Clothe Emojis & Symbols

⠀⠘⢀⡆⠀⠘⠂⠘⠃⠉⠛⠉⢹⠋⡏⠉⠉⠉⠛⠙⡓⠐⠂⢲⠒⠒⢶⠖⠖⠒⡖⠐⠖⠀⡤⠤⠄
⠀⢰⠏⢀⠂⠀⣦⡤⠄⢠⣆⠀⠠⢤⣆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠿⠀⠀⠀⠆⠀⡇⠀⡇⢠
⠀⠜⠃⢸⡆⠀⠀⣄⠀⠀⡈⠧⠀⠸⣾⠇⠀⠀⠐⠀⢠⠀⠀⠀⠀⠀⠀⣠⠀⠔⠳⡀⠀⠀⣷⠘
⠀⠀⠀⢸⡇⠀⠐⣽⠀⠀⢿⡄⠀⠀⠁⠀⠀⠀⠀⡄⠙⠀⠀⢀⡀⠀⡆⣿⠀⠀⠀⠀⠳⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠿⠀⠀⢸⣇⠀⢀⡀⠀⠀⠀⠈⡇⠶⠀⠀⠀⠀⠀⢀⡏⢀⠸⡇⠀⠀⠀⢿⠀⡇
⠀⠀⠀⢸⣷⠀⠀⠀⠁⠀⢸⠘⠀⢸⡇⠀⠀⠀⠀⠇⡀⡀⠀⠀⠀⠀⠈⠃⢠⡆⠁⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⡄⠀⠈⠇⢀⠀⠀⠀⠀⠛⣷⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⢸⢠⠆
⠀⠀⠀⠀⡏⢠⡇⠀⢰⠀⢪⡇⠀⠀⠀⠀⠀⠀⢰⠸⠿⡧⡁⠀⠀⠀⠄⠀⠀⠷⠀⡀⠀⠀⢸⡇
⠀⠀⠀⡄⡇⢸⡇⠀⢹⠀⠀⠁⠀⠘⠀⠀⠀⠀⠈⣆⣀⡾⢧⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⢸⣵⢀⡀
⠀⠀⠀⡇⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠈⠛⢣⠛⠀⠀⠐⢧⠀⠀⠀⠀⠃⠀⠀⢸⡷⠏⢁
⠀⠀⢠⡀⡗⠀⠀⠀⠸⡇⠀⣯⢰⣏⠀⠀⢰⠀⣀⣴⣶⣿⠈⣄⡴⢀⢈⠀⠀⠀⠀⠀⠀⠀⢸⠛⠓⠁
⠀⠀⡌⠁⡇⠀⠀⠀⣀⠈⠀⠀⣼⠁⡀⠀⠀⠈⣿⡃⠈⢻⠀⣿⠅⢰⢠⠆⠀⠈⠀⠀⠀⠀⢸
⠀⠀⢣⡀⣷⣠⠀⠄⠀⢐⠀⠀⢸⢰⡇⠀⠀⠀⣿⡿⣴⠆⡇⣿⠀⢸⡼⠀⠰⠀⠚⠀⠀⡀⢸
⠀⠀⠈⠁⢸⢹⠆⣀⠀⢠⠀⠀⣿⠸⡇⠀⠀⠀⠟⡀⠀⠀⡇⣿⠀⠸⣧⡅⠀⠀⠀⢀⠀⡇⣿
⠀⠀⠀⠀⢸⠘⠁⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠿⠆⡿⠹⠀⠈⢣⠇⠀⡄⠀⢻⠀⠃⡿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠀⢸⠙⠃⠀⠀⠀⠀⠀⠀⢀⡁⡀⠀⠀⠦⠀⠀⡇⠀⠸⠄⡀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⠛⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠠⠀⠀⠀⢴⠓⠀⠀⡇
⠀⠀⠀⠀⢸⠀⢀⡴⠀⢠⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⡤⠀⠄⠄⢀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠺⡼⠀⡇
⠀⠀⠀⠀⠚⢀⣀⣾⣀⢠⡀⠀⠀⠀⢠⣄⣈⡀⠀⣰⠀⣄⠀⢀⠘⠀⣧⡀⠰⢀⣀⣉⢁⣈⠧⢀
⠀⢰⠦⠤⠤⠬⠉⠉⠉⠛⠓⠀⠀⠠⠈⠁⠉⠁⠀⠿⠀⠿⠀⠬⠭⠤⠤⠥⠤⠤⠭⠤⠤⠥⠶⠦⠢⡀
⠀⣬⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡵⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡤⠤⢄⣈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢙⡆⠀⠀⠀⢨⡍⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⣻⠴⢚⣀⣈⡁⣠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⡱⠏⡼⠉⠉⠉⡻⣌⢉⠹⡿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢂⡌⡰⢺⡇⠀⠀⠀⠀⢈⠀⢂⠑⡕⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⠶⠞⠛⠀⠁⢸⣿⣄⠀⠀⠀⠀⠇⠀⠀⠈⢦⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⡎⠈⢙⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠠⠋⠀⢠⠎⢠⢿⡀⠀⠀⠘⡄⠀⠀⠠⠁⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠃⠀⢉⢀⠊⠈⣷⣄⠀⠀⠙⡇⠀⡆⠀⠀⣧⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⡦⣄⠀⠀⠀⢰⢠⢈⡜⠀⠀⡇⠀⠑⢀⡀⠘⠀⢱⠀⣸⡿⡦⡤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢻⡀⠀⢀⠄⠔⡼⠑⢆⠀⠀⠀⠀⢀⡇⠀⠀⡰⠀⠘⠅⠡⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠙⢦⣼⡀⡎⢸⠁⠀⠈⠉⢢⠀⣿⡇⣠⠎⠀⢠⡆⠀⢠⠠⡻⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠘⠛⢿⡀⢀⠀⠀⠀⠑⠸⡄⢻⣷⠟⠀⢸⠀⠻⠀⠀⠳⡉⠢⠀⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠰⠀⢠⠀⠀⢠⠸⣷⡈⠀⠀⠀⠈⠀⣇⠙⠛⠀⠠⠃⠀⠀⠀⢀⣀⠈⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠈⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠈⠓⠄⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠉⣿⠉⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠻⣧⣄⣀⣀⣿⣀⣀⣤⡾⠛⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠉⠉⠉⣿⠉⠉⠁⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⢼⡇⠀⠀⠀⠀⠀⢠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡄⠀⠀⠀⠀⠀⢹⡇
⠀⢠⡾⢷⣄⡀⠀⠀⣰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⢿⡄⠀⠀⢀⣤⡾⣷⡄
⠀⠈⠛⢶⣍⣻⡶⠾⠛⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠻⠶⣶⣟⣥⡾⠛⠁
⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⢸⣿⠷⠶⠶⠶⠶⠾⣿⠶⠶⠶⠶⠶⠞⣿⠁⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡇⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢡⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠿⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⣿⠟⠉⢿⠋⣿⣿⡿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠇⠀⠀⠀⠀⠈⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡖⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣼⣷⡀⠀⢰⡃⠀⢠⠆⢀⡴⠃⢀⡤⠒⣦⠀⢀⠐⡏⠀⣠⠋⣠⠆⢠⡄⠁⣠⠶⡆⢠⠄⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠿⣿⣿⡿⠁⠀⠀⠁⠀⠀⣠⠞⠀⠀⡏⠀⢾⠁⠰⣅⣸⠇⣴⠋⢰⡋⢰⠏⡀⣾⢁⠔⢰⡿⠂⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⣛⠃⢦⣀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠁⠀⠈⢳⣍⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣠⠀⡿⡿⠀⠀⡄⠀⣆⠹⣦⡀⠑⢄
⠀⠀⠀⠀⣠⠤⡸⠟⠀⠁⡇⠀⠀⣷⠀⢹⣆⢹⣿⣦⢢⡑⢄
⠀⠀⠀⠀⠀⣾⡇⢰⠀⢀⠁⠀⢰⣿⠀⠘⣿⣶⣿⣿⡇⠙⡌⠳⡀
⠀⠀⠀⠀⡰⠏⣀⠘⢀⡏⢰⠀⢸⡇⢸⣆⣿⣿⣿⣿⣷⠀⠘⣆⠙⣆
⠀⠀⠀⠐⠸⡦⣄⠔⣸⠃⢸⢠⣾⣇⣿⣿⣿⣿⣿⣿⣿⡇⢰⡹⣧⠘⣇
⠀⠀⠀⡰⠀⢰⡇⢀⣿⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠂⠈⠋⠁
⠀⠀⠀⠑⠒⠿⠷⠲⢦⣬⢭⣤⣬⣙⣿⡿⡏⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⣵⣿⣷⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⠿⣿⢿⣿⣿⣿⢿⣿⢿⣟⣶⣄⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠢⡄⢹⡟⢛⢋⡻⢼⣯⡏⢹⢇⠉⡖⢙⡅⠈⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠻⠂⠈⠈⢻⣾⣶⣵⣌⣛⣦⣌⡦⣹⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⣿⠟⣿⢌⣴⣳⢎⡼⣿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⡸⣿⢜⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡋⢿⣿⣽⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣇⣾⣏⡒⢽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡉⣿⣧⣜⢛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⢏⡃⢘⣋⢀⡀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⣬⠥⠽⣿⣤⠭⡁⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣓⢏⣛⣚⣻⣟⢒⣸⠗⠆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣗⣲⠟⣭⣯⣭⣻⡥⠺⠤⠆⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣬⣧⣽⣬⢿⣿⢣⣨⣥⣬⣭⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣼⢃⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⣿⣿⣿⣿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠊⡿⠏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠓




⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⣶⡆⠀⠀⠻⢿⡿⠀⠀⠘⠛⠿⠀⢼⣿⠷⠀⠀⡀⠀⠀⢿⣿⡟⠀⢸⣿⡿⠀⠀⠘⡟⠲
⠀⠘⠻⠿⢃⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⢀⠁
⠀⠀⠀⠰⣿⣿⣄⠀⠒⢺⣿⣇⢀⣤⣤⡄⠀⢀⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣀⣀⡄⠀⠀⣿⡇
⠀⠀⠀⠀⣿⣿⠟⠀⠀⠸⣿⣿⣼⣿⣿⡇⠀⣼⣿⡆⠀⢻⠁⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠹
⠀⠀⠀⠠⠛⣿⡀⠀⠀⠀⠿⣯⠈⢿⣿⡗⠀⠘⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⢻⡇⡇⠀⠀⠀⢿⡀⠈⢿⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⡇
⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠧


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣄⠐
⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠐
⠀⠀⠐⠒⣓⡒⢐⣒⣒⠂
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠖⢀⠀⠀⠀⠀⣮⠀⠤⠚⠁⡀⠴⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠀⠀⠐⠁⠐⠀⠀⠜⠀⡀⠤⠤⡀
⠀⠀⢀⡴⠃⠀⠀⠀⠀⢀⠔⢁⠔⡁⠀⢀⠁⠀⢀⡀⠘⠄⡁⠀⣀⠔⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⠴⢪⡄⠊⠀⠀⠀⡄
⢠⠒⠫⠄⠀⠀⠀⠐⠀⠐⠈⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⢀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡖⠉⠀⣀⠀⢁⡰⠋⠀⠀⢀⡠⠊
⠀⠀⠒⠐⠂⠀⠁⠀⠀⠀⢁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣆⠄⠀⠀⠀⡀⡀⠀⠀⠀⡜⠰⠁⠀⠔⠁⠠⠁⠀⢠⠄⠀⠈
⠀⢰⠛⠓⠀⣤⠀⠀⠀⠻⠀⠁⠁⠄⠀⠀⠀⠀⠀⠀⠘⠠⠄⣊⡔⠭⢊⡀⠀⠀⡐⠀⠀⠀⠀⢨⠽⡇⠁⠀⠀⠀⡄⠀⠁⣬⣶⣶⡖⣶⣾⣷⣆
⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⡄⠀⠀⠀⣀⡀⠀⠀⠀⠀⡄⢠⠞⠋⠤⠤⠀⣀⣀⠀⠀⠁⣀⠴⠊⢁⡰⠀⣶⠀⠀⠈⢰⡄⠈⢿⣿⠟⠁⠉⠛⠿⠋
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠻⠃⠷⠄⠚⠀⠁⠘⠄⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠔⠉⠀⣠⣿⣄⣀⣠⣿⣇
⠀⠁⠀⠀⠀⡘⠀⠀⠀⠀⢈⠀⠀⠁⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠉⠀⠒⠂⠀⠠⠚⠁⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⡐⠃⠀⠀⠀⢀⠃⡀
⠀⠤⠀⠀⠠⠀⠄⠀⠀⠀⠀⠐⠉⠂⠀⠀⠆⡇⠐⠂⠜⠀⠀⠠⠖⠀⠂⠀⠂⠀⠰⠦⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠏⠀⠀⠈⢂⠀⢀⠀⠀⡁
⢀⠄⣀⣀⡀⠀⠀⣀⣀⡀⡄⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢐⠀⠘⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠁⠀⠀⠁⠁⠀⠂⠁
⠀⠈⢿⡿⠃⠀⠘⢿⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠁⠄⠀⡐⠀⠰⠀⠈⠀⠀⢠⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠤⠤⠄⠀⠀⠀⠠⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠀⠀⠂⠀⠀⠀⠀⠀⠃⠀⡌⠀⠀⠈⠛⠿⣿⣿⡿⠟⠛⠘⢅⠀⠀⠀⠀⠀⢀⠜
⠀⡈⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢄⡁⠀⠀⠀⠀⠀⠀⠃⠸⠁⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠑⠠⠄⠠⠔⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠸⡄⠀⠀⡠⠂⠐⡄
⠰⡀⠀⠀⠀⢴⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠒⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠐⠁⠈⠆
⠀⠀⠁⠀⠀⠉⠂⠀⠀⠀⠁⠀⠀⣠⣤⣄⠀⠀⢀⠀⠀⠈⠁⠀⠈⠑⠀⠄⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡉⡄⠀⢀⡘
⠀⠠⠂⠀⠈⠈⠐⠀⠀⢶⣿⡧⠀⠙⠿⠟⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠈⠓⠠⠀⠄⡀⡠⠄⠠⠐⠈⢸⠀⢀⠃⠀⠀⢀⠇
⠀⠣⡀⠀⠀⠰⠶⠀⡀⠈⠉⠀⠀⠀⠀⠀⠀⡑⠤⠔⠃⠀⠀⠀⠀⠀⠰⢄⠀⠈⠀⠀⠀⢀⠀⢀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⠂⠊⠀⠅⠀⡈
⠀⠀⠀⠙⠦⣐⠒⠀⠉⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠀⣀⠀⠀⢀⠁⠀⠀⠤⠀⠀⠀⠀⠀⠐⠀⠚⠁⠁⠀⠒⠀⠄⢀⠁
⠀⠣⠀⠀⠀⠀⠉⠐⠒⠁⠀⠀⠀⠖⠀⠈⢂⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⠄⡰⠆⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠂⠐⠂⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠂⠀⠀⠉⠄⠀⠀⠀⡅⠀⢠⠦⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠠⠀⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⢠⠤⠀⠐⠒⠀⠀⠀⠆⠐⠀⠐⠂⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠈⠀⢨⠂⢀⠀⠀⠈⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⠄⡌⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠊⡠⠀⠀⠀⠀⢀⠀⠀⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣂⠘⠄⣀⠀⠀⢀⡀⠀⠀⡀⠠⠃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠈⠂⠀⠁⠀⠀⠂⠀⠤⠤⠤⠂⠀⠀⠀⠈⠒⠀⠀⠊⠂⠀⠂⠈⠀⠀⠀⠀⠉⠉⠁⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠶⠒⠚⠛⠛⠓⠦⡴⠖⠒⣷⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣿⣦⣀⣈⠙⠲⣄⡀
⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⢒⡎⠉⠁⣀⣠⡏⠀⠉⠉⠉⠉⠛⠛⡆
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠪⡭⠀⣀⡠⠤⠔⠒⠉⠉⠀⠀⠉⠉⠛⠓⠒⠶⠶⠶⢧⣀
⠀⠀⠀⢸⣆⡀⠀⠀⠀⢀⠤⠒⠈⠿⣀⡠⠤⠔⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣓⣦⡀
⠀⠀⠀⡏⠀⠙⠦⣄⣀⠇⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⠖⠒⠛⠋⠉⠉⠀⢀⡇
⠀⠀⠀⢧⠀⠀⠀⠀⡹⠳⣴⡁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠛⠉⠉⠉⢀⣀⣀⣠⣤⠤⠴⠶⠒⠚⠋⠉⣩⠇
⠀⠀⠀⣸⠓⢦⣀⠀⡇⠀⡎⠙⠲⣄⠀⠀⠀⣠⠞⠉⢁⣀⣠⡤⠤⠶⠒⠛⠋⠉⠉⠀⣀⣀⣠⣤⠤⠶⠒⠛⠉⢉⡇
⠀⠀⠀⣇⠀⠀⠈⠓⢧⡀⡇⠀⠀⠈⠙⠦⣄⣇⠀⠈⠉⢁⣀⣀⣠⣤⠤⠴⠖⠒⠋⠉⣉⣠⣤⠤⠴⠖⠒⠛⠋⢙⡇
⠀⠀⠀⠙⢦⡀⠀⢀⠇⠉⡷⢤⣀⠀⠀⠀⠀⡽⠛⠛⠉⠉⢉⣀⣀⣤⠤⠶⠒⠛⠋⠉⢉⣀⣀⣤⠤⠴⠖⠚⠛⢻
⠀⠀⠀⠀⠀⠉⠳⢬⡀⢠⠀⠀⠈⠙⠦⣄⢠⡇⠀⠀⠘⠉⠉⠁⢀⣀⣠⣤⠤⠶⠒⠛⠉⠁⢀⣀⣠⡤⠤⠶⠒⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣄⠀⠀⠀⠀⠈⠙⣷⠶⠶⠖⠒⠛⠉⠉⠁⣀⣀⣤⠤⠴⠖⠚⠋⠉⠁⠀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⢰⡇⠀⢠⣤⠤⠴⠒⠛⠉⠉⠀⣀⣀⣠⡤⠤⠶⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣧⣀⣀⣀⡤⠤⠶⠖⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠀⠈⠛⠉⠋⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⣀⣀⡀⢀⣀⣠⣀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⣿⣍⣻⣿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠻⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⠀⠀⠀⢀⠉⣙⢿⣿⡇⠀⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⣧⡀⠀⠀⠀⢀⣤⣑⢮⣿⣿⣇⠀⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⣄⠀⣰⣿⣅⠈⠙⢛⡿⢿⣧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣶⣤⣌⡒⠽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⠋⣯⠙⠿⠿⣿⣷⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣸⣷⡏⢠⠉⠸⠀⠀⡞⠻⣎⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣰⢃⡟⠀⣀⣠⣤⣤⣰⡀⠀⠘⢳⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠰⠋⡜⢀⣴⠿⣿⣿⠿⢿⣿⣦⢁⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠴⠂⢰⠀⣼⣿⠀⢿⣿⠀⢸⣿⣿⣿⠣⠹⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡔⠁⠀⢠⠁⠀⣿⣿⣇⠘⣿⡄⢸⡟⣿⣿⣆⠟⣿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠺⠀⠀⠀⡌⠀⢰⣿⣿⣿⡄⢸⡇⣾⣷⠋⣿⣿⡆⠘⢿⣿⣌⢷⡀⠉⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸⠀⠀⡼⠁⢠⣿⣿⣿⣿⠷⢼⣷⣿⢿⠘⢸⢻⣇⠀⠈⣿⡿⡿⣿⣄⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠈⠀⣰⢃⣿⣿⣿⡿⠀⢸⣿⣿⢻⠀⠚⡇⣿⣎⠀⣿⡁⠁⣈⢿⣧⡈⣿⡇
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⡇⠀⢸⣿⡿⣘⣆⠀⡇⣿⠹⣧⣹⣧⠀⠈⢎⠿⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⡌⠀⠀⢀⣼⣻⣿⣿⣿⣿⡇⠀⣸⣿⠃⠈⡟⠀⡇⣿⠀⠈⡟⠻⣷⣌⠢⢣⣿⡇⠈⣿⡀
⠀⠀⠀⠀⢀⣌⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⠀⢸⡿⠀⠀⡇⢸⣇⠸⣆⠀⠁⠀⠈⠻⣦⠀⢻⣷⠀⢻⡇
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⣠⡶⢋⣽⣿⣿⣿⣿⣿⣿⡇⢸⣇⠀⣸⠁⢸⡏⡄⢻⡀⠀⡄⠀⠀⢸⣧⠀⣿⢇⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⣿⣴⣿⣿⣿⢸⣿⢿⣿⣿⢻⣼⡇⠀⠻⠀⢸⡇⠰⢸⣇⠀⢰⣤⣤⣤⡿⢠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⣿⣿⣼⣿⡏⣾⠀⣿⣀⡀⢀⣸⣿⣿⣿⣿⣦⣈⣿⠉⠉⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⣧⡟⠁⣸⡟⠛⠛⠛⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠛⠃
⣿⣿⣿⠿⣿⡿⠿⡿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣶⣶⣶⣶⣾⣶⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⣈⠀⠈⠘⣿⣿⡇⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⢉⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡌⢈⡉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢻⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠚⠋⢸⣿
⠀⠀⡠⠖⢒⣛⣛⣛⠒⠲⡄⠀⠀⠀⣾⣿⡿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡦⢐⣷⡆
⠀⠀⡓⠶⠤⠭⠭⢭⢤⠔⣻⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡂⠀⠐⠹⠆⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⢏⠒⠦⠤⠤⠤⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠗⠷⠚⠛⠒⣄⠀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⢸⣿⣶⣿⡿
⠀⠀⠀⠁⠒⠀⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠸⡇⢠⠤⠔⠒⢲⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠸⡜⢋⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢹⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠄
⠀⠀⠀⠀⠀⠰⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⣰⢶⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠈⠻⣏⣀⡇
⢀⠤⠚⠆⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢠⠑⠁⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⡒
⠀⠀⠄⠀⢃⠀⠀⠀⠀⠀⠈⠉⠛⢦⣘⣷⠀⡀⣠⣛⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣦⠀⠀⠀⠘
⢂⠉⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠁⠀⠀⠀⠀⠀⠀⠀⢷⣺⣿⣿⣿⡿
⠀⢣⠄⢀⠈⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠛⠛
⠀⠀⠳⡤⢤⠊⡧⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⢀⠀⠰⠷⣶⣶⡶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡆⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠊⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠤⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠢⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠉
⠀⢰⠀⠀⠀⠀⠀⠤⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⢀⠀⠼⠂⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡾⠑⠒⠓⠒⠬⣉⠹
⠀⠀⠓⠀⠀⠀⠀⡀⠙⢄⡠⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠈⡀⢀⢠⠀⢑⡬⠂⠀⠀⠀⠀⠀⠀⠁⣀⣠⣶⣒⣓⣓⣶⣀
⠀⠀⠀⠀⢀⡴⠛⠷⡤⠊⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⠠⠄⠀⢠⡤⠒⠁⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠢⡀⠀⠒⢀⡤⠚⠁⠀⠀⠀⠀⢀⣸⡍⢆⠀⠀⠀⠘⣿⣿⣉⣉⡉⠛⠛⣿⣿⡇⠀⠀⠀⢠⣤⡴⢦
⠀⠀⠘⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⢈⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢧⣠⠏
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠍⠉⠉⠋⠙⠭⡆⠀⠀⡠⠤⠤⣤⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠂⠀⠰⠂⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢲⡐⣀⣿⠀⠀⠈⢹⠁⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠄⠁⠀⣠⢀⡀⠀⠀⠈⠀⠁⠁⠀⠀⠀⢸
⠀⢀⡴⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠈⠉⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠠⠆⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠰⠃⠀⠀⠐⠀⠀⠀⠠⣂⠄⠀⠀⢰⠀⠀⠃⠀⠀⠰⠘⡄⠀⠀⣗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡠⠄⠈⠁⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠌⠂⠀⠀⠀⣀⠔⠉⢀⡴⠊⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠄⠂
⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⢀⠤⠊⢀⡠⠞⠁⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⡠⡠⠁
⠤⠈⠀⡀⠄⠀⠀⠀⠀⡠⠖⠁⣀⠔⠋⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⠂⠀⠀⠀⠒⠀⠀⠀⣴⣾⣧
⠘⠁⠀⠀⠀⠀⣀⠔⠊⢀⡤⠚⠁⠀⠀⠂⠀⠀⢀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠀⠸⣿⣿⡡
⠀⠀⠀⠀⡠⠞⣡⢀⠖⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⣠⠺⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⠀⣀⠔⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⣀⠈
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣤⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⢀⣠⣤⢠⣄⣤⢠⣤⣤⣠⣤⣄⡤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠂⠀⠀⠘⣿⣤⣤⡿⠇⠀⠀⠐⠃⠀⠈⠁
⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠶⠶⠶⠶⠶⠶⠦⢦⠶⠶⠲⠶⠶⠶⠶⠶⠆⠀⠀⡀⡀
⠀⠀⠀⠀⢿⣏⠉⠀⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⢊⣷⡄⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣮⠙
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢤⡄⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣡⠾⣧⣤⡤⠦⢠⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠉⠀⠀⠀⢀⡤⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠲⠛⡟⠓⢀⠀⠛⠁⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⢠⠀⠀⠀⠸⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠈⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣿⡆⠀⢰⡀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⠟⡇⠀⠸⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢲⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠃⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠁⡳⠀⣈⣀⣁⣀⣀⣀⣠⡤⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢃⣺⠋⠀⠀⠀⠀⠀⠛⠉⢁⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⡉⣹⣄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⢋⠀⠀⠀⠒⡀⠛⠚⠛⡹⢿⣻⣿⢿⣿⣿⣿⣟⠛⣛⡻⢽⣯⢿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣀⡴⣂⣈⠗⢀⢠⡔⣤⡀⢠⡀⠀⣿⠀⠀⠀⠒⠓⠚⠛⠛⠛⠛⠛⠃⣈⠃⠈⠻⠒⠛⣻⠟⠋⡽⠿⠿⠆⠹⠟⠛⠱⠶⠾⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠘⡟⠁⢻⠇⢨⣷⡟⣡⣶⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⣀⢀⡷⢠⠾⠧⠴⠇⠠⠤⠿⠡⠾⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠜⠋⠀⠀⠀⠀⠀⡤⠀⠐
⠀⠀⠀⠀⠀⠀⣤⣷⠐⢦⣤⡄⢠⣄⢠⡀⡄⢠⣠⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⢸⡿⢹⡏⣿⣭⠟⣴⠞⣰⣿⣿⡿⣿⣿⣟⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠶⠠⠄⡰⠷⢌⣴⠯⣵⠿⠥⠀⠧⠄⠮⠇⠀⣦⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠉⠀⠉⠈⠉⣉⡉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠈⠉⠁⠈⠉⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⡠⠀⠊⠁⠀⢉⡀
⠀⠀⠀⠀⠘⡧⠀⠀⣀⡤⣿⠷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠙⠚⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣠⡶⠟⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠂⠇⠀⠀⠈⠈⡃⠀⠀⠀⠃⠀⠀⠀⢀⠄⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠂⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣤
⠀⠀⠴⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢱⡆⠀⠀⠀⠀⠀⠄
⠀⠀⡇⢀⠖⠉⠁⠉⠢⡀⢰⠉⠉⡆⡊⠀⠙⠄⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠞⠃⠀⢀⠀⠀⠀⢀
⠀⠀⡇⡌⠀⠀⠀⠀⠀⠱⠈⡲⣒⠁⢙⡶⡊⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⠀⠠⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠄
⠀⠀⡇⠡⡀⠀⠀⠀⠀⡔⢸⠀⠀⡇⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⡅⠀⠬⠀⠀⢀⣀⣀⡀⠀⠠⠀⠰⠀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⣇⠀⠑⠢⡤⠄⠊⠀⠀⠉⠉⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠌⡆⠀⠀⠀⡇⠘⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⡈⠂⠀⠰⠰⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠁⠀⠀⢮⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡾⢩⠏⢿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⢀⠠⢄⡀
⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⡅⡆⠀⠹⢍⡘⢹⠀⢀⠔⠛⠋⠲⡄⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⢻⡀⢀⢈⡬⢷⡾⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⢠⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠢⡉⠓⠛⠛⠉⠀⠀⠀⠓⠤⠤⠖⠁⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⢄⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠀⠘⠀⠀⠀⠀⠸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣤⣤⠤⣤⣤⡀⠀⢀⣀⣤⡤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⢯⠉⠉⠀⠀⠀⢠⠇⠀⠀⢣⡀⠀⠀⠀⠀⣴⠁⠀⠈⢳⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠤⠠⠤⠠⣸⠀⠀⠀⠈⡗⠂⠐⠂⠀⣿⠀⠀⠀⠸⠆⠔⠐⠤⠒⣼
⠀⠀⠀⠀⡤⠴⠒⠒⠚⠃⠐⠀⠐⠒⠚⠒⠒⠒⠚⠃⠀⠀⠀⠁⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⣉⠱⡄
⠀⠀⠀⠀⢹⠀⢐⠆⠀⠉⠁⠀⠀⠀⠘⠉⠉⠉⠈⡃⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⡇⠀⠇⢰⠃
⠀⠀⠀⠀⢸⠀⠈⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢸
⠀⠀⠀⠀⠸⡇⠀⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⡇⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇
⠀⠀⠀⠀⠀⡇⠀⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⡇⠀⡆⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠃⢸⡇
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡷⠀⣰⠄⠀⠧⡀⠀⢀⣰⠂⠀⠐⠂⠲⡀⠀⠀⠀⢠⠇⠀⠀⠸⡀⠀⠀⠀⡸⠁⠘⠀⡀⠳⡀
⠀⠀⠀⡠⠞⢁⡜⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠘⣄⠘⠦⡄
⠀⠀⠰⣁⣀⣈⣁⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣈⣉⣉⣉⣉⣩⣭⣭⣭⣥⣤⣤⠤⠬⠃

