Censored swear word Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣼⣶⣄⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣦⣀⠀⢀⣠⣶⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣄⠈⠃⠀⠀⢻⣷⣶⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⢠⣄⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⠆⠀⠀⢀⡬⠛
⠀⠀⠀⠀⠀⠻⠛⠛⠉⠉⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡿⣿⢻⡟⠻⢋⢙⡿⢛⣩⣭⡙⠿⠙⢹⡁⠖⢻⢁⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⠄⠰⣇⣶⡄⢹⠁⡏⠾⠀⢃⣾⣶⣯⡘⢃⣜⣹⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣠⣦⣾⣭⣷⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⠿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡶⠶⢾⡶⠿⡿⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠹⠟⠿⢻⠻⡟⢿⢻⠿⡿⢿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⠻⠉⠅⠭⠈⠁⠁⢉⢙⡛⣿⣿⠟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠰⡃⠰⠆⠶⠆⢀⠀⠀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡠⡄⠀⣦⣴⡄
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣪⢵⣛⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠋⠁⠀⠋⠛⠁⠀⠂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠐⢠⣤⠀⠀⠠⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠼⠇⠀⠐⠇⠈⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⢀⠀⣄⠀⠀⡀⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣾⣻⣿⣻⡆
⠀⠀⠀⠀⠀⣶⡂⣼⣇⣰⡆⠀⠀⠀⠀⠀⠛⠁⠸⠀⠐⠃⢠⠀⠀⠀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢿⣾⡟⠁
⠀⠀⠀⠀⠀⠛⠙⡿⠁⠝⠁⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠠⡀⠘⠺⠁⠏⠛⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣛⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⢐⠀⠀⡀⠂⠐⠐⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢼⣷⣄⠀⠈⢿⡀⠀⠀⣀⠀⠀⣀⣠⡤⠚⠁⠀⠉⠛⠲⠤⠤⠤⠔⠚⠁⠡⡄⠠⢤⣶⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠳⢄⠈⠃⠀⠀⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⠛⠁⡀
⠀⠀⠀⠀⢠⣤⣀⣀⣀⡀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠻⠛⠛⠉⠉⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣤⣤⡀⢰⡏⠀⠀⠄⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠁⠀⠀⢀⢀⣀⣠⣤⣄⢰⣆⣸⣧⢸⣇⣿⢠⡾⣩⠴⣶⢈⣿⠸⠇⠀⠀⠆⢇⠀⠀⠚⣉⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢻⣿⠇⢉⡾⠋⣻⣏⣿⣯⢸⡏⣿⢺⡇⠿⠶⠿⠟⠁⠾⠆⠀⠀⠈⢬⠢⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⣸⣿⣆⢨⣥⠀⠻⠏⠻⠁⠘⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⡀⠀⠋⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣧⠀⢤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⢀⠴⠚⠋⠁⠀⠀⠀⠀⠈⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⡦⠄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠴⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠐⠒⠂⠂⠛⠒⠐⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠉⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⡴⠁⣀⡀⠀⠀⢀⡀⡀⡀⠀⡀⠈⢧
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠰⡋⠁⡯⡇⠊⣭⡁⣿⠝⠘⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⣇⠀⠣⠟⠔⠃⠘⠛⠃⠋⠇⠀⠀⣸
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠀⠀⠁⠑⠂⠀⠀⠀⠈⠀⠀⠀⡠⠂⠂⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣀⣀⣀⣀⠀⣀⣀⣀⠀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢀⡠⠶⠤⠤⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣴⠒⠒⠛⠀⠉⠉⠁⠀⠉⠉⠉⠉⠳⠭⠤⠤⢄⡀
⠀⠀⠀⠀⠀⢀⡎⠀⢠⠀⡀⡀⡄⢠⠀⢀⢀⠀⢁⠀⠀⠀⠀⠀⠀⡔⠊⠁⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠘⡄⠀⠐⠃⠁⠁⠀⠘⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⡿⠄⠉⠰⡏⠁⡷⣏⠸⠀⠇⠃⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠰⡍⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠁⠈⠈⠀⠁⠁⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠒⠂⡇⠀⣠⠎⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⡀⠀⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⠒⠉⠓⠜⠀⠈⠉⠉⠉⠙⠢⠤⠵⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡀⠀⠀⠀⣠⣾⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠉⠁⠀⠀⠈⠉⠘⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢰⡶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⣄⢠⠀⡄⠀⡤⠀⢄⢀⢤⡀⠀⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⢸⡇⠀⠹⠸⠀⠃⢸⡸⠼⠌⠘⢦⠉⠀⣷⡗⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠉⠒⠁⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠈⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣷⣶⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣶⣶⣦⡀⠀⠁
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠀⠀⠐⣒⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⣣⣶⣿⣧⣿⣿⣯⣽⣿⣿⣿⠀⠀⠐⠄⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢸⣿⣧⣿⣧⣴⣿⣿⣿⣸⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⢀⠈⠀⠄⠀⠈⠉⠻⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⡿⠁⠀⠰⢠⠄
⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⡁⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢀⠒
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⢀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠆⠀⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⢀
⠀⠀⡇⠀⠀⢜⠟⢫⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁
⠀⠀⢁⠀⠀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣯⣿⣿⣿⣧⣿⣿⣿⣷⣀⠀⠀⠀⠂⠐⠀⠂⠀⠈⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠷⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⣴⠞⡋⠉⠉⠓⢦⠀⢠⠶⠦⠤⠤⢤⡄⢠⣶⠆⣠⣤⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⠃⣀⣛⣀⣛⡂⠈⡇⠘⢸⢋⡍⣻⢸⡇⢸⡟⣰⠟⠁⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠘⣇⡧⡥⣭⣬⣿⣰⠃⠀⣿⠘⠓⠋⣼⠀⠟⠐⠋⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠈⠛⠲⠶⠖⠛⠁⠀⠀⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣏⣠⣴⠞⠋⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣬⣭⣭⣒⣒⡶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣫⡴⠶⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠲⠦⣤⡀⠀⣀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢬⣙⠦⣄
⠀⠀⠀⠀⠀⢠⢞⣥⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣮⡣
⠀⠀⠀⠀⠠⢫⠞⠁⠀⠀⠀⠀⠀⣀⢀⣤⢀⡀⠀⢀⠀⠀⠀⠀⠀⡾⢁⡾⠁⠀⠀⠀⠀⢀⠀⡀⢠⢦⢀⠄⠀⢀⣤⢀⣤⡀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣤⣧⠈⢣⡀⠁⡼⣋⡄⠸⠀⡽⢇⡄⢸⡇⢸⠁⠀⠀⠀⠀⠀⢸⡀⢳⠈⢊⠊⡞⡆⠮⡿⢈⢳⡄⡼⢀⡄⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢻⠺⠈⠋⠀⠀⠑⠉⠃⠉⠘⠤⠋⠀⠸⣇⠸⡆⠀⠀⠀⠀⠀⠀⠣⠘⠀⠀⠀⠈⠀⠀⠀⠈⠉⠐⠢⠈⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠈⠪⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣷⠀⠀⠀⣠⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠁⠀⠈⠙⠓⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠶⠖⠒⢾⣧⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠛⠶⠬⣷⡄

⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⠞⠉⡀⣀⡀⢀⣀⠀⡄⣉⠛⢦⠀⠀⠀⠤⠠⠤⠊⠙⠒⠒⢶⠀⠀⠀⠀⠀⠀⢤⡀⢦⠀⠀⠀⣶
⠀⠀⠀⠀⣇⠀⢘⣯⣽⠀⠻⠼⠂⠁⠘⠀⢀⡇⠀⠀⡀⠰⡶⣦⢇⢰⣦⠈⢛⡶⠂⠀⠀⠀⠈⣿⠾⠓⠦⠚⠘⠦⡤⠤⡞
⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠺⠥⡀⠁⠉⢀⡲⢥⡒⣘⣇⠀⠀⠙⡖⠲⠋⠰⠀⢠⡀⢠⢤⠠⡄⠃⠐⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠙⠚⠃⠀⠀⠀⠀⠀⢹⣄⣄⣀⢀⡤⠤⠏⠀⠀⢀⡠⠆⠀⠀⢏⠆⠙⠁⠐⠚⠐⠀⠀⠈⢃⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⠀⢠⣚⡆⢹⡿⠀⠀⠀⡴⠉
⠀⠀⠀⠀⡰⠚⠉⠉⠉⠉⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣄⡀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠈⠉⠀⠈⠀⠀⢀⣄⣳⡀
⠀⠀⠀⠀⡇⢀⣀⡄⠞⢹⢴⠦⣧⡄⢹⡄⠀⠀⠀⠀⠀⠈⠢⠴⠋⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠔⠋⠉⠙⡴⠊⠙⠂⠀⠉⠂
⠀⠀⠀⠀⢿⠀⠟⠓⠀⠉⠀⠀⠈⠀⠸⡇⠀⠀⢤⣀⣸⠀⢀⣲⠤⣄⠉⠉⢩⠟⠀⠀⠀⢀⣾⠞⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣀⣀⣠⣤⡼⠇⠀⠀⠀⠙⣦⠀⣿⣼⣲⡟⠀⠀⢯⠀⠀⠀⢀⡞⠁⠀⢀⣠⡤⠤⠤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⢉⣂⣀⠘⣯⣉⣀⠀⠀⠀⠀⠀⠀⣤⣞⣁⡀⠈⠉⠉⠀⡶⠶⠬⠷⠀⠀⠈⠀⢀⠞⡩⠐⠢⡄⢠⣄⢀⢠⢨⡙⢆
⠀⠀⠀⠀⠀⠈⠉⠿⠶⣶⣄⣛⣶⠀⠀⠀⠀⠀⠀⠀⣼⠴⠲⣄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡀⢧⡓⢣⠆⠸⣒⡇⠋⠋⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⢀⡀⢀⣀⣀⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠒⠀⠂⠀⠈⠈⠒⠰⠒
⠀⠀⠀⡜⠁⠀⠀⠰⠀⠄⠀⠀⠀⡀⠀⠀⠰⠀⠀⣀⠀⠀⢄⡀⢀⣀⠀⠠⡁⠀⠀⡄⠀⣴⣄⠀⠞⢰⡶⠀⠀⠠
⠀⠀⠀⠑⠄⡀⠀⠀⠀⠈⠀⠂⠀⠀⢀⡠⠊⠀⠐⡀⠑⠂⠀⠉⠁⠀⣀⠀⠲⡀⠀⠘⠀⠙⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠒⠒⠢⡀⠀⡀⢀⠄⠂⠁⠀⣴⡄⢰⠃⠀⠀⠠⠂⠀⠄⠀⠛⠉⠉⠑⠈⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⢀⠀⠱
⠀⠀⠀⢀⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⠢⡠⠃⠀⠀⣀⠤⠤⠤⠤⠄⢀⠀⡀⠤⠀⠐⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⠀⠀⠤⠀⠀⠀⠀⡀⠄⠂⠐⠢⢄⠀⠀⠰⠋⠀⠀⠴⢠⠀⠀⠪⠉⠀⠀⠀⢒⢦⠀⠀⠈⢆
⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡎⠀⠀⠉⠀⠀⠀⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣙⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢀⢀⡀⠀⠠⠐⠁⠀⠀⠀⡅⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠠⢄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠶⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⣀⡠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡞⢡⠄⣄⡇⠸⠽⣠⠞⠀⢸⠸⠀⢠⡧⢼⠤⠄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢧⣈⠉⣀⠄⢠⠞⡡⠄⠀⠀⠃⠀⢰⠓⡞⠂⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠦⣄⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠏⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠯⠒⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⠶⠦⣤⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⣶⠆⠀⠀⢀⣀⣉⠛⢦⡀⠀⢀⡴⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⡟⠀⠀⡗⠛⣯⢀⠷⣄⢰⣲⣤⠈⣿⣿⠇⠀⢻⠀⣾⠁⢠⢩⠲⣏⡀⣴⠟⣹⢠⡖⡲⣀⢫⠗⠀⠘⡇
⠀⠀⠀⠀⠀⠻⣄⠀⠟⠖⠓⠘⠶⠋⠘⢻⠇⠀⡿⠁⠀⣠⡟⠀⠹⣦⠀⠾⠙⠵⠈⠴⠾⠃⠈⠳⠖⠃⣤⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣀⣀⡀⠀⠀⠀⢀⡀⠀⣴⠚⠉⠀⠀⠀⠈⠙⣦⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠙⠲⠾⠓⠀⠀⠀⠀⠀⠘⠳⠖⠋⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣠⠤⣄⠀⠀⠀⠀⠀⢠⡤⢤⣀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠉⠁⠀⠀⠀⠀⠉⠉⠀⠸⣅⡀⠀⠀⠀⢀⣠⠿⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⡾⠁⠀⢀⣴⡤⣶⠄⢠⡴⣦⡀⣶⣰⡀⠀⠹⣦⠀⣰⠟⢁⡔⣋⢉⡓⣄⠰⣲⣶⡲⡄⣶⢢⡶⠙⣧
