⢀⠆⢻⠀⠱⣄⠀⠀⢁⠈⠳⣄⠀⠀⡴⠋
⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡆⠀⢠⠊⠀⡏⠀⢣⠀⠀⢀⠎⠀⠘⡇⠀⠈⠳⣄⠘⠀⠀⠈⠳⣄
⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⣠⠞⠁⠰⢀⠔⠁⠀⢸⠃⠀⠈⡄⠀⠌⠀⠀⠀⢿⠀⠀⠀⢈⣢⣦⡤⠶⠒⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡼⠁⠀⢀⡷⠁⠀⠀⢀⡟⠀⢀⣀⣰⣜⣀⣤⣤⠤⢼⡶⠚⠛⠉⡹⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡛⠛⠛⠻⡛⠉⠉⠙⢯⠉⠉⠉⠉⢃⠀⠀⠀⠀⣸⠀⠀⠀⠠⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠑⢄⠀⠀⠈⢧⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⢠⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠱⡄⠀⠈⢧⠀⠀⠀⡆⠀⠀⢰⠇⠀⢠⠃⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⠢⡀⠈⢧⠀⠀⢁⠀⠀⣼⠀⢀⠂⣰⠋⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⡐⢄⠈⢧⠀⠘⠀⢀⡏⢀⢎⡼⠁⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⠌⢧⠀⠆⢸⠃⣬⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⣷⣀⣾⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠁

⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠿⠛⠛⠛⠛⠛⠋⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄
⣠⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⣿⡿⠋⠀⠀⠀⠀⠀⣀⣴⣿⡿⠟⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡀⠀⠀⠀⠀⠉⠻⣿⣿⣦
⠋⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⢿⣷⣦⣀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⢀⣤⣾⡿⠟⠉⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠈⠛⢿⣷⣦⡀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠘
⠀⠀⣴⣿⡿⠛⠁⠀⠀⠀⣠⣴⣿⠟⠉⠀⠀⠀⣠⣴⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣷⣤⡀⠀⠀⠈⠻⢿⣶⣄⠀⠀⠀⠈⠻⣿⣷⡀
⠀⣼⣿⡟⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⣠⣴⡿⠛⠉⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣦⣄⠀⠀⠙⠻⣷⣄⡀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠘⣿⣷
⣰⣿⡟⠀⠀⠀⢠⣿⡟⠋⠀⠀⢀⣤⣾⠟⠉⠀⢀⣠⣶⠟⠋⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠙⠿⣦⣀⠀⠈⠙⢿⣦⣄⠀⠀⠈⢿⣷⠀⠀⠀⠹⣿⣧
⣿⡿⠁⠀⠀⢀⣿⡿⠀⠀⢀⣴⡿⠋⠁⠀⣀⣴⠿⠋⠀⢀⣴⠾⠋⠙⠛⠛⠉⠉⠉⠉⠙⠷⣤⡀⠈⠙⢷⣤⡀⠀⠉⠻⣷⡀⠀⠈⣿⣧⠀⠀⠀⢹⣿⣇
⣿⠁⠀⠀⠀⣼⣿⠁⠀⠀⣼⡿⠀⠀⣠⡾⠛⠁⢀⣠⡾⠛⠁⣠⡶⠛⠛⠛⠛⠛⠛⠛⠷⣄⠈⠛⢶⣄⡀⠉⠻⣶⡀⠀⢻⣧⠀⠀⠘⣿⣇⠀⠀⠀⢻⣿⡆
⠃⠀⠀⠀⣼⣿⠃⠀⠀⣰⣿⠁⠀⢰⡿⠀⢀⣶⠟⠁⣠⡴⠞⢁⣠⠞⣛⠛⠛⠛⣛⠛⢦⡈⠻⢦⣄⠈⠻⣦⠀⠹⣧⠀⠀⢿⣇⠀⠀⢹⣿⡆⠀⠀⠘⣿⣿
⠀⠀⠀⢰⣿⡏⠀⠀⢠⣿⠇⠀⢀⣿⠃⠀⣼⠇⢀⡾⠉⣠⠶⢋⣡⠞⣩⢭⣍⣭⢭⡑⢦⡙⠲⢤⠈⢷⠀⢹⡆⠀⢻⡆⠀⠘⣿⡄⠀⠀⢿⣷⠀⠀⠀⢹⣿
⠀⠀⠀⣾⣿⠁⠀⠀⣾⡟⠀⠀⣼⡏⠀⢰⡟⠀⣸⠃⢸⠃⡶⢫⠴⣚⠕⣵⣒⣊⡱⢝⡲⢍⢳⠘⡇⠸⣇⠈⣿⡀⠈⣿⡀⠀⢹⣷⠀⠀⠸⣿⡆⠀⠀⠘⣿
⠀⠀⢠⣿⡏⠀⠀⢰⣿⠃⠀⢰⣿⠀⢀⣿⠁⢠⡏⢀⡟⢠⠇⡾⡸⢰⢭⣺⣷⣿⣯⡵⢮⠸⡘⣆⢻⡄⢻⡄⠸⣧⠀⢹⣇⠀⠈⣿⡆⠀⠀⢿⣷⠀⠀⠀⢻
⠀⠀⣼⣿⠁⠀⠀⣾⡏⠀⠀⣾⡇⠀⢼⡇⠀⣿⠀⣾⠁⡏⢸⢱⠳⡷⣾⣿⡉⢹⣿⠶⢇⡗⡵⣸⢂⡷⢀⡗⠀⣿⠀⢀⣿⠀⠀⣽⡇⠀⠀⣸⣿⠀⠀⠀⣸
⠀⠀⢹⣿⡄⠀⠀⢹⣷⠀⠀⢹⣧⠀⠘⣷⠀⢹⡆⠸⣆⠹⡌⣧⢡⢱⠞⣻⣿⣿⣟⠿⣬⢸⢰⠇⡼⠁⡾⠁⣸⠇⠀⣼⠇⠀⢰⣿⠁⠀⢀⣿⡇⠀⠀⠀⣿
⠀⠀⠈⣿⣧⠀⠀⠈⣿⡆⠀⠈⣿⡄⠀⢻⡆⠀⢿⡀⢹⡀⣧⠸⢌⡓⢌⡪⠑⠚⠵⡩⢒⣩⠞⣠⡇⢸⠇⢠⡟⠀⢰⡟⠀⠀⣾⡇⠀⠀⣸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⢻⣿⡄⠀⠀⢹⣷⠀⠀⢸⣷⠀⠈⣿⡀⠘⣇⠈⢧⣌⠙⠦⣌⠳⡭⠭⠬⠭⠴⢋⡴⠚⢉⣴⠟⠀⣾⠃⢀⣿⠁⠀⣸⡿⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠘⣿⣧⠀⠀⠈⣿⣇⠀⠀⢻⣇⠀⠸⣧⠀⠙⠷⣄⡈⠛⢦⣈⠓⠒⠒⠒⠒⠒⢋⣤⠞⠉⣀⣴⠞⠁⢀⣼⡇⠀⢠⣿⠃⠀⢀⣾⡟⠀⠀⠀⣸⣿⡏
⡆⠀⠀⠀⢹⣿⣆⠀⠀⠘⣿⡆⠀⠈⣿⣄⠀⠙⠻⣦⣀⠈⠛⢶⣄⠙⠛⠛⠛⠛⠛⠛⠋⢁⣤⠞⠋⠀⣠⣶⠟⠉⠀⣠⣿⠇⠀⠀⣼⣿⠁⠀⠀⢰⣿⡟
⣿⡄⠀⠀⠀⢻⣿⡄⠀⠀⠹⣿⡄⠀⠈⠻⣷⣄⡀⠈⠙⠷⣤⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⣀⣴⠿⠋⠀⢀⣤⣾⠟⠁⠀⠀⣸⣿⠃⠀⠀⢠⣿⡿
⣿⣷⡀⠀⠀⠀⢿⣿⡀⠀⠀⠻⢿⣦⣀⠀⠀⠙⠿⣦⣄⠀⠈⠛⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠋⠁⠀⣠⣴⠿⠋⠀⠀⢀⣴⣾⠟⠃⠀⠀⢀⣿⣿⠁
⢹⣿⣷⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠙⠿⣷⣄⠀⠀⠈⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠛⠁⠀⠀⣠⣶⡿⠛⠁⠀⠀⢀⣤⣾⡿⠃
⠀⢿⣿⣧⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠈⠻⢿⣶⣄⡀⠀⠈⠛⠛⠛⠛⠛⠻⠿⠛⠛⠛⠛⠛⠛⠁⠀⠀⣠⣴⣾⠿⠋⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⢠
⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠉⠻⢿⣶⣄⣀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣠⣴⣿⠟⠋⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⣠⣶⣿
⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠀⠀⠀⢀⣠⣴⣿⡿⠛⠁⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋
⣷⣆⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠁
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠴⣀⠀⡗⢀⡤⠆⠀⠀⠀⠠⠀⢀⠀⢀⠀⠀⠀⠀⢠⣶⡞⣟⢳⣶⡄⠀⠀⠀⠾⣷⣿⣿⣶⡦
⠀⠀⠀⠀⠀⣀⠑⡷⢀⡀⠀⠀⠀⠐⠀⠀⠻⠢⠀⠀⠀⠀⠀⢠⣭⡜⠿⢧⣽⡄⠀⠀⠀⣴⡿⣿⣿⣿⣦
⠀⠀⠀⠀⠛⠁⠀⡧⠀⠑⠂⠀⠀⠀⠈⠀⠠⠀⡀⠁⠀⠀⠀⠈⠙⠱⣿⠎⠙⠁⠀⠀⠀⠀⠀⠻⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠀⠀⣅⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠉⠀⣤⡄⠀⠀⠀⢠⠄⠀⡅⠀⢤
⠀⠀⠀⠀⠀⢘⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢀⣀⠀⠗⠀⣀⡀⠀⠀⠀⢀⡀⠐⠇
⠀⠀⠀⠀⠐⠈⠉⠛⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣦⠀⠉⠁⠀⠀⠀⠈⠁⠀⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⣰⡀⠙⠏⢰⡄⠀⠀⠀⠀⢠⣤⣿⣤⡄⠀⠀⠀⠀⠰⣶⢘⡛⣴⣶
⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⣉⡀⠜⠓⢤⣼⠀⠀⠀⠀⠠⠿⣿⡿⠇⡀⠀⠀⠀⢠⣷⡘⡟⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢤⡦⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠸⡿⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠻⠦⡄⢘⡃⣤⠞⠇⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⢀⢀⡄⠳⠜⣤⣀⡀⠀⠀⠀⠀⠀⠣⠼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠚⠊⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⢰⡷⠂⠀⡀⠀⠀⠀⠀⢦⠀⠀⡰⠁⠀⠀⠀⢀⠀⠀⢻⡇⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠰⢫⢤⠖⠛⢦⡞⠹⠂⠀⠀⠀⠀⣱⢤⠁⠀⠀⠀⠀⠛⠳⢦⠹⢣⡴⠟⠃⠀⠀⠑⠂⣤⣦⡀⠰⠂
⠀⠀⠀⠀⣀⣸⣄⢛⣸⢇⢤⡀⠈⠉⠉⠉⡳⠺⡁⠉⠉⠁⠀⣀⣤⠶⢠⡐⠶⣤⡀⠀⠀⣀⠀⠛⡿⠓⢀⡀
⠀⠀⠀⠈⠓⠁⢈⣽⡀⠀⠋⠀⠀⠀⠀⡜⠀⠀⠱⡄⠀⠀⠀⠈⠁⠀⣼⡅⠀⠈⠁⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠃⠉⠁⢈⣦⢔⠂⠁⠀⠀⠉⠐⢢⣴⡁⠈⠉⠙⠛⢦⣄
⠀⠀⠀⠀⠀⣠⣖⣫⣋⣰⣀⣤⣒⣉⣠⣂⣀⣁⣢⣀⣀⣄⣊⣁⣈⣄⣉⣒⣤⣀⣇⣙⣝⣲⣄
⠀⠀⠀⠀⠀⠙⠧⣍⠢⡈⠳⣄⠀⠀⠈⠅⠀⠀⠀⢈⡁⠀⠀⠀⢠⠋⠀⠀⣠⠟⢁⠔⣩⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢦⡙⠷⡄⠀⠘⡄⠀⠀⡈⢁⠀⠀⢀⠂⠀⣠⡾⢋⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⢪⠢⡀⠘⡀⠀⡇⢸⠀⢀⠎⢀⠔⡕⣡⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣷⡈⠢⡱⠀⠄⠀⠀⣌⠔⢁⣾⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⡈⢷⠀⠀⡾⢁⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⣸⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⣿⣡⠄⢄⢸⣇⡤⠀⠀⠀⡆⣶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠑⢄⠀⢹⡏⢀⡴⠃⢀⡿⠯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⢰⠈⠀⣤⠑⢼⡷⢋⣄⠀⠈⡆⠀⢰⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢤⣠⠀⡄⠠⠤⠷⢇⠀⢸⠀⠘⣿⠇⣸⣇⠸⡿⠀⠀⡇⢀⡼⠯⠤⠄
⠀⠀⠀⠀⠀⠀⢘⣛⣷⣇⢀⣀⣀⣠⣵⣾⠀⠀⡠⠊⢸⡏⠳⣄⠀⢀⣷⣋⣀⣀⣀⡀⠀⢀⡔⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⡱⢎⠀⢠⢾⣧⡀⢈⡵⢏⠀⠀⠀⣀⠀⠐⠚⡻⣟⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣄⠈⠳⣄⠺⠿⠗⣠⠞⠁⢀⡝⢇⢸⣇⡽⠫⡀⠀⠑⢄⠻⠿⠛⣠⠊⠀⡨
⠀⠀⠀⠀⠀⠰⠶⠾⡷⠶⠾⡷⠶⢾⠷⠶⢶⡷⠶⢶⣿⣿⠶⠶⣾⠷⠶⢾⡷⠶⢾⡶⠶⢾⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⡊⠀⡠⠋⣤⣶⣦⠑⢄⠀⢉⡶⣋⢸⡇⢱⣞⠁⢀⡴⠋⢴⣾⡦⠙⢦⡀⠙
⠀⠀⠀⠀⢀⣀⣦⣽⣮⡤⠀⠀⠉⠀⠀⢀⡵⢋⡀⠈⢻⡷⠃⠀⡱⢎⠀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠋⠜⠁⠀⠈⠉⠉⢉⡽⣿⠀⠀⠙⢦⣸⣇⡠⠊⠀⠀⡟⢏⠉⠉⠉⠀⢹⢿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⡿⡏⠀⢹⠀⠀⣾⡆⢹⡏⢰⣿⡄⠀⡇⠀⣷⢖⠒⠂⠘⠀⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠇⠀⠘⡀⠀⠙⣡⢾⡗⣄⠛⠀⠀⠇⠀⠸⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣲⣾⠁⢠⠞⠁⣸⣇⠀⠑⢄⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠿⠸⠀⠀⠀⠚⢹⡇⠑⠐⢋⣿⣍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠉⠉⣉⣉⣛⣛⣛⠛⠛⠛⠛⠛⠛⢛⣛⣛⡛⣛⣛⠛⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⢦⡀⠸⣿⡛⠛⠛⣻⣿⡿⢃⡴⢦⣄⠙⣿⣟⠛⠛⢛⣿⡿⢃⡴⣮⣻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⡾⠃⠈⠻⣆⠈⢷⣴⡾⢟⣡⡶⠋⠀⠀⠙⢷⣤⡙⢷⣤⣾⠏⣰⡟⠁⠈⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠟⣴⣿⣥⣤⣤⣤⣽⣷⡄⠉⣴⣿⣯⣤⣤⣤⣤⣤⣤⣽⣿⣦⠉⢁⣾⣯⣤⣤⣤⣤⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢰⣏⠀⣉⣉⣉⣉⣉⣉⣉⣩⡀⠀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⠀⢀⣉⣉⣉⣉⣉⣉⣩⣥⡈⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⣧⡉⠉⠉⠉⠉⠙⣷⠀⢻⡍⠉⠉⠁⠀⠈⠉⠉⠉⢩⡿⠀⣼⠁⠈⠉⠉⠉⢉⣽⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣦⡀⠀⠀⠀⢹⣧⠈⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣰⠇⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⢷⣄⠀⠀⠈⣿⡆⢸⣷⠀⠀⠀⠀⠀⢀⣿⠏⢠⡟⠀⠀⠀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⢷⣄⠀⠸⣿⡄⢿⣧⠀⠀⠀⠀⣾⡟⢀⣿⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⠻⣦⡀⢻⣷⠸⣿⡆⠀⠀⣼⡿⢁⣾⠇⣠⣾⢿⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣝⢿⣾⣿⣧⢹⣿⡄⢰⣿⠃⣾⣟⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡻⣿⣿⡆⢻⣷⣿⡏⣸⣿⡿⣫⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⡻⣿⠈⢿⡿⠀⠿⣫⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡴⠞⣉⠥⠖⠒⠒⠤⢍⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡔⡰⢋⡴⠋⣀⠴⠒⠒⠓⠲⢤⡉⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣾⠇⠀⡼⡹⢡⠏⣔⡝⠁⣤⠞⠋⠹⣷⣄⠹⡄⢳
⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⣿⠀⢰⢣⠇⡞⢸⡸⠀⣼⠁⠀⣰⣶⣬⣿⠀⡇⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⢸⢸⠀⡇⢿⢁⠀⢿⠀⠀⠘⠛⠛⠁⠜⠁⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡀⡇⠀⡇⢸⢻⠀⢸⡞⡇⢳⠸⡌⣆⠈⢧⣀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡰
⠀⠀⡀⠀⠀⡇⢣⠀⢳⠈⡞⡇⠈⢷⣿⡄⢣⠙⢎⠢⣀⠈⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⡴⠁⠀⠀⡠⠀⢠⠃⠀⠀⡰