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠔⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡂⠀⠀⢀⡀⠀⠴⠟⠛⠿⢄⡖⠀⠀⢸⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡴⡦⠶⣦⣴⣤⡶⢦⡴⢷⢶⡿⠿⠿⠻⣿⡟⠒⠚⠀⠃⠨⣧⠀⠰⠾⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠧⢶⣳⢾⠦⣔⣻⠷⠛⠏⣾⠛⠛⠓⠂⠈⠁⠉⠀⠀⠈⠙⡏⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⡆⠀⠈⠃⠂⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⡇⡀
⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢡⠃⠀⠀⣷⠆⠀⠐⠒⣨⠄⠀⠀⠀⠀⡇⠀⠀⣿⡇⠀⠀⠀⡇⠃
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⣃⠀⠀⠟⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠳⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⡀⠀⠀⠘⠀⠤⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠃⠰⡄
⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠒⠀⠇⣠⣦⡀⢤⢤⢤⡀⣀⣀⣢⠀⠘⠀⠀⠀⡇⠀⠀⠀⢀⠀⡇
⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⢀⡀⠀⠀⠈⠀⢀⣰⣂⣃⣸⣜⣃⡒⣢⡿⢿⡈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠇
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠿⠅⠀⠀⠁⠚⠂⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠘⠂⠀⠀⠀⠀⠀⠀⡇⢠⠶⠿⠿⠭⢦⣜⠁⠈⠉⣑⡄
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠠⠻⠿⠿⠿⠿⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠙⠉⠛⠀⠀⠀⢀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠈⠁⠈⠁⢀⠙⢰⣤⣄⣀⣀⣤⠀⠰⢻⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠀⡀⠈⡅⠀⡤⢹
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠘⢦⠀⠐⠀⠲⣄⣰⡀⠆⠅⢧⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠰⠤⣴⣤⠤⠶⠒⠾⢥⠄⠀⠀⠀⠀⠀⠸⠆⠴⠀⠠⠬⠵⠀⡀
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⢠⠷⡆
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠃⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠂⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⣀⠡⠀⠀⣍⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⣇⣀⣀⣀⣤⣀⣀⠊⠋⡀⢈⠙⢲⡇⠀⢀⠀⣿⢀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡞⠻⠚⠿⢷⠿⡶⡾⠻⢶⡟⣿⢻⣟⠛⠛⠛⠻⢿⡋⢉⠉⠁⠈⢀⢸⣷⠀⠈⠛⠛⢻⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡷⢶⣟⣶⢿⢦⣾⣩⠿⠞⢹⠉⣾⠋⠉⠉⠉⠉⠈⠉⠉⠁⠀⠉⠉⠙⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⣿⡄⠀⠘⠃⠰⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⡈⠀⠀⠀⢸⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠀⣦⣄⠀⠀⣠⣄⣐⡀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣶⡇⠀⠀⠀⢸⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⣽⠂⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⡀⣧⠀⠀⠈⣿⠀⠀⠀⠀⢸⠈
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⠀⢸⠀⠸⠆⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⡀
⠀⠀⢀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠘⠀⠋⡆
⠀⠀⡸⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃⣠⢶⠦⠠⡤⣤⡤⠤⢄⣀⣘⡂⠄⢸⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⢰⡇
⠀⠀⠰⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢠⣀⢀⡠⠀⠀⠀⠁⠀⢀⢰⣚⣚⣒⣧⣚⣃⡒⣀⣲⡷⢇⠁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠁
⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡇⠀⠈⠃⠺⠤⠀⠀⠀⠀⠀⠸⠉⠉⠁⠁⠀⠉⠉⠉⠈⠁⠀⠙⠩⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠀⠁⠀⠀⠀⠀⠀⡀⣀⡀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠠⠤⣄⡀⠀⢀⠀⠀⠀⠀⠀⡇⠀⣀⣴⣾⡿⠦⡀⢠⠄⠀⠠⠤⣄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠋⠉⠉⠉⠛⠙⣷⣤⣤⣤⣤⣼⣇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠂⠀⠀⠀⠀⠐⠘⠛⠛⠛⠛⠛⣺
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠈⠉⠉⠋⠀⠀⠀⢄⣀⡀⢀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⡀⠉⠀⡈⠍⢠⣄⣀⣀⣀⣀⣤⠀⠰⠞⡿⠧⠀⠀⣿
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢸⡇⠀⠈⠉⠈⡇⠀⠀⢀⣛⢀⢀⡀⢻
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⢸⣃⠀⠀⢀⢀⣆⠀⢫⢘⢘⢰⢸⡅⢸⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⡀⠀⠀⠀⠀⢁⣀⣀⣤⠀⠀⠙⠁⠀⠀⠀⠘⢳⡊⢆⠈⠀⡈⠻⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠁⣀⣀⡀⠙⠛⠛⠛⠛⠋⠁⠉⠋⠚⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠉⢉⠉⠈⠐⠂⠠⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⢀⡆⠀⠄⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠐⣚⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢻⠿⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⡠⠶⠖⠀⠖⠀⠆⠀⠆⠀⠛⠒⠠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀⣈⠁⠀⢠⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣀⠀⢐⠀⠀⠁⠀⠀⠄⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡯⠖⠀⠀⢹⠁
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⢒⠒⠐⠂⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠓⠋⠉
⠀⠀⠀⠀⠠⡀⢰⠀⠀⡆⡆⠘⠀⠀⡇⠀⠀⡏⠀⠀⡔⢸⣽⢲⡄⢁⣈⠀⠀⢀⡀⠐⠃⠀⢀⠉⠀⠀⠘⡁⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠁⠈⢀⠟⠛⢻⡁⠀⢠⡇⠄⢠⠃⠀⠸⣚⣚⣗⣰⡇⢀⠀⠀⠀⠈⠀⠀⠀⣰⠛⢿⡄⣴⠀⠀⠀⠀⣄⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠈⠁⠀⠀⠙⢋⠏⠃⠄⢀⠁⠀⡀⢠⠀⠀⠀⠘⠳⠾⠃⢸⠀⠀⠀⢰⡟⠊⠃⠀⢠
⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⣿⠀⠘⠓⠀⠀⢸⢠⡖⠀⠸⠀⢰⠀⢸⠀⢀⣇⢀⠀⠀⢰⠛⠉⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠈⠆⠀⢰⠏⣀⠯⠀⠀⠀⠈⢸⡇⠀⠀⠀⢸⠀⠈⠀⠐⠶⢺⡀⢀⡀⠧⠔⠰⠶⠆⠀⠀⠐⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢒⡋⣀⢹⠀⠀⡄⠀⠀⠠⠁⠆⡏⠀⢸⠀⠀⢠⡆⠀⠀⠀⠈⢱⢸⠀⠀⢆⠉⠀⠀⠀⢰⡇⠀⠁
⠀⠀⠛⠒⠋⠁⠀⠀⠀⠸⡝⠹⢸⡀⠀⠳⠀⠀⡄⠀⠀⠁⠴⠞⠀⠤⢹⠀⠘⠌⠀⠀⠈⢘⠀⠀⢸
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠑⠃⠀⢡⣤⣤⡄⢰⠁⠀⠀⠀⢠⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠇⠀⠀⠀⣀
⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠓⠒⢢⣤⣤⣤⡄⢸⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⢀⡃⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠘⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠃⠀⠀⠳⠐

⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⢶⣶⡶⠶⠶⠶⠶⠶⠶⢶⣶⢶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣤⣿⠇⠀⠀⠀⠀⠀⠀⠘⢋⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⣠⣾⠟⠛⠛⢿⣯⣀⣽⡟⠛⠛⠻⣿⣟⠛⢻⣯⣀⣽⡟⠛⠛⠻⣷⣄⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⣠⣾⠟⢁⣤⡀⠀⠀⠉⠛⠉⠀⠀⢠⣤⡈⠻⣷⣄⠉⠛⠉⠀⠀⢠⣤⡈⠻⣷⣄⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠻⣷⣶⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣶⡿⠋⠀⠀⠀⠀⠀⢸⣿⢿⣶⡿⠋⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠈⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⢻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣾⡏⠀⠀⢻⣧⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⣿⣍⣍⣩⣉⣉⣉⣩⣍⣍⣽⡗⠀⠀⢿⣯⣉⣉⣉⣉⣉⣉⣉⣩⣽⣿⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣇⣀⣀⣀⣿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣻⣷⣀⣀⣾⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣀⣀⣀⣸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣿⣷⡆
⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣾⡥⣄⠀⠀⢄⠀⢀⣠⠀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠁⠀⠀⢦⠀⠀⠱⠂⠀⢀⣀⣀⣨⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠖⠁⠀⠙⠛⠁⠀⢀⣀⠁⠊⡠⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣸⡇⠈⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣼⡇⠀⠀⠐⠒⠉⡄⠀⠸⣠⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⠆⠀⠛⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠁⠀⠀⠀⠡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠀⠀⣀⡜⠁⣀⠆⠀⠀⠀⠀⠀⠘⣄⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠆⠘⠀⠀⠀⠀⠀⢄⡀⠀⠌⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⣠⣤⣠⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢻⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣿⣿⡇⠀⢰⡇
⠀⠀⠀⢸⣷⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⣿⣿⣷⠀⠸⠇⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣾⠀⠀⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡏
⠀⠀⠀⠀⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡞⠂⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡷⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡇
⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⣴⣧⠀⣿⡇⠀⠀⠀⠀⣿⣇⡀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⣿⢰⣾⣷⡆⠀⠀⢀⣘⣿⣧⣇⡀
⠀⠀⠀⠀⢿⣿⣿⠃⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⢠⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⢸⣿⢈⡇⠀⠀⠘⣿⠂⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠈⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣀⣤⣄⣀
⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢹⣶⣾⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⡾⠋⠀⠀⠙⢷⡄⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣋⣠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣿⣿⢶⣶⣶⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠉⠉⠉⠉⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢹⡄⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠲⠒⠓⠓⠚
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠙⢶⣤⣾⡷⠏⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⢚⣛⣾⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣈⡇⠀⠀⠀⠀⠀⣾⠉⠙⠻⣿⣿⠟⠋⠉⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⡆⠀⠀⠀⢠⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠦⣄⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⣴⡾⠃
⠀⠀⠀⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠙⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⢨
⠠⠤⠤⠠⠤⠤⠤⠤⠤⠠⢤⣄⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠉⠉⠉⠉⠉⠙⠉⠈⠉⠉⠉⠐⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠄⠀⠀⠀⠀⠂⠄⠤⠀⠄⠠⠄⠰⢄⠀⠀⠀⠀⠀⠀⢀⠠⠤⠸⠀⠧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠂⠒⠒⠒⠛⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠻⠐⠋⠙⠈⠁⠀⠀⠀⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠐⠐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢈⣥⠀⣀⠀⠀⠀⠀⡀⠀⣀⠂
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠈⠁⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⢤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐





⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⡂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⡇⠈⠉⠀⠁⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠠⠤⠤⠤⠤⠤⠦⠤⠄⠠⠤
⡗⠒⠒⠂⠲⢦⠖⠂⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠄⠲⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠂
⡇⠀⠀⡠⠀⠒⠠⢀⠀⢀⢀⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈
⡇⠀⠊⠀⣀⠀⠀⢀⠃⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠤⠀⣰⡊⠂
⡇⠀⠄⢘⡛⢃⠘⢿⠀⢰⣶⡶⢰⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠂⠀⠀⠀⠀⠤⠄
⡇⠀⠀⠀⠀⠘⠃⠀⠂⣍⠁⠸⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠤⡀⠉⠀⠀⡄⠈
⡇⠀⠀⠀⠈⠈⠘⠁⠀⢀⠱⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠈⠀⠀⢹⠀⠂
⡧⠤⣄⠠⠸⣀⡤⡑⠤⣀⣀⣻⣁⠥⠖⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠠⠠⡤⠤⣜⡙⠃⠀⠀⠀⠈⠆⠀⠀⢠⠀⠀⡀
⣇⠀⠈⠉⠉⠁⠘⣄⠀⠀⠈⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠁⣄⠜⣀⠀⠁⠁⠀⠀⠐⠀⠀⠈⠀⠀⠐
⠏⡁⠀⠀⣀⡆⢸⠓⠄⠁⠀⠄⠁⠀⠀⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⡵⠊⠀⠒⡄⠀⠀⠀⠀⢂⠀⠀⠀⠄⢢
⠀⠀⠀⠁⠐⠁⠈⡄⠀⠀⠀⣤⢥⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠢⡀⢈⠍⠀⢣⡀⠀⠀⠁⠀⠈⡆⠀⠀⠈⡀⠀⢀
⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠂⡀⠐⠊⠀⢑⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠵⠁⠀⢀⠌⠑⠈⠄⠀⠀⡀⢣⠀⠀⠀⠐⠈
⠀⠀⠀⠀⣀⡀⢴⢃⠀⣂⠂⢀⡤⢒⢂⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⡀⠔⠁⠀⠀⡆⠰⠀⠀⠹⣼⡀⠀⠀⠀⠀⠁
⠁⠀⠁⠴⠸⠁⡇⠈⠇⠑⠂⠘⠀⠁⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠈⠃⠀⠀⠀⠠
⠂⠈⠑⡤⡀⢀⡱⡎⠂⠉⡶⢄⠀⠔⠱⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢸⠀⠈⠀⡘⠉⠀⠘⡆⠀⠀⠀⠀⣸⡉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡓⠂⠚⡀⠀⠀⠀⠀⡄⢆⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁⢰⠀⠀⠀⡀⠀⠀⠀⡀⠠⠰⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠩⠛⠀⠃⠀⠀⠀⠀⠁⠘⠾⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠒⠛⠛⠓⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣭⣴⠶⠞⠛⠛⠳⠶⣦⣬⡛⢦⡀
⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠦⠴⠶⠶⠋⣴⠟⢉⣀⣤⡴⠶⠶⢦⣤⣀⡉⠻⣦⠙⠶⠶⠶⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀
⠙⢿⣿⡟⠒⠒⠒⠶⠶⠒⠒⠒⠒⣒⣒⣒⣒⣂⣀⣀⣐⣒⣉⣥⠶⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠶⢬⣉⣓⣂⣀⣀⣐⣒⣒⣒⡒⠒⠒⠒⠒⠶⠶⠒⠒⠒⢻⣿⡿
⠀⠀⠈⠻⣟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠛⠛⣻⠟⠁
⠀⠀⠀⠀⠙⢦⠀⠀⠙⣿⡿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⣿⠃⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⢀⣠⣄⡀⠀⢀⣠⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠟⢻⡟⠻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠀⢸⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡏⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⢸⡇⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⣀⣠⣤⣄⣀⡀⠀⠀⠀⢰⣿⢸⠋⢸⡇⠹⡇⣿⡆⠀⠀⠀⢀⣀⣠⣤⣄⣀⠀⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣇⣠⣶⠟⠉⠉⠉⠉⠉⠙⠻⢶⣄⣸⡿⢈⡆⢸⡇⢸⡀⣿⣇⣠⡴⠟⠋⠉⠉⠉⠉⠉⠻⣶⣄⣸⡏⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠈⠀⣸⣇⠈⠁⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⠀⠀⠀⣿⣿⠀⠀⠀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢠⣿⣿⡀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡀
⠀⠀⠀⠀⠀⢀⡿⠋⠉⢩⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣿⡍⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢿⡄⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⢠⡿
⠀⠀⠀⠀⠀⠀⣾⠃⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⣷