⠀⠀⠀⠀⠀⢷⡀⠀⠠⢼⠶⡿⠂⠘⠷⠶⠃⠋⠈⡏⠀⠀⣽⠀⢿⠀⢸⣰⣛⣖⣧⡸⠀⡗⠶⢻⠃⠇⠏⠀⠀⣼
⠀⠀⠀⠀⠀⠈⠳⣦⣀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⡼⠃⠀⠈⠳⣤⡙⠒⠒⠋⠁⠀⠉⠉⠉⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠶⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⢤⣀⡀
⠀⠀⠀⠀⠀⡠⣔⡤⠶⠒⠛⠉⠉⠉⠉⠉⠛⠒⠲⣤⢀⣠⠴⠚⠉⠉⠁⠀⠀⠀⠈⠉⠉⠓⠾⣕⡦⡀
⠀⠀⠀⢠⣮⠚⠁⠀⠀⠠⡄⢰⡄⢠⠄⠀⠀⢀⡞⡱⠋⠀⠀⠀⠀⠀⣤⢠⠖⢦⠀⡤⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢧⠸⡇⡼⠀⠀⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⣿⠈⢠⠞⢠⠇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠘⠀⠃⠃⠀⠀⠀⠸⡄⢇⠀⠀⠀⠀⠀⠀⠙⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡔⠦⠤⠤⠤⠤⠤⠖⠒⠋⠁⠀⠈⠙⠒⠲⠤⠤⠤⣤⣤⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⠡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠷⠦⣌⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⢄⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠴⠲⠟⠉⠁⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠛⠁⠀⠀⠉⢢⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡔⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢰⠃⠀⠀⣀⡀⢀⡀⡀⢀⣤⢄⢠⡄⣤⠀⠋⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠃⠠⣤⢀⠀⢠⣤⠀⠀⢀⢜⠄
⠀⠀⠀⢾⠀⠀⠸⡥⡽⠈⣯⠓⣝⣱⡯⠘⠘⠁⠀⠀⠉⠢⡀⠀⠀⢈⢦⡀⠀⠀⡟⢲⠀⢩⠘⠋⢚⡿⠋⠀⠀⢻⠃
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠣⡄⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠐⠒⠒⠒⠮⠋⡇⠀⠀⡠⠋⠀⠀⠀⠀⠀⠘⠒⢶⠀⠀⠀⣰⠦⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠴⠊⠀⠀⠀⠀⠀⠀⠀⣀⡴⢃⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⢀⡤⠤⢤⣄⣒⣂⡞⠉⣷⣀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢁⡴⠛⠉⠉⠉⠉⠛⠀⠀⠀⠀⠉⠁⠀⠀⠉⠘⠋⠉⢉⣷⡭⠭⠭⢥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡤⠶⠶⣄⠀⠘⣇⢸⡇⠀⢀⣇⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⠀⢀⡟⣰⠒⣦⢸⡇⠀⢿⢸⡇⢈⣩⣯⣽⠤⠄⠀⠀⠀⠀⢀⣤⠞⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠀⠀⠀⠀⣷⠶⠒⠀⠘⣧⠘⠶⠛⠊⡀⠀⠘⠘⠁⠀⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡆⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠓⠶⠶⠚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⣠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡿⠀⠀⢀⡼⡳⠤⣤⡤⠴⠖⠛⢶⠀⣠⣤⠦⣄⣀⣀⣸⠞⠉⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣁⣀⠴⠋⠚⠉⠁⠒⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⢀⣠⣤⣤⣀⣴⠶⠶⢦⣬⣴⠋⢹⣦⣄⣤⣄⡠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣥⣾⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠼⠓⠛⠛⠓⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⣀⣀⠀⠀⠀⠶⣆⠀⠀⠀⠀⡄⢠⣀⠀⢠⣦⢀⣤⡀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⡾⢴⡶⠦⣄⠀⣠⣾⣶⣦⡀⠚⣷⠦⣯⠀⣿⠃⣾⡟⠁⠀⠀⣀⡴⢏⠄
⠀⠀⠀⠀⠀⠀⠀⢈⣿⠂⠀⠀⠀⠿⣷⡞⢣⣴⡿⠀⣿⣿⣿⣿⡇⠀⢻⡆⠊⠀⠋⡼⠋⠀⠀⠀⠀⣙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡇⠀⠀⠀⠛⠻⠛⠋⠀⠀⠈⠛⠛⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⠴⣆⠀⠀⢠⣄⠀⠀⠀⢀⣠⡀⠀⠀⡀⠀⠀⠀⣀⣤⡶⠲⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⣴⠯⠯⠟⠛⠛⠉⠀⠹⣤⠟⠋⠓⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠶⠶⣶⣤⣤⣀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣭⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡏⠀⠀⠀⠀⠀⠀⡄⢠⠀⢀⡴⠖⠲⢦⡀⠀⣤⡄⠀⣖⡦⠀⠀⡆⡆⡶⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠠⢾⢗⣟⡒⢾⢠⡖⣲⠄⣿⠈⠙⠓⣠⠟⣧⡆⠀⠇⠇⠇⠀⠀⢠⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⡆⠀⠀⠀⠀⠈⠿⠹⠋⠀⠀⠹⠶⠿⠴⠃⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠂⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢈⣱⠶⠶⢦⣤⣤⣤⣤⣴⣶⠶⠾⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣠⡤⠶⢛⠵⠊⠙⠓⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄
⠀⠀⢀⣔⡊⣤⣶⠃⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣋⣡⣴⣶⣷⡆
⠀⠀⠀⠙⢾⢝⡿⠁⠀⠀⢀⢗⡬⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣿⣟⣛⣁⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⣿⢯⣩⣥⣿⠁
⠀⠀⣀⠀⠀⠈⠩⠀⠀⡀⠨⠇⠀⠀⠀⠀⠀⢀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡿⠁
⠀⣰⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢔⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠈⠉⠉⠓⠂⠀⠀⠀⠀⠔⠨⡑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠄⠀⢀⠄⡀⠀⠀⠀⠀⡀⠀⠠⡔⠀⠃⠤⠂⠔⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠳⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢰⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠂⠀⠨⠛⡠⠂⠁⠀⠀⠀⠀⠀⠈⠁⠀⠃⠈⠀⠀⠀⠀⠈⣁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠑⠄⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠀⠠⠥⠄⢮⢈⢁⣀⣄⠀⠀⠀⠀⠠⠀⢐⠀⠐⠂⢀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⡀⠀⠨⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠑⠂⡄⠀⠮⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡄⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢿⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠐⠓
⠀⣀⠀⠀⠈⢳⡀⠸⡇⠀⠀⠀⠀⢀⢀⢤⣰⠄⠀⠀⠀⠀⠂⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⢀⡀⢀⠀⠀⠈⠁
⠀⠈⠛⢦⣀⠀⠓⠀⠀⠀⠀⢤⡺⠜⣊⢌⢆⠷⠀⡀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⣍⠂⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢳⠿⣘⣌⡦⢞⢋⠀⠀⠀⠀⢨⣀⣤⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡰⠘⠐⢠⠀⠀⠀⠀⠀⠀⢠⣘⣷⡆
⠀⠀⠀⠀⠀⠰⡄⠀⠈⠉⠀⠐⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⠂⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠐⢁⠂⡈⠆⠀⠀⠀⠀⠀⠀⠞⣿⣽⣿⡗
⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢢⢨⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠠⠀⠐⠄⠀⠀⠀⠀⠀⢀⠀⠆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠋⠉⠀⠀⠀⠀⠀⠀⡀⠈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠁⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠻⣿⣿⡇⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢨⠂⠀⠀⠀⠀⠀⠀⠀⢀⡄⠸⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡄⠀⣇
⠀⠀⠀⠠⣤⣈⣁⣠⣞⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢳⠀⠛
⠀⠀⠀⠈⠋⠉⣽⠋⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣄⣀⣄⠀⠀⣀⣄⠀⠀⢰⠀⣠⠀⠀⠠⡶⠀⠀⡖⣿⣀⠀⠀⣤⣴⢤⡆⠀⢰⢤⠄⢀⣄⢠⡄
⠀⠀⢈⣿⣭⡧⠀⠀⣯⣘⡽⠀⠸⠀⢹⠇⠀⢰⢤⡀⠀⠓⣷⠋⠀⠀⣻⣀⣸⡋⠀⢈⠃⠀⠀⢽⣉⠇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠑⠚⠁⠀⠀⠁⠀⠀⠀⠉⠘⠉⠁⠀⠙⠁⠀⠀⠘
⠀⠀⠀⣴⣶⣦⠀⢀⣠⣦⢆⠀⠀⢰⣿⡦⠀⠀⣠⠖⡊⢒⢦⠀⠀⢦⣤⡤⡄⠀⣤⢠⡖⠀⠀⣀⣠⣀
⠀⠀⠀⠸⣿⠃⠀⣼⢋⡴⡟⠀⠰⢦⣉⡡⠦⠀⣇⣼⣷⣿⣄⠇⠀⣾⠦⠟⡇⠀⢻⠸⠁⠀⢿⣬⢣⣼
⠀⠀⠀⠀⠋⠀⠀⠘⠉⠋⠁⠀⠘⠋⠉⠙⠂⠀⠈⠓⠒⠚⠋⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⡶⠶⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⠶⠿⠟⠛⠛⣉⣉⡁⠠⠤⠖⠲⠤⠀⠹⡿⠇
⠀⠀⠀⣀⣀⣠⣤⣤⣶⡶⠾⠿⠛⠛⣛⣉⣉⠥⠤⠄⠒⠒⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢲⣿
⣠⣾⣿⠟⢋⣉⡩⠤⠤⠒⠒⠚⠉⠉⡁⠀⣠⡄⠰⠆⠸⠇⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⢏⡇
⣿⣿⠁⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣧
⢹⣿⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡀⢸⣇⢠⣤⠀⢰⡖⠀⠀⠀⠀⡅⠘⣿⡄
⠐⣿⡇⢸⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⢀⣠⣤⣤⡀⢀⠠⠛⢻⡇⠸⣿⠀⠻⣧⣾⡇⠀⠀⠀⠀⢘⠀⣌⣁
⠀⢿⣿⠈⡁⠀⠀⠀⠀⠸⣿⠎⠻⣷⠀⣡⡴⢻⣧⠸⣷⣀⣸⣶⠀⢿⠇⠀⢰⣿⠀⠀⠀⠀⠀⠈⡆⢹⣿
⠀⢸⣿⠂⢡⠀⠀⠀⠀⠀⣿⣆⣠⣿⠀⠿⡶⠞⠟⠀⠉⠋⠁⠁⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⡼⠃⣸⣿
⠀⠀⣿⣧⠈⡀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠀⠐⠋⣁⣐⣿⡿
⠀⠀⢉⣿⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠄⠤⠔⠒⢒⣋⣀⣭⣤⣤⣤⠶⠶⠾⠛⠓⠃⠉⠁
⠀⠀⠈⣿⣧⡈⠳⠤⠤⠤⠤⠒⠀⠂⢉⣩⣥⣄⣴⣶⠶⠿⠟⠛⠛⠉⠉⠉
⠀⠀⠀⠹⢿⣿⣶⣦⣶⠶⠶⠿⠛⠓⠂⠉⠉
⣿⡿⠻⠛⢾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢉⠁⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⡌⠀⣴⣿⣿⣿⡆⠀⠀⠣⡀
⠀⠀⠀⡇⠀⢻⣿⣟⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⢦⠀⠀⠙⣿⣿⡷⠀⠀⠂⠀⠀⠀⠀⠀⠐⠈⢀⠀⠀⢀⠀⣿⠸⣇⠀⡆⠀⠀⠀⠀⠠⢊⣽⣿⣿⣿⣆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⡀⡆⢸⣀⣻⣿⣦⢙⢤⠼⠀⠁⠀⠀⠀⠀⡗⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠂⠐⠈⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⢳⢉⠘⣿⠀⠟⠁⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠊⠰⣾⣷⡯⠘⠞⡂⠋⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣺⣿⢻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠀⡀⠀⠐⠀⠁⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⡠⠀⠂⠈⠀⠀⣦⢸
⠀⠀⠀⠀⠀⠔⠂⠡⡄⣎⠁⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⢀⣤⡀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣀⡀⢿⠘⣳⠀⠁
⠀⠀⠀⠀⠀⢀⣶⣧⠉⠌⠄⠃⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠈⣄⢮⡻⣗⠌⠀⠀⠀⢠⢖⣛⢲⡘⠿⡇⠰⠈⠁
⠀⠀⠀⠀⢦⣤⡻⢯⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⢽⣤⣉⠊⢀⠀⠀⠀⣿⢿⣹⠞⠁⠀⠛⠀⠀⠀⢀⠠
⠀⠀⠀⢠⡆⣋⠳⠄⠀⠐⠀⠀⠀⡀⠄⠈⠂⠀⠀⠄⠀⠑⠀⠀⠹⡄⠠⠀⠀⠀⠀⠘⠳⠖⠋⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⢉⣉⡇⢀⠂⠀⠀⠄⠀⣀⡄⣯⡅⣶⣦⠐⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠆⡀⢸⡿⠂⠿⠟⠿⠧⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠉⠀⠉⠁⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠷⡆⢀
⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣰⢦⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠘⡋⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⠀⢠⡞⣋⣳⡀⣾⣄⢠⣾⣿⣓⡂⣼⣅⣶⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡿⠇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⡅⠀⠘⣎⣛⣿⠉⢩⡇⠈⠏⠏⠀⠘⡿⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠴⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠒⠒⠦⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀
⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠢⣄
⠀⡠⠊⠁⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⣴⣿⡿⠿⠿⣿⣷⠄⢸⣿⡷⠀⠀⠀⣰⣿⡏⠀⠀⠀⣿⣿⠀⠀⠀⠙⢦⡀
⡼⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⡿⠁⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠉⠀⠘⣿⡇⠀⠀⣰⣿⠟⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢳
⡇⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⢿⣿⡇⠀⠘⠛⣻⢿⡟⠛⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠾⣿⣿⡃⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢸
⠹⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠻⠆⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⣀⠀⢀⣿⡇⠀⠈⢿⣷⡀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢀⡾
⠀⠘⠦⣀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣿⠿⠃⢸⣿⣷⠀⠀⠈⢿⣿⣆⠀⠀⠀⣶⣶⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠀⠀⠀⠀⠀⣠⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣾⡭⠴⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠄⠠⠀⠀⠄⠠⠀⠀⠄⠠⠀⠀⠄⠠
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠉⠲⢴⣀⣀⣂⣐⣀⡠⠶⠚⡀⠀⠀⢀⣠⡆⠂
⠀⠀⠀⠀⠀⠈⠛⠿⣦⣀⠀⠹⡆⠀⠀⡶⠲⠶⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢤⡌⢙⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠛
⠀⠀⠀⠀⠈⢷⣶⣶⣶⡤⠤⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⣤⡄⢀⣤⡶⠿⠿⣶⡄⢸⡇⠀⠀⠒⢐⠀⠀⢀⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢠⡄⣤⢤⡶⣶⣆⣾⣧⣿⣷⢸⣧⣿⣧⣿⢡⡞⢛⣿⣸⡟⢘⠁⠀⠀⢡⠸⡄⠀⠈⠠⠤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠘⣿⡏⠀⣼⠟⢈⣿⣯⣿⣶⢸⡇⣿⡟⣿⠘⠗⠛⠛⠋⠀⠛⠃⠀⠀⠀⠳⣅⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢰⡿⣷⡀⣴⡆⠈⠿⠃⠛⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⣀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢠⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠊⠁⠈⠠⠠⠄⠄⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠉⠉⠉⠉⠉⠀⠀⠅⠠⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣿⣅⡈⠀⠀⠀⠐⠀⠀⠂⠐⠈⠓⠀⢀⠜⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣶⠀⣴⠆⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠠⠀⠀⠁⠀⠔⠁⠀⠀⠄⠀⠄⢠
⠀⠀⠀⠀⠀⠘⠟⠼⡿⠋⡿⠃⠀⠀⠀⠀⠀⠀⣶⠀⡀⠁⠀⢀⠀⠉⠁⠀⠐⠓⠀⠑⠀⠀⠀⠄⠘⠀⠀⠐⠀⠀⠨⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠃⢐⢶⠇⠠⣿⣿⠆⠀⡀⠁⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⣤⡀⠀⠁
⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠂⠀⠀⠀⠀⠀⢷⣿⣾⠇
⠀⠀⠀⠀⠀⣿⣻⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢦⣝⣥⠾⠂
⠀⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠲⠏⠁⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠘⠛⠁⠛⠘⠁⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠈⠛⠲⣯⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡴⠒⠀⢀⣀⣠⠤⠤⠴⠤⢤⣀⠏⢹⢾⠁⠀⢄⣠⠿⢁⣀⣴⣯⡁⠀⠀⠀⠈⠑⢦⡈⠁⡽⢯⡀
⠀⠀⠀⠀⠀⠀⢐⡾⡁⠁⣠⠖⡩⠀⠀⠀⡄⠀⠀⠀⠈⠙⢦⡈⠁⠀⡼⠉⡴⠋⣽⠽⠾⠛⠲⣄⠀⢀⡀⠀⠑⠦⣤⡄⠁
⠀⠀⠀⠀⠀⠀⠞⠀⠀⡼⠁⣼⠁⠀⢀⡜⠹⡄⠸⣧⠀⠀⠀⢳⡄⠀⠀⡾⠀⠀⡇⢠⠀⠐⠶⠈⢙⡒⠿⢶⣶⣶⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣤⡇⢀⣴⠏⠀⠤⠞⢦⣯⣷⣄⠀⠀⡷⡄⢰⡇⠀⢰⠇⠉⠀⠀⠀⠀⢋⠁⠀⠀⠛⠀⣷⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⡟⠁⠘⠀⠒⢦⠀⠀⠀⢀⣨⠓⣼⢧⠽⠼⣇⢰⠋⠈⠉⠁⠈⢀⣠⢾⢷⡀⠀⠘⡷⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠙⢶⠀⠀⢀⠀⠀⠀⠐⠀⠈⠀⠀⡗⢸⠀⠀⢸⠙⣇⠀⠀⠀⢾⣯⠖⠋⢀⡇⠀⣰⠃⠀⡼⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡄⠈⢧⠀⠘⣟⠒⠶⢤⡴⣇⣀⣀⡇⡾⠀⢰⡻⡗⠾⢆⠠⡗⢄⡙⠓⠒⠋⠀⣰⠻⣄⣀⠙⠚⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡲⢦⣽⡦⣨⠿⠛⠭⢚⣩⣵⣿⣠⣇⠀⠈⡇⣇⠀⠈⢿⣹⢶⠉⣿⢹⣫⠞⠁⡼⢡⠞⢳⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠉⠙⣇⣸⠃⠀⠀⠈⣭⣭⠖⠊⠀⠀⢀⣾⡱⡜⢦⣿⡭⠭⠵⣀⠈⠻⣟⣆⣸⠃⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⠟⢧⣀⠀⣠⣾⠶⢮⡿⠃⠀⠀⢸⡦⣵⡿⡁⢹⡟⠿⠭⠭⡀⠀⠈⢻⠓⣄⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡴⠻⣄⣀⠉⣹⢿⠹⡷⡼⠙⢲⠀⠀⠀⠙⣟⢙⣧⡼⣇⡇⠀⠀⡟⣲⡴⠋⠀⠈⡷⣄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡞⠁⠀⠀⠈⣹⠃⢸⡆⡇⠀⢸⠘⡇⠀⠀⠀⠘⡏⠁⠀⣸⡇⠀⠀⣷⢹⠲⣄⣀⡼⠁⠈⠳⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⣰⠃⠀⢸⠃⡇⠀⠈⡇⢳⠀⠀⠀⠀⢹⠋⠉⠉⡇⠀⠀⢸⢸⡄⠈⠻⡄⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡰⠃⠀⢀⡞⢰⠃⠀⢀⡇⠸⡆⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡜⡇⠀⠀⠙⠲⠶⡴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡤⠴⠋⠀⠀⢠⠎⡴⠋⠀⢠⠏⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⢷⠀⠀⠀⡇⡇⠀⠀⠀⠀⢀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠼⠼⠥⠤⠤⠼⠦⠤⠤⠼⠀⠀⠀⠀⠙⠲⠴⠾⠤⠤⠤⠧⠿⠶⠶⠿⠯⠭⠤⠽⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⠀⠀⠖⠑⠤⠠⡄⡄
⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠁⠀⠀⠀⡀⠀⢠⢠⠀⣀
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⡁⠀⠀⠤⢄⡀⡈⠐⣄⡠⠄⠀⠀⠀⠆⠀⠀⠀⠧⠀⢸⠒⠆⠀⠃⠀⠛⠀⠀⠀⡂
⠀⠀⠀⠀⠘⠢⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⠊⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡀⠀⠀⠀⠁⢀⠀⠀⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠒⠒⠤⡀⠠⡀⠀⢀⠔⠀⠁⠀⢠⣴⡀⠈⠏⠀⠀⠀⠠⠂⠀⠠⠀⠐⠉⠉⠉⠀⠁⠉⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠂⡀⠀⡄⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠚⠀⠀⢀⡤⠖⠉⠉⠉⠉⠉⠉⢁⢢⠔⠉⠉⠀⢀⣀⠀⠉⠉⠲⣄
⠀⠀⠀⠀⠈⠀⠨⡀⠒⠀⠐⡁⠀⠀⠘⠈⠀⢀⠀⠀⡠⠂⠀⡩⡀⠉⠁⠢⡀⠀⠀⠈⠀⠀⠀⠃⠃⠚⠀⠀⠁⠁⠀⠀⠀⠸⠈⠜⠘⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠁⠀⠀⠠⠤⠤⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠦⠞⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣞⡶⢾⡿⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⡿⠀⠈⠉⠉⠛⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣠⠤⠶⠚⠉⠉⠉⠀⠀⢹⡀⢸⢰⠀⠀⠄⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢠⣏⠈⠳⣄⡀⠀⠀⠀⠀⢠⠤⠶⠒⠛⡆⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⢸⠀⠀⠂⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⢷⡀⠀⠀⠀⠀⠈⢯⠭⠿⠟⠃⠀⠀⠀⠀⢸⢇⠀⠀⠀⢿⠁⠸⣇⠀⠀⠀⠀⠁⠀⢠⠴⠒⠋⡟⢸⢸⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⢀⡠⢼⡌⢆⠀⠀⢸⡄⡸⡿⠶⠒⠚⠆⠀⠀⠘⣄⣀⣰⣯⢿⢸⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⠖⠛⢧⣳⡀⢸⡅⠀⡀⢷⡘⡆⠀⠀⢷⠁⢻⣄⣀⡀⢰⠀⠀⠀⢧⡠⠊⠁⢸⠸⣤⣀⣀⡾
⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⢻⠀⠀⠀⢀⠬⢧⠀⠈⠋⠁⠀⠛⠉⠹⡎⣧⠸⡄⠀⢸⡆⠀⠄⠈⣇⢸⠀⠀⠀⢸⡆⠀⠀⠘⢛⣻⣿⣋⠁
⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⣀⠤⢾⡤⠒⠈⢠⡤⠞⠃⠀⠀⣀⢤⠀⢴⠊⣧⣼⣆⣙⣩⢟⣅⢁⠀⠀⢿⠀⣆⣠⠤⣶⠇⠀⠀⢠⡏⠀⠀⠘⣧
⠀⠀⠀⢠⡇⠀⠠⠄⠀⠐⢇⣴⣚⣁⣀⠀⠈⢧⠔⠚⢢⠀⢳⣶⠇⠈⠉⠀⠘⡎⠉⣼⠉⠙⡆⠀⠘⠸⣦⠤⠴⢞⠟⠁⠀⠀⢿⠧⣀⣀⣠⠟
⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡘⠓⣚⣻⡆⠀⠀⠀⣀⠀⢰⣊⡿⠐⣇⣙⡿⢱⡀⠀⠀⠀⠀⠾⠥⣄⣀⣀⠀⠈⠳⠶⠛⠁
⣤⣖⡉⠀⠻⣦⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⢳⠀⢿⣀⠤⡄⢰⢉⣨⣆⠬⡏⠀⠀⠈⠉⠀⠀⠈⠁⢀⣀⣄⣀⠀⠀⠀⠉⠉⠛⠒⣦⡤
⠰⢧⠄⠀⠀⠙⠳⠦⠶⠶⠶⢬⡆⠀⠀⠀⠀⠈⣧⠘⠧⠶⢷⣠⣏⠁⢧⣤⠇⠀⠀⠀⠀⠀⢀⣀⡄⢸⡏⣍⠉⣡⡄⠀⣀⡠⠀⠛⠉
⠀⣱⠖⠀⠀⠀⠀⠀⣀⣀⣠⠴⠃⠀⠀⠀⠀⢰⢹⡆⠀⠀⠘⠧⠾⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠘⠂⢿⣈⣧⣿⠐⠉
⠀⣠⠟⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⡠⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠘⠒⢶⡄⠤⠀⠀⠠⠤⠤⠌⠛⠐⠛⠛⠃
⠀⠈⠽⢃⡀⠀⠀⣿⣀⣀⣀⣀⣀⡤⢔⣫⣴⠞⠁⠤⠄⠐⠂⠀⠀⠈⢹⡗⠒⣳⢠⢿⡇
⠀⠀⠐⠚⠓⠒⠒⠚⠻⣤⣤⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡎⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠳⣄⡀⠀⠀⢠⠏⠀⢹⡀⠀⠀⠀⠀⢀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⠦⣴⠃⠀⠀⠀⢧⡤⠴⠒⠋⠉⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠑⠎⠁⠀⠉⠆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢀⠀⠠⣆⠀⠀⠀⠉⠳⣄⠀⠀⠈⠉⠉⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡓⠒⠒⠶⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⢸⠀⠀⣨⠂⠀⠀⠀⠀⠀⠙⢦⡀⠀⣤⣧⣾⣠⠎⣩⢭⠙⡆⢠⣶⣠⠄⢸⡇⣸⠇⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢡⣼⣧⣇⣸⡸⣇⣼⠴⠋⡻⣿⣟⠃⡾⢠⡏⠰⢏⡁
⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⢀⣠⡖⠋⠁⠀⠀⠀⠘⠘⠀⠀⠓⠤⠴⠀⠀⠀⠁⠀⢠⡅⣬⠀⠀⠀⠙⠢⣄
⡜⠁⠀⠀⠀⢡⠔⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠙⠛⠒⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠶⠶⠖⠚⠓
⢇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠋⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⣀⡤⢦⡀⠀⠀⠀⢠⠖⢤⡀⠀⠀⢸⡆
⠸⠁⠀⠀⢀⠀⢀⡈⠁⠀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠈⠁⠈⠲⢤⡀⠀⠀⢀⣾⡥⠖⠚⠉⠀⠀⠀⠱⣄⠀⢠⠏⠀⠀⠉⠓⢦⣀⣧
⠐⢄⣀⣠⠄⠙⠢⡍⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠳⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠒⠒⠦⢤⡐⠄⠀⠴⠊⠉⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠄⢀⡄⠀⢀⡏⠀⠀⠀⠀⢀⣀⣼⣉⣩⠇⠀⠠⡀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢠⣿⣷⣶⣶⣶⣶⣶⣿⣿⡇⣠⢏⣀⡤⠴⠒⠛⠉⠁⠀⠀⠀⣀⡤⠄⠙⠈⠀⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢷⠾⣏⣙⠛⠛⠛⢿⣿⣽⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⡏⠀⠀⠈⠉⠉⠉⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⡚⠁⠀⠀⠀⠀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⣼⠶⣇⠀⠀⠀⠀⠀⢀⡟⠒⠶⠤⠤⠤⠴⠒⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣤⠤⠤⣤⡤⠤⠤⠶⠖⢺⡃⠀⠀⠀⠙⢻⣀⡽⠂⠀⠀⠀⠀⣸⣡⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⣆⣀⣠⠴⠋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⣠⡴⣺⣿⣿⣷⠁⠀⠀⠀⠂⢠⡄⠒⠀⠀⠀⠀⠀⢸⡃⠄⠀⠀⠀⠀⠀⠀⠀⣶⣂⠂⠀⠀⠀⠀⠀⡠⠂⠈
⠀⠀⠞⣗⣻⡭⢟⣯⣹⡆⠀⠀⠀⠁⠄⠐⠈⠁⠀⠀⠀⠀⠹⠛⠁⠀⠀⢀⠀⠀⠀⠀⢯⠭⠀⠀⠀⠀⠀⠀⠢⣖⣉⣈⢉
⠀⠀⢀⠘⠯⡿⠿⠩⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠊⠒⢇⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢑⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡤⣀⣴⠀⠀⠀⠀⠀⠀⠈⢙⡄⠀⢀⣨⡁⠀⠀⠀⠀⡀⠲⠰⢀⡀⠀⠙⠚
⠀⠀⠀⠀⢀⢠⠐⡴⠀⠀⠀⢀⣠⠝⠉⣘⣲⡂⢹⠋⠁⠀⠀⠀⠀⠁⠈⠕⠁⠀⠀⠀⠀⠀⠀⢉⡀⠛⠠⡄
⠀⠀⠀⠪⡄⣕⠌⠀⠀⠀⠀⠀⠀⢈⠡⢸⣁⡆⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢀⡄⠀⠀⠀⠘⠈⠂
⠀⠀⠀⠀⢰⡌⠀⡀⠀⠀⠀⠀⠀⠁⢠⠏⠀⠙⠀⠀⢀⠀⠀⡀⠀⠀⠀⠈⢳⣢⢴⡼⣠⡤⠀⠀⠀⠀⠀⢰⠀⢀⡄
⠀⠀⠀⣄⠸⠁⠜⡃⢀⡠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⢀⠃⠴⠀⠀⠉⠉⣿⣺⣍⣅⠀⠀⠀⠀⠘⠦⠆⠁⡚⠅⣠⠆
⠲⠦⣤⠊⠠⡞⢤⡎⠘⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠀⠛⡀⠙⠂⠀⠀⠀⠏⠀⠃⠈⠀⠀⠀⠙⠲⠀⢲⠈⠳⠶⢣⣀
⠀⠀⣀⣇⡐⠓⣔⠉⣸⣄⠀⢠⠄⣒⠶⣦⣴⡀⠀⠀⠁⠐⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⠨⠏⠙⢀⣌⡀
⠀⠀⠀⠀⠈⣧⠤⠼⢄⠀⠀⢡⡿⢿⣿⣗⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠁⢲⠎⠁⠈⠉
⠀⠀⠀⢀⢘⡁⠀⠀⠀⠀⠀⠘⣿⣳⠿⣿⣿⢍⠀⠀⠀⠀⠀⠀⠀⠱⣠⢀⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣎⣉⣟⠁⠀⠀⠀⠀⠰⢿⣽⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⣦
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⠁⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣧⢾⣧⡯⣿⡄⠀⢠⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠄⠠⠀⠀⠈⠇⢩⠜⠠⣄⠇⣀⠀⠀⠀⠀⠀⢠⣶⣕⠀⠀⠀⠀⠰⢿⡿⣻⡿⠆⠀⢳⡸⠃
⠀⠀⢰⠀⠀⠀⠀⠀⢠⠋⣴⡒⠃⠀⠀⢠⠆⣘⢢⠤⠏⡎⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⠀⠚⠉⠁⠀⠁⠀⠐
⠀⠐⠂⢠⠄⣈⠀⠀⠀⠸⢵⠛⠀⠀⠀⠀⠀⠀⡧⠊⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠡⠆⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⣴⢖⠘⣷⣾⠀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠠⠆⣀⠀⠀⠀⠎⣀⠄⠀⠀⠀⣦⢿⠻⣶⣫⡿⠛⠃⠄⠀⢀⠐⠀⡬⢃⠐⡏
⠀⠀⠀⢀⠐⣅⠆⠀⠀⠀⠀⠀⠐⠂⡀⢶⠎⠥⠀⠀⠀⠌⡡⠎⢉⡀⠀⠈⠀⠹⢤⠞⠈⠀⠀⠀⠈⢉⡆⣸⡩⠇⢀⠜⠒
⠀⠂⠲⠄⠳⠈⠀⠀⠀⠀⠀⠀⠀⠋⢡⠆⠲⠀⠀⠀⠀⠀⠁⠺⠥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⣄⣁⡎⠈⠓