⠀⠀⡇⠀⠀⢸⠸⡄⠘⡆⠱⡹⡄⠘⢿⣷⡄⠑⢤⡙⠢⢄⣀⠀⠀⠀⢀⣀⠤⠒⢁⠴⠊⠀⠀⢀⠔⠁⡰⠁⠀⠀⡰⠁
⠀⠀⠸⡀⠀⠀⢣⢳⡀⠘⣄⠱⡝⣆⠈⠻⣿⣦⣀⠉⠓⠲⠤⠭⠭⠭⠥⠤⠖⠊⠁⠀⠀⢀⠔⠁⣠⠎⠀⡀⢀⠜
⠀⠐⡄⢣⠀⢣⠈⢦⢳⡄⠘⢦⠘⢮⡳⣄⠈⠛⠿⣿⣶⣤⣤⣀⣀⣀⣀⡠⠤⢔⣊⠥⠊⢁⡠⠊⢁⡠⠊⡰⠋
⠀⠀⠹⡄⢣⠀⢣⠀⠳⡙⣦⡀⠳⣄⠙⠮⣗⢦⣄⡀⠉⠉⠛⠒⠒⠒⠒⠊⣉⣁⠠⠔⢊⣡⡤⠖⢉⠴⠋⠀⣀⠄
⠀⠀⠀⠙⡄⠱⡀⠑⣄⠘⢮⡻⣦⣀⠙⣦⣈⠑⠪⢝⣳⣶⣦⣤⣤⣤⣬⣭⣤⡶⠶⠟⢋⡡⠴⠊⠁⣀⡤⠊
⠀⠀⠀⠀⠈⢮⡻⣦⠈⠳⣄⠉⠪⣝⢷⣬⣛⠿⣶⣦⣤⣉⡉⠉⠉⠉⠁⠤⠤⠒⠒⠉⢁⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠙⢾⣿⣦⡈⠓⢄⡈⠙⠪⢝⣻⢶⣯⣽⣛⣳⡶⠶⢶⡶⠶⠶⠶⠞⠛⠋⠉⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⣻⢦⢌⡓⠦⣔⡨⢭⣒⡪⠭⢭⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣌⡓⠦⢍⣙⠒⠯⠭⣿⣓⣒⣒⣒⣒⣒⡚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢷⣦⣬⣉⣙⠒⠒⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⣀⡀⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢭⣉⣛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠿⠟⠓⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠂⠤⠤⠤⠤⠤⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣿⡇⠀⠀⢸⣿⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠙⢿⡇⠀⠀⢸⡿⠋⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢻⣷⡄⠀⠈⠃⠀⠀⠘⠁⠀⢠⣾⠟⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⣿⠟⠉⠻⣿⡄⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢠⣿⠟⠉⠻⣿⠀⣀⣤⣤⣀
⠀⠀⠀⠀⣼⡿⠋⠙⠻⢿⣿⣧⠀⠀⠹⣿⡄⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣼⡿⠁⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⡿⠟⠋⠙⢿⣧
⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠈⠛⠦⠀⠀⠹⣷⡄⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠏⠀⠀⠴⠛⠁⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⠈⣹⣿⣷⣦⣄⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣏⠁
⠀⠀⠀⠀⠀⣼⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣿⡇⠀⠀⢸⣿⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣇
⠀⠀⠀⠀⠀⠸⣿⣦⣤⣤⣤⣶⣶⣶⣶⣶⣦⣀⠀⠀⠈⠙⠻⡇⠀⠀⢸⠟⠋⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣤⣤⣤⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄
⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⠿⣶⣶⣶⣶⣶⡿⠛⠉⠀⠀⢀⣠⡆⠀⠀⢰⣄⡀⠀⠀⠉⠛⢿⣶⣶⣶⣶⣶⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⢺⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⣿⡇⠀⠀⢸⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗
⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠟⠀⠀⠀⠀⠀⢰⣿⠟⠋⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠙⠻⣿⡄⠀⠀⠀⠀⠀⠻⢿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⣀⡄⠀⠀⢠⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠸⣿⡄⠀⠀⢤⣀⠀⠀⠈⠙⠿⣷⡄
⠀⠀⠀⠀⢿⣇⡀⢀⣠⣴⣿⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⣴⡿⠃⠀⠀⠘⢿⣦⠀⠀⠀⠀⠹⣿⡄⠀⠀⢿⣷⣦⣄⡀⢀⣼⡿
⠀⠀⠀⠀⠈⠛⠿⠿⠛⠉⣿⣇⠀⣠⣿⠏⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⣨⣿⠉⠛⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⣰⣿⠋⠀⠀⡀⠀⠀⢀⠀⠀⠹⣿⣆⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⢀⣼⡇⠀⠀⢸⣧⡀⠀⢘⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⡿⣿⡇⠀⠀⢸⣿⢿⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣾⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠈⠀⠉⠀⠀⠈⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢩⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠉⠀⠀⠈⠁⠘



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⣀⣜⣿⣟⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢦⣿⡴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡂
⠀⠀⠀⣽⢿⣿⡈⢹⠋⣸⣿⢿⡅⠀⠀⠀⢻⣿⣶⣨⣿⣅⣰⣿⣿⠂⠀⠀⠀⢳⣾⣄⠀⣿⢀⣠⣷⡚⠀⠀⠀⠈⡿⣷⣆⢉⣏⢁⣶⡿⡟
⠀⠀⠀⠰⣏⣁⣹⣿⣿⣁⣉⡷⠀⠀⠀⠀⠀⣈⣙⣿⣿⣿⣏⣉⠀⠀⠀⠀⠀⣍⠀⣈⣽⣿⣯⡁⢀⣉⠀⠀⠀⠀⠀⣍⣈⣿⣩⣏⣀⡅
⠀⠀⠀⠽⣿⣿⢁⣼⣄⢸⣿⡾⠅⠀⠀⠀⡼⣿⠿⢙⣿⣍⠹⢿⢿⠄⠀⠀⠀⠼⢿⠉⠀⣿⠀⢙⡿⠧⠀⠀⠀⠠⢿⡟⠏⣀⣇⡀⠿⣷⠧
⠀⠀⠀⠀⠁⠈⠩⢾⠮⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⣿⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆

⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⢤⡀⣦⠙⢾⠞⢡⣆⣠⠄⠀⠀⠀⣴⡆⢿⠶⣿⡴⣿⢀⣦⠄⠀⠀⠠⣤⣴⠀⢙⣿⠋⢀⣆⣤⠀⠀⠀⠠⣤⣄⠀⣸⣿⡁⢀⣤⣤
⠀⠀⠀⢠⠽⠛⣦⠞⢦⡞⠻⢥⠀⠀⠀⠀⣉⡽⠿⢦⣿⡤⠿⢯⣉⠁⠀⠀⠀⠹⠛⣷⢯⣿⡽⡾⠛⠏⠀⠀⠀⠀⠙⠛⡿⣬⣯⡼⢿⠛⠁
⠀⠀⠀⠘⣳⣶⠛⢶⠞⢳⣶⡚⠀⠀⠀⠀⣍⣹⣶⠚⣿⠙⣶⣟⣉⡀⠀⠀⠀⣰⣤⡿⣟⣿⣻⢷⣴⣆⠀⠀⠀⠀⣠⣼⢷⢛⣟⢳⢿⣤⡄
⠀⠀⠀⠉⠁⠟⡤⢾⠶⡌⠇⠉⠁⠀⠀⠀⠛⠃⣾⠞⣿⠳⢿⠈⠟⠁⠀⠀⠈⠛⠛⠀⣠⣿⣄⠀⠋⠛⠀⠀⠀⠈⠉⠉⠀⢩⣿⡁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⢖⣒⡿⠛⠻⣿⡷⠶⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠻⠉⠉⠐⠀⠀⠀⠀⠈⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠂⢩⣽⣟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣤⣶⣿⣿⣿⣿⣿⣮⣟⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡤⠴⠖⠛⢉⣹⣴⠛⠋⠉⠁⠀⠀⠀⠈⠉⢉⣷⢦⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣯⣿⠁⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠚⠉⠀⠀⠀⠀⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⢀⣠⡴⣟⢿⣗⢛⡳⣄