⠀⠀⠸⠿⠿⠿⠃⠀⢀⠀⠀⠀⠀⣀⠀⡀⣶⣶⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠓⠐⠒⢐⡒⠒⠒⠐⠒⠀⠀⠀⠈⢭⡘⠛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢉⣀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡞⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡰⣿⣿⣷⣼⠏⠃⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣥⣿⠛⡁⣥⣴⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡯⣾⣧⣿⠈⣵⣼⣟⢹⡟⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣩⡶⠟⠀⣴⣷⣿⣽⡏⠉⢠⡞⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⢈⣼⠟⣋⣤⠞⠻⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠤⠤⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠉⠻⢿⣿⣿⣿⣿⡛⢻⣿⣟⣿⣿⢿⣷⠀⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠋⠀⠘⠛⠻⣷⣿⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠀⢄⠀⠀⠀⠀⠙⢳⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⡞⢀⠀⡀⠈⠀⠄⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠈⣏⣛⠀⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⢠⠈⠁⠉⢁⣀⣴⠏⠀⠸⣿⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⣶⣶⣶⣿⣿⡿⠁⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠘⠃⠀⠀⠀⠶⠄⠶⠰⠀⠁⠀⠘⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠰⠶⠒⠂⠒⠒⠀⠖⠒⠀⠄⠂⡘⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⢾⣿
⠀⠀⠀⠀⠀⠀⠐⠛⠈⠛⠀⠒⠒⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯⣿⣄⣀⣠⣤⡄⠀⣰⣾⣿⣿⣿⣿⣿⣿⣯⣼⣿
⠀⠀⠀⠀⠀⠈⠁⢉⢀⡐⠉⡁⠀⡈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢿⠛⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿
⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿
⠀⠤⠂⢸⡟⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡄⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠸⠁⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠲⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠃⢀⣀⣀⢀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠉⠀⠁⠀⠙⠛⣿⡿⡟⠻⣿⠿⡶⠀⠿⠀⡶⠙

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠉⠑⠲⡄⠀⠀⠀⠀⠈⠀⠒⠠⠀⢀⣰⠀⠀⣈⣉⣉⣉⣉⣉⣉⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⡇
⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠶⠶⠶⠶⠶⠖⠄⠉⠉⠉⠉⠉⠉⢉⠛⠯⠭⠍⠛⢛⣛⡇⢰⠁
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠀⢸
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⠀⠠⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣆⠀⣀⣀⣀⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠼⡀⠀⠁⠗⠐⠂⠀⠀⠐⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⠖⠀⠒⠒⠀⠀⠐⠂
⠀⠠⠀⠀⠀⠀⠀⠀⡆⠣⢀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⠉⠉⣉⣻⣦⠀⣔⠄⢠⣠⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⡀⠀⠀⠀⠀⣀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣽⠍⢈⢿⣇⢘⣷⡀⣻⠂⣒
⠀⠀⠀⠀⠀⠀⠀⠐⡒⡈⡀⠈⡏⠀⢠⠂⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠼⢸⢸⠀⡇⡏⠸⢘⠹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢃⠘⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢀⣉⣻⢸⠀⠀⠁⠀⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡅⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢻⣿⠘⠀⡀⠀⠠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⢀⠀⡠⢤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⠀⠀⠀⠀⠀⠀⠀⠐⢠⣤⣴⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠑⢀⠉⠠⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣶⣶⣇⠀⢸⡿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠐⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠙⠛⠉⣉⣬⡀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣶⡄⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠉⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⢸⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠉⠉⠋⠈⠀⡂⠈⠈⠉⠉⠉⠁⠙

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⣄⣀⣀⣀⣀⣀⠶⠶⠶⠶⠶⢶⣶⠶⢶⣤⣤⡄
⠀⠀⠀⠖⠀⠀⠀⠀⠀⢀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⠉⠉⢩⡟⠁⠀⠀⠀⢠⣇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠀⠀⢰⡏⠂⠀⠀⠀⠸
⠀⠀⠀⠀⡀⠰⠐⠊⡙⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠷⢆⡀⠀⣀⡸⠷⠆⠀⢀⢀⡀
⣀⠀⠀⠀⠀⠄⠃⠈⠆⠀⠈⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠶⠶⠶⠶⠒⢾⡀⢀⡀⠀⠀⢀⠀⠀⠀⠁
⠁⠶⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⣿⡃⣸⡇⢻⡅⢻⠀⣺⠄
⠀⠀⠈⠑⠁⢂⡠⡀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠞⡁⠀⠇⡇⠻⠙⢇⠈⠃
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣴⡃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡽⡇⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⢦⣄⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡀⡉⢉⢉⠉⡇⠀⠀⠀⠠⠤⠂⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠔⡟⠠⠁⠃⠂⠦⠤⡀⣈⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡆⠀⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠐⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⢀⣀⠀⡀⣀⠠⠄⠒⠂⠉⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠚⠓⠂⠠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣿⣿⣄⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣴⣿⣿⣦⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣴⣿⣿⣦⣤⣤⣤⣤⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣶⣷⣾⣷⣿⣿⣿⣶⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⡿⠿⠛⠋⠉⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡳⣦
⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣵⣿⣏⣿⣄
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⣠⣴⣾⣿⣛⣯⠭⠶⠶⠶⢶⣶⣯⣭⣻⣷⣦
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣴⡿⣟⣿⣿⠋⠁⠀⢀⣠⣴⠶⣟⣻⣯⣭⡭⣭⣿
⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⣩⢾⣿⣿⡿⣷⣦⣴⢟⣯⣾⣿⡫⣿⣿⣿⣶⡿⠟
⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢟⣵⣾⡷⣄⣸⣿⣟⣾⡿⣱⣿⢿⣷⣿⣿⣿⣍⠉
⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣡⣿⣿⣿⣿⣷⣯⣭⣿⡿⣰⣯⣿⣿⣿⣿⣿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣟⣿⣿⡿⣿⡿⢻⣿⢿⡇⣿⣷⣿⣿⣌⠛⢁⣴⠆⢨⡟
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⡿⣻⣿⡘⣿⡀⢷⡸⣷⡿⣻⣿⣿⠋⠛⠶⡾
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣯⣼⢿⣿⡻⣿⣷⡜⢿⣾⣷⣿⣿⣿⣽⢻⣷⣄
⠀⠀⠀⠀⠀⣿⣿⣠⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡿⢣⣶⣮⣅⣹⣟⠛⣮⣻⣿⣿⣿⡿⠿⣟⣽⡟
⠀⠀⠀⠀⠀⡿⣿⠿⠟⠋⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣱⣿⣿⣿⣿⣧⣼⡷⠛⠛⠿⠿⠿⠿⠿⠛⠋
⠀⠀⠀⠀⣸⢰⢿⣿⠛⣇⠛⠃⠀⠀⠀⠀⠀⠀⣠⣏⢱⡀⠀⢸⣿⡟⢿⣿⣿⣿⡇⠉⠁
⠀⠀⠀⢠⣿⣢⣾⣿⣄⣻⣿⠁⠀⠀⠀⠀⣠⡾⣿⣿⣼⠇⠀⢸⣿⣏⣸⣿⣿⣿⡇⢀⣠⣴⣶⣦⣄⡀
⠀⠀⠀⣼⡐⣧⣿⡏⣹⣿⣇⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡿⣻⣽⣿⣿⣿⣇
⠀⠀⣼⣿⣷⡟⠛⠻⠟⠛⠉⢉⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣾⡟⣿⢻⣿⢻⡿
⠀⠰⢿⣿⡿⠀⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢳⣿⣟⣾⣟⣼⢃⡿⠁
⠀⠀⢘⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⣿⣿⣿⣿⡿⢃⡾⠁
⠀⠀⣼⠃⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡄⣿⣯⣛⣋⡴⠟
⠀⢰⣇⣴⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡏⣿⡿⠋⠁
⠀⡾⠛⢻⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣻⣿⡇
⠀⠁⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⡇
⠀⠀⢠⡟⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⠃⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⢰⡟⣀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄
⠀⣿⣿⣿⣶⣶⣦⣾⡟⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⣿⠋⠀⠈⠉⠛⢫⡇⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣄⣀⡀⠀⣀⣿
⠜⠁⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠉⣂⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠤⠢⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠂⡀⠀⣐⡬⠇⠈
⠀⠀⠀⠀⠈⠠⠈⠀⠣⠴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⢐⠀⠀⠰⠄⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⠂⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⡾⠀⢀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠄⠀⠆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢰⣷⡎⡙⢦⡗⠀⢀⣧⠀⠠⢤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠏⢀⠀⢰⡍⠂⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠳⠄⠀⠈⠇⠀⠠⠀⠀⠨⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠠⣀⠐⢡⠐⠀⠟⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠚⠀⠈⠄⠀⠀⠈
⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠰
⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⢤⣤⡬
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠋⠉⠉⡩⠅⣂⠀⠢⠄⣉⡀⠡⣤⣍⡄⠀⠀⠀⠀⠀⣠⣀⣀⣀⣄⣤⠀⠀⠀⠠⢌⠳⠤⠖⠠⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡉⡉⡁⠀⢈⠉⠈⢁⡀⠀⠀⡉⠙⠀⠠⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠐⠀⠀⠀⠉⠈⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢤⡉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⢁⢸⣿⣤⣤⣤⣤⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠸⢸⣿⣟⣓⠀⠀⠒⢺⣿⡟⠟⡟⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣽⣽⣍⣭⣭⡍⠉⣡⣬⠉⣭⣍⣠⣍⣁⣉⢹⣟⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣩⣅⠈⢉⣿⢫⣭⣿⣍⣿⣋⣿⣯⢻⠿⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⡭⠉⠸⣿⣿⣗⡉⠉⣻⣯⣠⡽⠋⠙⣿⡏⠛⠛⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⡤⠤⢿⣿⠌⠛⢙⡿⣿⣾⣥⡀⡆⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡓⠛⠓⠒⣾⣿⠂⢀⣼⠀⠸⣿⡌⠁⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣁⣉⣁⣀⣿⣿⢠⡌⠀⠀⠰⢾⡇⠀⠁⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠋⣉⢉⣿⣿⡿⠁⠀⠀⠐⢸⡷⠀⠰⠀⠀⠀⠀⠀⡇⠀⣀⡀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⢶⣭⠤⣽⣿⡀⠀⠀⠀⠀⠉⣇⠀⠀⠰⢆⠀⠀⠀⡆⠉⢻⠀⠝⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⣿⣴⣿⣤⣴⢿⣿⡄⠀⠀⠀⠀⠀⣿⡀⠀⠀⠘⠀⠀⠰⡇⠀⢸⣇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⢸⣯⣹⣧⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⣹⠁⠀⢤⣤⠦⠀⢐⡁⠀⠿⣿⠧⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣏⠉⠐⠂⢺⣿⣄⠀⠀⠀⠀⠀⠸⠃⠀⢀⡟⠀⠀⢸⡃⠀⡎⣿⠀⡄⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢧⣤⣴⣤⣿⣿⠀⠀⠀⠀⠀⠀⡄⠀⠈⠇⠀⠐⣾⠇⠀⢤⠟⠤⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠒⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠉⠀⠀⠠⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣟⠗⠀⠀⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠥⠤⠀⠀⠈⢼⣇⠀⠀⠀⠀⠀⠀⢰⣦⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡀⣄⠀⣺⡛⣤⠇⠀⠀⠀⠀⠀⠀⠘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠁⠁⠉⣹⠋⣿⣿⠆⠀⠀⠀⣠⠒⣎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣏⡙⢻⠃⠀⢿⣿⣃⡴⠒⠛⠀⠀⢼⠿⡆⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣾⣿⣿⣤⠤⠤⠀⠀⠈⠀⠈⢻⡗⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⣿⡇⠀⠀⠠⠀⢿⣯⣿⣷⣤⡀⠀⠀⠀⠀⠀⣻⣅⣀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠏⠒⠲⡖⠐⣚⠉⣿⣭⠭⠥⠨⠥⢼⣿⣈⣉⡈⠉⢴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⢿⠠⣟⢺⣿⣨⣧⠀⣿⣿⠆⠀⠀⠀⠀⣿⣟⡉⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣓⠀⠀⠀⠀⠀⢸⣷⣭⣄⣽⣛⣙⣀⣛⣟⠛⣛⣛⣛⣛⣉⣙⣏⣙⣛⠺⣿⢿⣷⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢲⣤⠛⠃⢸⡏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣾⠁⠀⠈⠙⠓⠦⣄⠀⠀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣿⡄⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣛⣙⠆⠀⠀⠀⠀⠀⠀⠀⠘⠻⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣛⣛⣋⣛⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣭⣉⣽⣿⣿⣿⣉⣟⣋⣿