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠒⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⣀⠆⠐⠤⠃⠀⠡⠄⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣾⠃⠀⠺⠀⡷⢠⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠜⠀⢤⣌⠀⠀⠀⠀⠀⢠⣖⡀⠧⠤⠄⠠⠀⠀⠀⠀⠀⠀⢀⢤⡠⠡⢄⠀⠇⠀⠠⠆⠀⠆⠻⠆⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡄⠀⠀⠲⢟⠂⠀⠀⠀⠀⢫⠟⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⣠⠞⢢⠐⠀⠀⠈⠒⠀⠤⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢠⠤⡄⠀⡀⠀⠀⠀⠀⠀⢠⡄⡤⣄⠀⠑⢢⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠈⠳⡆⢈⣴⣌⠆⠠⢿⡦⠈⡇⠠⡇⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠒⠠⠄⠙⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠈⠆⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⠄⠀⠀⠀⠀⠤⠤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢀⢄⠌⢀⡄⠀⠀⠀⠀⢠⡷⠇⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠊⠀⣞⡃⣰⠀⢠⡀⠀⠀⠀⠀⣶⠀⠱
⠀⠀⠀⠀⠀⢀⡴⠥⠘⡠⠊⠀⡀⠄⠀⠀⠈⠉⠀⠀⢠⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠠⠇⠘⠷⠂⠈⠋⠀⠻⠓⠀⠇⣀⡀⣤
⠀⠀⠀⠀⠀⠋⠀⠀⠛⠀⠀⠉⠀⠈⡤⠊⢣⠄⠑⢄⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠀⠀⠈⠁⠀⠐⠖⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠐⠒⠂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⢀⢻⡄⠑⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣀⡈⠢⡀⠀⠀⠀⠀⡝⢄⠀⠀⠋⠀⢀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠙⢦⡸⢾⡆⠒⠀⠠⠀⠀⠀⠀⢀⠂⢀⡀⢠⣰⣴⣀⢠⣿⡶⠀⠀⠀⠀⠀⠀⢀⠀⠡⡜⠀⠦⠉⡴⠀⡀⢀⡀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⢠⡐⣦⠺⣽⢦⡉⠀⠟⠀⢀⠆⠀⠀⠀⠀⠀⠀⠸⠃⠼⢿⠿⠇⠀⠈⢀⠜⠀⠀⠀⠀⡄⢨⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⢢⡈⠳⣼⠇⠀⠼⠇⢀⡀⠔⠁⠀⠀⠀⠀⠀⠘⠄⣈⠁⠀⠈⠀⠀⢀⠄⠂⠀⠀⠀⠀⡀⠰⢀⠀⠀⡤⠀⠀⠀⠀⠐⠀⠀⠉⢐⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⢠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠋⢮⠄⠀⠀⠀⠴⠦⠡⠤⡄⠘⠀⠀⠀⡀⠂⠀⠀⠀⠂⢀⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⡀⠀⠀⠀⠉⠂⠂⠀⠤⠈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⡆⠀⢀⠄⠂⠈⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡡⠆⠀⡀⠆⢰⢸⠆⠴⢂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⢠⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠊⠀⠰⠎⠈⠆⢰⠈⠈⠤⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠋⠀⠀⠈⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠂⠀⢈⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠒⠒⠢⢤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢆
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠺⡆
⠀⠀⠀⢸⠁⠀⣤⣤⣤⡀⢀⡤⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⢠⡄⣤⠄⢀⣠⣦⣀⢠⣤⠄⠀⠘⣏⢻
⠀⠀⠀⣾⠀⢰⣿⠀⣿⡇⣸⠃⠀⠀⠀⠀⣰⡟⢁⣴⣦⣤⠌⣿⡄⣤⣿⣧⣿⡄⠈⣿⢿⡍⠈⣿⠀⠀⠀⣏⠛⡆
⠀⠀⠀⣿⠀⠀⠛⠿⠟⢡⡏⣴⡾⢷⣆⠀⣿⠀⣿⡏⢰⣿⠀⣼⡇⣤⣿⣼⣯⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⠉⡇
⠀⠀⠀⢹⠀⠀⠀⠀⠀⣾⠁⣿⣇⣸⡿⠀⣿⡀⠻⡷⠾⢿⡴⠟⠀⢸⡏⢸⡇⠀⠀⠀⠀⠀⢀⣍⠀⠀⠀⡧⣙⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠈⠃⠀⠈⠛⠋⠁⠀⠘⠷⣦⣤⣤⣤⠀⠀⠀⠘⠃⠙⠁⠀⠀⠀⠀⠀⠈⠛⠀⠀⢸⡳⢌⡇
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣍⢲⠇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⢮⡹
⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢯⡑⢤⠇
⠀⠀⠀⠀⠀⠀⠳⣼⢛⠖⠶⠶⡤⢤⡤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡤⣤⠤⡴⢶⡒⢞⠻⡍⠙⣄⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠓⠾⠴⠮⢴⣧⣾⣞⣠⣏⡼⠁⠀⠀⠀⢀⡜⠣⡈⣧⣸⣤⡽⠬⠷⠞⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢀⣴⠫⡍⢢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⡴⣞⠳⣈⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣴⣶⣏⡹⠤⠷⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣒⣒⣒⣒
⠀⠀⠀⢰⣷⣄⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣦⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠉⠓⠄⠙⠀⢠⢖⣥⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣄⣐⠠⡀
⠀⠀⠀⠘⣿⡶⠶⠖⠂⢠⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣊⣥⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⠻⣿⣿⡿⠿⠛⠛⠿⣿⠟⠟⣿⠋⣤⣼⣿⠁⣾⣿⣿⣧⢣
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠉⠿⠀⢻⠇⣜⠁⢦⣼⠋⣴⢞⡛⢻⡆⢹⠅⡀⡼⢂⣬⠀⣾⣰⣿⣿⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⡧⠀⠂⠐⢻⣠⡿⠷⠀⣧⠘⣇⣘⣃⣈⣠⣾⣿⣿⣧⣈⣉⣴⣧⣼⣿⣿⣿⡟⠘
⠀⠀⠀⠀⠀⠀⢂⢻⣿⣿⣿⣿⣇⣰⣦⣼⣧⣤⣷⣆⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠣⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⡿⠻⠿⠟⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠨⠭⠐⠈⠁⠈⠉⠉⠭⠅⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠙⠻⠿⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣶⣀⣤⣆⣠⣤⣴⠀⠀⠀⠀⠀⡀⣰⢃⢠⡞⣀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⣼⢿⣿⡿⣿⣛⢻⢻⣧⡀⠀⠀⠀⠀⠀⠓⠂⠘⠂
⠀⠀⠀⠀⠀⠰⠝⠪⠀⠀⠀⠀⠀⠸⠃⠀⠐⠄⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣻⣿⣦⣾⣿⣏⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⢿⣿⣿⣿⢿⡏⠛⠓⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⣧⣼⣿⡇
⠀⠀⠈⠃⠀⠀⠀⢀⣾⢿⡿⢿⡛⣟⣿⡿⣷⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠹⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠿⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣷⣼⣧⣿⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠊⠀⡠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠄⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣴⣶⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸
⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⢀⠀⢀⠀⣀⠀⡜⠀⢀⣼⣿⣿⣿⣿⣿⠿⣿⠛⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠘⠀⠙⠘⠃⠐⠙⠀⠀⠘⠂⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⢂⠀⠂⠒⠀⠀⠀⠈⠛⠿⠿⠟⠿⠿⠿⠛⠛⠉⠘⠁⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣝⣛⣩⣛⣻⣛⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠀⠀⠀⠠⠤⠀⣀
⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠠⠤⠤⠤⠤⠀⠤⠤⠤⠤⠄⡀
⠀⠀⠀⠀⡴⠊⠀⠀⠀⡔⠁⢠⡀⠀⠀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠰⡏⠉⠀⣠⠖⣖⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⢠⠂⠀⠠⡴⠴⠀⠀⣰⣷⣿⣿⣆⠀⡀⠒⠰⢃⠘⣷⡛⠟⢀⣰⠇⣀⣠⡆⠀⠀⢀⣴⢆⡾⡆
⠀⠆⠀⠀⢚⠛⠓⠀⠰⢿⣿⣿⣿⠟⠀⠀⣉⣐⠃⠀⣿⡄⢀⣬⡏⢸⣿⣿⣷⠀⢀⣾⡏⣼⡿⠀⠀⠀⡘
⢰⠀⠀⢀⡀⡀⠀⠀⢀⠶⠉⠉⠀⠀⣴⡿⣄⣈⣀⣼⣹⠃⠚⠀⣀⠈⠛⠛⠁⠀⠘⠋⠘⠷⠁⠀⠀⡐
⢸⠀⠀⡊⠲⠄⠀⠀⡾⠙⠁⠀⠀⠀⠋⠀⠈⠛⠛⠋⠀⠀⡠⢀⠐⢢⠀⠀⠀⠀⠛⠀⠚⠃⠀⢀⠜
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣤⣤⡤⠶⠀⢲⣈⠔⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠇⠉⠁⠀⠀⠀⠀⠀⠁⡠⠤⠄⠀⢀⣀⠀⠠⠄⠂⠈
⠀⠀⠀⠀⠈⠒⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠶⠞⣛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠐⠂⠄⠀⠀⠠⠾⠗⣩⣾⣡⠴⢻⡎⠱⢊⣛⢋⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⡴⠤⠁⡀⠀⠀⢀⠁⠀⠈⠁⠀⣠⣿⡜⣠⠎⢹⣇⣥⣟⠨⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠐⠀⠀⠀⠄⠸⢿⣧⡀⠀⠀⠀⠉⠀⠀⠘⠉⠘⠋⢻⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⢀⣀⣤⣶⣾⡇⠘⠷⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⣏⣫⣿⡠⠔⠀⠀⠀⠈⠢⡉⠈⠟⠰⣿⠟⢛⡟⠉⠁⡘⠀⢠⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠡⠄⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠶⠀⡄⠀⠀⠠⠂⠊⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄⠠⡄⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠈⠀⠑⡄⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠊⠀⠈⠐⣶⣷⠀⠀⠀⠐⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠀⠀⠀⠀⣿⠹⡄⠀⢀⠠⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠚⠓⠛⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⢶⣾⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⣾⢿⣿⣿⡿⣿⣷⡄
⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡜⣿⣩⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⣀
⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶
⠀⠀⣿⣿⣿⡇⠀⠐⠂⠀⠀⠘⠁⢀⡞⢠⡎⢄⠀⠐⠀⠀⠀⠁
⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣶⣾⣶⣶⠇
⠀⠀⠀⡺⠏⠀⠀⢀⠁⠀⠆⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⣺⣿⣿⣯⣧⣰⣿⡛⠀⠀⠐⢀⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⢻⠿⣿⣿⡿⠏⠛⠀⠀⡀⠘⣿⣯⣿⣿⣯⣿⡟
⠀⠀⠀⠀⠀⢠⣾⣿⣻⣝⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠘⠀⠀⢹⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⢠⠀⣄⠀⠀⡄⠀⢠⠁⢠⣿⣿⣿⣿⣟⣿⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠻⣿⣿⣿⣿⣿⠿⠿⠣⠄⠀⠶⠶⠶⠶⠶⠀⠀⠀⠀⢀⡀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠤⠖⠚⠋⠉⠉⠙⠓⠲⠤⣄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠐⢯⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠙⠦⡀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡴⢦⡀⠀⠑⢶⠚⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄⠀⠘⢦⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡞⠀⠀⡽⢦⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢳⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣼⠀⠀⣸⠁⠀⡾⠀⠀⢱⢄⠀⠀⠑⢄⡀⢀⡀⢀⣀⠀⢀⠀⠘⡆⠈⣇⠀⠀⣧
⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⡇⠀⠀⣟⣚⢳⣄⠀⠈⠳⣼⠃⡸⢎⡀⢸⠀⠀⣿⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⢳⡀⠀⠁⠃⠘⢌⣳⣄⠀⠈⠳⣗⠚⠃⠐⠀⢠⠇⠀⣸⠀⠀⢸
⠀⠀⠀⠀⠀⢻⠀⠀⢹⡀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠳⣄⢀⡴⠋⠀⢀⡏⠀⠀⡟