⠀⠀⠀⢀⣤⡾⠛⠋⠛⣿⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⡅⠉⢸⡌⠛⢏⡛⣷⣄
⠀⢀⡴⠋⠄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠺⣿⣇⠀⠀⠤⠄⣀⣀⣄⣀⡀⠀⢤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣶⣴⣤⣀⡘⡇⠀⠀⠀⠈⢮⠳⣄
⣴⠋⠀⠀⠀⠀⠀⠀⡶⡏⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢀⣩⣽⣿⣿⣿⣿⣿⣟⠛⣋⠍⣿⣿⠿⣛⡹⠵⠛⠋⢽⢟⡷⠄⠀⠀⠀⢈⢧⠈⢳
⡇⢀⣡⡠⠐⠉⠀⡐⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⣀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢠⠾⠓⠀⠌⡔⠀⠀⠀⠀⠁⡇⠡⡀⠀⠑⠢⣬⣷⢸
⣿⠋⠁⠀⠀⠀⠌⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⣧⠀⠀⢼⣿⡿⠿⠛⡟⠋⢙⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡄⠀⠠⠜⢉⣿
⠈⠳⣌⠂⣀⠂⠀⠀⠀⢿⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⢴⡧⠀⣸⣿⣿⣿⣿⣿⣿⣷⣦⣀⠁⠀⠀⠀⢠⡅⠀⠀⠾⣆⣡⣠⡾⠋
⠀⠀⠈⠳⣼⡗⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⢶⣖⠂⠀⠂⣻⠑⣹⣿⣿⣿⣿⣿⡿⣗⣉⢿⣿⣷⣤⡀⠀⢘⠀⢠⠦⣄⣫⡿⠋
⠀⠀⠀⠀⠈⠻⣿⣶⣦⣬⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣏⣼⣿⡿⠉⣈⠼⠿⢻⢫⠟⢮⢟⠻⣿⣿⣷⣦⣴⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⣿⣷⣶⣦⣤⣄⣀⣚⣒⡒⠀⠠⠀⠄⠙⢿⣞⣽⣿⠿⠄⠥⠤⣤⠤⣀⢷⣾⣶⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⡻⣯⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣺⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡘⣎⠻⣟⢻⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠳⡀⠰⣵⡿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣌⡀⠀⠑⠉⠻⣶⣨⣿⢿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⡿⣋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠠⠘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠛⣿⣿⣿⣿⣿⣿⣟⢛⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣬⣩⣤⣭⣽⣭⣼⣏⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







⣿⣿⠿⢿⡿⢿⠿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⢤⡂⠀⠀⣄⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⡄⢤⠷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡤⡻⣄⠐⠈⢷⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣔⣀⣤⠬⠶⠒⠃⣁⠆⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⢶⣄⡀⡉⠙⠛⠓⣾⣾⠾⢲⠾⠿⠿⠿⠟⠋⠉⠉⠉⠉⠁⠁⠀⢀⡠⠟⠀⡈⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡖⢊⠛⣷⡦⡤⣄⡉⡀⡀⢀⡠⠀⠀⠀⢀⡀⢀⣀⣀⣤⢴⠴⠋⠁⠀⢰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣵⣀⡷⠀⠀⠀⠀⠀⠁⠀⠀⠐⠐⠛⠛⠉⠉⠉⢉⠀⢠⣀⣤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠈⠹⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠑⠚⠉⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣫⣄⠈⠙⠛⠓⠗⠒⠳⠒⢸⣀⣣⠴⠋⠁⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣈⡛⠞⠄⠉⠉⠐⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣮⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡶⠒⠛⠉⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣴⣳⡔⣄⡠⢠⣩⣈⣤⣰⣏⣠⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡛⠛⠛⠛⠛⡯⡼⢟⣉⠙⢉⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠀⠀⠀⣼⣿⢏⠚⠛⣂⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢋⠿⠵⢶⣶⣿⣿⡷⡷⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣼⣿⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣇⠀⢿⣿⠀⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢟⡨⣻⠀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣄⢹⡆⠿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⢽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡌⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⣼⣷⡤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣾⠁


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

⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀⢠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡰⢞⣡⠾⠛⣒⣒⣀⡀
⠀⠀⠀⣠⣦⠀⢸⣿⡇⢀⣾⡟⠁⣀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⢰⣧⢨⡞⣡⠟⣃⣤⠿⠿⠭⣭⣭⣓
⠀⠀⠀⢻⣿⣆⠀⢿⡇⢸⡟⢠⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣶⣀⡇⠘⣽⠃⣸⠟⣃⣠⣔⡶⠶⣍⢉⠻⡄
⠀⢠⣄⠀⠙⢿⣦⡈⢷⡸⡡⢋⠴⠶⠿⠿⠿⢿⣿⣧⠀⠀⣤⣨⠘⣿⠐⡿⣸⡇⣠⢿⣟⡢⡉⢢⡈⢻⢷⣌⠂
⠀⠸⣿⣿⣦⣄⣈⡛⠒⣁⠀⠀⢝⡛⠷⣶⣤⣀⠈⠉⠀⠀⣈⡙⣧⢸⣄⢇⠻⣇⠀⠋⠹⣳⢸⡆⢿⡆⣄⢹⡄