⠀⠀⠀⢸⣿⡆⠀⠀⠈⣹⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⡄⠀⢸⡇⠀⡀⠀⢿⣿⠂⠀⣴⣶⣶⣶⣦⣴⣶⣶⣶⡄
⠀⠀⠀⣼⣿⣧⡀⠀⣾⣿⣿⣆⠀⠘⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣶⠀⠀⡇⠀⢸⡇⢰⡇⠀⢸⡟⠀⠀⡿⠉⠙⡟⠉⠙⡟⠉⠙⡇
⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢾⣿⠀⠀⣿⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠻⠦⠶⠿⠦⠾⠷⠦⠾⠃
⠀⠀⠘⣿⣿⣿⠃⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢺⣿⠀⠀⣿⡇⠀⣿⠀⢠⣷⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠐⠀⠐⠒⠒⠒⠒
⠀⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⠀⣿⠇⠀⣿⠀⠐⣿⠀⢸⡇⠸⡇⠀⠀⡇⠀⠀⠚⠂⠚⠛⠛⠛⠒⠒⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⣯⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⡟⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⡟⡇⠀⠀⢠⣤⡹⢿⠃⠀⢰⣿⣦⣤⣤⣴⣾⣷⣶⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⠀⠀⠀⠀⣬⣬⡉⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⡇⠀⠀⠼⠿⠇⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣷⠀⠘⢠⣶⣿⣿⣷⣤⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⡏
⠀⠀⢸⣿⣿⡗⠀⢁⠰⠶⠀⡇⠈⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⠀⠀⣼⣇⠀⠀⣼⣷⠀⠈⡏⠀⢠⣿⡈⠄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠿⠿⠇⠀⠸⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠸⠿⠿⠃⠘⠿⠿⠃⠀⠁⠀⠻⠿⠗⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⢿⠿⠿⠿⠷⡿⠿⠿⢿⡇
⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣄⣄⣄⣤⣠⣀⣠⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⢹⣟⢸⠠⠀⠆⠀⠀⠀⣿⣿⣧⣤⣼⣿⢿⡃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⡿⢻⡟⡝⠙⢻⣷⡀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠿⠶⠶⠶⠶⠷⠶⠶⠾⠇
⠀⠀⢸⡇⢸⢐⠀⡇⠀⠀⢸⡏⠈⡉⠀⠉⠁⢹⡇⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣿⢠⡿⡱⠀⢀⡿⢻⡷⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⡀
⠀⠀⢸⡇⢸⢈⠀⡇⠀⠀⠘⡅⠀⠁⠀⠀⠀⢨⡇⠀⠀⡆⢡⣠⡌⢰⠀⠀⠘⣿⣿⡱⠁⢀⣾⣣⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣞⣩⣶⠟⠋⡲
⠀⠀⢸⡇⢸⠘⠀⠇⠀⠀⠀⡟⠈⠉⣿⣿⣿⣿⠁⠀⠀⣇⠈⠉⠀⣾⠀⠀⢀⠈⢻⣿⣶⣾⣿⣿⠋⣀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠛⠁⢀⣤⡇
⠀⠀⠈⠃⠘⠈⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠒⠛⠋⠀⠀⠈⠛⠛⠓⠒⠒⠚⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⣀⠴⠚⠳⠦⣴⡋⣸⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⣦⣄⠀⣀⡴⠛⠁
⠀⠀⢈⣩⠿⠛⠻⢯⣉⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⢠⡟⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⢿⢏⣤⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣷⣶⡆
⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠋⢋⣼⣿⣧⡀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣧⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⣿⣦⣤⣄⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠔⠁⠀⠘⣿⣿⣿⠆⠀⠀⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠙⠲⠦⠶⠚⠋⠀⠀⠀⠀⠻⠿⠛⠤⠬⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡍⣿⠛⠿⠿⠿⠻⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠦⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⢉⡽⣍⠉⡽⣍⢹⣀⣤⣤⣤⣤⣤⣸⡇
⠀⠀⠀⠀⠀⠀⣠⠞⢤⠤⠖⠻⣌⡆⠀⢀⡀⠀⠀⠀⢸⢸⡇⢹⢠⡇⢸⢸⢹⠟⠛⠛⠛⢻⠻⡇
⠀⠀⠀⠀⠀⠀⢳⠀⢘⣆⣀⡴⣫⠃⣀⣼⣦⣀⠀⠀⢸⢸⠃⢸⢸⡇⢸⢸⣏⣉⣉⣉⣉⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠈⠳⠉⢑⠟⢾⡁⣻⡏⢧⡸⢹⡟⠀⢸⢸⠀⢸⢸⡇⢸⢸⠀⣀⣤⣷⡄⡀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠃⡄⠘⣆⡆⠉⢹⠀⠈⠳⣤⡇⠀⢸⢸⠀⢸⢸⡇⢸⢸⠛⣿⠀⠉⠀⣟⢳⡆
⠀⠀⠀⠀⠀⠀⢠⠇⠹⣄⠘⢯⡒⢛⡧⠤⠤⠼⡇⠀⢸⠸⠤⠼⠸⠦⠼⢸⠀⡇⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⢳⢄⣹⢮⠀⠀⠀⠀⢧⠀⢸⠒⠒⢒⣒⠒⠒⢺⢰⠇⠀⠀⠀⠸⣼⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢰⠃⠸⠄⠑⠞⠁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢸⠿⠤⠤⠤⠤⠴⢿⡇
⠀⠀⠀⠀⠀⠀⣧⠀⢸⣇⠀⢶⢸⠇⠀⠀⠀⠀⠘⡇⢸⠋⠙⠫⠭⠉⠙⢻⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⢿⡀⢸⣾⠀⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⢠⡤⠬⠤⠤⠤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⡇⢸⡟⠦⠔⠦⠴⠢⠤⠇⢸⠉⠉⠩⠽⢸⡏⠉⠉⠉⢹⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣼⠀⡾⢸⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⢸⡯⠭⠭⠭⢽⡇⣚⣛⣻⡇
⠀⠀⠀⠀⠀⠤⠿⠶⠧⠼⠷⠾⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⠷⠶⠶⠶⠾⠧⠤⠤


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠈⠀⠀⡀⠀⠀⠈⠀⡐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⡖⢈⣀⡀⠀⠀⠀⠀⣐⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣤⡤⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⡇⢰⣄⣯⣻⡂⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⢱⠃⠈⢿⣿⡧⠽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⠿⡆⠀⡴⠞⠉⠀⠀⠉⠐⠯⢠⡈⣺⡿⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢏⠻⠿⣤⡫⢿⣇⠀⠀⣂⠒⠀⢐⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠹⠀⠸⣿⣿⣶⣶⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠘⠻⢿⠿⠿⣿⣿⣿⣿⡿⠿⡿⣿⠿⠿⠿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣸⠁⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡱⢸⡇⣎⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣓⠒⢒⣒⣒⣒⣒⣒⣒⣒⢒⠒⠚⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠉⠉⠉⠉⠉⢩⢛⡍⠉⠉⠉⠉⠉⢸⠉⠉⠉⠉⠉⡝⣩⠉⠉⠉⠉⠉⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⢸⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠦⠤⠤⠤⠤⠤⠔⠒⠒⠒⠒⠒⠒⠛⠿⠿⠷⠞


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

⠀⠀⠀⢀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⣯⢺⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠘⣎⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠙⡆⠀⠀⠀⠐⠋⢹⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣮⣿⢫⣿⣿⣦⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣷⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⢮⡙⢿⣿⣿⣷⣄⠀⠀⠀⢀⣧⣤⣤⣤⣤⣤⣧⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠻⣿⣿⣿⣦⡀⠀⢰⣿⡀⢀⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡜⠁⢺⣿⣿⡄⠘⣛⣣⣬⣭⣭⣭⣭⣄⣀⠀⢸⣿⣿⠀⠀⠀⠀⣠⡾⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⢀⣀⣤⣶⣦⡀⠀⠀⠀⠻⣄⠈⢛⣩⣶⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣷⣌⡻⠀⠀⠀⣰⡟⢀⡄⠈⢙⣿⣿⣿⡿⠃⠀⣠⣶⣦⣄⡀
⢾⣧⡤⢿⣿⣿⡟⡆⠀⠀⠀⠈⣱⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⣰⡟⢠⣾⠁⢠⣾⣿⣿⡿⠀⠀⠀⡇⠀⠈⠙⢿⣦
⢺⣿⣷⠀⣿⣿⣷⢹⡄⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣟⣠⣿⠃⢠⣿⣿⣿⡿⠁⠀⠀⡜⣰⡀⠀⠀⠀⢹⠂
⠈⢿⣿⣧⢻⣿⣿⣧⢻⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠟⢤⣿⣿⣿⡿⠁⠀⢀⣼⣿⡟⢡⠆⣠⠎⠁
⠀⠘⣿⣿⣇⢻⣿⣿⣯⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣾⣿⣿⡿⠁⠀⣠⣾⡿⠋⣰⣿⡿⠁
⠀⠀⠸⣿⣿⡆⠿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⣿⣿⠙⠺⣿⣿⡿⢁⣤⡾⠋⠎⢀⡼⣿⡿⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠹⣿⣿⣷⠹⣿⣿⣿⣷⠀⠀⠀⣠⣴⣾⡿⢿⣛⡿⠭⠭⠭⠭⠭⠽⣟⣿⢿⣿⣧⣄⠀⣼⡿⢡⣾⣿⣦⣀⠀⠞⢱⣿⠁⠀⢠⠂⢿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣆⢻⣿⣿⣿⣧⣴⣿⣿⡯⠗⠋⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠉⠺⢻⣿⣿⣿⢡⣿⣿⠛⣿⣿⣷⣤⣼⣿⠀⣰⠟⣡⣿⡿
⠀⠀⠀⠀⠀⢿⣿⠈⣦⡹⣿⣿⣿⣿⡿⠋⢀⡠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⢹⣿⣿⣿⣿⠧⢄⣿⣿⣿⣿⣿⠃⣴⠃⣴⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣦⠛⠛⣾⣿⣿⠏⢀⠔⠉⠀⠀⢀⣄⣀⢸⣧⣀⡤⢖⣀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣧⢀⣼⣿⣿⣿⣿⠃⠚⢅⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣄⣸⣿⣿⡀⠁⠀⠀⠀⠀⣀⡤⠟⠋⢻⣥⠶⣈⣭⠉⢀⠀⠀⢀⣼⣿⣿⣿⣿⣸⣿⣿⣿⣿⠇⠀⠀⠀⣰⣹
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⣻⣿⣧⡳⣄⠀⠀⠐⠿⢥⣭⣶⣒⣻⡧⠞⣋⡤⠖⠁⣀⣴⣿⣿⣿⣿⣿⣏⣝⣻⣿⡿⣵⡆⠀⠀⡴⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠙⣿⣿⣷⣬⡑⣢⣄⣀⣀⠀⠀⠉⠉⣉⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⡿⠛⣽⣽⡇⢀⣼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠀⠀⠀⠑⢦⡙⠻⢟⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⡛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⣉⣠⣽⣿⠟⠀⠀⠀⠀⠀⠀⢰⢸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣯⣿⣿⣿⣿⣿⣥⣴⣶⣶⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇⠀⠀⠀⠀⠀⣠⣾⣾⣿⡟⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⢶⣤⣤⣤⣿⣾⣿⡿⢋⣤⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⠾⠉⠁

⠀⠀⠀⠀⠀⠀⠥⠂⠒⢛⡷⠒⠐⠚⡷⠂⠒⠒⠒⠚⡿⠒⠀⠒⢛⠗⠒⠒⠚⡷⠂⠐⠒⢛⡷⠒⠐⠒⠒⢫⠗⠐⠲⠨⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢤⠈⢁⣤⡄⠨⠅⣄⢀⢀⣠⣨⣅⣤⣀⡄⠉⠠⣄⣤⠈⠁⣄⣀⣄⠈⢁⣄⣀⣀⠀⠉⠀⣀⣀⣀⡀
⠀⠀⠀⠀⡀⠒⠁⠀⡤⠒⠈⠀⠠⣠⣤⠀⠈⠀⠀⡩⠟⠋⠁⣠⠶⢊⡇⠻⢿⠭⡟⢸⠛⠯⡍⢸⣿⡿⠭⣟⠉⢿⠙⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢸⠁⠂⠀⠀⠀⢹⠛⠋⠉⠉⢙⡽⠋⠙⢛⠻⠁⠘⢿⡭⠽⠃⠸⢏⠉⢋⠀⠀⠑⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢠⠂⠰⠀⠀⠀⠈⠀⠀⠀⡀⠀⠂⠀⢠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠐⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠉⠉⠑⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣤⣤⣤⢤⡀⠀⠀⠀⢰⠠⠠⠤⠤⠀⠠⠄⠀⠀⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠐⠐⠄⠀⠀⠨⠤⠀⠄⠄⣬⠀⠀⠀⡈⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠉⠉⠉⠉⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⣠⢃⣀⣀⣀⣀⠀⠂⡀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⣐⣉⣉⣈⣁⣁⣒
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠘⠂⠓⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠂⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣤⣄⣀⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⢠⣿⠛⢦⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠈⣿⡀⢸⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠛⠹⣧⠀⠀⠀⢿⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣿⡄⠀⠀⢸⣷⠀⢹⠀⠀⠀⢀⣿⣿⡇⠀⠉⢹⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣹⣷⠀⢠⣾⣿⡖⠘⣿⡇⠀⢸⣿⣿⡇⠀⠀⡞⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⣹⠿⢇⠈⣿⣿⣷⠆⢿⣿⠀⢸⣿⣿⠃⠀⢰⠇⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠸⡀⣿⣿⣿⡂⠸⣿⡇⢸⣿⡿⠲⠤⡜⠀⡼⢁⣼⣿⠏⠙⠻⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣷⣾⣿⣿⡇⠀⢸⣇⣿⣿⡇⠀⣾⠃⡼⢡⣾⣿⡟⠀⠀⠀⢈⡿⠛⠋⠉
⠀⠀⠀⠀⠀⣠⣴⣾⠿⠿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣷⡀⠸⣿⣿⣿⡯⢉⣿⡼⣡⣿⣿⣿⣄⡀⠀⢠⠎
⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⠀⣿⣿⣿⠙⢺⡿⣵⣿⣿⣿⣯⣀⣼⣷⠋⠀⠀⢀⠀⠀⢐
⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⠁⠀⣼⣿⣿⣿⣿⣟⣵⣿⣿⣷⡶⣶⡆⢸⣷⣴⡟
⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠀⢹⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⡇⣿⡇⢸⠛⠛⡇
⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⣿⣿⣿⣷⡼⢤⣤⠧⣄⠠
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⠀⣸⣿⠀⢸
⢻⣿⣿⣦⣀⡀⠀⠀⢀⣀⣤⣶⢿⣿⣿⡿⠛⠉⠉⢙⣿⣿⣾⣿⣿⣿⣿⣿⣀⢐⣗⣀⣽⠀⢸⣿⣿⣿⣿⠁⣿⣿⠃⢹
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠋⠉⠻⣦⣤⠞⠋⠀⢈⣹⢿⣿⣿⣿⣿⣮⣽⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢹
⠀⠀⠉⠛⠛⣻⣿⡿⠋⠉⠉⠻⣦⣴⠞⠋⠉⢙⣷⣶⡞⠉⠀⢀⣉⣿⣿⣿⠫⣭⣿⣯⣿⠀⢸⣿⣿⣿⣿⠀⣿⣿⡇⢸
⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⠶⠋⠉⠙⣷⣶⠞⠋⠁⢀⣙⣷⣾⣿⣿⣿⡿⢿⠀⢿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⣿⣿⡇⢸
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⠖⠋⠁⠉⣻⣶⣾⣿⣿⣿⣿⠿⠛⠉⠀⢸⡇⢸⣿⣿⣿⠀⠘⠻⠿⠿⠟⠓⠛⠛⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠒⠒⠒⠒⠒⠂⠒⠆⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⡔⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡚⠀⣀⣀⢘⢲⡀⠐⠀⠀⠀⢰⠒⢢⠤⠄⠀⠀⠠⠄⠀⠀⠀⠀⢃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡔⠃⠊⠙⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠘⢀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂⠘⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⡆⠀⠀⠀⠀⢀
⠀⠀⠀⠖⠲⠖⠒⠒⠒⠂⠒⠂⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⡠⠒⠂⠐⠒⢤⠀⠀⡴⠂⠑⢢⠀⠖⠉⠙⢆⢸⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠇
⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⠀⢱⡀⢣⡀⢀⡼⠀⢦⣀⣀⠎⢸⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠄
⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣠⠆⠠⢄⠀⡴⠒⠢⡄⢸⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠧⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⡇⠱⡀⠀⠀⠀⠀⠀⣰⠁⣇⠀⠀⣸⠀⣄⠀⢀⡄⢸⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠰⠄⠀⠀⠠⠄⠄⠤⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡇⠀⠈⠢⠤⠀⠤⠞⠁⠀⠈⠉⠈⠁⠀⠈⠉⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡀⠀⢀⣄
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠉⠒⢄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⢀⣀⣀⣀⣀⡀⠠⠊⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⣅⠼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠊⢠⠘⠅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠀⡀⠤⢀
⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠄⡀⠀⠀⠀⠈⠀⠄⠀⠀⠤⠂⠀⠘⡆⠀⢀⡔⠚⠒⠒⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠀⠀⠀⢨⣀⠠⠀⠠⠐⠨⠀⠐⡇⠀⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⡠⠀⠀⠀⠀⠑⢤⡐⣀⢶⠡⡈⠎⠀⠀⠡⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠔⠉⠑⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠛⠂⠑⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⢐⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡦⠀⠀⠠⠄⠀⢠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠢⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠊⠀⠁⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⠶⠶⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣛⣭⠶⠖⠛⠛⠛⠛⠛⠳⠶⢬⣍⣛⡳⠶⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢒⣋⣭⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⣿⡗⠮⠭⣙⡒⠢⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠁⠀⠀⠀⣀⣤⠶⠚⠛⠙⣿⠙⠛⠳⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡀⠀⠉⠉⠉⠒⠒⠀⠀⢹⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⡀⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⡇⠀⠀⠀⠀⢸⡇⢸⠀⡇⢸⢰⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠃⢸⠀⡇⢸⠈⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡄⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠘⠛⠒⠲⠶⠤⣤⣄⣼⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣻⣿⣶⠶⣤⣤⣄⣀⡈⠀⠀⠈⠛⠒⠶⠶⢤⣤⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣌⣉⠉⠛⠛⠒⠶⠤⠤⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⠔⣋⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠤⣄⡀⠀⠀⠀⠈⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠠⠀⠀⠄⠄⠄⠀⠆⠄⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠂⢀⠂⠀⠀⠆⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⠀⡀⠀⠤⡀⠀⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⢰⠃⠀⠒⢒⣚⠒⠒⠀⠀⣠⡃⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠴⠂⠀⠁⠀⠦⠖⡩⢑⡘⢒⣶⠢⠑⣀⠵⣠⢀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠙⡲⠊⠉⠈⠢⣀⣈⠂⠀⠀⠀⠀⠖⠅⠊⠀⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠄⠀⠀⣃⠀⠠⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡅⡇⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⠠⠉⠀⢀⠀⠀⠸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡴⡇⡃⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠶⠦⠀⡈⠀⢀⠀⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠃⠀⠀⠀⣄⠀⠀⠀⢐⠂⡌⣀⠀⢀⠃⠒⡞⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢃⡧⣀⡀⢴⠀⠀⣀⡁⠒⡚⠇⠉⠀⠈⠀⠨⠁⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠛⠒⠒⠚⠀⢀⠂⠀⠀⡘⠀⠀⠀⠀⠀⠂⠀⠘⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣀⠀⣄⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠰⠀⠀⠄⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠈⠙⡀⠀⠀⠀⠸⠀⠠⠤⠬⢀⠀⠀⠀⠀⡀⠀⠰⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠂⠤⠀⢴⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠉⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⡀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡃⠀⢀⢘⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠙⡀⠈⠈⡏⠉⡇⠈⠀⠀⠀⠀⢨⠉⠉⠉⠉⠉⠉⠉⠩⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠈⢄⠀⢁⢀⠑⠂⢄⠂⡀⠀⢘⡀⠀⠀⠀⠀⠀⠀⢐⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⡁⠞⠛⠓⠚⠛⠛⠁⠒⠚⠀⠀⠀⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠠⠤⡀⠐⢫⠤⠠⠤⠯⢁⣉⠀⠀⣀⡀
⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠒⠀⠀⠀⠀⠂⠒⠖⠂⠒⠆⠀⠀⠀⠆⠀⠀⠀⠰⠀⠂⠒⢰⠀⠂⢠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡄⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠃⠀⠀⠆
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⢸⡄⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠤⠀⠀⠀⠒⠀⠀⠀⠀⠄⢤⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠄⠀⡂
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠱⠆
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⣷⣼⣰⣀⣆⣄⡄⠀⠀⠀⠀⠑⠓⠂⢐⠂
⠀⠀⠀⠀⠈⠀⠀⡀⠀⠰⠖⠂⠀⠀⠀⠀⠀⣀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠉⠉⠀⣠⠈⠉⠉⠀⠀⠰⣄⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿

⠀⠀⡂⠒⠀⠂⠂⠀⠀⠀⠀⠬⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠀⠒⠒⠐⠂
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠀⠀⠀⠀⠀⠸⠯⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⠶⢴⣤⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠀⠃⠀⠋⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠠⠤⠀⠀⠤⠤⠀⠀⠀⠀⠅⢁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠐⠐⠀⠀⠐⠐⠀⠀⠀⠀⡃⢠⣠⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢷⠁⢱⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⣀⣀⣀⣀
⠀⠀⡒⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢠⢐⠰⠀⡄
⠀⠀⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⡂⠀⠀⠀⠀⠈⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠘⢿⣿⡋⠉⠈⡇⢰⣿⣿⣷⡄⠀⠘⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⣿⠁
⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣆⠀⠀⠘⠛⣷⡀⠸⣿⣷⡀⠀⣷⢸⣿⣿⣿⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡰⢃⣼⣿⠃
⠀⠑⠤⡀⢀⣠⣴⣄⠀⠀⠀⠀⠹⣉⠀⠀⠀⢸⣿⣧⠀⢿⣿⣷⡀⢹⠀⣿⣿⣿⣿⠀⢸⠀⠀⡿⠀⠀⠀⠀⢠⣮⣀⣿⣿⠃
⠀⠀⠀⠈⢻⣿⣿⣿⣦⡀⠀⠀⠀⢻⣧⢣⠀⠈⡿⣿⣆⠘⣿⢿⣿⣹⡇⢻⣿⣿⣿⡆⢸⠐⠒⡇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⢻⣧⢣⡀⢹⣿⣿⡄⢹⣽⣿⣀⣷⢸⣟⣿⣿⣇⢸⠈⠉⡇⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣶⣦⣤⣌⣿⣧⢳⡀⢿⣿⣷⠀⢿⣿⣿⣿⡀⣿⣿⣿⣿⡆⠀⢸⡇⠀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡳⠘⣿⣿⣧⠸⣿⣿⣿⡇⢹⢹⣿⣿⡟⠀⣼⣿⡏⠉⠛⠿⣿⣃
⠀⠀⣴⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⡟⠙⡆⢻⣿⣿⣿⠘⡟⣿⣿⡇⢸⣿⣿⣿⣿⣶⣦⣄⡙⠳⣦⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⠀⢹⡈⣿⣿⣿⡄⣧⢿⣿⡇⠀⣿⣿⣿⡿⠟⢿⣿⣿⣶⣄⡙⢦⡀
⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠻⢇⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢧⢹⣿⣿⣇⢸⣸⣿⡇⢰⣿⢿⣷⣍⠀⠀⠉⠛⢿⣿⣿⣦⣽⡄
⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⣠⣔⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⡆⢿⣿⣿⣼⣷⣿⣦⣼⣯⣾⣿⣿⣷⣦⣀⠀⣰⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣅⣀⣠⣴⣿⠾⢋⣽⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⠸⣆⣽⣾⣿⠿⣛⠛⠉⠙⢛⡻⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⡃
⢻⣿⣿⣿⣿⣿⣿⣿⣯⢁⣤⣾⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⡿⣰⣿⡿⣫⣖⣭⡶⠾⠟⠛⠛⠻⢶⣌⠻⣿⣿⣆⠉⠛⠻⠿⠿⠟⠁
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠐⠂⠈⠳⡜⣇⠘⣇
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣯⡿⠿⠟⠛⠛⢿⣿⣿⣿⠃⠀⠠⠀⠀⠀⠀⠸⠗⠀⠀⠀⢀⢹⣿⡄⣿⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡁⠀⠤⢤⣤⡀⢸⣿⣿⡏⠀⠰⣦⣶⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠈⠳⣌⣧⣾⣀⣀⣸⣿⣿⣷⡀⠀⢨⠙⠓⠀⠀⠀⠀⠀⠆⠀⠀⣸⣿⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⡏⠀⣤⣀⣀⣤⢀⣀⠈⠓⢦⠜⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢯⣾⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉⠹⣿⠌⠉⠑⠂⢁⣤⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣤⣤⣤⣤⣶⣾⣿⢟⣫⠶⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⡤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠛⠛⠋⠉⠉⠉⠉⠉⢉⣻⠀⠀⠀⢸⣏⠉⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀⠻⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠙⡇⠀⠀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠢⣤⠦⢤⡤⠤⢄⣸⠀⠀⠀⠀⠀⠀⣿⠉⠋⠀⠳⠒⠀⠲⣾⠀⠀⠀⠀⠀⠀⣷⠦⠴⠉⠑⠤⠞⠳⣄⡇
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⠀⢿⣤⣤⡤⠤⠤⠤⠷⠤⠤⠴⠶⠶⠶⠤⠚⠓⠒⠲⠶⠶⠶⠷⠦⠤⠀⠀⠀⠀⠒⠚⠛⠒⠒⠲⢦⡀
⠀⠀⢸⡏⠉⠁⢀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⣴⠄⠀⣧
⠀⠀⠀⣷⠀⠀⢱⠏⠉⠉⡉⠁⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢰⡇
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⢸⡇
⠀⠀⠀⢸⡆⠀⠘⡆⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⡇
⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⣿⠀⠀⡇
⠀⠀⠀⢸⠃⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⢸⡆⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⠀⢠⡧
⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢹⡀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠁⠘⡇
⠀⠀⠀⠈⡇⠀⠀⢻⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⣧
⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⠀⡄⠀⢻
⠀⠀⠀⠀⣿⠀⠀⢸⡤⠠⠤⠾⣇⠀⠀⠀⠀⠀⣰⠃⠒⠒⠒⠒⣒⣚⣆⠀⠀⠀⠀⠀⠀⠀⡏⠉⠭⠭⠭⠭⣇⠀⠀⠀⠀⠀⠀⣸⠦⠤⠚⠁⢃⠀⠸⣇
⠀⠀⠀⣰⠏⠀⣰⠋⠉⠉⠉⠀⠈⠓⠒⠶⠒⠋⠉⠉⠉⠉⠉⠀⠀⠀⠈⠓⠤⣀⣀⣀⡤⠚⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠚⠁⠀⠀⠀⠀⠈⢦⡀⠈⢳⡀
⢠⡖⠛⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣹⡄⠀⠙
⣾⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣠

⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⢰⣄⣀⣀⣤⣾⣇⢁⡄⢠⡀⣬⠁⣦⢀⡄⣠⠀⣄⢀⡄⢠⡀⣤⠀⡄⣠⠀⣤⢠⡄⢠⡀⣤⢠⡤⣠⠀⣧⠘⣄⢠⡄⢠⡀⣈⣳⣤⣠⣠⣤⣆
⠀⠀⠀⢸⣤⣦⣤⣾⣯⣹⣿⣏⣿⡛⠃⠀⢿⠀⢉⣭⡤⣉⣠⣥⣌⣁⣩⣄⠑⣨⢀⣥⢨⣥⣈⣄⢩⣌⣥⣤⡌⣥⠀⠘⣏⣽⣿⣿⣿⣿⣿⣶⣵⣾⣏
⠀⠀⠀⠐⠀⠀⠈⠝⠓⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠐⠒⠚⠋⠀⠀⠀⠋
⠀⠀⠀⠀⣆⣀⣀⣇⠀⠀⠀⢀⡀⠀⠀⠀⣠⣀⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣴⠄
⠀⠀⠀⠀⢸⣉⣟⠀⣤⣄⢴⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠠⣤⣠⣤⡀⣻⣀⣇
⠀⠀⠀⠀⢻⣿⣽⢋⣿⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣿⡋⢿⣦⡞
⠀⠀⠀⠀⢸⠁⠸⡀⣀⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣀⣀⣀⡀⢸⡿⡇
⠀⠀⠀⠀⢸⡇⠀⠂⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⢸⣿⡿⣿⡇⠸⠃
⠀⠀⠀⠀⢸⣷⢸⡂⣿⠅⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠈⣿⡇⠀⠇
⠀⠀⠀⠀⢸⣿⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⢸
⠀⠀⠀⠀⠸⡇⠀⠀⣤⣤⣤⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣤⣤⣄⡇⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⡉⣉⠉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠈⡉⡈⢉⠁
⠀⠀⠀⠀⢠⠘⠀⠀⣶⢏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢤⡜⢷
⠀⠀⠀⠠⡋⠉⠉⡶⡇⠀⠻⠀⠀⠀⠀⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⡁⢸⢦⢉⣉⢁⠄
⠀⠀⠀⠘⢄⣀⣀⡜⡗⡏⢆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠷⢸⣿⠣⣀⣀⡠
⠀⠀⠀⠀⢸⠀⢨⡇⡆⠙⠻⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠻⢹⠀⠋⠈⠃
⠀⠀⠀⠀⢸⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⠀⢠⠀⣠⡾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣾
⠀⠀⠀⠀⢸⣄⣰⡆⠍⠊⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠸⠀⣄⠀⡄
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠚
⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