⠀⠀⠀⠀⠀⠘⣇⠀⠀⢧⠀⠀⠀⠀⠙⠲⢤⠀⠀⠀⢀⣈⣳⣄⠀⠈⠻⣄⠀⠀⡼⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠳⡄⠀⠀⣠⣴⣋⣀⡤⠖⠋⠀⠀⠈⠳⣄⠀⠈⠳⠞⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠲⣄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⠒⠦⢤⣄⣀⣀⣠⡤⠴⠒⠋⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠛⠋⢉⠉⢉⠛⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠛⠛⠿⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⡀⠀⠌⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣥⣤⣬⣤⣤⠤⠤⢤⣤⣼⣿⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⢤⠀⡀⡀⠀⠆⡄⠀⠄⠈⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣉⣉⣉⣉⣉⣉⡉⣲⣤⣊⣉⣉⣹⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣆⠈⠉⠀⠁⠒⠀⠀⠐⠃⠀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣉⣤⣴⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⢘⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣼⣷⣶⡝⣿⣿⠟⠋⠁⠹⡛⠻⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣹⠻⣿⣿⣿⡆⠀⠀⠀⠀⢠⣿⣿⣿⣧⢻⡉⠉⠉⠉⠉⠉⠉⠉⣹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠿⡟⠋⠙⢿⣿⣿⣷⣤⣼⣿⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⡜⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡃⠀⠀⢧⣀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠻⠶⠶⠶⠶⠶⠶⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⠝⣿⣿⣿⣟⠝⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠶⠀⠉⠉⠉⠉⠉⠉⠁⠰⠶⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⡴⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠒⠠⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⠔⠺⠿⠈⠀⠀⣴⠞⢙⣫⡿⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠃⠀⠀⢤⣼⣤⣦⠀⠀⢀⣼⣿⣿⣿⣿⡄⠀⡇⠐⠖⠰⠎⠆⠘⣷⣿⠻⡿⢀⡀⣰⠇⢀⣀⣰⡦⠀⠀⠀⠀⣴⣿⢂⣯⣷
⢀⡈⠀⠀⠀⣴⠧⣴⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⢰⠐⠛⠀⢠⠃⠀⣿⣿⠀⠀⣌⡻⡏⢰⣿⣿⣿⣦⠀⠀⠀⣼⣿⠃⡾⣤⠋⠀⠀⠀⢀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⢹⢿⡿⠟⠛⠁⠀⢧⡤⠒⠲⠜⠀⢀⡿⣿⠀⣴⠏⠿⠀⠹⣿⣿⣿⡿⠀⠀⣾⣿⠏⣼⢣⡏⠀⠀⠀⠀⡜
⡇⠀⠀⠀⡠⠤⠄⠀⠀⠀⢀⣻⡃⠆⠀⠀⠀⠀⣴⡿⢣⣤⣤⣤⡴⢟⣱⠟⠐⠋⠀⣠⡤⠀⠈⠉⠉⠀⠀⠀⠛⠁⠀⠙⠛⠀⠀⠀⠀⡜
⡇⠀⠀⢴⠙⣷⡘⠀⠀⠀⣼⠋⠛⠀⠀⠀⠀⠐⠉⠁⠀⠘⠛⠛⠛⠛⠁⠀⠀⣀⠔⣉⠲⠀⡄⠀⠀⠀⠀⠘⠓⠀⠘⠿⠀⠀⠀⢠⠊
⢃⡀⠀⠘⠦⠤⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⠤⠖⣡⠞⠁⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣿⣟⣻⣿⠿⠟⠛⠋⠀⠀⠀⣳⠞⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⠁
⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⣀⣀⣀⣀⣀⠀⠤⠀⠈⠁
⠀⠀⠀⠀⠈⠁⠲⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠰⠖⠀⠉⠉⠳⡀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢶⣶⣶⡶⢟⠛⢫⠛⠷⣤⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠂⠤⠤⡀⠀⠀⠀⢠⣾⡵⠚⢫⡽⢋⣉⡶⢾⡇⠀⠻⡨⢉⡛⢛⣋⡱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⠀⣄⠀⣄⠀⡇⠀⠀⠀⠀⠐⠀⠀⠛⠛⠋⠉⢀⡾⢑⢠⢄⣵⠛⣿⠠⠊⣈⢢⡹⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⢉⠀⠁⡰⠀⠀⠀⠀⠘⢀⣠⣄⠀⠀⠀⠠⡾⠛⣏⡵⠞⠁⢀⣟⡴⢿⣿⣀⡡⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⡌⠁⠀⠀⠀⠀⠃⢘⠿⣿⣧⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠘⠋⠉⢿⡤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⢸⠀⢿⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣷⠀⢺⣥⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠀⠀⣼⢳⡤⣾⠀⠀⡃⠀⠀⠀⠀⠈⡄⠰⠏⠻⣿⡧⢠⣤⣴⣶⣾⣿⠿⠟⠛⢻⠋⠀⠀⠁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣀⣀⣀⣸⣯⣤⣿⣿⠆⠋⠀⠀⢸⡇⠀⠀⠘⠢⠀⠀⠈⠁⠘⠟⠋⠁⢸⡷⠀⠀⣠⠎⠀⠀⡷⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠲⠄⠤⠤⠚⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠲⠒⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠀⠀⠰⡏⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡄⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢡⣀⣀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠴⠟⠛⠓⠚⡄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠒⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠤⣚⠆⠈⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠈⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠃⠁⠀⠀⠀⣴⡎⠁⠐⠚⠛⠛⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢠⠚⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠦⣀⡀⢀⣀⡀⠀⠀⠀⠀⢃⡀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⢻⣷⣿⠀⠀⠀⠀⠈⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⢸⡇⢻⡄⠀⠀⠀⣀⡾⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⣨⣿⣤⣿⠖⠊⠉⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣈⠒⠀⠒⠊⠀⠀⠀⠀⠀⠠⡀⠰⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣽⣷⣦⣤⣤⣤⣤⣤⡤⠤⠤⣤⣤⠴⠶⠶⣻⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⡠⠄⠒⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⠃
⠀⠀⠀⢠⠂⢀⣴⣾⣿⣶⡀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠠
⠀⠀⠀⡇⠀⠸⣿⣿⣿⣽⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠀⠀⣁⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢃⠀⠀⠙⢿⣿⣿⣇⠀⠀⡘⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⢶⠈⡆⠀⢂⠀⠀⠀⠀⠀⠀⡤⢻⣿⣿⣶⣄
⠀⠀⠀⠈⢆⠀⠀⠈⠛⠛⠁⢀⠔⠁⠀⠀⠀⠀⠀⠁⢀⠀⣶⠀⣴⣴⣀⢸⢀⢹⡆⢸⠀⠀⠀⠀⠀⣌⣼⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⢡⠀⡀⠤⠀⠒⠁⠀⠀⠀⠀⢀⠎⠀⢰⡜⡇⣿⣷⠞⣿⡟⠰⠈⠋⠁⠄⠀⠀⠄⠀⠀⠃⢻⣿⣿⣿⣿⠏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣄⣠⠄⣧⣶⠀⡟⠀⠉⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋
⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠂⢀⣷⣿⡵⠃⢘⡨⠀⠁⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣽⢿⡟⡇⠀⠀⠀⠀⡠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠰⠀⠀⠁⣀⠄⠂⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⢸⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠠⠂⠉⢰⡴⣆⠀⡀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡠⢐⣦⡀⠱⠀⠀⠀⠀⡄⠀⠀⠀⢸⣄⡄⢸⡆⢙⡷⠀⠠
⠀⠀⠀⡠⠀⠀⣰⣾⡥⠡⠩⠀⠃⠀⠬⠀⠁⠀⠀⠀⠀⠀⠀⢀⠈⣄⢦⣽⣿⠦⠁⠀⠀⡐⣠⢞⣛⢲⡄⠿⣧⠀⠆⠉⠀⠀⠀⡃
⠀⠀⠀⠀⢠⣤⣜⢿⡝⠆⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣽⣆⣉⠠⠁⡀⠀⠀⠐⡇⣏⣹⠾⠃⠀⠹⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⡤⠙⠛⣦⠀⠀⡐⠀⣀⠀⠀⡠⠔⠢⠀⣀⣀⠀⠀⠣⠀⠀⠻⡌⠁⡐⠀⠀⠀⠀⠛⠮⠥⠞⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠐⠀⠛⠛⢳⠄⠠⠊⠀⠀⡀⠈⠁⠀⣦⣒⢠⣠⡀⢆⠀⠀⠁⠂⠒⠓⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠤⠂
⠀⠀⠀⢂⠀⠛⠋⠀⠃⠀⢀⡄⠀⢰⣿⡏⢻⣻⢾⣿⡃⠈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⠢⠈⠻⠀⠨⠤⠀⠀⣁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠐⠀⣤⡄⠈⠐⢄
⠀⠀⠀⠀⠈⢀⠄⠀⠀⠀⠀⠀⠀⠃⠂⠀⠠⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢠⡍⣙⠀⡆
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠻⣯⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠀⢈⣁⣀⠀⠀⡤⠀⠀⢰⣤⣀⡀⢀⡖⠀⠀⢀⠀⠀⠀⠀⠀⢁⠀⠙⠙⣄⣤⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠⣀⡴⠀⢠⡏⣵⣮⣷⢸⣷⡆⢸⣿⣿⠭⠅⣼⡷⣼⡅⠀⠁⠀⠀⠀⠀⠀⠀⢄⠀⠸⠛⠀⡠⠊
⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠚⠻⠆⠀⠈⠳⣭⡽⠇⠀⣼⠁⠸⠇⠇⠀⠀⠿⠁⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌
⠀⠀⠀⠠⠈⠀⠀⠀⠀⠠⠀⡀⠀⢀⠀⠄⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⡆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣿⡇⠀⣿⣿⡇⣠⣤⣤⣸⢿⣿⠿⢿⣿⣟⣛⡛⢻⢡⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠇⢠⣿⣿⣷⣿⣟⡛⠿⣿⣿⠀⢸⣿⡿⣿⣷⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⣿⣠⣾⣿⣿⣿⣿⣿⠿⣷⣿⣿⡇⢸⣿⢠⣿⡏⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⢻⣿⣿⣿⡿⠛⠙⣿⣿⣿⣇⠀⠉⠛⣿⣾⣿⠘⢿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢻⣿⡟⠁⠀⠀⢻⣯⠙⠛⠿⣶⣾⡿⢿⣿⣶⡀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣀⢤⣀⡤⠴⠖⠒⠚⠛⠛⠒⠒⠶⠦⢤⣀⠀⢀⣠⠴⠖⠛⠉⠉⠉⠉⠉⠉⠛⠓⠾⢭⣒⢤⡀
⠀⠀⠀⠀⡠⣪⠖⠋⠁⠀⢀⡀⢀⡀⠀⡀⠀⠀⠀⢀⡴⢫⠖⠉⠀⠀⠀⠀⢀⡀⢀⣤⣄⠀⣀⠀⠀⠀⠈⠙⢮⡂
⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⠀⠀⡼⢠⠋⠀⠀⠀⠀⠀⠀⢸⡇⠙⢀⡼⢀⡏⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢹⠀⡇⠸⠀⠀⠀⠀⣧⢸⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡞⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠊⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡬⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⠏⠙⠒⠒⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⣒⣶⠶⣷⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠮⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠦⠽⡄

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⢈⡉⠛⠛⠿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣷⠀⠀⢰⣿⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⣤⣤⣤⣤⣬⣍⣙⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣿⣤⣀⣀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⣀⣯⣉⣉⣉⣉⣉⣉⠉⠉⠉⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⠿⢷⡀⢸⣏⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠸⣏⣉⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠌⢿⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣾⣦
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠛⣋⣹⣿⡿⠿⢿⣿⡏⠀⠸⢿⣿⡁⠆⣿⢋⣽⣿⠇⣸⣿⣿⣿⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⣾⣿⣿⣿⡏⢰⠲⡆⢻⣷⡤⠀⣸⣿⣿⡿⢣⣾⣿⣿⡀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⢉⣡⣴⣿⣧⠘⢦⡴⠟⣿⡧⠀⣠⣿⣟⣱⣿⣐⣠⡿⢛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡟⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣶⣶⣾⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⡿⠓⠖⠒⠒⠚⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⢠⡀⠀⠀⠀⠀⠘⠀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⠃⠰⢺⣿⣥⣄⣾⣟⣀⣈⣷⡀
⡇⠀⠀⠀⠀⠑⣄⠀⠀⣼⣿⣙⣿⡄⡰⢘⣿⣿⣿⠿⠿⠉⣛⡻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⠈⠲⠐⢄⠙⢿⠀⠀⣁⣺⣿⣿⡿⠿⠷⣦⣌⠉⠀⠻⢢⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣭⣽⣦⣤⣿⣿⡿⠟⠈⠁⠴⠄⠙⢧⡀⣀⢠⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠛⠉⠀⢀⡄⠀⠀⠀⠤⢬⣷⣳⣿⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⡉⡈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⡀⠀⠀⠘⣤⠀⠰⠂⠀⠉⠈⠀⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡦⠴⢄⠀⠀⠀⠀⠀⠀⢈⣸
⡇⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⢀⠈⠡⠔⠈⠀⠀⠀⠀⡤⠀⢌⠁
⡇⠀⠀⠀⠀⢀⡄⠀⠀⡀⠤⠀⠀⠀⠈⠏⠀⠀⣤⠀⠀⠀⠀⠀⠀⢈⠈⡀
⡇⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠈⠲⣄⠘⠃⠀⠀⢀⠄⠀⡦⠔⠁⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⢑⠀⠀⠘⠛⢀⠀⠀⠀⠀⠀⠈⠣⣍⡁⠀⠈⠀⠐⢁⣾⠀⠀⠀⠀⠐⠠⠁
⡇⠀⠀⠀⠀⠀⠘⡷⣤⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡑⢂⡂⢀⣤⣿⢣⣿⣦⣤⣤⠐⠶⠀⠐⠠⣶⣶⣄
⡇⠀⠀⠀⠀⠀⢸⡙⢦⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⢿⣏⣡⣿⣿⣿⣿⣿⣷⠀⢠⠀⠀⣿⣿⣿⡆
⡇⠀⠀⠀⠀⢠⠜⠳⠦⠠⠃⠀⠀⠀⠀⣴⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢠⠸⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠁⣶⣦⣤⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⠟⢁⡈⢻⣿⠇
⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠨⣿⣿⣿⣦⠀⠏⢸⡝⢤⡀
⡇⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⠀⠊⠁⣼⣦⡀
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠢⣤⣀⣼⣿⣿⣿⣆