⠀⠀⠀⠈⠉⠉⠉⢉⣩⡵⢹⠎⣆⠹⣦⡈⠻⣿⣷⡄⠀⠀⠙⠻⣌⢃⠻⠿⣦⣘⡾⠶⠞⢋⣼⡁⢸⠇⣿⢀⠁
⠀⠀⠹⣿⣿⣿⠿⠛⠉⣰⡟⢀⣿⠀⢻⣷⡀⠈⠿⠁⠀⠀⠈⠛⢙⠻⠷⣤⣤⣝⣛⣃⣈⣽⠟⢡⣿⠀⡟⠈
⠀⠀⠀⠈⠀⢀⣠⣴⣿⠟⠀⣼⣿⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠛⢙⡶⠶⡭⣉⣁⣬⣿⠞⣀⡼⡋⡸⠃
⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⣼⣿⡟⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠖⢺⡛⣠⠴⣟⠥⠊⠁

⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠓⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⢶⣬⡙⠳⣤⠀⣄
⠀⠀⠀⣠⠞⢉⣤⠶⠚⠋⠉⠓⠒⢤⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠛⠿⣶⣄⠙⢿⡄⢹⣧⠈⣧
⠀⠀⣰⠏⣰⠏⣠⠴⠒⠛⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⡶⠶⠶⢶⣄⠙⣧⢸⡇⢀⣿⠀⣿⡆⣆
⠀⢠⡟⣸⠇⣼⢃⡴⠖⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣁⣤⣶⠶⠦⣌⣳⣹⣸⢃⡾⠃⣰⡿⠀⣿
⠀⢸⡇⣿⢸⡇⣾⢡⣖⣂⡀⣀⣀⢠⣤⡀⣤⡄⣤⣤⠀⠀⠃⣼⠟⢁⣤⠶⢒⡲⠅⡂⡱⢭⠴⠾⠋⣠⣾⠇⡄
⠀⠘⣷⢹⣎⣿⡹⣧⣟⣛⣵⣿⢟⣾⡿⣹⣿⢧⣿⡟⠀⠀⢸⡏⢠⡿⠁⣴⠏⣴⢱⡘⣌⠓⠶⠶⠟⠛⢁⡼⠁
⠀⠀⠹⣧⡻⣮⡻⣾⣽⣿⣯⣵⣿⢟⣵⣿⢋⣾⡿⠁⠀⠀⠈⠇⢾⡇⢸⣟⠀⣿⠈⣷⡈⠻⠶⢶⡶⠾⢋⠁
⠀⠀⠀⠘⢿⣮⣻⢷⣿⣭⣭⣷⣾⠿⣻⣵⣿⠏⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⡀⢻⣧⡈⠻⢷⣦⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠈⠛⠿⢶⣿⣿⣶⣾⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠳⣤⡙⠻⠶⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠸⢦⠥⡴⠁⢠⡆⢀
⠀⠀⠀⡀⠀⠀⠀⠠⠾⣖⣠⣐⡾⠆⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣡⠚⠤⣄⠌⡎⢅⡀⠜⢢⣁⣠
⠀⠀⠈⠂⠲⢢⣖⡐⢗⣁⣽⣄⣱⢗⣐⣤⠶⠀⠊⠀⠀⠀⣄⡈⠀⢥⠱⠄⢆⣓⠆⡴⢫⢅⠀⢀⡀
⠀⠀⠀⠀⠀⠈⢡⡧⢴⣟⠩⢙⣷⢤⡧⠁⠀⠀⠀⠀⠀⠠⠌⡗⡪⠥⢬⢱⠡⣷⢹⠸⡤⡭⡒⡏⠤⠄
⠀⠀⠀⡀⢀⡨⣗⢓⣼⠿⢶⠿⢯⣔⢶⡧⣀⠀⡀⠀⠀⠀⠔⠋⠁⣱⢈⡥⡁⡆⡋⣬⡐⡹⠈⠑⠤
⠀⠀⠐⠐⠁⠀⠈⠠⣍⣖⠲⢒⣎⡅⠈⠐⠀⠑⠈⠀⠀⠀⠰⠶⠲⣁⠯⣖⡄⡇⣔⡨⢅⣱⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠉⠀⠈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣸⠀⢀⡼⠬⢆⠀⢸⡆⠑
⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣤⣀⠀⣦⠀⢹⠁⣠⡆⢀⣠⠄⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠄⠀⡆⠀⢄⠀⢀⣤
⠀⠀⠀⠀⠀⠘⠱⣦⢰⠓⣈⠀⢳⢠⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⢠⡸⠿⣸⢈⡰⠎
⠀⠀⠀⠀⠈⠻⢴⡒⡵⣯⠻⢻⠷⡔⡲⠜⠋⠀⠀⠀⠀⠀⠀⠐⠉⠠⣭⠔⡡⠨⡉⢨⡥⠄⠕
⠀⠀⠀⠂⠗⠒⢊⠘⡟⣂⠪⢂⡺⡧⡠⠒⠒⠗⠂⠀⠀⠐⠂⠒⠒⠿⣀⠨⡀⠒⡨⢠⡘⠟⠐⠂⠒
⠀⠀⠀⠀⠠⠾⠙⣒⢝⠧⣾⡮⢟⢕⡚⠱⠦⠀⠀⠀⠀⠀⠀⠐⠅⠊⣥⢐⡮⠈⣦⢠⣭⠃⠕
⠀⠀⠀⠀⠀⣰⣞⠋⣘⠎⢲⠈⢞⡈⢻⣶⡀⠀⠀⠀⠀⠀⠀⠀⡄⠟⢀⠊⠘⡟⠸⢠⠘⢳⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⢼⠄⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⡃⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣙⠻⠀⠟⢋⡽⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣋⠳⠿⠸⠷⠊⣹⢀⣤⡀
⠀⠀⠀⠀⣀⠀⡏⢹⢀⣠⡖⠮⣷⠀⣾⠵⢲⣄⡀⡏⢹⠀⣀⠀⠀⠀⠀⢠⠶⢤⡇⢸⢠⠬⣕⣦⢠⣖⡫⢤⢸⡀⣧⡴⢦
⠀⠀⠀⠘⢏⡙⠃⢸⣸⠀⡟⠲⣤⠀⣠⠖⢻⠀⣇⡇⠘⢋⡹⠇⠀⠀⠀⣈⡷⠄⠀⢿⡞⢠⣄⡉⠈⣉⣤⠘⣯⠇⠀⠴⣏⡀
⠀⠀⠀⣴⠚⣡⠴⣦⡉⠀⢧⣄⣸⠀⣇⣠⠼⠀⠉⣴⠦⣌⠓⣦⠀⠀⠘⠥⠴⣚⡽⠆⠀⠸⡤⠿⠘⢧⡼⠀⠀⠾⣝⡲⠤⠽
⠀⠀⠀⠈⠉⠱⣏⣡⠖⠛⠲⣌⡙⠀⢋⣡⠖⠛⠲⣌⣹⠎⠉⠁⠀⠀⣞⠳⣄⢧⡀⢾⣉⡗⠀⠀⠀⠀⠐⣏⣹⠆⣠⢇⡴⢛⡆
⠀⠀⠀⣠⢤⣘⢧⣉⠓⠶⠚⣉⣤⠀⣤⣉⠓⠶⠚⣉⡼⣃⡤⣄⠀⢀⡬⠷⠈⠛⣋⠀⢩⣤⠀⠀⠀⠀⢠⣬⠁⢈⠓⠋⠰⠯⣄
⠀⠀⠀⠙⢦⣌⠙⢋⣡⠀⡟⠁⢸⠀⡇⠈⢹⠀⣌⡙⠋⢡⡴⠋⠀⠘⠲⢲⠂⡾⡽⠀⠷⠼⠃⡴⠶⡄⠻⠤⠇⠸⡽⡆⢲⠲⠚
⠀⠀⠀⠰⣏⡤⡆⢸⢹⣀⡷⠞⣉⠀⣉⠓⢾⣀⡏⡇⢰⢦⣹⠆⠀⠀⠀⠻⠴⢃⣙⣒⣲⠂⣤⠙⠞⢡⡄⢲⣒⣚⣁⠳⡼⠃
⠀⠀⠀⠀⠀⠀⢧⡼⠀⠉⢓⣫⠽⠀⠿⣝⡚⠉⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⢯⣥⣤⠀⡈⢯⡳⠴⣫⠏⠀⢠⣬⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡤⢶⠀⡶⢤⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡼⠳⣄⣳⢰⣃⡴⠳⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡶⢼⠉⣧⠶⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣙⠾⠹⢚⣩⠇
⠀⠀⠀⠀⠀⢠⡶⣴⢋⣇⣠⢽⣶⠀⣶⡯⣅⣸⡝⣧⢶⡄⠀⠀⠀⠀⠀⠀⡴⣄⢠⣄⠰⣟⠻⢿⢰⠿⢚⡽⠀⣀⢠⡤⡄
⠀⠀⠀⠀⢠⡴⢛⣀⡸⡿⣸⠓⢮⠀⡵⠚⣇⢻⠇⣀⡛⢦⡄⠀⠀⠀⠀⡴⠇⣿⣿⢸⣀⡬⠟⣂⢀⡚⠯⣄⣸⢹⣿⡆⠷⣄
⠀⠀⠀⠀⣀⠉⣹⣛⣋⣤⡻⣄⢸⠀⡇⣠⠞⣠⣘⣛⣯⠉⣁⠀⠀⢀⡴⢋⣤⣬⠋⠘⣩⡖⠋⢹⢸⡏⠓⣮⡙⠈⢫⣤⣌⡓⣦
⠀⠀⠀⣘⣏⢳⣧⡹⣄⣀⣙⣮⡻⠀⢟⣡⣊⣀⣠⠏⣼⡾⣹⣃⠀⠀⠉⢹⣋⡵⣶⢰⠦⣝⠲⢾⢸⠷⢚⡥⢶⢰⡶⢍⣳⡍⠁
⠀⠀⠘⠯⡭⢠⣭⢄⡬⠭⠭⣭⠅⠀⡨⣭⠭⠭⢥⡠⣭⡄⢭⠽⠃⠀⠀⣠⢤⣀⣿⢸⣀⡤⠟⣂⢀⡚⠯⣄⣸⢸⣇⣠⣥
⠀⠀⠀⠸⠥⠋⣯⠾⣤⣠⢞⡵⢻⠀⡟⢮⡳⣄⣤⠷⣽⠙⢮⠇⠀⢠⡶⢼⣶⣬⠋⠘⣭⡖⠋⢹⢸⡍⠓⣮⡝⠈⢫⣴⣾⠖⡦
⠀⠀⠀⠀⢠⣖⠾⠿⢖⡀⢿⠀⣸⠀⣇⠀⡿⢀⡲⡾⠷⢲⡄⠀⠀⠀⠉⣗⡈⣱⣶⢰⠦⣝⡲⢾⢸⠷⢚⡥⢶⢰⣶⡍⣐⡏⠁
⠀⠀⠀⠀⠀⢩⣟⣤⢸⡿⣼⣋⣥⠀⣬⣙⣧⢿⡇⣤⣻⡍⠀⠀⠀⠀⠀⠉⣇⣹⠻⠼⢀⡤⠟⣂⢀⡘⠧⣄⠸⣼⢿⣇⡏⠁
⠀⠀⠀⠀⠀⠀⠉⠘⠷⠇⢠⢟⣫⠀⣝⡻⡄⠸⠶⠃⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⢒⡿⠟⠘⠻⣷⡋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠶⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠖⠛⠞⠛⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠛⠓⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠏⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠈
⠀⢀⡟⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠒⠈⠉⠉⠉⠙⠒⠢⣄
⢠⠟⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠈⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠈⢳⡆⠀⠀⠐⠒⠉⠉⠉⠀⠀⠀⠀⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠄⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠀⠀⠉⠒⢲⡶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⡀⠀⠀⠉⠉⠒⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠐⠻⣍⠉
⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠄⠀⠀⢀⡴⠒⠲⣌⠢⠀⠀⠑⠲⢄⡀⠀⠀⠀⠉⠁⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢄⣀⡼⠀⠀⠀⠀⠀⢀⣈⠑⠄⠀⠀⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⣹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⡀⠀⠀⠀⠘⠀⠃⠀⠀⠀⢀⠀⢔⡄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⡛⠀⢀⠀⠀⠅⠀⠀⢚⣥⠒
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠊⡄
⠀⠀⠀⠀⠤⠀⢀⠄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠁⠐⠀⠢⠄⡀⢁⣄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠈⠤⠛⠀⠀⠈⠀⠠⠔⠀⠳⠠⢁⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⠋⠡⠄⢀⠀⠀⠀⠀⠂
⠀⠀⢀⣢⣀⠀⠀⠀⢀⢰⡀⠀⠀⠀⣀⣐⠄⠂⠀⠀⠀⠀⠠⠠⢤⡂⠆⠂⠈⠁⢠⠀⠀⠀⠋⠐⠤⠤⢣⠄
⠀⠀⠀⠀⠉⠐⣰⠄⣀⠈⣀⠰⣂⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⢠⡀⠀⢾⡀⣰⠶⠂⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠘⠓⢒⣉⠡⢴⣄⠀⠰⠦⠄
⠀⠀⠀⠀⣀⠠⠻⠀⠉⡀⠁⠰⠏⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠂⠀⠠⠶⠋⠀⣷⠀⠈⠁⠀⣆
⠀⠀⠀⠍⠁⠀⠀⠀⠈⠏⠁⠀⠀⠀⠉⠹⠄⠀⠀⠀⠀⠀⠀⠀⢪⠔⠃⠆⢠⠀⠀⠀⠃⠀⣀⠰⠰⠎⣟⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢠⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⣿⣿⣶⢿⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣰⣟⢩⣭⢿⣷⠋⣶⣾⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠞⣁⣴⣿⡿⠛⡯⢚⣿⣿⣿⣟⣻⣻⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣰⣿⣿⣿⣿⣿⣶⣿⡿⣬⡟⠛⠛⠟⠛⠦⠐
⠀⠀⠀⡀⠀⠻⢱⠜⣿⣿⣿⣿⣿⡿⢿⠋⣽⠛⠓⠃
⠀⠀⠀⠸⠷⢸⣿⣼⣿⣿⣿⣿⡿⢶⠖⢛⡇
⠀⠀⠀⠀⠀⠹⠿⣿⡿⢿⡛⢿⡷⣬⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠈⠁⠀⠀⠈⢻⣷⡠⢀⣀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠤⠄⠀⠀⠚⠛⠚⠻⠿⠶⠿⠿⠿⠷⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣦⣻⣟⣴⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⡀⢀⡈⢻⡟⢁⡀⢀⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢿⣿⣿⣧⢸⡇⢸⡇⢸⡇⣼⣿⣿⡿⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⢀⣈⣉⣻⣿⣇⢸⡇⣸⣿⣟⣉⣁⡀⠀⠀⠀⢀⣴⣿⣿
⠘⢿⣿⣿⣷⡄⢸⣆⠀⠀⢿⣿⣿⡇⣀⡀⣶⣤⡉⠉⠉⠉⠻⣿⣿⠟⠉⠉⠉⢉⣠⣶⢀⣀⠸⣿⣿⡿⠀⠀⣰⡇⢠⣾⣿⣿⡿
⠀⠈⠻⣿⣿⣿⣮⣿⡀⣴⣄⡻⣿⣰⡿⠁⢸⣿⣿⣶⠀⢀⠀⢸⡇⠀⡀⠀⣶⣿⣿⡇⠈⢿⣆⣿⢟⣠⣦⢀⣿⣵⣿⣿⣿⠟⠁
⠀⠀⠀⢠⣴⡶⠿⠛⠿⣦⣍⡛⢿⡟⠀⠀⠘⠻⣿⣿⣀⣿⠁⢸⡇⠈⣿⡀⣿⣿⠟⠃⠀⠀⢻⡿⢛⣩⣴⠿⠛⠿⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣝⣻⣾⣿⣀⠀⠰⢶⣮⣿⣿⡏⠀⢸⡇⠀⢹⣿⣿⣵⡶⠆⠀⣀⣿⣷⣟⣫⣴⠾⠛
⠀⠀⠀⢀⣴⣾⣿⣿⣷⢿⣿⠟⠉⠉⠛⠷⣦⣄⡀⠈⠹⣷⡀⢸⡇⢀⣾⠏⠁⢀⣠⣴⠾⠛⠉⠉⠻⣿⡿⣾⣿⣿⣷⣦⡀
⠀⠀⠐⠛⠛⠻⠿⠟⢡⣾⠃⠀⠀⠀⢶⣄⠀⠙⠻⢶⣤⡘⣷⣼⣧⣾⢃⣤⡶⠟⠋⠁⣠⡶⠀⠀⠀⠘⣷⡌⠻⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣴⣾⣿⣷⣦⣽⣷⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣾⣯⣴⣾⣿⣷⣦⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠙⠻⠿⠟⢋⣽⠟⠉⠉⢉⣭⡿⣿⣿⣿⣿⢿⣭⡉⠉⠉⠻⣯⡙⠻⠿⠟⠋⣩⡀
⠀⠀⠐⢶⣶⣾⣿⣷⣌⢻⣆⠀⠀⠀⠛⠁⣀⣴⡾⠛⠉⣰⡟⢹⡏⢻⣆⠉⠛⢷⣦⣄⠈⠛⠀⠀⠀⣰⡟⣡⣾⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠙⠻⠿⠿⠟⣿⣿⣷⣤⣤⣶⠟⠋⢁⣀⣠⣼⡟⠀⢸⡇⠀⢻⣧⣄⣀⡈⠙⠻⣶⣤⣤⣾⣿⣿⠻⠿⠿⠟⠋
⠀⠀⠀⢀⣀⡀⠀⠶⠟⣋⣵⡾⢻⡿⠀⠀⠘⠛⣫⣿⣿⣧⠀⢸⡇⠀⣼⣿⣿⣝⠛⠃⠀⠀⢿⡟⢷⣮⣙⠻⠦⠀⢀⣀⡀
⠀⠀⠀⢈⣙⣛⣿⣶⡿⣋⣥⡶⣿⣷⡀⠀⢰⣾⣿⣿⠀⢿⠄⢸⡇⠠⡿⠀⣿⣿⣷⡆⠀⢀⣾⣿⢶⣬⣙⢿⣶⣿⣛⣋⣁
⠀⢠⣾⣿⣿⡿⢫⣿⠀⠙⢁⣾⣿⠘⣷⡄⣸⣿⡿⠛⠀⠀⠀⣸⣇⠀⠀⠀⠛⢿⣿⣇⢠⣾⠃⣿⣷⡈⠋⠀⣿⡝⢿⣿⣿⣷⡄
⠰⠿⠿⠿⠟⠁⠸⠃⠀⠀⣿⣿⣿⡇⠀⠀⠛⢉⣤⣤⣤⣤⣾⢿⡿⣷⣤⣤⣤⣤⡉⠛⠀⠀⢸⣿⣿⣿⠀⠀⠘⠇⠈⠻⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⢀⣠⣤⣾⢿⡗⢸⡇⢸⡿⣷⣤⣄⡀⠀⠀⠀⠀⠙⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣿⣿⣿⡟⢸⡏⢸⡇⢸⡇⢻⣿⣿⣿⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠋⠀⠀⣠⣾⣷⣄⠀⠀⠙⠛⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢋⣾⣷⡙⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣠⣤⣤⣤⡤⣠⢶⡺⣍⡲⣝⡲
⣀⡀⠀⢀⣀⡠⢖⣺⣭⣍⣓⠢⣤⢖⡫⢽⣒⣾⢯⣭⣭⣭⣯⣿⣿⢗⣽⣿⣻⠭⣽⣪⣪⡳⣝⠦⣝⠦⣝
⡯⣟⢝⡿⡫⡾⢿⣞⣓⡲⠬⣝⡲⣽⢾⣷⣾⣽⣟⣿⢿⡻⢟⣝⣵⡿⠯⢗⣒⣛⣓⣺⣷⣝⠮⣓⠮⣗⡮
⡿⢥⣛⡺⠭⣭⣓⣒⡮⠭⢽⣶⠿⠿⢭⣶⣒⣒⣛⣳⢯⣶⢽⣚⠯⠭⢭⠭⠵⢖⣒⣒⣿⣿⣿⣮⣭⣭⣭
⣭⣓⠶⢭⣝⣓⣒⣚⣛⠿⣻⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠲⢭⣟⣒⣚⣯⠽⠒⠚⠉⠉⠉⠛⠛⠶⣿
⠀⠈⠙⠲⠶⢬⣭⡭⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤
⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠀⠀⠀⣿⣿⣿⠀⠀⢠⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠙⠛⠛⠻⠿⢿
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⡀⠀⠸⣿⣿⠀⢠⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⡀⠹⣿⢀⣿⠟⠁⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⣀
⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠉⠛⠻⠦⡝⣜⣥⡶⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⡕⣯⠲⣶⣤⣄⡀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠛⠛⠉⠁⢀⣴⣿⠁⢹⣧⠀⠙⢿⣿⣷⣦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠃⠀⢸⣿⣆⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⠋⠀⠀⣾⣿⣿⡀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣌⢹⡆⣿⢩⣤⣀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢦⣄⠀⠀⠀⠻⣄⠈⠻⠇⠛⠋⣠⡟⠀⠀⠀⠀⡼⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠹⣆⠀⠀⠀⠈⠙⢦⠀⣴⠛⠁⠀⠀⠀⢀⡾⠁⣼⠃
