Golf Course Emojis & Symbols

⣀
⣿⣀⣀
⣿⣿⣿⣷⣀
⢻⣿⣿⣿⣿⣀⠀⠀⠀⣠⣄
⣶⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣦⣄⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣄⡀⣀
⡿⣿⡄⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⢴⣤⣄⣀⡀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄
⠋⠀⠀⠈⢸⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣾⢻⣿⡿⣿⡟⠏⡟⣿⣿⣿⠛⣿⣿⣯⢽⣿⣯⣿⣟⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⢾⡟
⠀⠐⠀⠀⠀⢸⠟⠹⣿⡇⠱⠆⠸⠻⠏⢩⡝⠛⠏⢁⠃⠀⠈⠓⠠⠿⠶⠤⢬⣽⢓⠞⡌⣻⢻⠥⣽⣿⣿⣟⡋⠀⠩⢷⡻⠽⠟
⠀⠀⠀⠀⠀⠀⠃⠐⢪⡇⠠⣤⡃⣷⠅⠀⠁⢢⠀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠐⠃⡁⠂⣀⠋⣀⢒⡐⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠁⠀⠈⠀⢠⠂⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠞⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⡀⠀⢀⣀⣠⣤⣶⣶⣿⣟⣉⣉⣀⣤⣀⣀
⣿⣿⢛⠿⡛⠛⢿⠟⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡈⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠀⡂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡃⠀⠀⢀⠇
⠀⠀⠠⠀⠂⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢸⠅⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠄⠀⠀⠀⠀⣸⡆⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠨⡇⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⣼⠔⠀⠀⠀⠀⠀⢀⠀⠀⡼⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠠⠀⡀⠐⠂⡥⢘⡩⠀⠀⠀⠀⠀⠀⠊⠀⢰⢧⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⠄⣀⠐⢢⠇⡾⠘⠔⢌⣀⠀⠀⠀⠀⠶⠲⠂⠀⠶⠖⠐⠱⠁⠂⢀⣀⣀⡠⠤⣀⣒⠠⠬
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠓⠂⠚⠁⠀⠀⠀⠀⠁⠀⠀⠀⠂⠐⠒⠒⠒⠐⠒⠀⠐⠒⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠡⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠂⠀⠀⠀⠐⠊⠀⠀⡀⠀⢠⠇⠀⠒⠒⠀⠐⠀⠐⠂⠀⠂⠀⠘⠀⠂⠂⠀⠒⠀⠀⠀⠀⠂⠀⠐⠒⠒
⠠⣀⢄⡁⠀⢄⣄⠤⠀⢀⠀⣀⠀⢀⠒⢈⠂⣀⣠⢸⣔⢀⠀⠀⠠⡀⢡⢠⠄⠄⠀⡄⢆⠄⢀⢐⠀⠀⠀⠀⢐⠆⢀⠀⠀⠀⠄⠀⡌⢀
⠀⠈⠛⢃⠔⠂⠀⠀⠡⠀⠆⠦⠂⠠⠐⠶⠁⠁⠉⠉⠈⠳⣪⠄⢢⡜⠊⠈⠕⡤⡰⠀⠀⠈⠀⠱⠐⡀⠀⠐⠰⠟⠐⠈⠜⠦⠁⠆⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢂⠀⠀⠐⠀⠁⠀⠀⣈⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠈⠀⠀⠀⠚⠃⠀⠀⢈⡀⢸
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⢸
⠈⠛⠋⠁⢀⣀⠀⠀⠀⠀⠀⠀⢠⣐⣆⣀⠀⠄⢶⡆⢀⠀⢀⡀⠀⠈⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠚⠂⠙⠀⢸
⠀⠀⠀⠈⠾⠯⠁⠀⠀⠀⠀⠀⠀⠰⠾⠏⠀⠀⠛⠂⠐⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠮⠳⠦⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⢠⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢑⠔⢰⣃⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠘⠀⢼⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠀⠲⠂⠀⢰⣷⡀
⠀⠀⠀⠀⢀⣀⣄⠀⣡⣘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⢤⡄⠀⠀⡀⠀⣦⢁⡂⠂⢠⣤⣾⣿⡘⡷
⠀⠀⠀⢠⣿⣿⣿⣿⣦⣿⣿⡃⠀⡀⢀⠀⣀⡀⣀⢀⠼⡿⠿⡻⣦⡏⠀⠀⢧⣤⣽⣴⡟⠻⠿⠛⠉⠑⢀⣤
⠀⠀⠀⠀⠻⣿⣿⣻⡙⢻⣉⠉⢀⡀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠀⢈⣀⡲⠤⠤⠩⠽⠭⠠⡆⠤⢴⠶⢠⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣿⠓⢀⣀⠀⠀⠀⠒⠉⣉⣡⣤⠤⠤⠤⠤⠤⢄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠋⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠦
⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⣀⣠⡤⠤⠤⠶⠶⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⠂⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⣤⣖⡄⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠠⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠈⠉⠙⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠙⠛⠻⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⣉⡑⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠠⠴⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠀⠀⠀⠛⠇⠀⠀⠀⠀⠠⣏⡿⠂⡗⠾⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠉⠉⠉⠁⠁⠒⠒⠦⠤⢄⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡋⣀⣅⣀⣸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⡠⠀⣠⣰⣮⣽⡿⠿⠿⡟⠛⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⡿⠛⣿⡉⠭⠑⠒⠈⠃⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡵⠶⠓⠉⠀⠀⢀⣀⣤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠋⠁⠀⠀⠀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣤⣤⣴⣧⠄⠊⡀⢰⣦⡄⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⡿⠛⠻⠋⠳⠟⢀⣈⣽⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴
⠀⠀⠀⢀⣀⣀⣀⣀⣠⣬⠤⠶⠶⠒⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁



⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⢀⣤⣤⡀⠀⣤⡤⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠠⣼⡅⣿⡃⠀⣿⠄⢾⡇⢀⠀⢸⣧⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠃⠈⠓⠚⠋⠀⠛⠓⠚⠀⠚⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⠀⡀⠄⠒⠄⠠⠀⠂⡴⠠

⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣾⡿⠟⠛⠷⢾⣿⣷⣶⣶⣷⣴⣶⣾⣷⣾⣿⣿⣿⣿⣷⡶⣷⡾⠾⠟⠃
⣿⣿⣿⡿⠾⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠿⠒⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣇⢀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⣩⡥⠀⣀⣶⣄⠰⣶⠆
⣿⡿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣒⣒⣲⣟⡒⢠⣼⣿⠿⣿⣿⡞
⣿⣷⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣄⡀⢠⣾⣿⣿⣯⣄⡤⢽⣿⣿⣿⣿⣷⣶⣶⣾⣿⡉⢿
⣽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣼⣿⣧⣽⣿⣿⢿⣽⠟⢛⡿⢩⡍⣽⣻⣏⣹⡟⣻⣿⡝⢉⡿⣩⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⣠⠀⠠⠤⠤⠼⢇⠚⠷⠖⠳⠚⠉⠍⠉⣛⡉⢑⠌⠑⠀⣀⠐⡀⠀⡀⢐⡀⡀⠒⠂⢀
⣿⣿⣿⣿⣿⣿⢻⡗⢒⣲⠒⡶⢒⠒⣒⣶⣶⣷⣶⠖⠒⠒⠒⠒⠒⠒⠔⣤⣄⣈⣀⣐⣀⣀⣀⣀⣁⣒⣀
⣿⣿⣿⣿⢛⣗⠿⣴⢿⠖⠾⠖⢒⣑⠛⣾⣟⣿⠏⠖⠀⠀⢀⡆⠀⠀⣴⣿⠟⠀⡈⡡⢡⠃⣠⣿⠏⣹⠿
⣿⣿⣿⣿⠀⠀⠀⣀⡀⠀⣀⠀⠓⠀⠀⠭⠭⠭⠭⠭⠥⠠⠟⢃⡖⢺⣿⢇⣀⡀⠐⠁⣀⣰⣿⡿⣿⡷
⣿⣿⣿⡿⠀⠀⠀⠀⠈⠉⠀⣀⣀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠭⠬⠩⣩⡍⠉⠐⠦⠉⠉⢉⣛⡒⠒
⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠀⠀⠀⠈⣉⣉⢀⣙⡃⠀⣈⠀⠉⠉⠉⠉⠉⠀⠒⠒⠒
⣿⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⡍⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠭⡉⣒⣖⣀⠀⠒⠒⠠⠤⡀
⣿⣿⣿⡇⢉⡙⢛⢛⠶⠶⠶⠤⣧⣤⠤⢼⠤⢤⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢀⣓⠲⠤⡭
⣿⣿⣿⡇⠛⢳⣄⠀⠀⠀⠀⠀⠇⠀⠓⠼⣦⣀⣀⠀⠀⡀⣾⣮⠉⠉⠉⠛⢲⣦⡀⠀⠀⠀⠀⠀⠐⠚⠙
⣿⣿⣿⡇⠀⠀⠈⠉⠉⠉⠉⠉⠛⠐⠒⠂⠱⣤⣌⣁⣘⢹⣿⠏⠀⠀⠀⠀⠀⠉⠉⢛⠛⢛⣓⣒⠒⠲⠤
⣿⣿⣿⠁⠀⣀⠀⡀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣀⣀⣀⣀⣈⣐⡄⠀⠁⠉⠙⠛
⣿⣿⣿⠀⠉⠁⡨⢡⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡧⠈⠛⠤⠤⠤⢌⠈⠁
⣿⣿⣿⠀⠀⠀⠀⠉⠆⠖⠰⠁⠴⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⣔⠋
⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡸⠿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⠤⣤⣄⣀⡀
⣿⣿⣿⠀⠀⢘⣶⡇⠀⢀⡤⠖⠒⠦⣐⡇⢀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠠⠦⢶⡆⠤⣀⠀⠀⠀⠉⠉
⣿⣿⣿⡆⣰⡁⠀⣨⣗⣼⢄⠀⠀⠀⠀⢻⡾⡀⢀⣻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡥⢠⢄⡀
⣿⣿⣿⣷⡟⢱⣾⡿⡾⠋⠈⠑⠢⡀⠀⠘⡇⣷⡀⠭⠹⡏⠑⠒⠶⠤⡤⣤⣀⣀⠀⠀⠀⠀⠀⠈⠀⠂
⣿⣿⣿⣿⡇⡌⠀⣤⡇⠀⠀⠀⠀⣸⠂⠀⢱⠹⣷⣴⢿⡇⠀⠀⠀⠀⠀⠰⠃⣬⠗
⣿⣿⣿⣟⣇⠇⣾⠹⣧⠀⠀⠰⡉⠀⠀⠀⠀⢇⠇⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠤⠤⣤⣀⣀
⣿⣿⣿⣿⣿⣶⣛⣾⣁⣀⡀⣀⡈⠑⠂⠀⠄⢸⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠋⣉⣲
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣤⣤⣤⣤⣤⡴⠶⠶⠿⡿⢟⠟⡛⠩⠭⠭⠝
⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⡿⢟⠻⢿⣿⡟⣿⣿⣛⣻⣿⣟⣛⣛⣭⣉⣱⣖⣚⣲⡤⠦⣄⣰⣵⡂⣿

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣤⣴⣦⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⠪⣛⢟⡫⣙⠌⢋⢫⠉⠋⠋⠉⠉⠉⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠉⠈⠀⠑⠙⠈⠫⠱⡙⠜⡴⣫⢾⢟⡽⣻⣿
⣿⣷⡯⢂⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⡁⡊⣚⢵⣿
⣿⣟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⡵⣻⣿
⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⣀⢀⣼⠀⢻⣅⡀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⣿
⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⡄⣀⡈⡷⠂⡔⠃⠀⠱⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡉⠉⠁⡸⠋⢀⡼⠀⠀⠀⠀⠱⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣷⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣀⣀⣀⣀⠀⢀⡴⠿⣤⠞⠀⣴⣿⠧⣀⣠⣠⡤⠲⣿⣄⠀⠀⢈⡧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⢀⠴⣋⣴⠶⠋⢰⣾⣿⣷⣼⣿⠃⠀⠀⠀⢸⣿⡃⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡜⢡⡏⠀⠀⠠⣵⣿⣿⣿⠋⠀⠘⣶⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠸⡀⠳⢤⣤⠖⣼⣿⣿⠏⠀⠀⠀⠘⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠹⣄⠀⣠⣾⣿⣿⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠾⣿⠀⠀⢠⠀⣠⣠⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⢠⣠⣆⡀⢄⣀⣸⠆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣿
⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢰⡿⠔⠛⠋⡉⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⣶⣦⣄⣀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢷⣤⣙⣆⠀⡠⠶⢶⣤⣄⣀⡀⠀⠀⢠⠔⢶⣿
⢸⣿⠀⠀⠀⠀⠀⠀⣠⣤⣀⣠⠖⠁⠀⠀⠈⠉⠙⢻⣿⣶⣤⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠁⢸⠏⠀⠀⠀⠈⠻⢿⣿⣿⡶⠃⠀⠀⢹
⢸⣿⠀⠀⠀⣠⠔⠋⠀⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠉⠛⢻⣿⡀⠀⡀⠀⠀⠀⠀⠀⣼⣦⢀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢸
⢸⣿⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⡇⠀⠠⣑⢦⣄⡀⢀⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣰⣗⣿⣿⣿⣿⠀⠀⠪⣿⣾⣿⣿⣿⣿⣿⣿⣿⢻⣿⠇⣤⡄⠀⣀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⣿⠄⣠⠀⠀⢠⣸⣿⣷⣿⣿⣿⣿⣿⣆⠀⢬⣻⣽⣿⣿⣿⣿⣿⣿⣿⢈⣿⣶⢸⣿⣴⢻⣷⡤⣼
⢸⣿⠀⣰⡀⣾⡀⣿⢇⢸⡇⢸⣇⣿⡆⣽⡀⣦⢸⣿⣿⣿⣿⣿⣛⠛⠻⢹⠀⡀⡍⠛⠻⠛⠟⠛⠉⠀⣿⢘⣿⣿⠸⣿⣿⢸⣿⣿⣿
⢸⣿⣆⢿⡇⣿⡇⣿⣿⣿⣇⢸⣯⣿⣿⣿⣧⣿⣿⣿⣿⠿⠟⠛⠀⠀⠀⠀⢷⠀⠀⠀⠀⠘⠷⡶⠾⠿⣿⡘⢿⣿⠰⣿⣿⢨⣿⣿⣿
⢸⣿⣿⣿⣷⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣠⣶⣶⣶⣶⣶⠿⢦⠀⠀⠀⠘⢿⣿⣦⡀⢻⠘⠿⣿⠲⣾⣿⠠⣹⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⢋⣁⣠⣤⣴⣶⠾⠟⠛⠉⠉⠉⠉⠀⠀⠈⢳⢆⠀⠀⠀⢻⣿⣷⡉⢆⢲⣿⠆⢨⣿⡀⢙⣿⣿
⢸⣿⣿⣿⣿⠿⠿⠟⠛⢛⣛⠉⠉⠉⠉⠉⠉⠉⠉⣡⣾⠀⠠⢀⡴⠋⠀⠒⠒⣢⣼⣟⡄⠀⠀⠘⣿⣿⣿⡌⠳⡏⠘⢬⡟⢡⣸⣿⣿
⢸⣿⣭⡥⠶⠒⠉⠉⠀⠀⠀⠀⠀⢀⣀⡴⠊⠀⠀⠛⠃⡀⠀⢸⠁⠀⠀⠀⠈⣩⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⡶⠧⢤⣸⣇⠀⠹⡃⣿
⢸⣿⣧⠀⠀⠀⠀⣀⡤⠒⠀⠀⠉⠉⠀⠀⠀⠀⣠⣶⠟⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠟⣿⣷⡀⢸⡏⠻⣿⣿⣿⣆⣀⠀⠈⠉⠛⠳⣿
⠘⣿⣿⣷⣄⣠⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣁⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣷⡀⡇⠀⠀⠙⢿⣿⣿⣿⣶⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠷⠿⡀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⣀⣀⣤⣤⣴⠶⠶⠶⠛⠛⠛⠛⠋⠉⠛⠛⠂⠀⠠⠀⣸⠧⣀⢀⣷⣄⠀⠀⢙⣿⣿⠀⠀⠀⠀⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠻⣿⣦⡀⠀⣹⣀⣀⣸⣿⡟⠀⠀⠀⠀⣿
⢸⣿⣛⣛⣿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠉⠁⠀⠈⢻⡀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣄⣀⣠⡤⢶⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣦⡀⠀⢀⣨⡋⠁⢰⢏⣴⣁⣀⣤⡶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡜⠁⠀⠀⢙⠓⠛⠯⠜⠁⣀⣴⡟⠁⣬⠟⣋⣽⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡿⢩⣅⢤⡿⠚⠋⠀⠀⢀⣤⣸⣿⣿⡇⠀⠴⣋⠥⢖⣻⣿⣿⣏
⠀⠀⠀⠀⠀⠀⣴⡟⢀⡏⢀⡀⡇⠀⠀⠀⠀⡌⢰⡏⠉⠁⠀⠀⠀⠀⠀⠊⠭⠒⠛⣿⢀
⠀⠀⠀⠀⠀⢸⣿⠀⢸⡏⠀⠀⢧⡀⠀⠀⠀⢧⣿⠀⠐⠛⢶⡀⠀⠀⢀⣀⡀⢠⡶⣿⣁
⠀⠀⠀⠀⠀⠸⣷⠀⠀⡇⠀⠀⠸⡏⠓⢤⣀⠈⣿⠀⠀⣠⡜⠃⠀⠰⠋⠉⠀⠀⢀⡿⡿
⠀⠀⠀⠀⠀⠀⠙⠷⣄⣻⡀⠀⠀⠙⢦⡀⠀⠉⢿⠀⠀⠙⠁⠀⠀⠀⠿⠃⠀⠀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠉⠓⠶⢬⣧⣀⠀⣰⢢⡆⠀⠀⢀⣠⠾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠞⠓⠚⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⠿⠶⠶⢶⠴⠶⠶⠖⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣶⡦⢤⣄⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣏⢀⣿⣀⣨⣗⣙⣿⣏⣻⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢛⣽⡁⢸⣏⢀⣽⡁⢸⣏⢈⣿⡁⣸⣏⢉⣿⡛⣲⡦⣤⣀
⠀⠀⠀⠀⢀⣤⣶⠛⣻⡟⢙⣿⠃⢻⡟⠘⣻⠓⢚⣟⢘⣛⠛⢻⡛⢘⣟⠋⢻⡛⠛⣿⠛⢳⠦⣄⡀
⠀⠀⣠⣶⡟⢛⣿⠉⢻⡟⠙⣿⠉⠹⣿⣽⡿⠿⠟⠛⠛⠛⠿⠿⣿⣼⣿⠇⢿⡷⠺⣿⠖⢾⠷⠺⣿⠶⣄
⢀⣾⠟⢿⡗⠺⣿⠶⣿⡷⠲⣿⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣾⡗⢰⣿⡄⣾⣶⢤⣶⡦⣼⣷⣄
⢸⣷⠤⣼⣧⣴⣿⣤⣾⣧⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣿⣄⣼⣤⣀⣼⣄⣀⣯⣹⡆
⠀⠻⢦⣼⣧⣸⣿⣀⣼⣧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⡁⣹⣍⠉⣹⡇⠉⣿⡿⠃
⠀⠀⠀⠀⠀⡿⣿⡿⠿⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣧⣿⣟⣉⣿⣏⡿⠟⠁
⠀⠀⠀⠀⠀⠙⣶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⢬⣙⣛⣻⠟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡼⠉⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢈⡇⠀⡇⠀⠀⠀⠀⠀⠀⢾⣄⡼⠂⠀⠀⠀⠀⢀⣠⡼⠁⣰⠋
⠀⢀⣤⣤⣴⡚⠉⠙⢲⣷⡆⠀⠀⠀⠀⠀⢠⡿⡀⠀⠀⠀⠀⠀⣾⣿⣏⡉⠉⣲⣤⣤⣄
⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠶⠤⠤⠤⠾⠤⠷⠤⠤⠤⠤⠤⢬⠤⠤⠭⠿⠿⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣤⢇⡏⠀⠀⠀⠀⢠⠞⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⢾⣷⡀⢰⡇⠀⠀⢸⠟⠠⠀⠀⢀⡔⠁⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⢀⡄⢠⣶⣶⡶⠀⠀⢰⣎⠁
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠃⠀⠀⠀⡠⠋⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠛⠷⣤⣤⠜⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⡀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⠀⠀⠠⢄⡜⠁
⠀⠀⠀⢧⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣿⣀⢀⡠⠋
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣩⣩⣏⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⡴⠁⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣧⣴⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⢿⣫⠽⠚⠉⠉⠛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣡⣞⠕⠋⠀⠀⢀⣠⡤⠴⠶⣾⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣷⣶⣿⡿⠛⢉⣠⣴⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢾⠐⠣⠘⠑⢮⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⣴⣾⣿⠿⣿⣯⠛⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⡉⠉⠁⠀⠀⠑⢦⣴⣴⠿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣻⣿⣧⠀⠀⠀⠀⠸⠽⡄⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣀⢤⣐⣶⣭⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⠿⣿⣧⡀⠀⠀⠰⣶⣾⠓⢨⠁⠀⠀⣀⠤⣐⣢⡭⠾⠿⠛⠋⠛⠒⠺⢿⣿⣿⠇⠀⠀⢸⣿⣿⡶⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡶⣿⣿⣷⣄⡀⠀⠀⠀⠀⣸⣦⠭⠷⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⣾⣿⣭⣭⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⢘⣿⣿⣿⣿⣿⣶⠶⠿⣽⣄⣀⣀⡀⠀⣀⣀⣠⣤⡤⠤⠴⠶⠚⠛⠀⠀⠀⠀⠀⣼⢫⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡿⣻⠟⢉⣡⣤⣤⣤⣤⣤⣀⡉⠉⠉⠉⠁⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣦⠞⢡⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⠿⠟⢿⣿⣿⡿⢀⡞⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⢀⣴⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣤⡴⠶⠞⠛⠉⠁⠀⠀⣀⣾⣿⣿⠃⢸⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣏⡉⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇
⣰⣡⡠⡖⠋⠁⠀⠀⠀⠀⣠⡴⢶⣿⣿⣿⣿⡇⠀⢸⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠀⠀⠉⠙⠀⠈⠙⢦⣀⣴⣿⣿⣿⣿⣿⣿⠏
⣿⣿⠀⡵⠀⠀⠀⢀⣠⣼⣥⣶⣿⣿⣿⣿⣿⡇⠀⠘⣧⡘⣿⣿⣿⣿⣿⣤⣬⣶⡿⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠏
⣿⣿⣤⠁⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣷⣬⣛⠿⠿⢿⠿⠟⢋⢆⣾⣿⣿⡆⡀⠀⠀⣀⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋
⠘⠻⠿⠛⠁⠀⠀⠀⠀⢿⣿⢁⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣟⠛⠒⠃⢀⣾⣿⣿⣿⣿⣿⣧⣴⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡾⣋⣼⠿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡗⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠉⠙⠛⠁
⠀⠀⠀⠀⠀⠀⢀⠴⣋⣽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠚⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡄⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣸⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⡇⠀⣸⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⠃⠀⣿⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡿⠀⢸⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡾⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣤⡤⠶⠟⠁

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠐⠂⠀⠀⠀⠂⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠐⠀⠐⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢃⡿⠀⠀⠀⢸⡟⡉⠁⠀⡙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣸⠃⠀⠀⠀⢸⡇⠲⣄⠲⡝⣆⠠⣍⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⣄⣤⣄⡀⢸⡇⠀⠸⣦⣑⠘⢧⡸⣕⠂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠉⢀⣈⡙⠎⣰⠀⠀⠘⣿⣧⠈⣷⠈⠓⢤⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡈⠻⡀⡇⢰⠀⠀⢸⡏⢀⢹⡄⠀⣼⠇⠠⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⠀⠈⠻⣷⠀⠑⢸⠀⠀⠀⢻⣌⠪⡷⠈⠀⠀⣾⠹⣸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢀⣾⠟⠀⠱⣄⠀⠀⢻⡀⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⣿⠀⢠⠞⠁⠀⣶⠈⢿⠀⣠⠿⠃⠘⣺⡷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⢰⡄⢻⡀⡅⠀⠀⢠⡟⠀⠻⠋⢁⡠⠖⢉⢹⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣃⠜⣸⠇⠘⣷⠳⡙⣆⠈⢧⣄⡀⠀⡨⢠⣆⢨⡸⣧⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠴⣫⡵⠚⠁⠀⠀⠈⠳⢑⠈⣷⠀⣿⢃⠞⣵⠏⢹⡼⣧⠀⠈⣹⡆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⣁⣤⠾⠋⠀⠀⠀⠀⠀⣠⠞⠋⣰⠃⢠⡇⠊⣾⠃⠀⠀⠛⣎⠁⠸⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡉⠉⠀⠀⣀⣀⣀⣠⣴⡾⡯⠀⣸⠇⠀⢸⡇⠀⡿⠀⢀⣠⠄⠈⣀⠀⣹⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⡴⣾⠛⠉⣉⡁⠠⢔⣚⣥⠾⠋⠀⠀⠸⡇⠀⠃⣴⠏⠀⣠⣞⠥⠚⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡠⠞⣉⡥⠞⠋⠉⠐⠛⠉⠉⠀⠀⠀⠀⠀⣠⡤⠶⠟⣉⡤⢊⡵⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣁⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣁⣤⡶⢾⣛⣿⡿⡿⢛⢿⣟⣳⣦⡀⠀⠀⠀⠀⠀⢀⡶⠴⠒⠒⢏⢡⢠⡙⢦⡀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⢸⣿⣫⣼⠟⠛⠉⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⢘⡏⠑⢦⠀⢻⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀⣠⣦⠀⠀⢸⣿⣿⠀⠀⣀⣤⠾⠛⠻⡤⠚⠃⢉⠛⠒⠶⠞⠛⣧⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣠⡤⠀⠀⢈⠁⢠⣦⠀⠀⣿⠋⡍⠿⠋⠀⠀⢀⠞⠁⠀⢠⡎⠀⠀⢸⠀⠀⠸⣆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⣠⡄⠀⢸⡀⠀⠉⠀⠀⠀⠀⠙⣧⠀⢀⡔⠃⠀⠀⢠⡟⠀⠀⠀⢸⡆⠀⠀⢻⡄⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⠸⠇⠀⠠⣤⡀⠀⠐⡟⣁⠔⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣷⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡸⠛⠁⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⢷⣀⠀⠀⠤⠔⠋⣀⡤⠖⠉⠀⠀⠀⠀⢀⣤⠿⠃⠒⠒⠒⠒⠒⠛⠛⠉⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠙⠶⣤⣤⠴⠛⠉⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣶⣟⠁⠀⢠⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⣼⡏⣷⣄⠈⣇⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⡴⢟⡿⠋⠀⠀⠸⣇⣿⠛⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠉⠁⠔⢋⡴⠀⠀⠀⠀⢻⣿⠀⣿⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡾
⣼⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⡴⠋⠀⠀⠀⠀⠀⠈⢿⣠⣿⡏⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⡼⠁
⢸⡆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⢻⡀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡾⠁
⠀⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀⠀⠀⣠⠔⢲⡾⢿⠟⣹⣆⠀⣠⠞⠁⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣹⣟⣿⣟⣼⡫⢿⣎⣿⣿⡁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⣿⢎⡵⣯⣚⣽⡦⣿⠏⣻⣷⡀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢯⣿⣧⣛⣼⡷⢋⣾⡿⣿⣛⢌⣻⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠽⣳⢞⡶⣩⣿⣵⡿⣻⢎⡳⢉⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢏⠶⣭⢻⣵⡿⣻⢏⡱⢯⠛⣽⢻⣝⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢪⡟⣴⡳⢾⡷⣭⢳⡜⡳⣛⠾⣱⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡳⢎⡲⣉⣾⣟⠶⣙⢮⡵⢯⡚⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡷⢫⣝⠤⣿⢎⡳⣭⠛⣜⣣⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠚⠉⢹⡟⣬⡳⢎⠷⣿⢻⣝⡦⣛⢾⣽⢯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠸⣟⡶⡝⢫⣾⡾⣳⢎⡱⢯⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢼⡳⣟⠶⣉⢲⣝⡿⣋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣮⣽⢯⣝⡦⣋⣾⡱⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢹⡳⢌⣱⣿⠳⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣴⣿⡓⢮⣛⢤⣹⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣝⡳⣏⣳⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢺⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣟⣉⠛⠛⢋⣩⣿⠇

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡔⠚⠩⣕⠦⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⣦⠉⠉⠛⢯⡑⢠⡀⠻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡌⡇⢹⡄⡠⣄⡀⠀⠀⠀⢀⡿⢴⢋⠈⠳⣤⣀⠀⠉⠓⠉⠻⣆⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡞⣤⡧⠃⣾⡇⠹⣄⢙⢦⣤⠴⡯⠞⠰⠃⢀⣄⠀⢭⡳⡄⠀⠀⠀⠹⡄⠙⣆
⠀⠀⠀⠀⠀⠀⢸⡀⠋⣇⠀⠻⡅⢲⠘⢧⡱⡄⠎⠀⠀⠀⣠⠶⢬⡻⠳⡅⠙⠀⠀⠀⠀⢓⢆⡟
⠀⠀⠀⠀⠀⠀⢸⠃⣾⠘⢧⠘⢁⡞⠀⠀⢻⣎⣆⠀⠀⡠⣁⡤⠤⣉⠒⠌⢳⠀⠀⢠⢞⣟⡞
⠀⠀⠀⠀⠀⠀⠸⠀⢿⣄⠪⣛⠋⠀⠀⠀⠀⠙⠮⠁⠞⠀⣡⠤⠒⢈⡷⢠⡟⠀⡴⠋⣨⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⣧⠀⠀⠀⢀⣴⣾⢏⠉⠉⠁⠀⢠⡞⣀⡟⠀⣸⠁⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠌⢦⢀⣤⣮⢚⡕⠁⠀⠀⠀⠀⠘⡴⣹⢁⡴⠋⠜⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠒⠓⠋⠀⠀⠀⠀⠀⠀⠸⡜⠃⣨⡴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣄⠀⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠃⠀⠆⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠀⠈⠀⠀⠀⠀⠀⠀⢀⣶⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⢵⡖⠾⠉⠀⠀⢀⠀⠀⣰⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣇⠀⢘⡀⠀⢀⠀⠊⠀⢀⠃⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⣿⣦⡴⠋⠉⠀⢀⡴⠃⠀⣂⠈⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠁⠀⠀⢸⡾⣅⣴⣿⢁⣻⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⣠⡖⠈⠁⢻⢿⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢤⣸⣿⡇⠀⠀⠘⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⣻⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⣟⣿⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠁⠉⠙⠛⠿⠖⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣰⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣥⣶⣾⠟⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢈⠔⣫⠔⠁⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠰⠋⡄⠀⠀⠀⠀⠀⠀⠀⢰⠃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⣠⡄⣤⣤⣄⣤⣀⣀⣀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠘⠉⠀⠀⣄⣠⣤⣠⣦⣤⣤⣤⡤⣤⣤⣀⣀⡀
⠀⠀⠈⠀⠀⠀⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠀⠀⠘⢧⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠲⣄⣤⡴⢞⡛⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⢹⣦⢀⣀⣤⡍⠀⠠⢏⣴⣥⣤⣴⣞⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠇⠀⡀⢀⡍⠉⠹⠖⠃⣠⣾⡟⠁⠰⢚⣭⠽⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢈⣿⠏⡱⠔⢾⡏⠋⠀⠀⠀⡴⣤⣿⡻⠧⠀⠘⠩⠖⢻⣽⠿⣿⣧
⠀⠀⠀⠀⠀⢠⣾⠃⢸⣅⠤⢼⡇⠀⠀⠀⢰⢰⡏⠀⢀⡀⠀⠀⠀⠀⠀⠐⠛⠉⣿⡠
⠀⠀⠀⠀⠀⢸⡏⠀⢸⡁⠀⠈⣧⣀⠀⠀⠸⣾⠃⠀⠉⠹⡆⠀⠀⣠⣴⠄⠰⠟⣿⣤
⠀⠀⠀⠀⠀⠘⣧⡀⢸⡇⠀⠀⠻⡌⠙⠲⢤⣸⠆⠀⢰⡦⠁⠀⠀⣡⡀⠀⠀⢠⢟⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠦⢿⡀⠀⠀⠙⠢⣄⡀⠘⡇⠀⠀⠀⡀⡀⠀⠙⠁⠀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠉⠑⠻⠦⠤⣴⢁⣇⣀⡀⠀⠔⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠙⠛⠛⠉⠉⠩⣤⣀⣀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣀⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⢸⡏⠙⣿⠼⢿⡟⢷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⡿⠛⢿⠓⢺⡟⠚⣿⠓⢿⡟⠻⡿⠛⠶⠦⢤⣀
⠀⠀⠀⠀⠀⣀⡤⠾⣿⠷⢾⡿⠨⣿⠇⢿⡿⠬⣿⠥⢿⠧⢼⡿⠴⡿⡧⢾⡿⠿⣷⠦⣤⣀
⠀⠀⢀⣤⡾⢿⣷⠲⣿⡖⢾⡷⠒⣿⢖⣾⣷⣶⡿⠶⠿⣶⣾⣶⣐⣷⡆⣼⣷⣤⣿⣤⣼⣭⢽⣦⣄⡀
⠀⣴⡿⣿⡦⣼⣧⣤⣿⡦⣼⣧⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⣼⣧⢠⣿⣀⣼⣤⣀⣭⣈⣹⣦
⢸⣏⣀⣼⣇⣸⣇⣀⣿⣅⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣏⠈⣯⡁⣹⣉⠈⣻⡉⢹⡏⣷
⠈⠿⣄⣹⡇⢹⣟⠈⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣿⠋⢻⡛⠙⢻⠋⠻⣿⣿
⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣿⣟⠚⣿⣗⣾⠟⠁
⠀⠀⠀⠀⠀⠳⡶⠶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣝⡛⠿⣿⠟⠉⠉
⠀⠀⠀⠀⠀⠈⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡽⠋⠁
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢸⡆⢸⠃⠀⠀⠀⠀⠀⠰⣇⣨⠇⠀⠀⠀⠀⠀⣀⣴⠃⣠⠞⠁
⠀⢀⣤⣤⣴⡚⠉⠓⣾⣶⡀⠀⠀⠀⠀⠀⣼⢇⠀⠀⠀⠀⠀⢸⣿⣏⡉⠉⢲⣤⣤⣄
⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠧⠴⠤⠤⠤⠴⠧⠼⠦⠤⠤⠤⠤⠬⠥⠥⠬⠿⢿⢿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⢀⡼⢁⣾⣿⣿⡿⠋⠀⣸⣿⣿⣿⠟⠀⠄⣀⣠⣶⣿
⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⢀⣯⣶⣿⣿⣿⠟⠁⠀⣰⣿⣿⡿⠁⠠⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣯⣤⠶⠞⠋⣀⣴⣿⣿⣿⣿⡿⠁⠀⠀⣰⣿⣿⡟⠀⠀⢠⣾⣿⣿⣿⡿⠋
⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⢀⣠⣴⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⣰⣿⣿⠋⠀⠀⣴⣿⣿⣿⣿⡟⠁
⣠⣾⣿⣿⡿⠛⡥⠒⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣠⣾⣿⠟⠁⠀⢀⣼⣿⣿⣿⣿⡟⠀⠐⠂
⣿⣿⡿⠋⣴⡿⠁⢀⣴⣿⣿⣿⣿⣿⠿⠿⢿⠟⠋⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⣠⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀
⣿⠟⠀⡼⠋⠀⣠⣿⣿⣿⠟⠋⠁⠀⠀⠀⢀⣀⣀⣤⣶⣾⠿⠛⠉⠀⠀⣀⣤⣾⣿⣿⣿⣿⡿⠃⠀⠀⣠⣶⣿
⠋⠀⡞⠀⣠⣾⣿⣿⠟⠉⠃⠀⠀⠴⠶⠟⠛⠛⠋⢉⣁⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣠⣾⣿⣿⣿
⠀⢨⣧⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⣀⣼⣿⣿⣿⡿⠋
⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠉
⡿⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⠿⠋⠀⢀⣀⣤⣾
⠀⠀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠛⠁⠠⠴⠶⠿⠿⠿⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣿⠿⠟⠋⠉⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶
⣿⣿⣿⣿⣿⣯⣭⣥⣄⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉
⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉
⠿⠿⠿⠿⠟⢛⣛⣛⡋⣉⣀⣀⣤⣤⣤⠤⠀⢀⣾⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⡾⠿
⣶⣾⣿⣿⣿⡿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⣠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⢁⣀⣠⣤
⣿⣿⣿⣭⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡀⢀⣤⣾⣿⡿⠋⠁⣠⣴⣾⣿⣿⣿⣿
⠉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⡴⠋⣰⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⠿⠛
⣀⣤⣶⣶⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣾⠁⣴⣿⣿⣿⠏⠀⣴⣿⣿⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠂⢠⡀⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢛⠋⠉⠀⠀⠀⠤⠧⠀⠀⠀⠒⠀⢸
⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠂⢸
⠠⣴⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⣬⠁⢸
⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠸⠲⠻⣴⠆⠉⢉⣿⠁⠐⠂⢠⣶⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣠⣴⣀⡄⠀⢀⢠⣀⡀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢿⠓⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢠⣟⠆⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣽⡶⢀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠁⠀⣤⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠀⠀⠀⢰⣿⡵⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣆⠀⠀⠀⢼⡿⠗⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠙⠛⣶⠟⣷⠆⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢻⣧⠀⣤⢀⠄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣧⣴⢛⣿⣶⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠸⣿⣿⡟⣻⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⢰⣿⡿⢁⣼⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⣿⣿⢃⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⢂⣾⣿⡏⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⣿⡿⠠⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢂⣿⣿⣿⠃⢾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢰⠰⣿⣿⡏⣀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⢹⣿⣿⣿⣧⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠒⠀⠒⠒⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠀⢸⢻⣿⣿⡇⠀⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⣿⣇⠀⢻⣰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠙⠉⠉⠃⡀⢿⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠘⠂⠐⠒⠒⠐⠀⠀⠀⠀⠀⠀⠐⠆⠴⠄⢀⡀⣠⣤⣦⣾⣿⣷⠞⠂⠚⠁⣴⣶⣶⣦⣤⣤⣤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠏⠀⠀⠀⠰⠶⠀⠉⠉⠉⠁


⣶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠂⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠸⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⠀⡆⠀⠀⠀⠒⠒⠐⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠐⠀⡀⠉⠁⠀⡿⠀⠀⠀⢸
⠀⠀⠈⠀⠀⠂⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣏⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⡀⠀⠀⠁⠀⠀⠀⠀⠐⣿⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠀⠀⠁⠀⠀⠂⠀⠀⡀⠀⣹⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠆⣥⡗⠀⠐⠁⠀⠀⠀⢀⠌⠀⡸⠫⠀⠀⡄⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢉⢰⠂⣧⠖⠁⠀⠀⠀⠀⠀⠑⠀⠀⠟⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⣆⣀⡌⠩⠞⢸⠋⠕⠛⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⡝⠀⢀⠎
⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠩⠋⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠯⠀⠀⠀⠀⠆⠀⢰⠂⠀⠀⠀⠀⠀⠈⠡⠀⠘
⠀⠀⠀⠀⠂⠀⠀⠐⠐⡐⠀⠁⠀⠈⠀⠂⠀⠀⠀⠂⠀⡜⠀⠐⠒⠂⠀⠐⠀⠀⠒⠀⠒⠀⠘⠁⠐⠐⠀⡐⠃⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠐
⠀⡀⠄⡁⠀⢠⡠⢀⠄⠁⡀⠐⡀⠀⢀⠒⢀⠂⣰⣠⠀⣇⠆⡀⠀⠀⢀⠀⡡⢠⠀⠄⠀⡄⢔⠠⠀⠀⠀⠀⠀⠀⠀⠐⡄⢀⠠⠀⠀⠄⡀⢀⠁
⠀⠉⢟⠖⡄⠢⠁⠁⠊⠄⠰⠀⡅⠄⠊⠦⡤⡁⠉⠋⠋⠃⠳⢄⣣⡠⣤⡕⠘⢚⡥⡠⣰⠍⠈⠐⠀⠋⠇⢂⠀⠀⠆⢸⠚⠸⠘⠜⢤⠃⢰⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠉⠉⠉⠙⠛⠓⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣦⡄⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⡀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠈⣿⡄⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⣸⣿⠇⠀⠀⣀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⢿⢂⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠙⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡉⠉⠁⠀⠀⠀⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡖⢶⣶⢞⣿⣷⣶⣾⡿⡛⢡⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣿⣧⣽⣿⡅⢻⠿⢫⣽⣿⠟⣿⣦⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣿⣎⣿⣏⠹⣿⡿⢇⣿⣏⢱⣶⣆⠻⣿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣽⣆⣹⣯⠘⣿⡟⢡⣿⣿⡞⢿⠿⢋⣿⡋⣴⣦⡼⣷⡼⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣹⡝⣻⡉⠿⣟⢺⣿⡿⣠⣿⣍⢰⣿⣿⠜⢿⡿⢉⣛⢱⣮⡔⣾⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠿⠻⣿⠿⣿⣿⠇⣾⡆⢻⣿⠟⣠⣭⡁⣾⣿⣧⠻⣿⡏⣛⢣⣤⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣷⣴⣿⣏⣵⣶⣍⣽⣿⣷⠸⣿⣿⡇⣙⠛⢡⣶⣦⣾⣿⡿⠛⢣⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡍⣥⡝⢛⣭⡻⠿⣟⣙⡛⢫⣶⣿⡅⣾⣿⣷⠘⠿⠟⣠⣍⢰⣿⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣿⠏⢻⣿⡟⠰⣿⣿⡗⢘⠻⠟⢃⣬⣍⢱⣾⣷⡜⣿⡿⣀⡉⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣼⣿⡆⣼⣿⣮⠉⣾⣿⣿⡆⣿⣿⣿⠈⠛⢛⣥⣤⠸⣿⢏⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁⣨⡛⠃⣘⡛⠋⣀⣙⡛⢛⣤⣤⡉⣵⣿⣶⠸⠿⢟⣴⡤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠸⣿⡿⠘⣿⣿⠗⣙⣿⠿⣃⣽⡛⣿⣿⣆⣸⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠐⢿⣿⡆⢾⣿⡿⣚⣿⢟⣷⣾⢁⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⣿⣿⣦⣸⣿⣿⣬⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠠⠤⠐⠒⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⢀⣤⣶⣤⡤⠀⠀⠚⠛⠻⠆⠹⣿⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣿⣿⣷⣶⠄⠀⠈⠀⢤⣤⠃⠀⠀⠀⠰⠶⠀⠀⠙⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠸⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠋⢡⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠁⠀⢀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⢃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢤⡀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡀⠀⣀⣀⣀⣀⣀⠼⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⢄⣡⠊⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣿⡏⠛⠛⠉⠉⠉⢉⠉⠀⠀⠀⠛⠀⠤⠄⠀⠀⠀⠀⠀⠀⠆⠀⢀⡠⣌⠁⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠁⠠⢤⡈⠠⠖⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢸⠄⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠁⠀⠀⠈⠉⠠⢄⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠰⠆⢀⡴⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⢀⠆⠀⠻⠖⠐⠶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠽⠀⠀⠀⠀⠀⠀⢀⣤⠞⠳⠋⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠐⢢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⢃⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣽⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⣄⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠻⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡈⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠃
⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠠⠄⢀⣀⡀⡀⠀⠀⠀⠀⣀⣀⣀⡠⠆⠈⡹
⠀⠀⠀⠔⢉⠀⠀⠤⠄⠈⠀⠀⢈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠁⡀⠊⠀⠰⡖⠒⣦⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠣⠀⡜⠁⡋⠈⡟⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠠⢀⠀⠀⠠⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠈⢦⠀⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠆⢀⠀⠃⠀⠀⠐
⠀⠘⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡇⠀⠀⠀⠈⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⣤⣶⠟⠁⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠉⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠒⠤⠤⡤⠤⣤⡤⠟⠀⠀⠀⠀⠘⠦⠤⠘
⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⢠⡇⠀⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤
⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂
⠀⠈⠳⠄⣀⣀⣀⣀⣠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉

⠀⠀⠸⠀⠀⠀⠀⠱⠖⠃⠄⢢⡆⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡰⠀⠀⠠⢀⢬⠀⠀⠀⠀⢘⠀⠀⢀⠆⡀⠀⠀⠀⠀⡆⠀⠀⠀⣀⣀⠤
⠀⣀⢰⡁⢀⡀⣭⠀⠀⡄⠀⠈⠑⢴⠤⠤⠤⠠⢼⠀⠔⠀⠢⠠⠋⡖⠰⠒⠊⠀⠈⠑⠲⠂⠀⠀⠓⢰⡂⠀⠈⠘⡁⠀⢀⡉⠈⠐⠒⠊⠁⠄⠀⠀⠈⠁
⠀⠀⠀⠈⠈⠀⠀⡈⣰⠁⠀⠀⢀⡏⠀⠀⠀⠀⢘⡆⠀⠄⠀⠀⢀⡂⠈⢀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠌⠈⠂⠀⠈⣇⠀⠀⠰⠀⠀⠀⠀⠀⠘⠀⠀⠀⢈⡀⠀⢀
⡀⣀⡈⢀⠦⠒⠊⠀⠉⠀⠆⢀⣈⣀⠜⠂⠈⠙⠁⠀⠘⠀⡀⠀⠀⠈⠀⡠⠲⠀⠤⡖⠁⠀⠀⠀⠈⢃⠀⠀⢠⠊⠀⠀⠀⠲⡀⠀⢀⡀⣀⡼⢅⠀⠀⢠⢀⠀⢀
⠀⠀⠀⢓⠀⠀⠀⠀⢀⠄⠂⠀⢰⠁⠁⠀⠀⠴⠁⠐⠀⡀⠈⠁⠂⣸⠋⠁⠀⠀⠀⡧⠀⠀⠤⠀⠂⢠⠁⠁⢓⠄⠀⠂⠄⠀⠙⠉⠉⠀⠈⠀⠀⠈⠁⠁⠀⡘⠈
⠀⡀⢠⠘⠤⠀⠀⠀⢮⡀⠀⠀⠐⠁⠀⠐⠄⠀⠄⠠⠒⠉⠀⠐⢋⠀⢀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣀⠼⠀⠀⢤⡀⠹⢄
⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠠⠄⠢⠠⠄⢠⠃⠀⠀⢀⠀⠀⠈⠁⢤⠔⠂⠀⠀⢨⠐⠔⠂⠀⠁⢮⠀⠀⠤⢀⠀⠔⠁⠀⠢⡄⠀⠀⠀⠀⡘⠀⠀⠀⢀
⡄⠀⠀⠁⠀⢀⠀⠀⠄⠃⠀⡀⠔⠀⠀⠁⠀⠀⠄⣰⠆⠀⠀⠀⠱⠄⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⡠⢄⡀⠤⠤⣀⡀⠀⠀⠀⠓⠀⠀⢀⣴⠁⠀⠀⠀⠔
⠡⠀⠄⠂⢠⠀⠢⠔⠀⠀⠀⠘⠐⡀⠀⡀⠎⠀⢀⠉⢀⠀⠀⠀⢀⠑⠢⣀⣠⡀⣀⡰⠚⠀⠀⠠⠒⠀⠀⡁⠀⠀⠀⠰⠀⠀⠄⠐⠀⠉⠂⠇⡁⠀⣂⡀⠤⠈
⠁⡀⠀⠀⡀⠀⠀⠘⠐⠄⠀⠀⠀⡆⠀⠀⠀⠀⡌⠀⠈⠀⠀⠑⠁⠀⠀⠉⠀⠀⠁⠈⠐⠀⠲⡀⠀⠀⠀⡁⠀⠀⢠⠌⠀⠀⠀⠀⠀⠘⠀⠀⠨⠀⠈⠀⠓⠀⠄
⠀⠀⠀⠐⠠⣄⣀⠀⠀⠀⠃⠀⢸⠁⠀⠈⠀⠀⠈⡇⠀⠀⠀⠀⠂⠀⠄⠀⠈⢣⠀⠂⠀⠀⠀⠈⠀⠀⡠⠤⠀⢀⠡⠀⠠⠀⠀⠈⠁⠃⡄⠀⠀⠈
⠀⢈⠀⡀⠀⠀⠀⠉⠁⠀⠀⠠⣎⡀⠀⠀⠄⢀⠄⠰⠀⠤⡄⠀⠰⠂⠒⠀⠀⠢⠀⠀⠀⠀⠈⠅⠂⠈⠀⠀⡀⠀⡆⠀⠀⠀⠈⠀⣀⣀⠴⠄⠀⠊⠋⠉⠑⠤
⠀⠀⠀⠀⠂⠀⠀⠰⠀⡤⠀⠁⠀⠡⠄⠤⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⢀⠀⠐⠀⠁⠀⠉⠀⠀⠐⠀⠀⠀⠀⡄
⠂⠠⠀⠉⠐⠂⠀⠀⢄⠀⠀⠀⠀⠤⠜⠢⣄⠀⠀⠀⠀⠀⠀⠂⠓⠀⠀⠀⠀⠠⡊⠀⠀⠀⠒⠈⠈⠢⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠠⠢⠄⢀⠄⢂
⠀⠀⠠⠄⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠄⠐⣂⠁⠀⠀⠀⡄⠒⠂⠀⠐⢢⠐⠀⡅⠀⢀⠀⠉⠁⠂⢉⠱⠀⠂⠀⠈⠄⠀⠀⠀⠀⠐⠀⢀⠂⠂
⠀⠀⠀⠉⠐⠂⠀⠁⠉⠁⠈⠀⢡⠀⠀⠀⠀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠒⠻⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠳⡀⠀⠀⢀⠀⠚⠁⠀⠀⣡
⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⡄⠈⠀⠀⠡⡀⠀⠀⠀⡃⠀⠀⠀⢀⠴⡄⠀⠔⠀⠤⢀⠀⠀⢀⠄⠉⠈⠑⠢⣎⠀⠀⠀⠀⡀⠗⠈⠀⠀⠀⠠⠂⠀⠒⠒
⠈⠆⠀⠀⢀⠀⠀⠀⠁⠀⠁⠠⢌⡀⠀⠀⠄⠤⠀⠀⠀⢈⠅⠉⠒⢈⠁⠀⠀⠀⡇⠀⠀⠈⠑⠀⠸⠀⠀⠀⠀⠀⠘⠀⠁⠀⠐⠡⠖⠀⠀⠀⠀⠸⠀⠀⠀⠀⢣
⢀⢠⡀⠈⠉⠁⠀⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⡂⢀⢀⡈⠀⠀⠀⢐⠀⠀⡄⢀⠒⠠⠀⠰⠤⠀⠊⢀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠸⡃⠐⠂⠀⠤⠨⠀⠀⠀⠀⠜
⠀⠀⠠⠀⢆⠀⠀⠀⡀⠈⠀⠀⠀⠀⠂⠀⠀⡠⠀⠀⠀⠱⠄⢀⡄⠀⠀⠀⢘⠀⠀⠀⠄⠀⠂⠀⠀⠁⠱⠘⠀⢀⠀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒
⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⠐⢀⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⣀⠰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⡀⠄⠉⠀⠠⠀⣄⠀⠠
⣀⢀⢀⠀⠀⠀⠀⡂⠀⠀⡨⠈⠀⠀⠈⠀⠀⠀⠄⠀⠀⠌⠂⠀⠀⠲⠤⠄⢤⠀⠠⡀⠈⠀⠀⠀⡀⠀⠀⠀⠈⣀⠀⠀⠀⢠⠑⠀⠂⠀⠀⠠⠀⠠⡀⢀⠄⠀⠤
⣤⣤⣤⣤⣬⣤⣤⣤⣥⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣬⣤⣤⣤⣬⣦⣬⣥⣤⣭⣭⣭⣥⣭⣵⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣛⣛⣿⣹⣙⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣯⣽⣭⣿⣿⣭⣭⣭⣿⣽⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠁⠀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠠⠤⠀⠀⢰⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢀⣤⠶⣥⠄⠀⠐⠳⠖⠘⣿⣿⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠑⠒⣲⣿⣿⣿⡶⠈⠀⠀⠲⠼⠀⠀⠀⠙⠓⠀⠈⠛⣿⡿⠿⠆
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢄⠀⠀⠀⠀⠂⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠑⢄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣾⠛⠶⠚⠛⠛⠛⠁⠀⠀⠆⠠⡄⠀⠀⠀⠀⢠⠀⠈⣀⡝⢉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⠀⠀⠈⠀⠃⠠⢤⠀⠔⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠁⢸⠆⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⡘⢀⡔⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⡂⡰⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⡄⣠⠾⠴⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠦⡀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⢃⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⠃⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠛⠒⠤⠄⣀⣀⠀⠀⠀⠀⣀⣀⡀⠤⠐⡪⠐
⠀⢠⡈⠀⠀⠤⠈⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⠨⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⢥⡔⠁⠀⢛⠁⣆⡀⡱⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠐⠁⠠⢐⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⡀⠀⠀⠰⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉⠀⠈⣄⠠⠄⢀⠀⠊
⠀⠀⠀⠀⠀⠀⡅⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⣀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠖⠃⠠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⠞⠛⠉⢻⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠊⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣄⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠈⠉⠚⠉⠛⢁⢀⡀⠀⠀⠈⠉
⡀⠠⠀⠀⠀⠆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⡀⠤⠰⠈⠉
⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡀⡀⠤⠐⠆⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠻⣄⣀⠟⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⣠⠴⠖⠚⠛⠋⠙⠛⠓⠲⠦⣄⠀⠈⠓⠒⠋
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠙⠻⠭⣉⠙⠒⠒⠶⠤⣤⣄⡀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢀⣠⣤⠤⠴⠒⠒⠋⣉⠭⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⡀⠀⠀⣹⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⣏⠀⠀⢀⣠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠓⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⡀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⠀⡸⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢇⠀⠀⠈⠙⠲⠦⣄⡀
⠀⠀⠀⠀⢀⣠⣴⣚⣉⠤⠤⠴⠒⠚⠋⠉⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠉⠙⠒⠒⠢⠤⠤⣉⣓⣦⣄⡀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⡀⠀⠉⠓⠲⠤⢤⡤⢤⡤⠤⠖⠚⠉⠀⢀⡴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⣼⠉⠉⣧⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠿⠟⠛⠛⠛⠿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⣠⣽⡿⠉⠀⣴⡄⠀⠐⠿⠀⠀⠀⠈⠙⠛⠿⢷⣶⣤⣀⡀
⠀⠀⠀⠀⣾⣿⣿⣟⣉⠉⠙⠛⠛⠛⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠀⠀⢈⣉⣛⣿⣿⣶⣤
⠀⠀⠀⠀⣿⡇⠉⠙⠻⠿⣶⣦⣄⣀⠀⠘⠋⠀⠀⠀⢠⣴⣶⠶⣶⣶⣤⣀⣤⣤⣾⡿⠻⣿⡟⠛⢹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣦⣄⣀⣀⣸⣿⣄⠀⠀⢈⣿⠟⠋⠉⠙⢿⣾⠿⠁⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣴⡿⠿⢿⣷⡀⠀⠀⠀⠉⠙⣿⡟⠛⠙⠿⣷⣶⡿⠋⠀⠀⢀⣄⠀⠀⠠⣶⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣿⣇⠀⢀⣿⡇⠀⢠⣶⠀⠀⣿⡇⠀⠠⣶⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠈⠻⠿⠿⠋⠀⢀⣀⣀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠐⠿⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⠛⣿⣧⠀⣿⡇⠀⠀⠀⠀⠀⢾⣿⣉⣿⡇⠀⠀⢀⣀⣀⠀⢸⣿
⠀⠀⠀⠀⢿⣷⣤⣀⠀⠀⣀⠀⠈⠻⠿⠿⠃⠀⣿⡇⠀⠰⠶⠀⠀⠈⠛⠛⠋⠀⠀⣴⡿⠛⠻⣷⣾⡿
⠀⠀⠀⠀⠀⠈⠙⠻⢿⡿⠻⣿⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣤⣤⡀⠀⣀⣠⣴⣿⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣤⣀⠀⠀⣿⡇⠀⠀⢰⣿⠋⠙⢿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣿⣧⣶⡾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠒⠀⠲⣖⡶⠒⢲⠖⠒⠒⠒⠒⠒⠒⢒⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠤⡄⠀⠀⠎⠂⠉⢦⠈⠀⢠⠛⣄⠠⠒⠦⣀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠦⡀⠀⠀⠀⢸
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡀⠐⠀⠀⠘⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢰⠀⠀⣠⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠒⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠣⣀⠤⠆⠒⠊⠉⠀⠈⠉⠉⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠢⣄⡀⠀⠀⢀⣀⡇⠀⠀⣇⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⡀⢸
⠀⣂⣀⣀⠀⠌⠀⡄⢨⣶⣀⡉⠦⢀⠀⣀⣀⡀⠀⠀⠉⠒⠉⠀⠀⡇⠀⠀⡏⠉⠁⠀⠈⠉⠁⠐⠒⠁⠀⠈⢣⣀⣀⠔⠒⠢⠖⠊⠁⠀⠀⠈⢾
⠀⠀⠀⠀⢈⠀⡘⢝⢸⣇⡜⢧⡤⠀⢩⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⡇⠀⠀⡏⠉⠉⠁⠉⠉⠀⠀⠐⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠒⢸
⠀⠀⠀⠀⠈⡶⢣⡀⡱⡊⠈⢉⠇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠠⣈⣚⣒⣚⠩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡀⢀⢆⠀⣾⠅⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣾⣷⣶⠶⠶⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣀⡐⣌⣾⣈⠀⡯⠀⣜⣰⠕⢲⠆⣀⣤⣴⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⡋⢰⡥⣟⡹⢒⡷⢻⣹⣏⣿⣝⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠒⠤⠀⠀⣠⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠰⣿⡆⢠⣾⠁⠀⠈⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠄⠠⠿⠛⠃⠀⠀⠀⠀⠀⠘⠀⠀⠠⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠉⢀⡀⠤⣿⣤⡌⠐⠠⠀⢀⣤⣤⣀⡀⠠⢤⠀⠙⠢
⣠⡤⠶⠶⠀⢀⡁⠀⠘⡉⢀⡠⢶⣦⣤⣐⣂⠈⠛⠇⠠⠤⠼⢿⣿⣿⣿⠿⠿⠶⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢂⡀
⠻⢶⣄⡀⠀⠀⠹⢷⡒⠂⡏⠉⠃⠀⠀⠀⠀⣀⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡥⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠳⢯⣀⢀⣾⣿⣿⠀⠀⠀⠀⢀
⠀⠀⠈⠙⠳⢦⣤⣸⡉⠀⠰⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣾⣿⣶⣦⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⠻⠟⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢻⠷⢦⣵⣄⣀⠀⠈⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣵⣿⣿⣿⣿⣻⣿⣦⡬⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡬⠵⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⡍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣟⣿⣿⣧⣠⣦⣤⣤⡤⠤⠶⠖⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡄⠿⠆⠈⣝⢿⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣧⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠈⠀⠒⠠⠄⢬⣖⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣮⣙⣤⣬⣩⣯⣵⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⡄⠀⠀⢀⠤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠈⠀⢁⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠙⢀⠔⠁⠀⠘⢢⠀⠈⣉⣒⡶⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣄⠀⠀⢀⡼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠥⠴⠃⠀⠉⠉⡁⠀⠰⣌⠣⡀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠦⣤⠴⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢸⡆⠀⢧⡆⠀⠈⠉⠉⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⠀⠀⠀⢀⡤⠀⠉⢷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡰⠉⠀⠈⠉⠉⠙⠉⠉⠀⠀⣠⠞
⠀⠀⠀⢀⠔⠋⠙⠲⡴⠋⠉⠉⠙⢦⡤⠶⠶⠶⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢦⠀⠀⠀⠀⠀⢰⡇⠀⠀⡀⠀⠀⠀⢀⡟⠛⠉
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠉⠛⠋⠛⠦⢤⠴⠚
⠀⠙⠒⠒⠻⣄⡀⢀⣀⡼⠲⠶⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢧⣀⡀⢀⣤⣀⠀⢀⣠⠏⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⠀⠀⠀⠀⢀⡠⠔⠲⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⡇⠀⠀⠀⠙⢦⣄⣀⣠⣤⡇⠀⠀⠀⡅⠀⠀⠹⣄⡀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢟⠀⠀⠀⢱⠀⠀⠀⠀⠘⣿⠇⢻⡟⠀⠀⠀⢀⠇⠀⠀⠈⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡧⢸⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠔⠁⠀⢀
⠀⠀⠀⠀⠐⠛⠷⠤⠀⣀⡀⠀⠀⢳⠀⠀⠀⠀⠀⢽⣿⡇⠀⠀⠠⢸⠇⠀⢀⡠⠞⠁⠀⠀⢀⡎⠀⠀⠀⠀⣠⡴⢦⠴⠶⣦⡀⣀⡀
⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠈⠑⠲⠾⣆⠀⠀⠀⠀⠀⢹⠆⠀⠀⠀⢸⡀⣰⠊⠁⠀⠀⠀⢀⡜⠀⠀⠀⢠⠞⠁⠀⢨⠀⠀⢸⡏⠉⠻⡆
⠀⠀⢠⠟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠈⠃⠀⠀⠀⢼⡼⠃⠀⠀⠀⠀⣠⡞⠀⠀⠀⢠⠏⠀⠀⠀⣶⠀⠀⠉⠀⠀⢠⣷⢤⡀
⠀⠀⠀⠞⠙⣻⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⣠⡿⠀⠀⠀⠀⢿⠀⠀⠀⣠⡖⠋⠀⠀⣷
⠀⠀⠀⠀⠔⠋⢻⡿⣿⠟⠛⣿⣦⡄⡀⠀⠈⠈⠻⣦⡀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢰⡞⠀⠀⠀⠀⢹⡇⠀⠀⠀⠠⣼⣤⡶⠟⠁⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠈⠛⠙⣷⡀⠀⠀⠀⠈⠻⣦⣀⠂⣾⠃⠀⠀⠀⣸⠏⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⢀⢀⣼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢸⡿⣆⡀⠀⠀⠀⠙⣷⣽⡏⠀⠀⠀⣴⠏⠀⠀⠀⢀⣤⣾⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⣸⣿⣿⣷⣶⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡀⠀⠙⣿⡇⢀⠐⣸⠇⠀⠀⠀⣠⣽⣿⠇⠀⠀⠀⢀⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠹⣁⣠⡼⠋⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⣠⡾⠁⠀⢀⠖⠛⠛⠛⠿⠿⠋⠀⣠⡶⠞⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠊⠋⠀⠀⠀⠀⠀⣠⠉⠋⠀⢀⢀⣼⡏⠀⠀⠀⠀⡀⠀⠠⠀⢀⣰⠾⠛⠉⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠲⠥⠀⠖⠉⠙⠛⠛⠿⠿⠿⠿⠳⠛⠶⣟⠁⠀⠀⠀⠀⠤⠶⢾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠚⠿⠤⢆⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠉⠛⠾⣄⡀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⢷⣷⠶⣦⣆⡄⠀⠀⠀⠀⠈⠉⠓⢤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠻⢻⡿⣶⣤⣶⣤⣤⣴⠞⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠋⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢸⢆⢠⢣⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠒⠦⢈⣃⣀⣁⣈⡋⠸⠔⡹⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣏⠉⡠⠊⠁⠀⠀⠀⠀⠈⠑⠢⡉⢡⣃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣦⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠉⠛⢶⡄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣔⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠓⠒⠉⠉⠉⠑⠒⠢⢄⡀⠀⠀⠀⢸⠠⣔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⡌⢠⡐⠓
⠀⠀⠀⠀⢠⠔⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⠊⠰⡒⠳
⡠⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⣓
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⣬⣵⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣯
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⣿⠿⣿⣦⣬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠒⢦⡀⠰⡟⠓⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠻⣦⡀⠀⠙⠆⠠⠬⡃⣰⠟⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⣀⡌⠀⠙⠦⣤⠀⠀⠀⠈⠙⢠⡀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡁⠀⠁⠀⠐⠀⠛⢤⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢶⣷⠂⠀⠀⠀⢻⣇⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠉⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣀⣀⡀⠀⣀⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠉⠉⠛⠻⠿⠿⢿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠐⣄⠀⠀⠀⠀⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠈⣷⡀⠀⠀⠀⢻⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡀⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣾⡇⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢻⡇⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢹⣷⡀⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣧⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⢰⡟⠘⣆⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡆⠀⣿⠃⠀⠘⢧⡀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⠀⢿⡀⠀⠀⠐⡅⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⣾⣧⠀⠀⠀⠹⣆⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠹⣿⠀⠀⠀⠀⢿⢧⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢻⡀⠀⠀⠀⠘⣦⣼⡿
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣼⠗⡾⠾⣧⣴⣦⣀⡄⣿⣿⣥⣤⣤⣤⣄⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠐⠚⠁⠀⠈⠉⠙⠉⠉⠀⠈⠁⠀⠈⠀⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠸⡄⢸⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠁⠀⢁⣀⠀⠁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠴⠋⠁⠀⠉⠲⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⡄⠀⠀⠀⠀⠀⡇⢀⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠢⡀⢀⠡⣄⡈⠋⣀⡴⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠁⠀⠀⠀⠀⠁⢀⡉⠉⢁⡠⠤⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⣀⠀⠀⠐⠋⠀⠀⠁⠐⠀⠀⠙⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢠⠔⠀⠀⣀⣠⣤⣄⣀⠀⢀⡤⠶⠒⠒⠦⢤⡀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠋⢀⡴⠊⠁⠀⠀⠀⠀⡴⠋⢀⠀⠀⠀⠀⠀⠙⠀⠉⠁⠉⠙⠢⠤⠔⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠚⠀⢀⣀⡤⠤⠤⠤⢤⣀⡀⠀⠀⠀⢀⡠⠴⠒⠒⠲⢦⣄
⠀⠀⠀⣰⠛⠁⠀⠀⠀⣠⠞⢩⠂⡀⢐⠆⠀⠀⠀⡭⠗⣦⠰⠋⠀⠀⠀⢀⣀⠀⠈⠳⣄
⠀⠀⢰⠃⠀⠈⠀⠀⡰⠁⠀⠀⠀⢀⢨⠆⠀⠀⠀⠦⣀⠉⢳⠀⠀⠠⣆⢠⠚⣢⠀⠀⠘⣇
⠀⠀⢸⠀⠀⠀⡀⢠⠃⠀⠀⠀⠉⠁⠀⢀⠠⠀⠀⠀⠀⠀⠸⡆⠀⠀⠈⠢⠜⠁⠀⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⢸⡀⠀⠠⠄⢠⠀⠀⢙⠀⠆⢐⠄⠀⠀⢰⡇⠀⠄⠀⠀⡠⠀⠀⠀⣰⠃
⠀⠀⠀⠈⠓⠦⢤⠀⢷⡀⢸⢀⡠⠃⠀⠈⠑⠁⠀⠀⠀⢀⡞⠀⠰⠦⢤⣤⣥⡥⠾⠛⠁
⠀⠀⠀⠀⠀⠀⢲⡀⢠⠙⢦⣉⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⣄⠸⡄⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⣷⠈⢰⠂⠸⡍⠛⠓⡚⠛⢁⠄⠀⠀⠀⠀⠸⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⡟⠀⣾⠀⠀⠙⡄⢠⠇⣰⠋⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇
⠀⠀⠀⠀⣠⠶⠒⠒⠲⠦⡀⠀⠀⡏⠀⣿⢠⣀⣀⠀⢀⡤⠤⣸⠁⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢫⡇⠀⣿⠀⠀⠈⠙⠲⠄⠀⠀⠀⠀⠀⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⠛⠛⠛⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠠⠀⠀⠈⠂⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⢠⣞⠁⣀⠀⠀⠀⠀⠀⢠⡀⠀⠘⠆⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⢠⠏⣄⠀⠈⠀⠀⠐⠆⠀⠀⢁⡀⠀⠀⠲⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⣿⡇⢀⡀⠈⠃⠀⠀⠠⢄⠀⠀⠘⠀⠀⠀⠀⠲⡀⠀⠀⠉⠂⢀⣀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣼⣿⣷⠈⠃⠀⠐⢲⠀⠀⠈⣀⡀⠀⠉⠙⠆⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⣿⣯⣿⣄⠘⡇⠀⠀⠠⣄⠀⠀⠙⠆⠀⠀⠀⠉⠳⠀⠀⠀⠀⠈⠂⠐⠄⠠⠄⠀⠀⢿
⠀⠀⠀⠀⣿⣿⣏⣿⣄⠀⢶⡄⠀⠈⠃⣀⠀⠀⠉⢳⠀⠀⠀⠀⠉⠳⢀⣠⡀⠀⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠀⢿⣿⣿⣏⢿⣧⠀⠃⣠⡀⠀⠉⢳⠀⠀⠀⠐⠙⢳⠀⢀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⡿
⠀⠀⠀⠀⠘⣿⣿⣿⣷⡟⣿⣦⠈⠻⢀⣀⠀⠈⠙⢳⠀⠀⠀⠀⠉⠙⠀⠴⠦⢀⠤⠀⠠⠀⣸⠇
⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣦⣿⢷⣦⡈⠙⠷⠀⣀⠀⠈⠉⠳⠀⣠⣄⠀⠀⠀⠀⠀⠀⡀⣰⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣽⣿⣦⣭⡿⣶⣦⡈⠙⠷⢀⣤⣄⠀⠀⠈⠀⠉⠁⠐⠉⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⣿⣭⣻⣿⣮⣽⡟⢿⣶⣄⣀⣉⠐⠛⠓⠠⠒⢂⣈⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣾⣿⣷⣭⣽⡿⢶⢾⣯⣭⣽⣛⣛⣟⣛⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡅⢀⠀⢨⠀⡈⠀⡀⢀⠀⢁⠀⡀⠈⠀⡀⠀⡄⢠⠁⢡⠀⡄⠀⡀⢠⠀⢄⢀⡅⢀⠀⡀⠀⡄⢠⠀⢀⢀⡅⢨⠀⡀⠀⡄⢠⠀⢀⠀⡄⠈⡀
⠀⡄⠀⠄⠠⠀⠀⠠⠀⠠⠀⡄⠀⠄⠠⠀⠠⠀⠆⠠⡄⠠⠀⠆⠠⠀⠠⠀⡄⠀⡄⠠⠀⢠⠀⠄⠠⠀⡄⠀⡄⢠⠀⢠⠀⠄⠀⠀⠄⠀⠄⢠
⠀⠆⠐⠀⠀⠀⠆⠀⠆⠰⠀⠰⠀⠂⠀⠀⠴⠀⠆⠰⠀⠰⠀⠂⠀⠄⠰⠀⠂⠰⠀⠰⠀⠂⠀⠄⠰⠀⠀⠠⠆⠰⠀⠆⠀⠀⠰⠀⠐⠀⠆⠐⠆
⠀⠂⠀⠂⠐⠀⠐⠐⠀⠐⠀⠒⠀⠂⠐⠀⠘⠀⠃⠀⠂⠐⠀⠂⠐⠀⠘⠀⠇⠀⠂⠐⠀⠂⠀⠂⠐⠀⠃⠀⠂⠐⠀⠐⠀⠂⠀⠂⠂⠀⠂⠐
⠀⡁⠀⠀⠈⠀⠁⠀⠁⠈⠀⡈⠀⠁⠈⠀⠃⠀⠁⠘⠀⠈⠀⠁⠈⠀⠉⠀⡀⠘⠀⢘⠀⠃⠀⠁⠈⠀⡈⠈⠁⢈⠀⠀⠀⠁⠈⠀⠈⠀⠃⢀⠁
⠀⡁⢀⠁⢈⠀⡈⠈⡀⢈⠀⢁⠀⡁⢈⠀⡈⠀⡀⢈⠁⢁⠀⡁⠈⡀⢀⠀⢁⢀⡁⢈⠀⡀⠀⡁⢀⠀⢁⢀⡁⢈⠀⠈⠀⡁⢀⠁⢁⠀⡁⠘⡀
⠀⡄⠀⡄⢠⠀⠀⢀⠅⢨⡀⡄⠀⡄⢠⠀⢠⠀⡄⠈⡀⠀⠀⡅⢠⠀⢀⠀⡄⠈⡄⢠⠀⢠⠀⡅⠠⠀⡄⠀⡄⢠⠀⢠⠀⡄⠀⠀⡄⠀⣁⢠
⠀⠄⠠⠀⠀⠀⡄⠀⠄⠠⠀⢤⠀⠀⠀⠄⡤⠀⠆⠠⠀⢠⠀⠆⠀⠄⠠⠀⠇⠠⠄⠠⠀⠄⠀⠄⠠⠀⠄⠠⠄⠠⠄⠄⠀⠀⢠⠀⠠⠀⠄⠀⡄
⠀⠂⠀⠆⠰⠀⠲⠰⠀⠀⠀⠀⠀⠆⠰⠀⠰⠀⠂⠀⠆⠐⠀⠆⠀⠀⠐⠀⠆⠀⠆⠐⠀⠂⠀⠂⠐⠀⠆⠀⠂⠐⠀⠰⠀⠆⠐⠂⠂⠀⠂⠐⠂
⠀⠂⠀⠀⠘⠀⠃⠀⠂⠘⠀⠐⠀⠂⠀⠀⠃⠀⠀⠐⠀⠐⠀⠂⠀⠀⠘⠀⠀⠐⠀⠐⠀⠂⠀⠃⠘⠀⠐⠐⠃⠐⠀⠂⠀⠃⠘⠀⠐⠀⠃⠀⠂
⠀⡃⠀⠁⢘⠀⡘⠈⠀⢈⠀⠃⠀⠃⠈⠀⠈⠀⡁⢈⠃⢋⠀⡁⠀⠀⢀⠀⠃⠀⡃⢈⠀⡁⠀⡁⢀⠀⠃⠀⡃⢘⠀⠈⠀⡃⢀⠃⢁⠀⡃⠘
⠀⡁⠈⡀⢈⠀⠁⢀⠁⢈⡀⡀⠀⡁⢀⠀⢁⠀⡁⢈⡀⣈⠀⡅⢀⠁⢈⠀⡈⠈⡀⢈⠀⢁⠀⡁⢈⠀⡈⠈⡁⢈⠀⢀⠀⡅⠈⠀⣈⠀⣁⢀⠁
⠀⡄⠠⠀⠀⠀⡄⠀⡄⢠⠀⢡⠀⠀⠀⠀⣠⠀⠄⢠⠀⢠⠀⠄⠀⡀⢠⠀⠅⢠⠁⢠⠀⠌⠀⠄⢠⠀⠅⢀⡄⢠⠀⠄⠀⠀⢠⠀⢠⠀⡄⠈⡄
⠀⠄⠀⠄⢠⠀⠠⠠⠀⠀⠀⠄⠀⠄⠠⠀⠰⠀⠆⠀⠄⠠⠀⠄⠠⠀⠰⠀⡆⠀⠄⠠⠀⠤⠀⠄⠰⠀⠆⠀⠄⠰⠀⠠⠀⠄⠐⠄⠄⠀⠀⠠
⠀⠂⠀⠀⠐⠀⠂⠀⠂⠐⠀⠐⠀⠂⠐⠀⠂⠀⠂⠐⠀⠐⠀⠂⠀⠂⠒⠀⠀⠐⠀⠐⠀⠂⠀⠂⠐⠀⠐⠐⠂⠐⠀⠀⠀⠂⠐⠀⠐⠀⠂⠀⠂
⠀⠃⠀⠂⠐⠀⠐⠐⠀⠘⠀⠃⠀⠂⠐⠀⠐⠀⠁⠀⠂⠂⠀⠃⠀⠀⠘⠀⠃⠀⠃⠘⠀⠀⠀⠂⠀⠀⠃⠀⠃⠘⠀⠐⠀⠃⠀⠂⠃⠀⠃⠸
⠀⡉⠈⡀⢈⠀⠁⠀⠃⢈⠀⡉⠀⡁⢈⠀⠁⠀⡁⠈⠀⠈⠀⡁⢀⠁⢈⠀⡈⠈⡁⢈⠀⢃⠀⡃⢈⠀⡈⠈⡁⢈⠀⢉⠀⡁⠈⠀⠈⠀⡁⢀⠁
⠀⡁⢀⠁⠈⠀⡀⠈⡀⢈⠁⢁⠀⠁⠈⠀⣀⠀⡁⢀⠁⢁⠀⡅⠀⡀⢀⠀⡁⢀⡁⢈⠀⡈⠀⡁⢀⠀⠁⢀⡁⢈⡀⡈⠀⡁⢀⠀⢁⠀⡉⠈⡀
⠀⠄⠀⡄⢠⠀⠥⢠⠀⠠⠀⠀⠀⡄⢠⠀⢡⠀⠄⠀⠄⠠⠀⡄⠀⠀⠠⠀⡄⠀⠄⠠⠀⠄⠀⠄⠠⠀⡄⠀⠄⠠⠀⢠⠀⡄⠠⠄⠄⠀⠄⠠⠄
⠀⠄⠠⠀⠐⠀⠆⠀⠄⠰⠀⠠⠀⠄⠐⠀⠆⠀⠆⠰⠀⠠⠀⠄⠀⠀⠰⠀⠠⠠⠀⠠⠀⠄⠀⠆⠰⠀⠠⠠⠆⠠⠀⠀⠀⠆⠰⠀⠠⠀⠆⠀⠄
⠀⠂⠀⠂⠰⠀⠐⠐⠀⠐⠀⠆⠀⠂⠰⠀⠰⠀⠀⠐⠆⠆⠀⠂⠀⠀⠐⠀⠂⠀⠆⠐⠀⠂⠀⠂⠀⠀⠆⠀⠆⠐⠀⠀⠀⠆⠀⠂⠂⠀⠂⠰
⠀⠃⠐⠀⠘⠀⠃⠀⠃⠘⠀⠐⠀⡃⢀⠀⠃⠀⠃⠘⠀⠘⠀⡃⠀⠂⠈⠀⠀⠐⠁⠘⠀⠃⠀⡃⠘⠀⠐⠐⠃⢘⠀⠂⠀⡃⠘⠀⠘⠀⠃⠀⠂
⠀⡁⢀⠁⠈⠀⡀⠈⡀⢈⠁⢁⠀⠁⠈⠀⣈⠀⡁⢈⠁⢉⠀⡁⠈⠀⢈⠀⡃⢀⡁⢈⠀⡉⠀⡁⢈⠀⠃⠀⡁⢈⠀⡈⠀⡁⢈⠀⢉⠀⡉⠘⡀
⠀⡅⠀⡀⢀⠀⢥⢀⠅⠨⠀⠈⠀⡀⢀⠀⢩⠀⡅⠈⡀⠨⠀⡄⢀⠀⢨⠀⡄⠈⡄⢨⠀⣁⠀⡀⢨⠀⡄⠈⡄⢨⠀⢀⠀⡀⠨⡀⡌⠀⠁⢀⠅
⠀⠄⠠⠀⠠⠀⠄⠀⠄⠠⠀⠠⠀⠄⠠⠀⠄⠀⠄⠠⠀⠠⠀⠄⠀⠀⠠⠀⠠⠠⠀⠠⠀⠄⠀⠄⠠⠀⠠⠠⠄⠠⠄⠄⠀⠄⠠⠀⠠⠠⠄⠀⠄
⠀⠆⠀⠄⠰⠀⠠⠰⠀⠰⠀⠆⠀⠆⠠⠀⠠⠀⠂⠀⠄⠄⠀⠆⠠⠀⠀⠀⠆⠀⠆⠰⠀⠀⠀⠄⠀⠀⠆⠀⠆⠰⠀⠠⠀⠆⠀⠄⠆⠀⠄⠰
⠀⠂⠀⠂⠐⠀⠂⠀⠂⠐⠀⠒⠀⠂⠐⠀⠂⠀⠂⠐⠀⠐⠀⠆⠀⠂⠐⠀⠐⠐⠂⠐⠀⠂⠀⠂⠐⠀⠐⠐⠂⠐⠂⠂⠀⠂⠐⠀⠐⠀⠂⠐⠂
⡿⢿⠿⠿⣿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣻⣟⣿⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⠛⠛⠂⠀⠀⣰⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠀⠀⠀⠀⣰⡿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣦⣤⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⠿⠛⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠻⣿⣿⣿⣶⣄⣠⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡾⠋⠀⠀⠀⠀⠀⠈⣿⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣼⣷⣄
⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄
⠀⠀⣠⣴⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⣿⣿⣿⣿⣷⡄
⣤⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣰⣿⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣿⣿⢿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡇⢀⣾⡇⠀⠀⠀⠀⠁⠀⢰⣿⡇⢸⣿⣿⣿⡇
⠘⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⢀⠀⢸⣿⠁⠈⣿⣿⣿⣿
⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡇⠀⠀⠀⠀⢀⡿⠀⣼⡟⠀⠀⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⢠⣾⠇⢰⣿⡇⠀⢀⣿⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣴⣿⡏⣠⣼⣿⠀⠀⣸⣿⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⣿⡏⣰⣿⠏⠋⣰⡆⣿⡟⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣴⣿⡿⠀⣼⣿⣿⣿⠁⠀⢠⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣼⣿⡏⠻⠃⣶⠀⢸⡇⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣾⣿⣀⣾⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣦⣄⡀⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡉⠉⠉⠛⠋⠀⠀⠀⠀⣼⣿⢋⣿⡿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣸⣿⠁⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣶⣶⣦⠀⠀⠰⠛⠁⠀⢰⣿⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠟⢛⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣶⣾⡿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠿⠀⠀⠀⠚⠛⣿⣿⣿⣿⣿⣯⡄⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠇⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠛⢿⣿⣷⠀⠀⠀⠀⣿⣿⠇⢨⣿⣿⣿⡇⠘⢿⣆⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠉⠁⠀⠀⠀⢀⣿⡏⠀⢸⣿⣿⣿⣷⠀⣈⠉⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⣾⣿⣿⣿⣿⡄⢻⣷⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⣿⣿⣿⠟⠻⣷⠈⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⣿⣿⡟⠀⠀⢹⣧⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⣿⣿⠇⠀⠀⠈⠻⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠻⣿⣿⣿⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⣿⣿⣿⡟⠀⠀⠈⠻⢿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⣀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⢿⣿⡟⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⠀⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠉⢉⣡⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠁⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣆⠉⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠋

⠐⠦⠤⢀⣀⡀
⠀⠀⠀⠀⠈⠁⠛⠖⠀⠀⣤⢀⡄⣤⠴⠒⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⠀⠄⠀⠀⠀⠀⠐⠀⠀⠐⠉⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠁⠒⠀⠠⠀⠉⠀⠀⠒⠀⠀⠠
⠀⠁⠀⠀⠂⠀⠀⠐⠀⠐⠀⠀⠀⠂⠀⠐⠀⠀⠠⡀⠀⠀⠀⠐⠄⠀⠀⠀⠁⠀⠀⠀⠒⢀⠀⠈⠀⠀⡁
⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠈⠍
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⣀⠀⠀⠀⠀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠠⣂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⡁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡀⠠⠄⠀⠄
⢠⣭⣤⡤⣌⣀⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣀⠀⠀⠠⠆⠀⡀⡀⠀⠀⠀⠀⠁⠀⡀
⠀⢡⣤⡈⠀⢠⢠⠀⠀⠀⣈⣄⡀⠀⡀⠁⠄⢤⡲⡲⢄⠀⡀⠀⢰⣴⡊⢁⠐⢋⡠⠁⠐⠂⠀⣀⠐⢀⡉
⠐⠋⠁⠐⠀⠀⠀⢠⠀⠈⠁⢻⣞⠉⡻⢁⠀⠀⢠⠀⠡⡄⠀⠀⠀⢀⣴⠀⠀⠰⢶⡖⠀⠀⡠⠄⠐⣴⡇
⠀⠈⠒⠀⠀⠀⣀⠼⡇⠀⠈⠁⠽⠀⠀⠀⢠⢖⡢⠕⠂⠀⡌⣂⡐⠎⠁⠁⠀⠀⠀⢰⠂⠛⢛⠂⢩⡬⡅
⠀⠈⠁⠨⠈⢁⡬⠏⠁⠀⠠⠤⡡⠄⠀⠀⠀⠉⣓⠀⠄⠚⢧⠓⠢⠐⠠⠀⢐⠲⢖⣒⠢⣌⠀⠀⠀⠉⣅
⠀⠁⠸⣦⡞⠁⠌⠀⠀⡀⠀⠀⠠⠈⢠⠀⠀⠀⣀⣀⠔⠦⣀⠇⠀⢠⠀⠀⠀⠀⠀⠈⠋⠁⠐⠀⢈⡀⡄
⠀⡀⠀⠪⠇⠀⢀⠤⠤⠤⠴⠊⠀⡒⠉⠂⠀⠐⠃⠆⡤⠶⠷⠷⠢⠀⠩⠀⠲⢰⠁⠔⡲⠯⣀⣈⢁⣠⣷
⠀⠉⢯⣗⢦⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣈⢄⠂⠁⠈⠀⠁⠚⠙⠉⢢⠀⠐⢂⣵⣈⠁⠁
⠠⠤⠈⠩⠊⡄⡀⠠⡐⠀⠀⠘⠘⢉⡀⠈⠀⠀⢼⣩⠬⠔⠋⠄⠀⠈⠀⠀⠀⠀⠐⠀⢀⣀⠀⠬⣣⣥⣖
⠀⠄⠂⠐⠙⢍⠐⠀⠠⠔⠤⢀⠀⠀⠅⢀⡠⠛⠏⠀⠰⣤⣄⠈⢁⠠⠄⠀⠀⠀⠀⠈⠉⠣⢀⠀⠀⢀⣂
⠀⠠⠀⠀⠀⠈⠀⠀⠀⣌⠓⠈⠀⢄⣰⠃⢁⠊⠀⢀⢀⢀⡵⠁⠈⠐⠀⠀⠠⠀⠐⢰⣜⠀⠈⢆⣀⢡⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢸⣇⠀⣿⠀⢸⡇⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⢻⡦⠘⣋⣤⠥⠴⠶⠦⠬⣥⣘⠃⢰⡟⠀⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠷⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠾⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡈⠻⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡰⠟⠃⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣃⣸⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⠚⠉⠉⠉⠙⢦⡙⠦⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⠙⠁⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠛⠮⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣤⣤⡀
⠀⠀⠀⠀⢀⣤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⠀⠀⠀⠀⠀⠀⠀⣼⢡⣄⡉
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡆⠀⠀⠀⠀⢀⡼⢡⣄⠉⠛⠷⠂
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣼⠀⠀⠀⣀⡴⠋⣴⣄⠙⠃
⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡕⠧⠴⠖⣋⡁⢲⣆⠈⠻⣷
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⡆⠸⣧⠀⠉
⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠏⠀⠈⠀⠀⠹⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⡀⠀⠐⡀⠀⠀⠀⠀⠈⠁⢰⠀⠀⡀⠀⠐⠼⠁⠀⠀⠀⠀⢀⠂
⠀⠈⠄⠀⠰⡄⠀⠀⠁⢀⡤⠀⠀⠀⠀⠀⠀⢸⡄⡞⠀⠀⠀⠀⢆⢤⠀⠐⠀⠆⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢀⣦⠘⢄⠒⠲⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⡄⠀⠀⠀⠊⠁⠔⠂⠀⠀⠀⠀⠀⠄⠐⠂⠀⠀⠀⠐⠀⡀⠀⠀⠈
⠀⠀⠀⡀⠸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷⠁⠀⠀⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⡀⠠⠀⠀⡀⠀⢀⠖⠀⠊⢀⠁
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠄⠀⠀⠀⠀⡦⠃⠀⢠⠀⡇⢀⠀⢰⡁⠀⢸⠀⡰⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠱⠠⠀⠀⠘⠁
⠀⠀⠤⠀⡤⠤⠒⡠⠔⠀⠀⠀⠀⠂⠀⡀⢀⡒⢦⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠒⠀⠤⠠⠠⣄
⠐⢀⣠⡀⠄⠀⠀⡀⠀⠀⣀⠐⠁⢀⠔⠁⠠⠉⠋⠁⠀⠀⠀⠀⠀⢀⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠐⠰⠲
⠀⠘⠛⠉⠀⠈⠀⠀⠉⠁⠙⠶⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠈⠢⣄
⠀⠀⠀⠀⠀⠤⢠⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠀⠀⠀⠁
⠀⡄⢠⠀⠀⠀⢐⡀⣠⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡾⠋
⠀⠻⠶⠘⡆⠀⠀⡼⠘⠛⠾⠧⠢⠀⠠⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠄⠀⠘⠂⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢶⡀⠀⠀⠀⢸⠟⠀⠀⢳⣿⣿⣿⣦⡀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⣾⣿⣦⠊⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⣿⡀⠀⢶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠠⣤⣹⣿⣿⡆⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣶⠖⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠁⢀⠀⠠⢈⣷⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⣇⠀⠐⣿
⣸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠞⠃⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡧⠀⠀⠀⢀⣼⣿⣿⣷⣄⡈⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣿⣿⠄⢻⣿
⣿⡆⠀⢠⣧⠀⠀⡀⠀⠀⠀⢨⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⢠⣿⠿⠛⣻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠈⠛⠉⠙⣿⣿⠉⠉⠉⣽⣿⣿⡤⣾⣿
⣿⡗⠀⣸⣿⡀⢰⡇⠀⠀⢀⣸⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⢾⣿⣿⠶⣿⣿
⣿⣿⡀⣻⣿⡃⣼⣧⠀⠀⠠⣽⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⠀⠘⢿⣿⣿⡿⣿⣿
⣿⣿⣽⣿⣿⣿⣿⣿⠄⠀⠴⣾⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿
⣿⣿⣭⣿⣿⣿⣿⣿⡃⢀⣤⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠘⡄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⣠⣶⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⢁⣿⠋⠉⠀⠀⠀⠀⣀⣠⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⠈⠓⠀⢸⣤⣴⣾⠟⠀⠀⢀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣼⡿⠟⠁⠀⠀⣠⣿⣿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡽⠟⠉⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢟⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠙⠿⠛⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⠋⠀⠀⢠⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢠⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢰⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡼⠁⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢰⠁⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣰⠇⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢿⠄⠠⠉⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣀⣀⣠⣾⣆⡀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣤⣭⣤⣄⡀⠠⠴⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠂⠈⠉⠉⢉⡉⠉⠓⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠈⠐⠲⠦⠠⣌⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡤⠊⠀⣠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣉⡓⠤⡀⠈⠐
⠀⠀⠀⠀⢠⠊⠀⠐⠋⠀⢀⡤⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⢠⠖⠒⡶⡶⠶⠶⠶⠒⠒⠒⠒⠒⠒⢒⣒⣒⣒⠒⠒⠒⢶⡞⡸⢣⠟⣢⣀⡀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⣾⢃⠄⠈⡃⠀⠀⠀⠀⠀⠘
⠀⠸⡀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢫⠙⣘⠞⠛⢄
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⡆⠘⢦⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⢙⡗⣹⡃⠀⠀⠀⠀⢀⠁⠀⡇⠀⠀⢳⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⣴⣫⣾⣁⡥⢄⡀⠀⠀⡘⠀⢠⠇⠀⢀⡼⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣰⣟⡁⠧⠞⠁⠀⠴⠓⡄⢀⠁⠀⣸⣤⠖⠋⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡌⣡⡄⠀⢄⣀⠤⠖⣹⠋⠙⣺⠁⠀⡱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠑⠂⠤⠤⢲⢺⠇⠀⠀⡏⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠃⠋⠀⢀⡼⠁⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡠⠤⣄
⠤⠤⠤⣄⡀⠀⡿⠦⠀⠀⠀⠀⠀⣀⡴⠋⠀⠉⠳⣄⡀⠀⠐⢄⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡖⠒⠒⠋⠀⠀⠀⠑⢄
⢀⣀⠀⣀⣈⣙⡓⠶⠶⠒⠖⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⠲⠒⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⣀⣀⣀⡀⢤⡤⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⠤⠄⠤⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠤⠀⠀⠠⠔⠚⠉⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⡤⢄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⢀⠞⠀⠘⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠎⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠜⠀⠀⠀⠀⠀⡆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢉⡀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢉⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠄⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⢠⢀⡠⠴⠚⠉⢉⠩⠔⡾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠤⠔⠒⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡄⠤⠠⠄⢀
⠀⠀⢠⣄⣶⠶⢤⣤⡤⠾⡄⠷⣲⣤⣿⣼⣼⠿⠶⠞⣇⠠⠄⠰⡢⣀⡤⡶⣼⣦⢠⡀⠤⠴⠖⢶⣀⣠⠄⣀⠆⡀⢀
⠀⠘⢛⣯⠍⠋⣀⡞⣊⣀⣬⢩⣿⠋⠀⠈⠀⢀⢠⡧⣿⠀⠀⣳⢏⣺⠉⣯⣻⠻⠻⢧⡀⠀⠀⠀⡘⢀⠉⣈⠿⠽⣉⣖⠳⠶⡠
⠀⡾⠋⠈⠿⠚⠻⡟⢻⣄⠀⠈⣇⠀⣠⠖⠆⠛⢺⠃⢷⠈⠋⠁⢘⠈⠁⢿⢩⣇⣀⡀⠁⢉⠛⣋⠙⡶⠟⠋⠳⠶⣎⠉⠙⠠⡿⠄
⣰⢅⡐⡄⢀⣄⢰⣵⣶⠿⣆⠚⠙⢤⠀⠀⠴⡱⠈⠳⣜⡅⠀⢈⠉⢠⠄⢠⡔⠇⠈⠁⢠⣀⠀⠀⢀⢁⡀⠠⢤⡀⠱⢢⡄⠠⠶⢄
⡉⢉⢿⠁⠸⠾⢿⣼⣟⡣⢝⣶⣤⣤⣦⣄⣴⣤⣁⠀⣸⣧⣀⠁⣨⣿⣞⣫⡭⠽⣦⠠⠤⣿⣶⣀⣆⢛⣠⡨⡌⠁⠀⠈⠠⠤⠀⠁
⡇⢀⡎⠀⡀⢰⠋⡔⠈⢻⣿⠚⠉⠉⠛⡍⠹⢿⣍⢚⠿⡶⢶⣿⣿⡃⠈⠁⢀⣼⣍⣓⣢⠜⣫⡽⠿⣿⡉⣗⢆⣀⠚⠀⠀⠐⢠
⠀⢨⡔⠛⢁⠜⣴⠆⢀⣿⡟⢶⣶⡶⠀⠹⠿⣾⠉⠛⠶⢼⡦⢹⣻⣯⡄⠺⠗⢻⣫⣿⡇⣸⡿⠁⠀⠈⠏⢿⣰⣅⠀⠠⠀⠀⢠⠅⣆
⠰⠶⢦⠔⠤⡄⠀⠀⠀⢉⣽⠆⠈⠀⣶⡄⠀⢑⠶⠉⠶⣶⠶⣾⣿⠃⠛⢁⠀⡈⡎⢉⣿⣚⠁⠀⣀⢀⠀⠘⣿⣧⢦⡆⣶⡐⢃⣃⠞
⠀⠡⡀⠀⠀⢦⠀⠀⠀⠈⠙⣤⣀⢀⣀⣄⠠⣊⡑⠳⠀⠀⠀⢚⡅⡘⠀⣀⣉⠉⣀⢸⡆⠻⠗⠂⠈⠉⠉⢬⡿⢺⣿⠀⠀⠙⡀⠏
⠀⠄⠈⡖⠒⢚⠤⠤⢤⡤⠖⠀⠿⣷⡶⢦⣎⣭⣀⣴⣧⡀⢠⢾⣧⣀⠈⠈⠃⣺⡯⢼⣧⢄⡀⠀⠦⢆⣸⠆⠒⠉⠁⠀⠀⠄⡉⠁
⠀⣀⡘⢆⢄⣀⣤⣄⣀⠿⣄⢶⠈⡏⣿⢻⢀⣩⡤⠿⣟⣿⡶⠫⡿⡿⡿⢦⣾⠉⠀⠀⠀⠀⠹⣆⡤⢤⢄⢰⣾⡿⠿⢦⣌⠓⠃⢠⢣
⠀⠘⢧⣶⠼⠈⠈⡍⢧⠚⢁⠀⠈⠁⠹⣿⣉⣀⠀⠀⣠⣭⡓⡬⣀⣲⠤⢤⣟⠀⠀⢀⣀⠀⡄⡈⠙⡿⢟⣿⡯⢝⠷⣞⣙⣖⡚⠈⢰
⠀⠠⢨⣧⠀⠀⠀⠀⠉⠄⠀⠠⡀⠀⠠⢸⡿⠿⠋⠀⠛⠿⠂⣿⠇⠠⣤⣼⡟⠋⡄⠈⠛⠉⠀⠅⡸⣥⢿⡉⠁⢠⣿⡍⠉⣙⠃⢄⣰
⠀⠀⠀⡄⠀⠀⠀⠀⣀⣦⡤⠰⠛⠻⡿⠋⢯⡀⠠⠤⠄⠀⢠⢅⠀⠀⠉⢉⠳⡔⠚⠂⠀⠀⠀⠈⠁⠀⠀⢃⢀⣷⣦⠆⢀⠋⠀⠂⠁
⠀⠀⠀⣾⠢⠶⢊⠩⢑⠃⠄⠀⠀⠀⠀⠀⢱⡄⡀⢄⡲⠀⡄⠀⠀⠀⠀⢄⣲⣮⠀⠂⢀⠀⠀⡀⠀⠀⠀⣸⢣⣄⡤⠄⠀⠺⠄⠂⡄
⠀⠀⡘⡧⢼⣷⡰⣴⠆⡿⠃⠀⠏⠁⠀⠀⢘⣭⠵⠶⠷⢿⣾⡓⢤⣄⡄⣄⣿⣟⣶⣶⡇⠰⠻⠿⠵⢀⣶⠋⠶⡳⣦⣀⠀⠶⠿⠿⡃
⠀⠀⠁⢰⠾⡏⣀⣈⠀⡴⠶⢦⠄⠀⠀⡰⠿⠋⢉⠱⠶⠸⠊⣷⢺⣯⢐⠀⣹⣿⣾⠀⠁⠀⠀⠀⠀⠀⣻⠑⠃⢈⣼⠗⠷⠖⢶⣿⣧
⠀⠀⠀⠈⠠⠳⡙⠸⢤⡜⠀⠈⢢⡄⢞⣭⡘⠿⠿⠶⠄⢲⠺⢿⠁⠀⢸⣤⣲⠁⢹⣖⠂⣠⣄⡐⡀⣸⠿⣶⠄⣈⢀⠀⠀⢠⣟⡼⠝
⠀⠀⠀⠀⠦⠈⣀⢤⡈⣋⡁⡴⢊⣙⢛⣽⡀⠀⠘⠰⠆⠈⠷⠰⠁⠀⢠⣤⣤⠀⣼⠱⣶⣭⣡⣠⡰⡿⠀⠀⠀⠋⢩⠄⠀⡈⡁
⠀⠀⠀⠐⢄⠳⣁⠀⠀⠙⠁⠔⠙⠋⣤⠄⠀⠀⠀⢶⠀⠠⠔⡰⠀⠀⠀⠀⠁⠐⣣⢭⠙⣯⣭⣻⡇⠊⠚⠂⣤⠀⠠⠄⢊⠠⠁⠉
⠀⠀⠀⠀⠀⠁⠚⠛⢀⠘⠀⡰⠀⢀⠐⠶⢂⠔⠛⠒⠠⠅⠊⠀⠀⠀⠒⠒⠐⠈⠀⠀⠘⠠⠨⠄⠁⠀⠀⠊⠀⠑⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢠⣄⢈⡤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⢁⠾⠛⠀⠀⠀⠀⠈⠄⠀⠠⣄
⠀⠀⠀⠀⢀⠀⢠⣄⠀⠀⠀⠀⢀⠾⣶⡄⠀⢀⣤⣶⣦⣄⣐⡀⠈⠑
⣾⣛⠉⠀⠰⣤⣀⠀⡴⠛⠛⠛⠘⠓⣮⣯⣹⣽⣿⣿⣿⣿⣿⣷⡖⠒⠒⠖⠲⠒⠶⠶⠶⠶⠶⢤⣤⠀⢠⣤⣆
⠀⠉⠳⠦⣤⣘⡟⠀⢀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⢿⡟⢀⡠⠔
⠀⠀⠀⠀⠀⠉⢻⠶⠾⣦⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣦⢵⡀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠽⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠋⣍⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣷⢷⠶⠒⠒⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠁⢉⣀⣐⣽⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠠⠀⠁⠈⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⢠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⡆
⢰⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣻⣿⣿⣿⣿⡟⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠟⠉⠁⠀⠀⠈⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⡏⣸⣿⣿⡏⠀⠀⠀⠀⠀⣴⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠠⣄⣹⢸⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢸⣿⣿⣿⣿⡿⠉⢿⣿⣿⣿⣿⣷⣤⣦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠋⠙⠛⠙⠛⠋⠙⠛⠻⠛⠛⠛⠛⠀⠟⠻⠿⠻⠛⠿⠿⠿⠿⢿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⠩⣿⣿⣿⣿⣿⡏⢹⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠉⠉⠁⠈⠁⠀⠈⠙