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣭⣽⣛⣿⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠿⠛⠛⠛⠛⠉⠙⠟⠿⣿⣿⣟⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⢿⠄⠀⠀⠀⠀⠈⠛⠻⠿⠿
⡇⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠉⠁
⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⢄⣀⣀
⠀⠀⠀⠀⠀⢀⠤⣒⡤⠶⠒⠚⠛⠛⠛⠛⠛⠒⠲⠤⣄⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠉⠉⠙⠓⠺⢽⣲⢄
⠀⠀⠀⠀⣔⡵⠋⠁⠀⠀⣤⠀⣤⠀⣠⠀⠀⠀⢀⡔⣡⠞⠁⠀⠀⠀⠀⣠⠀⣤⢤⡄⢀⡀⠀⠀⠀⠈⠳⣅
⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢸⡀⢻⠀⡟⠀⠀⠀⣼⢰⠃⠀⠀⠀⠀⠀⠀⢸⠀⠃⣰⠃⣼⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠇⠸⠀⠃⠀⠀⠀⢻⠘⡄⠀⠀⠀⠀⠀⠀⠸⠀⠰⠁⠀⠇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠽⠓⠈⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡶⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡠⠎⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⣷⣄⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⠓

⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠐⠿⣦⡀⠹⠀⠀⣤⣀⣀⠀⢰⣿⣿⣿⣶⣤⣴⣾⣿⣧
⠀⠀⠀⣀⣀⣀⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⡤⠀⠀⠑⠆
⠀⠀⠀⠈⠛⠉⠉⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡟⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡿⠙⢙⡏⢱⡖⣰⢡⠪⠍⢇⡧⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣏⣠⣰⣥⣬⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠿⠻⠻⠿⠿⢿⢿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠉⠨⠈⠈⠩⠹⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠒⠲⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⢹⠛⢦⡴⠀⠀⡀⢀⣷⡖⠀⠀⣤⡞⠋⠉⠀⠈⠉⠳⢤⡀⠘⠉⣳⣞
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠚⠧⠀⣀⡴⠒⠈⠉⠀⠀⠀⠀⠉⠙⠳⢤⡋⠹⠀⠀⢹⠿⢀⡵⠚⡾⣿⣹⣶⣄⠀⠀⠀⠀⠀⠙⢤⡈⠁⠈⠷
⠀⠀⠀⠀⠀⠀⠀⡼⠉⠃⢀⡾⠁⡼⠁⠀⠀⣰⢧⠀⠀⣄⠀⠀⠀⠹⣄⠀⠀⠋⢠⠞⠀⢸⠋⠉⠀⢀⣈⠓⠦⣄⣲⣄⣀⡀⣉⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡞⠀⣸⠁⠀⢀⡼⠁⠈⢧⡀⣿⢦⠀⠀⠀⢹⣆⠀⠀⡞⠀⠀⢸⢀⡿⠀⠀⠉⠀⣠⠤⠈⠉⠻⡽⠻⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⠒⣿⣠⠴⣿⠀⠐⠚⠃⠙⠿⠚⠷⣄⡀⢸⡟⣆⠀⡇⠀⢠⠏⣠⣄⡀⣠⠀⠀⢁⣄⠀⠀⠀⢀⢀⡟⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⠯⠁⠀⠁⠈⠙⠶⠀⠀⠀⠀⣤⠤⢹⡞⣷⠺⠗⢧⣀⡏⠀⠀⠀⠀⠀⣀⡴⢋⡟⣧⠀⠀⢸⡏⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠳⡆⠀⠀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡇⣿⠀⠀⢸⡏⢻⡀⠀⠀⠀⢿⣷⡞⠉⠀⡿⠀⠀⡼⠀⠀⡾⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣄⠀⢻⡄⠀⠻⡙⠒⠶⢦⡴⣻⢀⣀⣸⠃⡟⠀⢰⡟⡟⠲⢷⡄⢰⠳⣄⡙⠓⠒⠋⠀⢀⡾⢳⣀⣀⠙⠚⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠳⠦⣍⣲⡄⣈⡿⠖⣫⠴⢛⣩⣾⣏⣠⡇⠀⠀⡇⢿⠀⠀⠘⡟⣓⢦⠙⣶⢋⣟⡵⠋⠀⡼⢁⠼⢳⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠛⢿⠉⣳⠃⠀⠀⠐⣚⣉⣭⠵⠋⠉⠁⠀⣾⠻⡜⢆⢰⣒⣓⣛⣩⠀⠉⠲⣟⢦⠀⡼⠁⠋⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣸⢷⡁⠀⠀⠀⣠⣭⣝⣓⡶⠀⠀⠀⢸⣍⡳⣽⡶⠙⣿⢧⡴⢖⣚⠀⠀⠈⢻⡿⣅⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣴⡃⠀⠙⠲⢶⣾⠟⣧⡀⡿⢦⡀⠀⠀⠘⢦⣽⠿⣶⠀⣿⢀⡏⠉⠈⣷⣄⡀⣰⠃⠈⠳⣄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠁⠉⠒⠶⢤⡞⢸⡇⡇⠙⠁⡄⢷⠀⠀⠀⠀⢳⡤⠾⠛⠉⣿⡇⠀⠀⣷⢸⣟⠁⠀⠀⣠⠋⠳⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⠏⠀⠀⠀⠀⢀⡞⠀⢸⡇⣿⠀⠀⢧⠸⡆⠀⠀⠀⠀⢳⣀⣠⡤⢾⡇⠀⠀⢹⢸⡏⠳⢤⡞⠁⠀⠀⠈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠃⡿⠀⠀⢸⡄⢷⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⢸⡌⡇⠀⠀⠳⣄⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⠞⠀⠀⢠⡞⢰⠇⠀⠀⡼⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⠈⡇⣷⠀⠀⠀⠈⠓⠒⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠴⠋⠁⠀⠀⢰⢋⡴⠋⠀⠀⡾⠁⠀⠀⣇⠀⠀⠀⠀⣧⠀⠀⠀⣇⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⣀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⣤⠤⢤⣤⣤⢿⢼⠤⠤⠤⡤⠧⠤⢤⣤⠽⠀⠀⠀⠀⠈⠳⠦⠴⠿⡤⠤⢤⢿⠼⠶⠶⠶⣿⡭⡭⢤⣬⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠶⠖⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠲⠦⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⡀
⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢦⣀
⢠⠞⠁⠀⠀⠀⠀⠀⢱⣄⠀⠀⡠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⡿⠃⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⢠⣦⡄⠀⠙⠛⢃⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠙⢦
⡟⠀⠀⠀⠀⠀⢤⣄⣰⣿⣿⣿⣁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡗⠀⠠⠿⠷⣶⠆⠀⠀⠐⠿⠿⢷⣤⣀⣠⣤⠾⠿⠿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘
⣇⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡷⠄⠀⠀⢸⡟⠉⣽⣏⠉⢻⡇⠀⠀⠀⣼⠏⠀⠀⠀⢠⣶⣤⣴⠿⠛⠻⢷⣤⣴⣦⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀
⠘⣆⠀⠀⠀⠀⠖⠛⠋⣿⠛⠛⠻⣄⠀⠀⠈⠷⣾⣧⣸⣷⠛⠀⠀⠀⠾⢷⡶⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣼
⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠶⠶⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣠⣴⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣀⣤⣴⠶⠛⠋
⣀⣀⣀⣀⣀⣀⣐⣿⣷⣾⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠻⣟⠟⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀⣤⣤⣤⣀
⠀⠀⠀⠀⣠⣔⡮⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⢒⡦⣀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠯⣶⠄
⠀⠀⠀⢼⠟⠁⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⢠⠎⡜⠁⠀⠀⠀⠀⠠⡀⠀⠀⡀⣀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⢸⠀⠀⠠⣶⢈⠆⠠⣯⠀⢁⢘⠄⢸⢸⠀⠀⠀⠀⢰⢸⠈⠙⠷⠘⠇⠵⢀⠡⠂⠀⠀⠀⡇
⠀⠀⠀⠈⢆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠘⣆⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⠍⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⡼⠀⢀⠜⠉⠉⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠛⠶⠶⠿⢿⣄⠀⠘⡆
⠀⠀⠀⠀⠀⠐⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⠋⠀⠰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⢇⠀⠀⠀⠀⢿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠡⠐⠒⠀⠀⣼⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⣰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⡟⠛⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⠜⢁⡴⢿⣿⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣍⠒⠒⠒⠛⠉⢀⣡⠶⠛⢿⣤⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣿⣦⣽⣷⣤⣶⣶⣶⣟⣵⣦⣀⠈⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠐⠒⠀⠤⢄⣀⠀⢀⡀⠤⠒⠒⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣝⢦
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠠⠄⣀⠐⠃⢰⠆⠀⠀⠈⢦
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⢀⠞⢉⢍⠳⡄⠀⢰⠀⠼⢵⠄⠀⠀⣠⣃⣸⣀⠀⠀⠸⣷⣦⣼⣿⣀⡀⠀⠀⢸⠀⡜⠀⠀⡞⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠈⠦⣀⠼⢀⡇⠀⣮⢴⢠⠋⠀⠀⢉⡏⣁⣏⠀⠀⠠⢾⣿⣿⣿⣿⣿⡁⠀⠀⠸⠤⠇⡄⣸⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠓⠢⠤⠖⠋⠀⠀⠀⡿⠃⠀⠀⠀⡽⠉⢸⠁⠀⠀⠀⠼⠛⠉⠻⠇⠈⠉⠀⠀⠰⣵⢆⠍⣅⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠠⡙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠨⠲⠍⠒⠦⠤⠤⠤⠤⠤⠤⠤⠀⠒⠒⠂⠤⠤⠄⣀⣀⠀⠀⠀⣀⡠⠤⠒⠉⠉⠉⠒⠢⠤⠤⠔⠊⠉⠱⣄⠀⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠐⠂⠒⠀⠐⠉⠒⠀⠤⠤
⠀⠀⠀⢠⠊⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡌⠁⠀⠀⡄⠀⡠⡀⠀⢶⠀⣤⠀⠀⠀⡀
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⡠⠀⠀⠈⠑⠢⠆⠈⠳⠒⠉⠆⠀⠨⡄⠀⠀⠃⠀⠣⠭⠀⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠂⠤⠀⠤⠀⠠⣄⡀⠀⢐⠈⠀⠀⡀⠸⠀⠀⣀⡀⢠⡄⠀⠀⠀⠠⠀⠀⠂⢀⠦⠤⠔⠂⠤⠄⠤⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠒⠀⠊⢄⡀⠀⠀⠛⠁⠈⠁⠀⢰⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠤⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠚⠀⠀⣠⠴⠒⠂⠉⠉⠉⠐⡢⡠⠒⠈⠉⢀⡀⠉⠙⠓⢄
⠀⠀⠀⠀⠁⠀⡀⠒⠀⢀⠀⠀⠀⠻⠁⠀⠂⠀⡀⠀⠈⢍⠉⠉⠲⡄⠀⠀⠁⠀⠀⠘⠘⠚⠀⠀⠈⠀⠀⠀⠘⠈⠌⠆⠀⠀⠀⡇
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢦⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠⠄⠤⠐⠊⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠒⠲⣄⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠠⠃⠰⠆⠾⠇⠱⠀⠀⠀⠀⠀⠀⢯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⢠⣤⠀⣰⣴⣇⠀⠀⠂
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⣪⢽⣞⡂⠀⠀⠃⠀⠀⠀⠈⠀⠏⠀⠈⠉⠀⠙⠙⠉⠀⠘⠨
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠁⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠐⢠⣤⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⣀⡀⠐⠀⠀⠀⠀⠊⠀⠀⠈⠀⠄⠀⠀⠀⠰⠟⠀⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⢤⠀⠀⢀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⣟⣿⣟⣷
⠀⠀⠀⠀⠀⣴⡆⣴⣆⣰⣆⠀⠀⠀⠐⡀⠙⠃⠸⠀⠀⠓⢀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣀⠢⠀⠀⠀⠀⠈⢻⣷⣿⠋
⠀⠀⠀⠀⠀⠛⠙⡻⠃⠹⠁⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⠀⠀⠀⠀⡄⠈⠗⠇⠹⠸⠃⠹⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠢⣤⡀⠀⠀⠀⢀⡠⠴⠀⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠘⠻⢷⣄⠀⠹⡀⠀⢰⠦⠦⠖⠚⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠙⢄⢙⣿⠄
⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠀⠀⠀⠀⠹⠿⠿⠛⠃⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⡶⠀⠀⡂⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⠁⠀⠀⠀⣀⣀⣤⡀⣤⣀⣶⣰⡇⣿⢠⡞⣫⢭⡍⣿⢸⠇⠀⠀⡒⡂⠀⠔⢛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⣷⡏⢉⡾⠋⣿⣿⣯⣼⡏⣿⢿⡞⠷⠾⠟⠋⠾⠆⠀⠀⠁⢕⠄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢠⣿⣧⢨⡦⠈⠿⠙⠃⠘⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠒⠒⠒⠧⠈⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⣀⣶⣶⣾⣿⣿⣦⣥⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢿⣿⣿⣿⡏⣿⣟⣿⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢻⣿⣿⣿⣟⢿⣻⣿⡇
⠀⠀⠀⠀⠀⠓⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢨⣿⣉⣸⣷⣾⣾⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣤⡄⠀⠈⠉⠻⠿⡛⠿⠟⣭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠟⠀⠓
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠁
⠀⠀⢀⣶⣿⣿⣿⡄⠀⠀⠁⠠⠤⠀⠁⠀⠀⠏⠀⠤⠈⢷⠀⠹⡆⠄⠀⠐⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠠⠄⠀⠀⠒⠒⢀⠊⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠓
⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠻⣶⣾⣷⣶⣿⣶⣾⣿⠏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣽⣯⣻⣏⠀⣽⣿⠶⠀⠀⠀⠀⠂⠀⢰⣶⣶⣶⣶⣾⣿⣶⣶