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⣆⠀⢰⡖⢦⣽⠀⣿⡴⠲⣆⠀⢀⡾⠁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⣾⡛⠙⠛⢶⡄⢰⡟⢦⡀⠀⠀⠀⠘⣧⠀⠘⣆⠘⠳⣄⠉⠀⠋⢀⡴⠇⢀⡞⢁⡼⠁⠀⠀⠀⣠⢶⣄⠀⣴⠟⠉⠉⣿⡟
⠀⠙⢷⣄⣀⣈⡳⠾⡇⠸⡇⠀⣴⢦⡀⠘⢧⠀⠘⣦⠀⠈⢳⡄⣴⠋⠀⢀⡞⢀⡾⢁⡴⠶⡄⠀⡿⠀⣿⡶⢋⣠⣤⡾⠟
⠀⠀⠀⠙⢋⣭⠿⠶⠀⠀⠻⣄⣻⠀⢹⡆⠈⢧⣀⣸⡁⠀⢸⡇⣿⠀⠀⣸⢠⡞⠀⢸⡇⢠⣏⡴⠇⠀⠀⢾⣯⡀
⠀⠀⠀⠀⠾⢦⣤⡴⠞⠛⢳⣦⡉⠀⠘⣇⠀⠀⠉⢳⡳⡄⢸⡇⣿⠀⡼⣳⠋⠀⢀⣾⠀⠈⢩⡴⠛⠛⠲⠦⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢁⣠⡤⠶⢬⣛⠶⣤⡀⢳⡹⣼⡇⣿⣼⡷⢃⣤⠶⣋⡥⠦⣤⣈⠉⢻⡄
⠀⠀⠀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⠀⠉⠛⠶⣝⡳⢷⣹⡇⠿⡽⠟⣩⠴⠚⠉⠀⢀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣄⣤⣄
⠀⠀⠺⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣿⣿⣿⣿⣿⣛⣂⠉⠀⠀⢀⣻⣿⣿⣿⣭⣽⣭⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⣉⣉⡉⠉⠉⠁⠀⠀⢀⣤⠖⣫⢵⡆⡀⣤⢤⣍⡳⢦⣄⡀⠀⠀⣀⣤⠦⢤⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠛⢶⣄⣠⡴⢞⡭⠖⠋⢁⣞⣼⡇⣿⣜⣦⠙⠳⢮⡉⠓⠛⠉⠀⣀⡼⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠸⣟⠛⠳⢦⣈⣹⡶⠀⠈⣵⠞⠉⠀⠀⢠⢏⡞⢸⡇⣿⠘⣎⢧⠀⠀⢹⡆⠀⣘⣿⢥⡤⠖⠋⠉⢨⡟

⠀⠀⠀⠀⠀⠈⢙⣦⠀⠈⣠⠖⣷⠀⣿⠀⠀⠀⡴⠋⡞⠀⢸⡇⣿⠀⠘⣾⢧⡄⠀⣷⠀⣿⠙⣧⠀⣀⡲⣿⡉⣀
⠀⢀⣴⠞⠛⠚⢋⣥⡄⠀⡟⠀⢿⣀⣿⠀⢀⡼⠁⣼⠃⢀⡼⠇⢿⡀⠀⢿⡀⠹⣆⠸⣄⣸⡆⢹⡄⢹⡟⢻⣍⠉⠛⢶⣄
⠀⣸⣇⠀⢀⣸⠏⢸⡇⢠⡿⠀⠀⠉⠁⢀⡾⠁⡼⣡⠶⠋⢀⠀⢀⠙⠶⣄⠹⡄⠹⣆⠈⠉⠀⠘⢧⣰⡇⠀⠙⢶⣄⣠⣿
⠀⠉⠉⠛⠋⠁⠀⠀⠙⠟⠀⠀⠀⠀⢀⡞⢁⡾⣹⣃⣀⡴⢻⡇⣿⠳⣄⣸⣇⠹⡄⠙⣆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡞⠀⠈⠉⢉⡴⠟⠁⠙⢷⡈⠉⠉⠀⠹⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠀⠀⢠⡶⠋⠀⣠⡄⣶⣄⠙⢳⣄⠀⠀⠹⢶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠋⣽⠇⢯⡈⠷⠾⠟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡾⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠙⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣝⣴⠶⠀⠐⠻⢷⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠺⠀⠀⠀⢈⡔⢢⠀⡴⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡤⠤⠼⣦⢸⠀⣧⡀⣨⠷⠒⠒⠀⠐⠂⠄⠀⠀⠠⠒⠋⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠉⢹⠀⠀⠀⠈⠧⠤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⡳⢤⣀⡐⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠐⠒⠀⠐⠀⠀⠸⠤⠄⠀⠠⢏⠉⠉⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢶⣚⣠⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠉⠀⠀⠀⠂⠈⠁⢈⢧⡀⠀⠀⠉⠀⠈⠙⠒⠦⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡶⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠓⡤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⠞⠳⢄⣀⠀⣀⣠⠴⠋⠳⣄⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢬⡥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢬⣙⣋⡥⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐⠠⠀⠑⠢⢬⡥⠔⠊⢀⠀⠂⠀⠀⠀⠀⠀⢀⢠⠊
⠀⠀⠀⠀⠀⠀⠂⠤⠜⡳⢄⡄⡆⢀⢀⠀⠀⠀⠀⠰⠀⢸⠁⠀⠆⠀⠀⠀⠀⠀⡀⢠⢠⡬⢞⠣⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⠜⣳⠶⣸⡀⠀⡐⠀⠀⠀⠈⠀⠀⠀⠀⢒⠀⢀⣧⠶⣎⠃⢍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠠⠒⠉⢉⠲⢄⡁⠄⢈⡢⠔⡀⠠⢈⡤⠒⡉⠉⠒⠄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠑⠂⠁⠂⠀⣊⠀⠁⠀⠁⠐⠀⠐⠈⠐⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⡀⠄⠀⢄⢀⠀⢀⠀⡩⠀⠠⢀⠠⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠐⠤⣀⣈⠤⠊⡁⠂⢈⠔⠪⡁⠐⢈⠑⠦⣁⣀⠤⠂⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢠⡹⠶⢻⠁⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡏⠶⢏⡔⡊⠄
⠀⠀⠀⠀⠀⠀⠄⠒⢢⡴⡚⠃⠃⠀⠀⠀⠀⠀⠀⠰⠐⢀⡀⠂⠆⠀⠀⠀⠀⠁⠀⠸⠘⢑⢮⡔⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠁⠀⠀⠀⠀⠀⠰⠀⠁⡠⠔⢚⡓⠢⢄⠀⠂⠄⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢚⣩⣍⡓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢚⡓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣤⡀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣠⠴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⣏⠀⠀⠙⠳⣄⡀⡇⠀⠀⡇⣠⠴⠋⠁⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⢲⠀⠀⠀⠙⠦⣄⠀⠀⠙⠃⠀⠀⠋⠁⠀⣀⡴⠚⠁⠀⠀⢰⠚⠋⡏
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣰⠋⠈⠛⠦⣄⡀⠀⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⣀⡤⠞⠉⠈⢧⡀
⠀⠀⠀⠀⠘⠳⢤⡀⠀⠀⠈⠙⠲⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠷⠚⠉⠀⠀⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⢷⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⣀⡤⠞⠋⠀⠀⢀⠀⠀⠈⠛⠦⣄⡀
⠀⠀⠀⠀⠀⣴⠞⠋⠁⠀⢀⣠⠴⠚⠉⠛⠦⣄⡀⠀⠈⠙⠲⣄⣀⡇⠀⠀⡇⣠⡴⠚⠉⠀⠀⣀⡤⠞⠉⠙⠲⢤⣀⠀⠀⠉⠓⢦⡄