⠀⠀⠀⠀⣌⠻⣐⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣷⣾⣿⣿⣿⣿⣦⡀⠀⠀⡄⠀⠀⢸⣿⣧⣿⣿⣿⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠟⢿⣿⢿⡿⠻⠀⠈⠁⠀⢀⡜⠀⠀⠈⢻⠟⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠀⠀⠀⠀⠀⠉⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠈⠉⠢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠛⠛⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠠⠤⡔⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⣠⠶⠋⠉⠉⠉⠁⠀⣀⣀⡀⠀⠀⠘⠢⢄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠟⠉⠀⠈⢧⠀⠀⠀⢀⡀⡀⠀⠀⠀⢸⠂⠀⢀⡤⡖⠀⠀⠀⣾⠁⠀⠀⠀⠠⠀⠀⠀⠀⢳
⠀⠀⠀⡇⠀⠀⠀⠄⠀⠀⣿⠀⠀⠠⠤⠟⠀⠀⠀⣸⣷⡧⠶⠀⠀⢀⡄⠈⠁⡜⠀⣀⣀⣠⣯⣠⣄⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⠀⠚⠋⣿⣽⡶⠀⠒⠊⢁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⣀⣠⡤⠞⠁
⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠠⢶⡟⡟⠀⠀⠀⠀⣎⡴⠂⢸⠉⠀⠁⢀⡏⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠉⢹⡆⢀⣀⠀⠀⠀⠀⠀⣿⠀⡾⠸⠇⠀⠀⠀⠘⠋⠀⠈⣼⠀⠀⠀⠈⢧⣀⣀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢧⡀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⣀⣠⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠤⠶⠚⠋

⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⣀⠀⠀⠀⣄⠀⡀⠀⠀⠀⣤⠀⠀⢀⡶⡖⢀⡀⠀⢀⣀⣄⣠⠀⠀⢤⢤⡀⠀⢀⠀⣀
⠀⠀⠐⢺⡛⣻⠉⠀⠠⣟⠩⢇⡆⠀⣿⠰⢷⡆⠀⢠⣉⠀⠀⢸⢯⣭⠟⠀⠀⢼⡋⠀⡿⠆⠀⠸⠞⠀⠀⢻⡖⢿⠄
⠀⠀⠀⠹⠏⠛⠁⠀⠀⠙⠛⠋⠀⠀⢀⠀⠘⠀⠀⢸⣈⠇⠀⠀⠸⠃⠀⠀⠀⠸⠛⠞⠻⠀⠀⠶⠆⠀⠀⠈⠟⠈
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠻⣿⣿⡇⠀⢠⣾⠟⢻⡄⠀⢀⠻⣿⠇⠀⠀⣰⠋⠤⠀⡌⢳⡀⠀⢩⠿⢯⢹⠆⠰⣷⢸⡏⠀⢀⡴⣶⠷⣤
⠀⠀⠀⠀⢿⡟⠀⠀⣎⣡⣾⡿⠀⠀⣛⣳⣤⡖⠓⠀⠹⣼⠭⠯⢽⡸⠃⠀⣼⣘⣚⣸⠀⠀⠻⠘⠀⠀⠙⣷⣎⣶⠟
⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠉⠀⠀⠀⠙⠁⠀⠙⠁⠀⠀⠉⠓⠒⠋⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠳⢄⡀⠀⡼⠁⠘⡆⠀⠀⢀⣀⠤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠚⠀⠀⠀⠙⠒⠋⠁⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢀⠇⠀⠀⠲⣖⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢥⡤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢰⠀⠈⢱⠀⠀⠀⠀⠑⢦⡀⠀⣠⣀⣆⡔⣊⣑⢦⢀⣠⣀⠀⣶⢰⡆⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢀⢈⠀⠉⠀⠀⠀⠀⠀⢀⣠⠜⠂⣼⣽⣸⡅⣇⡿⠞⢹⠿⣟⢀⠇⡞⠰⢎⡁
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠴⣞⣉⣀⠀⠀⠁⠀⠀⠙⠒⠒⠀⠀⠁⠀⠤⠠⠅⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠄⠀⠀⠀⠈⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣀⡤⠤⠐⠁⢥⣀⠀⠀⠀⢠⢞⣠⠤⠒⠋⠙⢦⠀⠀⣸⠉⠙⠦⣄⠀⣇
⠀⠀⠀⠀⠀⠀⠘⣄⢀⣀⠑⠠⡀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠈⠑⢦⠀⠋⠉⠀⠀⠀⠀⠀⠀⠳⣴⠃⠀⠀⠀⠀⠙⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠒⠦⢤⡠⠀⠠⠖⠉⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣤⣀⣐⣂⣒⣒⣦⡆⢀⡼⠀⠀⣀⣠⠤⠚⠣⠚⠁⠀⢢⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣸⠿⠿⠿⣿⣿⣿⣿⡷⠾⠒⠛⠉⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⡿⠈⠑⠒⠒⠒⠛⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⢄⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣢⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⣄⡆⠀⠀⠀⠈⢱⡤⣄⣀⡀⢀⣀⠤⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⡠⠤⠤⡞⠀⠀⠀⠻⡅⣱⠀⠀⠀⠀⣸⣀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠧⠤⠴⠊⡝⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣬⣾⣿⣿⣿⣿⣿⣶⣶⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⢀⡀⠤⠀⠀⢂⠀⠀⠀⠀⣻⣿⡏⣽⡿⠟⣿⡸⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣿⣿⣣⣽⣿⣿⣿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣺⣷⣶⣿⣿⣿⣿⣿⠇⠁⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠂⠙⠿⢿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠀⡀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠹⠉⠉⠐⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⢠⣶⣿⣿⣿⡀⠀⠀⢀⣀⠀⠀⠀⠙⡟⠀⠀⢀⡠⠀⢀⡄⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠈⠉
⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠈⡀⠀⠀⠀⠀⠁⠀⠂⣼⠁⢰⣟⡐⡆⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐
⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣶⣀⣤⣦⣀⣤⣴⠄
⠀⠀⠀⠀⣴⣶⠄⠀⠀⠀⠀⠖⠚⠀⡀⠀⠀⠀⠀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⡿⣿⠟⠻⣿⣯⣀⠀⠀⠀⢀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⡮⠩⠊⠀⠀⢀⠄⠀⠀⠘⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠈⠀⠀⢀⣽⣿⣯⣾⣛⣿⣧⣼⣿⣯⡁⠀⠀⠀⠘⠀⢸⣿⣿⢻⣿⣻⣟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⣿⣿⣿⣿⣿⣿⡟⠙⠛⠀⠀⢠⠎⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⡟⢻⡙⣯⣿⣯⣿⠀⠀⠀⠁⠖⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠻⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣷⣾⣷⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢰⡂⡤⠀⣀⠀⠀⢠⠀⠆⢠⠁
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠙⢻⡿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠈⠖⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⣀⡀⡈⠀⠀⠨⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣀⢀⣙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠑⠀⠀⠀⠘⠛⠿⠻⣿⡿⠀⡰⢿⡿⠿⣿⠿⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣁⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⣤⣤⣾⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⣋⣩⣭⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠈⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠁⢀⣶⣦⣾⣦⠀⡀⢀⠞⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠂⠈⠛⠋⢉⣉⡨⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⡿⠛⠛⣿⣿⡿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠋⣉⣠⣤⣿⣿⡿⠛⠛⠻⣿⣿⡇⠀⠘⠛⠻⣿⣇⠘⢃⣼⠟⣠⣿⣿⡟⠀⣼⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⡟⠀⣴⢻⡆⢸⣿⣷⣦⠀⠀⣼⣿⣿⣿⣿⠋⣴⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⡇⠀⠟⠛⢉⣽⣿⣇⠀⢧⡈⢁⣼⣿⣿⣏⡀⠀⢉⣿⣿⡿⢁⣼⡏⢠⠈⣿⡿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣦⡈⠙⠛⢁⣼⣿⣿⠁⢠⣾⣿⣿⣦⣿⣿⣷⣤⣶⣿⣄⣼⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⣿⣿⣿⠷⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⣴⠶⠶⠶⢶⠀⠀⠀⠀⠀⠀⣼⠋⠙⠓⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⡇⠀⠀⣠⡇⢹⣀⣀⡀⠀⢠⡇⠀⠀⠀⡿⠀⣀⡴⣦⠀⢸⢹⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣆⠀⠀⠀⠀⢀⣀⡀⡴⢦⠀⠀⠙⠾⠇⠀⡞⢁⣀⡀⣀⢠⡇⠀⡼⡇⠀⠀⠀⠛⠋⠁⠀⠈⣧⢸⡜⡇⠀⠀⢸
⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠘⡄⠀⠀⠀⡼⡀⢣⣷⠀⠧⠖⠻⡄⠀⠀⣷⣌⣓⠁⠘⠒⠳⢾⠁⡇⠀⠀⠀⠀⠀⣠⠔⢺⠏⢸⡇⡇⠀⠀⡟
⢠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣹⠄⢀⣠⠧⠗⠀⢀⣀⠀⢰⣒⠇⣀⠀⠘⠶⢽⡀⢖⢢⠀⠘⡇⡇⠀⠀⠀⠀⢎⣠⠴⠋⠀⠈⡇⡇⠀⢰⡇
⢿⠀⠀⠀⠀⠀⠀⢀⡴⢚⠟⠁⠀⢸⡧⠤⠶⡄⢏⡠⠆⠀⠛⠋⠉⡇⠀⣾⠛⠃⠈⠉⢀⣰⠃⡇⠀⠀⣀⠀⠈⠳⣄⠀⠀⠀⣧⣭⣽⡛
⠈⣇⠀⠀⠁⠄⠀⠀⣶⣋⣀⠀⠀⠈⢙⡷⠔⠛⡀⢀⡠⡄⠀⣔⣊⡟⠀⢻⣖⣶⠀⣯⡵⣿⠀⡇⠀⠀⡟⢦⠀⠀⠈⢳⡄⠀⣴⡟⠉⢹⡆
⠀⠸⡄⠀⠀⠀⠀⠀⠉⠁⠈⢇⠀⠀⢸⡷⠒⡉⢃⠸⣤⣰⣀⣸⠁⠀⠀⠀⠀⠸⣷⠏⠀⣇⠀⠧⢤⣤⡇⠀⠳⣠⠔⢹⠇⠀⠻⠾⠶⠋
⠀⠀⢹⡀⠀⠀⠀⠀⠀⣀⢤⡾⠀⠀⠀⠛⠋⢿⣈⣻⠟⠧⠴⠛⠀⠀⣰⠛⢦⠀⠀⠀⠀⠻⠦⣤⣤⠞⠳⡄⢀⣠⠖⠋
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠸⣄⡤⢒⡾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠆⠁⠁⠀⠀⢀⠠⠀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⠱⡀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⢀⠂
⠀⠀⠀⠀⢀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠆⢠⢀⡀⡁⠀⠀⢀⠀⠀⠀⠀⠁⠀⠈⠧⠂⢾⠀⡡⠂⠀⠕
⠀⠀⠀⢀⠃⠀⠀⢀⣰⣶⣶⣶⣦⣄⠀⠀⠒⠢⠀⠀⠀⠀⠀⠀⠀⠤⠤⠌⠀⠀⠀⢸⠀⠀⠀⠀⢇⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠢⠯⠿⠿⠿⠿⢟⠑⠀⠀⡠⠀⠀⠀⠀⠀⠸⠀⠀⠤⠤⠈⠅⠀⡈⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡈⠀⠀⠐⠢⢀⡀⠀⢀⣀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⡀⠀⠈⢢⠀⠀⠀⠀⢀⠀⠐⠀⠀⠂
⠀⠀⠀⠘⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠋⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⠀⠀⠃⠀⠀⢀⠁
⠀⠀⠈⠁⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⡸⠋⠀⠀⢀⠃⠀⠄⠀⠀⡔⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢀⠠⠂⠀⠀⠂⠀⠐⠋⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠾⠿⠀⠀⠈⠀⠀⠀⠀⠀⠱⠂⠀⠉⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⢀⠄⠀⢰⠀⠐⡂⠀⠫⡀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠀⠀⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠛⠀⠈⠁⠉⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⠀⠄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⡰⠀⠀⠀⡘⠀⠠⢠⠀⣀⣤⡀⢠⣀⢢⠀⢀
⠀⠀⢀⡀⡀⠀⠀⠀⠀⠰⣠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠐⠒⠁⠐⠤⠉⠀⠈
⠀⠀⠒⡁⢀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠁⠂⠐⠀⠁⠀⠀⠆⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠱⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⣠⠖⠚⠓⢦⡀⠀⢻⠀⢸⡄⠀⠀⣿⠀⠾⡽⠂⡴⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠰⢶⡖⠃⠙⡶⠃⢠⡇⢠⠞⣶⠀⣷⠈⣙⣏⣹⣏⠀⠀⣿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣴⠷⣆⣤⠞⠃⠈⢧⡘⠓⠛⠚⠁⠀⠀⢣⠀⠇⠀⠀⣤⠀⠀⠜⠁⢾⡗⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⠈⠙⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣠⣄⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⣶⣾⣶⣶⡟⠀⠀⠀⠀⢲⡃⢰⠇⠂⠀⠰
⠀⠀⠀⠀⢈⠛⠀⠀⠀⠀⠘⠇⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⣺⣿⣿⡯⣿⣠⣿⡟⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⡿⣿⣿⡿⡟⠛⠂⠀⠀⠀⢻⣿⣽⣷⣿⣽⣿⡇
⠀⠀⠁⠀⠀⠀⣴⢿⡟⣯⢻⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠈⡿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠐⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣤⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⢀⠀⡀⠐⠀⢠⣿⣿⣿⣿⡟⣿⢻⣿⣧
⠀⠀⠀⠀⠈⠀⠁⠁⠈⠁⠀⠀⠀⠀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠲⠦⢤⡀⠀⠀⠀⠀⠀⢀⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⠋⠠⡤⡦⢠⡶⡄⠇⢦⠈⢦⠀⠀⠁⢀⣉⣀⠉⡉⠳⣄⣀⠀⠀⠀⢳⣌⣦⣀⣠⢷⡀⠀⣀⠄
⠀⠀⠀⠘⢦⣀⠋⠉⠀⠉⠀⠀⠀⣠⠞⠀⢠⣃⠘⠙⠏⢬⣛⠄⢸⠁⠀⠢⡤⣠⠏⡅⠈⠀⢀⡉⣉⠉⡀⣠⠄
⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠂⠲⠼⠆⠀⠀⠀⠈⢣⣀⣀⠉⡈⢱⡏⠁⠀⢀⠇⠀⢐⡢⠘⠃⠨⠝⠈⠀⠀⠧⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠀⠀⠀⠀⠈⠉⠒⡄⠀⠀⣖⡆⣻⡗⠀⠀⢰⠋
⠀⠀⠀⢰⠋⠉⠉⢀⠀⠀⢀⠈⣧⠀⠀⠀⠀⠤⡀⠀⢀⢴⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣀⡉⠀⣀⡤⠼⣄
⠀⠀⠀⢸⠀⣤⡂⠃⠗⠇⠻⠆⢻⠀⠀⠀⠀⢀⠈⠑⠋⠘⠧⠤⢄⡀⠀⠀⠀⡼⡠⠚⠁⠀⠘⠎⠀⠁⠀⠀⠁
⠀⠀⠀⠸⡆⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠐⢶⡊⢠⣗⣏⣷⠀⢠⡞⠀⠀⠀⣰⠏⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠓⡄⠀⢶⡖⢚⠋⠉⠉⠀⠀⣀⣴⡋⠈⠻⠛⠋⣤⣄⣱⡄⠀⠐⠁⢀⠴⡚⠉⡉⣉⣉⡉⡙⡲⣄
⠀⠀⠀⠀⠈⠉⠿⠬⣍⣻⣧⠀⠀⠀⠀⠀⠀⣽⠴⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⢺⠸⣴⢶⠜⢸⢞⠟⠛⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠲⡇⠀⠀⠀⠀⠀⠀⠀⢑⣆⡠⠠⠤⠤⠤⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⣠⠀⠀⢀⣲⣆⣶⢶⣇⣯⡞⣰⣠⣾⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣿⣿⣷⣤⣴⣿⣿⡆⠀⠉⠛⠛⠋⠛⠛⠋⠐⠙⠋⠉⠉
⠀⠀⠀⢠⡄⠀⢠⡀⠀⢠⠀⡤⠀⢹⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣶⠃
⠀⠀⠀⡾⣧⣿⣿⢷⣷⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠆
⠀⠀⣼⢣⣿⣿⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠎⠻⠛⠙⠛⠟⠙⠇⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣄⣀⡀⠀⣿⣿⣿⡿⢟⢿⣿⣿⣿⣛⠿⣿⡆⠀⠀⠀⠀⣀⢀⡄⢀⢰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠁⢸⣿⠟⠋⠀⠈⢣⡹⡿⠁⠈⠙⠺⠟⠀⠀⠀⠀⣿⠨⡇⢸⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣀⠀⠀⢰⣧⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠉⠉⠉⠉⠙⠓⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣿⣿⣇⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠘⠊⠀⠈⠂⠸⠃⠀⠀⠀⠉⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⣀⣀⣀⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣤⣶⣾⣧⠀⠀⠀⠀⠀⠀⣰⡖⠀⠒⠀⣰⡖⠀⢒⠀⠆⠀⠀⢀⡟
⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣶⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠛⠋⠉⠙⠋⠙⠲⢤⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⢉⡓⢦⡀⠀⡴⣚⡁⠀⠀⠈⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢩⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠻⠿⠀⢷⠄⠘⠿⠃⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢾⣠⡆⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢋⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣚⡭⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢠⣿⣿⣿⣿⣦⠀⢀⡏⠀⠀⠐⠒⠒⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠄
⢷⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢹⣿⣆⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⡤⠖⠶⢴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⢘⠀⢿⣿⣆⠀⢠⠴⠒⠛⠛⢿⠖⠒⠋⠀⠀⠀⠀⢹⠔⠒⠦⠤⣁⠠⠀⠀⠀⢠⡴⠋
⠀⠀⠀⠙⠇⠀⠀⢀⠀⠀⠒⢣⠞⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⣠⣶⡶⠋
⠀⠀⠀⠀⠀⠀⢴⣦⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⢤⢫⠉⠀⡇⡠⠋⠈⠲⡈⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⣀⡀⠤⢤⠀⠘⡏⠉⢹⠀⣀⣴⠃⠀⠀⣀⣀⣼⢸⠀⠀⠛⠁⠀⣠⠎⠀⣰⠃
⠀⠀⠀⢀⠖⠋⡰⡏⠉⠀⠀⠀⠀⢸⠏⠑⠛⠀⠘⠉⢀⣣⠀⢠⠏⠠⡜⢹⢸⠀⠀⠀⠀⢴⠁⠀⠀⠀⠙⣆
⣶⣦⣤⡏⠀⠀⠀⢷⠀⠀⡤⠐⣲⣏⣩⢶⠆⠀⡀⠈⠻⣅⠀⢇⠀⠀⢀⠞⠼⠀⠀⢠⡀⠈⠳⡀⠀⠀⠀⢸⣤⣤⣴
⠈⠉⠛⣇⠀⠀⠀⢸⠀⠀⠙⠉⠉⠩⡇⠧⣀⣠⡉⢢⡴⠇⠀⠈⠓⠒⠁⠀⢠⡄⠀⢸⠑⣄⠀⠈⡦⠀⠠⠿⠿⠛⠉
⠀⠀⢀⠼⢄⠀⠸⠘⡀⠀⢠⠤⠐⢲⠋⠑⠐⠁⠈⠁⢀⠈⠦⣀⠀⠀⣀⡴⠇⣇⣀⣨⣆⣈⡶⠿⣷⠀⠒⡦
⠀⠀⡏⠀⠀⠀⠀⡄⡇⠀⠀⡇⠈⠁⠀⠀⠀⢀⡀⠀⢀⡱⠄⠒⠬⣥⣾⠑⠉⡧⠴⡏⠉⢹⠁⠀⡅⠀⢠⠃⡄
⣀⣀⣷⡀⠀⠀⠀⢁⠷⠄⠲⢃⠔⠓⢄⡀⡠⠊⠙⠢⠋⠀⢀⡀⠀⠈⢿⠀⠀⡇⠀⡇⠀⢸⠀⠀⡇⠀⡞⠰⣤⣄⣀
⠿⠿⠿⢿⠆⠀⠀⠘⠀⠁⡠⠣⣀⠀⠀⠉⠁⠀⢀⡄⠀⢰⢁⠈⠇⠀⠀⠀⠀⣧⠀⡇⠀⢸⠀⣆⠃⢠⠃⠀⢹⡿⠿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⢄⠈⠓⢄⠀⠀⢰⡏⡇⠀⠰⣄⡥⠃⠀⣰⠀⠀⠻⠤⠃⠀⡸⠀⣸⢀⡌⠀⠀⣸⠃
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠁⢠⠺⠀⠀⢸⡇⠱⣄⠀⠀⠀⢀⡴⠁⠳⢄⣀⣀⢤⠞⠁⠠⢟⢙⡆⠀⢺⡁
⠀⠀⠀⢀⣠⣿⣶⡶⠂⠀⠀⠀⠀⠘⠀⣇⣀⣸⠈⢄⠈⠑⠒⣊⠋⠀⠑⠠⠤⠀⠄⠊⠀⠀⠀⠘⠉⠀⠀⠀⡇
⢀⣠⣶⠏⠉⠉⠀⠁⠀⠀⢶⠀⠀⠀⣦⠩⠤⠊⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠼⣿⣶⣄
⠿⠛⠉⠣⠄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠁⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠦⠤⠤⠴⡂⠀⠀⠀⠀⠀⣤⣀⣀⣤⠀⠀⠀⠀⠀⡤⠐
⠀⠀⠀⠂⠠⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠙⣶⣤⡤⠴⠊⠀⠀⢹⣿⣷⠤⡤⠔⠁⢣⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠑⣦⣦
⢀⢀⡀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢈⢻⣷⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⣦⡀
⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢹⡇⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⢠⡀⠀⣀⠀⠀⢠⡖⣶⠀⣰⠂⠀⠤⠤⣶⠶⠶⠆⠀⣾⠛⡷⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⣉⠀⠀⠁⠀⢀⣼⣧⡤⣿⠶⠂⠀⠉⠁⣰⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣰⠇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠉⠉⠛⢳⡄⠀⠈⣷⣀⣸⣇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣄⣠⣤⡾⠃⠀⠛⢻⡏⠹⠇⠀⠀⢠⡞⠀⢰⣉⡷⠀⠀⠸⠇⠀⠀⢠⣞⣷⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⢦⡀⠀⠀⢰⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⠀⠀⣄⠀⢀⣄⠀⠀⠀⢀⣤⣶⣤⣄⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢠⣄⠀⠀⠀⢸⣿⡇
⣿⣿⠀⠀⣀⣼⣿⣄⣼⣿⣀⠀⢠⣿⡏⣿⠉⠋⠀⠀⢸⣿⡁⠈⠙⠁⠀⠐⠿⣾⣷⡾⠗⠀⢸⣿⡇
⣿⣿⠀⠀⠉⣿⡟⢉⣿⡏⠉⠀⠀⠛⠿⣿⣦⣄⠀⠀⢠⣿⣷⣄⠀⢠⣄⠀⠰⠟⠙⠷⠀⠀⢸⣿⣧⣄⡀
⣿⣿⠀⠘⢻⣿⠟⢿⣿⠛⠃⠀⢀⣄⠀⣿⢹⣿⠀⠀⣿⡇⠈⠻⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣿
⣿⣿⠀⠀⠘⠟⠀⠻⠏⠀⠀⠀⠈⠻⠿⣿⠿⠋⠀⠀⠙⠿⣷⣶⠿⠻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣿
⠈⠻⣿⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠋⠀⠀⣿
⠀⠀⠀⢹⣿⡏⠉⠉⠉⣿⣿⠀⠀⣠⣾⣿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣴⣿⡿⠋⠁⠀⠀⠀⠀⣶⣦⠀⠀⠀⢰⣶⡄⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠸⡿⠃⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠘⠿⠃⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠻⣿⣶⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⡿
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⢻⣿⡇⠀⢀⣤⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⠟⠋

⠀⠀⠀⠀⠀⣸⢃⣀⡀⠀⠀⠀⠀⠀⠊⡀⠉⠀⠀⢀⡼
⠀⠀⠀⠀⢠⡿⠋⠀⠉⠓⠶⠤⣤⣀⣀⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣶⡄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿
⣼⣿⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣍⣻⡿⢿
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣤⠴⠋⠳⣄⣀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣷
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⣀⣚⣀⠀⠈⠉⠉⢻⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⠀⢀⢠⣾⣿⣿⢿⣷⡀⠀⠀⢹⡄
⠓⢤⣀⠀⠀⢀⡀⠀⠐⢾⡉⠀⠻⣆⠀⣿⣍⣿⣷⣾⣿⠇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣨⡉⠉⠉⡇⠀⠀⠀⠙⣦⡀⠙⠆⠘⠻⢿⠿⠟⠋⠀⠀⠀⢀⡜⠁⠀⠀⣠⠴⠊⠉⠉⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⣠⠞
⠘⣇⠘⡇⠀⠀⣇⠀⠀⠀⠀⠘⡇⠀⠀⠂⠀⠀⠀⢀⠀⣀⣠⣤⡞⠀⠀⠀⡼⠁⠀⣀⡀⠀⢲⠀⠀⠀⠸⡆⠀⠀⠀⣶⠋⠁⢰
⠇⠁⠀⠐⠀⠀⣨⠆⠀⠀⠀⠀⣷⡤⠤⠤⠤⠤⣤⠞⠋⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠙⢿⣄⠈⣛⡷⠀⠀⡇⠀⠀⠀⠘⡷
⠈⠀⠀⠐⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠠⣶⣿⠇⠙⢂⠉⠀⠀⢸⡇⠀⠀⠀⢀⡇⢀⣀
⠉⠙⠲⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢾⢿⠂⠀⠀⠀⠀⠀⡈⢧⡀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⢳⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⡀⢀⣀⣠⡴⠊⠙⠲⢽⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠃⣠⠤⣄⡀⢀⣙⠒⢒⡒⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣀⣀⠀⠀⠀⠀⢰⡏⠀⣾⣥⢰⣳⣾⣦⠧⣼⣿⠧⣼⡇⠀⠈⡇⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣧⡀⠀⠀⠈⢧⡀⠈⠷⠀⠙⢓⡂⠀⠙⠘⠀⠻⠃⠀⡼⠁⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿
⣿⣇⣿⣧⠀⠀⠀⢠⣟⣀⣀⣠⡞⠉⠉⠙⠲⠤⣤⠭⠶⠋⠀⠀⠀⣿⣿⣼⣿⡟⣿⠀⠀⠀⣀⣀⣀⣀⣠⠴⢺⡄⠀⠀⠸⣿⢿
⣷⣿⣿⠇⠀⠀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠀⠀⢠⣇⠀⠈⣤⠀⡀⠀⢳⡀⠀⠀⢻⣶
⠛⣫⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠏⠊⠀⢸⡏⣼⠃⣶⠂⠙⠲⣄⠀⠉
⠀⠉⠋⠁⠀⠀⢀⣠⠤⠶⠶⠶⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠤⢀⠁⠀⠃⠀⢀⡞⠁
⠀⠀⠀⠀⠀⡴⠋⠀⢠⡴⠚⠀⢀⢀⠀⠀⡈⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠮⠀⠀⠀⠍⢦⡀⠀⡀⠀⠀⠀⣾
⠀⠀⠀⠀⢸⡇⠀⠀⣼⠟⢁⣠⣿⣾⢤⣼⠇⣠⠆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⢳⡴⠒⠋⠉⠉⠋
⠀⠀⠀⠀⠀⢳⡀⠀⠿⠀⢀⣟⡟⠀⣼⠏⣼⠋⣀⠀⢸⣀⡀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⢛⢻⠛⡟⣛⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠅⠈⣀⡀⠈⣀⡀⠀⡉⠀⠁⠐⠀⠀⠐⠈⠀⠀⠁⠢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠻⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄
⠀⠀⠀⠀⠀⠀⢠⣿⡅⣼⣿⡄⣼⡧⠀⠀⠀⠀⠈⠀⠐⢀⣀⠂⠀⡇⠀⠀⠀⠀⣖⡆⠀⠀⡰⡂⠈⠔⠀⠀⠀⠀⠁⢀⡀⡆⡈⠁⠈⠁⢸⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠈⠏⠘⣹⠋⠀⠟⠁⠀⠀⠀⠀⠀⠢⡀⠸⠇⢀⠔⠀⠀⠀⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠅⠀⠀⠀⠄⠈⠀⠃⠀⠀⠀⠀⠐⠂⠀⣀⠌
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠈⠐⠄⠀⠀⠀⠂⢀⠀⠤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠠⢀⣀⠓⠀⠴⢴⠀⢀⣷⣾⣧⠀⠀⡀⠃⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⢀⣤⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠎⠀⠀⠉⠁⠀⠀⠋⠙⠈⠁⠀⠃⠬⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⣟⣿⣛⣷
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠚⠀⠀⠀⣴⠀⢠⣌⠻⣿⡿⣣⣄⠀⢰
⠀⠀⠀⠀⠀⠀⢿⣶⡟⣷⣾⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠚⠀⠀⠀⠒⠂⠀⠀⠀⠘⠀⠘⠛⢻⠶⣿⣋⣋⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠁⣄⠀⡄⣤⡄⣤⠄⡄⠑⠀⠀⠀⠈⠀⢐⠀⡐⠀⠢⠲⢂⣦⠀⠂⠘⠀⡀⠘⠀⠘⠿⠃⠀⠀⠙⠛⢀⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣄⠀⠙⠛⠃⠸⠀⠋⠀⠇⠀⠀⠁⠀⠈⠀⠈⠀⠁⠘⠊⠀⠈⠉⠁⠀⠠⠀⠀⠀⠠⠀⠠⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠠⠀⠤⠐⠀⠃⠀⠀⠈⠑⠐⠀⠤⠀⠀⠠⠄⠂⠁⠀⠀⠀⠀⠂⠀⠀⠤⠀⠐⠂⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⣤⣤⣄⣀⣀
⠀⠀⡠⠐⠒⠒⠒⢒⠖⢸⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡿⠀⠀⣴⠄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⢸⣿⣏⠉⠉⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠘⠛⠓⠒⠒⠀⠀⠘⠛⠛⠛⠛⠉⠉⠉⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡍⢉⡁⣀⢀⣿⣟⣿⣿⣿⢿⣿⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣤⠄⠀⠀⠀⠀⠜⠀⠄⠀⠀⠸⠈⠀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠀⢻⣿⣿⣿⣽⣿⣿⣿⣼⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠙⢿⣿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠔⠁⣿⡉⠁⠀⠀⣼⣏⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⡶⠀⠀⠀⠀⠂⠀⣄⠀⠀⠠⠂
⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⢈⠁⠀⠀⠀⠈⢿⣶⣤⣼⣿⣶⣾⣿⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠁⡀⠀⢀⣤⣾⣿⣿⣿⠄⢈⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⣽⡿⣿⣿⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠿⣿⣿⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠁⡀
⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣧⣒⣼⣯⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠛⠿⢷⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢀⣄⠀⠀⠀⠁⠀⠀⠀⠀⣒⡦⢠⡄⠀⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠁⠐⠋⠀⠘⠁⠀⠑⠀⠀⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⢴⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⣢⠏⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