⠀⠀⠀⠀⠀⠈⢧⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠉⠃⠀⠀⠋⠁⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⠄⠀⠀⠀⠀⢤⣞⠉
⠀⠀⠀⠀⠀⠀⡴⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⡀⠀⠀⡀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⡄
⠀⠀⠀⠀⠀⢾⣁⠀⠀⠉⠛⠦⢄⡀⠀⢀⣠⠖⠋⠁⠀⢀⣠⠴⠛⡇⠀⠀⡟⠲⢤⡀⠀⠀⠉⠓⢦⣀⠀⢀⣠⠴⠞⠋⠁⠀⣀⣹⠆
⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠉⠛⠉⠀⠀⢀⣤⠖⠋⠀⠀⠀⡇⠀⠀⡇⠀⠀⠉⠳⢦⣀⠀⠀⠈⠙⠉⠁⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣠⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣤⡀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠖⠋⠁⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠉⠓⢦⣀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠹⠞⠉⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠳⢦⣀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠀⠀⠈⠙⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣸⠀⠀⠀⢀⣠⠖⠋⠀⠀⡀⠀⠀⡀⠀⠈⠓⢦⣀⠀⠀⠀⢹⣀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠠⡖⠋⠀⢀⣠⠴⠛⡇⠀⠀⡟⠳⢤⡀⠀⠈⠓⡦⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠶⠋⠁⠀⠐⡇⠀⠀⡇⠀⠀⠉⠳⢤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣠⢀⣸⣇⡀⣄⣤⠆⠀⠀⠠⣼⡆⢹⡟⢁⣿⡤⠀⠀⠰⣤⣆⢶⣼⣇⡶⢠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠋⠙⣿⡍⠀⠀⠀⠀⣛⡋⣙⣿⣿⣟⢉⣛⡀⠀⠀⠨⣭⣿⣿⣿⣿⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⠻⠷⡾⠟⡶⣤⡀⠀⠀⠸⢿⡏⢹⣇⠉⣿⠏⠀⠀⢀⣴⡶⣻⡿⡿⣟⢲⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠏⠓⠈⠀⠀⠀⠀⠀⠀⠉⢼⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣀⠦⣽⠴⣀⣴⡶⠀⠀⠲⣤⣀⠀⣹⡁⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣳⣾⣞⣛⠌⠀⠀⠀⠀⠀⠉⣛⣾⣶⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⡇⣿⢬⡛⣶⣦⠀⠀⣠⡶⠞⠉⢺⠒⠉⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⠀⠘⡏⠀⣠⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣷⡚⠉⠁
⠀⠚⠒⠂⠒⠂⠒⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠉⡇⠉⢻⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠠⢄⠀⠀⠀⣀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠀⠒⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡼⠁
⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⡿⠉⠓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀
⠘⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠈⢿⣅⡀⠀⠠⠀⠀⠅⠀⠒⠠⠄⠀⠀⠀⢀⡀⠀⡐⠁⠀⠀⠈⠑⠀⠀⠀⠐⠢⣀
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⢌⠐⠀⢈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠢⡈⠂⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠑⢄⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⣀⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀
⠀⠀⠀⠀⣶⣾⣤⢼⣿⣿⢄⣸⣷⣆⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⡀⠀⠐⣷⣿⡁⠀⠀⠀⠀⠀⠀⠠⣼⡆⣀⣿⣿⣁⢰⣇⡄
⠀⠀⠀⣀⠉⡿⠿⣦⣻⣡⡾⢿⣏⣉⡀⠀⠀⠀⠀⠀⢀⠀⠾⢿⡇⢸⣷⣯⡍⠀⠀⠀⠀⠀⠀⣈⠉⣻⠿⣥⣼⣧⣨⠿⡟⠛⡀
⠀⠀⠰⣿⣿⡷⠶⣾⣿⣿⡟⠻⡿⢿⡟⠀⠀⠀⢠⣿⣾⣷⣤⣤⣿⣾⣧⣴⣿⣴⣿⠤⠀⠀⠀⢾⡿⡿⠶⣿⣏⣿⣿⠤⣿⣾⠥
⠀⠀⠀⠉⣤⣿⣿⣋⣼⣏⢻⣾⣧⣄⠀⠀⠀⠀⠀⠋⠘⠋⠶⣶⡏⢹⣷⣦⠝⠀⠛⠀⠀⠀⠀⢉⣀⣹⣶⠛⢻⠟⢳⣴⣃⣈⠃
⠀⠀⠀⠀⠛⠻⠉⢉⣽⣯⡉⠹⠟⠃⠀⠀⠀⠀⠀⠀⠠⢶⣾⡋⠃⠘⢫⣿⡶⠆⠀⠀⠀⠀⠀⠀⠚⣻⠉⢙⣿⣟⠋⢹⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠙⠃

⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠙⠻⡄⢠⡄⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⠁⣀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣃⠀⠀⣸⡿⠇
⠀⠀⠀⠀⠀⢰⣦⣹⣾⣧⣏⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠋⣷⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣸⠟
⠀⠀⢿⡿⠶⠶⣶⣿⣿⣿⣿⡶⠶⠶⣾⣷⠀⠀⢠⣶⣿⣦⣼⣧⣼⣿⡧⢴⣧⢤⣾⣵⡆⠀⠀⣾⡷⢶⡶⠶⣿⣿⠶⢶⡦⢾⣷
⠀⠀⠀⠀⠀⠘⠋⣱⢿⡟⣯⠹⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠾⢥⣼⠉⣷⣤⠿⠆⠈⠁⠀⠀⠀⠀⠀⠀⢀⣼⠋⢻⣦
⠀⠀⠀⠀⠀⢀⣴⠃⠘⠋⠈⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡙⠿⠋⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠀⠀⢹⣦⡄
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣄⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣤⡄⠀⢀
⠀⠀⠀⢀⣤⣧⣈⣿⡷⢾⢯⣄⣿⣆⠀⠀⠀⠀⠀⠀⠀⣻⣦⡿⠀⠀⠀⢻⣶⣟⡀⠀⠀⠀⠀⠀⢠⣤⡼⣻⣭⣽⣏⣳⢿⡃
⠀⠀⠀⣺⣉⡿⢷⣾⣿⣿⣶⣟⣳⣴⣧⠀⠀⠀⠀⢠⡌⠉⠛⢷⡄⣴⣠⡾⠋⠉⢉⠀⠀⠀⠀⣀⣨⢿⡿⣭⣷⣿⣾⣛⣧⣽⡿⠂
⠀⠀⠠⣟⢻⡟⣿⣾⣏⣹⣿⣿⣩⣏⣽⠅⠀⠀⠠⣤⣿⣦⣤⣿⡿⠛⣿⣿⣥⣴⣿⣥⡀⠀⠀⠙⢿⢿⣛⣳⣿⣹⣿⣿⣽⣇⣧⡄
⠀⠀⠀⢿⡟⢯⣹⢾⣽⣻⡽⢯⣼⣛⡿⠁⠀⠀⠀⠠⠟⠁⠀⢻⡿⣶⢿⣿⠃⠈⠻⠌⠀⠀⠀⢰⡾⣟⢏⣵⢿⡿⣟⢳⣾⣱⠋⠁
⠀⠀⠀⠈⢺⣿⠟⢶⣿⠼⣷⡛⢻⠿⠁⠀⠀⠀⠀⠀⠰⢶⣶⡟⠀⠉⠀⣹⣿⡷⠆⠀⠀⠀⠀⠀⠀⣼⡿⣝⣻⣗⣻⣥⠞⠻⠇
⠀⠀⠀⠀⠀⠈⠐⠻⠻⠼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠷⠀⠀⠀⠉⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠈⠛