Father Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⠄⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⡀⠤⠀⠋⠀⠀⠈⠃⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠔⠊⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⠀⠀⠀⠁⡄
⠀⠀⢰⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣄⠀⠀⠙⢇⠒⠒⠒⠂⠀⠛⠓⠲⣄⠐⠒⠒⠂⠀⠀⠀⠀⢁
⠀⠀⠀⠑⠄⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠃⠠⠄⣀⣱⣄⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⣀⠠⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢸⠀⠂⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢥⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⡀⢀⣀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠈⠳⠀⠀⠀⠀⠙⠋⠘⢃⠀⠂⠀⢢⡀⠀⠀⠺⠛⠃⠀⠀⠀⠀⠀⠀⠀⠠⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠴⠀⣰⣼⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠉⠁⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠒⣀⡀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡰⠟⠉⠁⠀⠐⠾⠏⠉⠈⠙⠳⣖⠖⢲⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠔⠁⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠘⠀⠀⡄⠀⠀⠀⠀⢀⡀⠤⠐⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⠀⠃⠀⠀⠙⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠶⠖⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡘⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣌⠁⠀⡁⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡅⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠐⠚⠁⠀⢠⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⢥⠀⠮⣀⣀⡀⠀⠀⣀⠠⢶⠊⠉⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡄⠀⠑⢦⠠⠤⠙⠓⠃⠯⣀⣸⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠈⣧⠀⠀⠀⢰⠀⣠⠺⢶⡉⠐⡀⠀⠀⢰⡆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣝⠀⠀⠁⠀⣧⣀⠀⢠⡅⠀⠀⠀⡜⠉⠢⢀⠀⠀⠀⠀⠀⣠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠚⠀⠀⠀⠀⠑⠦⡀⢀⠔⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⣶⡀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠁⣹⠦⡀⠀⠀⠀⠈⠉⠁⢸⣗⠃⠐⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠙⠆⠀⠀⠀⠟⠻⣦⡸⠦⡀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠢⣈⡇⠀⠈⠒⠤⢀⡀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣀⠀⠀⢀⡤⠛⠁⠀⠁⠓⠀⠤⠀⣉⡉⠉⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡩⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠀⠀⢀⠉⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠳⠛⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠏⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢰⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠉⠙⠖⢲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠈⠁⠒⠠⠄⣀⣀⠀⠀⣀⡠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢯⡀⠀⠀⠀⠀⠊⠡⠀⠀⠀⠙⠢⠤⠀⠀⠀⢀⠠⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠶⣄⠀⠀⠀⠀⠈⠒⢀⡀⣀⠀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠀⠤⠄⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉⠁⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⢸⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⡰⠋⠀⠈⠉⠒⠢⣤⣤⣄⡀⠀⠀⠀⢀⣠⣤⢤⡴⠒⠉⠀⠀⠀⠙⢦⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡸⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠁⠂⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢆
⠀⠀⠀⠀⠀⠀⣸⠁⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠿⠗⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠘⣆
⠀⠀⠀⠀⠀⢠⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡄
⠀⠀⠀⠀⢀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠻⠇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡀
⠀⠀⠀⢰⣿⣿⣿⣶⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⡀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣶⣾⣿⣿⡆
⠀⠀⠀⠙⠿⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠿⢏⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⠿⠃
⠀⠀⠀⠀⢶⠀⠀⠈⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢏⠀⠀⠀⣦
⠀⠀⠀⢠⡅⠀⠀⢠⠃⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠘⡀⠀⠀⢡⡄
⠀⠀⢀⣸⠁⠀⠀⡜⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢃⠀⠀⠈⢃⡀
⡤⠚⢫⠁⠀⠀⢸⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡁⠀⠀⠈⡝⠓
⡙⠛⡟⢦⠴⢤⢼⡃⠀⠀⠀⢻⡒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠰⠂⠿⠀⠀⠀⢸⠆⡠⠢⡔⢻⠛
⠃⠾⣤⣾⢀⣆⡀⠃⠀⠀⠀⠀⠉⠖⠒⠠⣤⣌⠉⠉⣁⣀⡐⠂⠀⠒⣀⣉⣉⠉⢩⣤⠄⠒⢶⠉⠁⠀⠀⠀⠈⣀⣠⡀⡤⠨⠖
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣄⣀⣀⣀⡼⢧⣤⣤⣤⣤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠻⠿⠿⠿⠛⢛⡹⠇⠸⢟⡛⠛⠻⠿⠿⠟⠛⠅
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠖⠓⠲⠶⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠂⠉⠉⠒⠤⠤⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠅⠈⠀⢈⠉⠒⠀⠈⠀⡄⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠉⢀⠈⠁⠀⢀⡀⢀⣄⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠂⠉⢀⠀⠀⣸⣧⠀⠹⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢅⠀⠈⠑⢃⠄⢀⢳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢀⡖⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⡀⠯⡄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢡⠎⠀⠀⠀⠀⠸⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠼⡠⠋⡥⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠊⡘⠀⠀⠀⠀⠀⠀⠋⢂⠐⢄
⠤⠀⠊⠀⠀⠀⢀⠔⠀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠠⠐⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠑⡄⠁⠀⠀⠀⢀⠀⡄
⠀⠑⠢⠤⠤⠐⠁⠀⠀⢂⢺⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⠔⡆⡰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⡄⠁⠀⣄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠤⢀⡀⠀⠄⠈⠀⠀⠀⠀⠈⠗⢊⡝⢠⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⡀⠀⠁⠀⢬⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⠐⣁⠆⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠢⣀⣀⣀⣀⣀⡀⠤⠴⠂⠀⠀⠀⠀⠈⢆⠰⡈⠳⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠡⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠶⠦⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠘⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⡀⠐⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⢀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⡀⠇⠀⠃
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡐⢈
⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠠⠐⠊⢁⡀⢹⡟⠚⠉⠉⠐⠢⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣠⣬⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣤⣤⣤⣤⣄⣀⣈⣁⣀⣉⣒⣲⣶⣶⣒⣁⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⡟⣟⣹⢛⣛⣛⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠿⠛⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⢀⣀⣀⡀⠀⣰⠟⠀⠀⠀⢠⡇⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠉⠉⠁⣈⣅⠀⠀⠀⠀⠈⠀⠠⠦⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠸⡿⠀⠀⠈⢙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠠⠔⠀⢀⣀⠀⠀⠀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠲⣄⡠⠚⠈⠉⠀⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠐⢦⡀⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢢⠂⠀⠀⢀⣴⠆⠀⠀⢀⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢈⡋⠴⠤⠐⠀⠀⠀⠀⠙⡖⠀⠘⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢳⡂⠑⠒⠒⠢⣄⡀⠠⠔⠁⠀⠀⢠⡿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢸⡇⠀⠀⠀⢀⡬⠋⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢀⠀⠐⠛⠻⠛⠋⠀⠀⢤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⣿⠀⠀⢠⠟⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣁⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⠶⠶⠖⠂⠀⠀⠀⠐⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⣾⠉⠓⠀⠀⡄⠀⠴⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⠀⢰⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢱⡀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢘⡷⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠆⠀⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡤⠖⠋⠉⠀⠀⠀⠀⠉⠻⢿⣷⣶⠞⣿⠁⠀⠐⢦⡀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠡
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢦⡀
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⣶⠶⠶⠚⠉⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢿⣆⢀⣠⣶⣾⡿⠟⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⢈⣿⡿⠟⠋⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⡀⠀⠀⠀⠀⠀⣿⢰⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀
⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠶⡀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠙⢷⣄⠀⠀⠀⣿⠇⠀⠀⠀⠈⠀⣀⠴⠀⠛⠉⠁⠈⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡀⣠⡶⠟⠋⠀⠀⠙⢷⡀⠀⠙⢧⡀⢀⠋⣀⠴⠈⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠻⡎⠀⠀⠀⠀⠀⠀⠐⠋⣀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⠤⠐⠛⠛⠀⠄⣀⠀⠀⠀⣀
⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣍
⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣶⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⣉⠉⠉⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⠶⣦⣤⣀⣀⡀⠀⠀⠀⣨⡗
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋
⠀⣸⠏⠀⠀⠀⣀⡤⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟
⢰⠟⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠻⠶⣶⣶⣶⠶⠾⠟⠛⠁
⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠃
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠰⠟⠛⠉
⠀⠀⠀⠀⠻⢦⣤⡀⠠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⠁⢀⣠⣤⣶⣶⣾⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣟⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⢀⣾⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣮⡙⠛⠛⠿⠟⠻⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠋
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⡟⠀⡈⢻⣿⠀⠀⠀⣠⠴⠶⣶⣶⣶⠀⠀⠀⢶⣶⠶⠷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢸⡇⢠⣶⠈⣿⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠀⠒⠛⠃⠀⣇⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠸⡇⢻⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⢻⣄⠉⠀⣿⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⣄⠀⠀⡇⠀⠀⠀⢠⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣟⣇⠀⠀⠀⠀⢀⣘⣷⣤⣤⣤⣴⣏⠀⢠⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣆⠀⣠⣾⣿⣿⡿⠿⠿⠿⠿⣿⣷⡞⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣉⣀⡀⠘⣿⣿⠀⠀⠀⠀⠉⢹⡟⠋⠉⣉⣉⠉⠉⠀⢀⣀⡀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣧⣼⣿⣿⡇⠀⠀⠀⡄⢹⡇⠀⢋⣉⡉⠀⠀⠀⠈⣉⣉⠃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣧⠐⠃⠀⠈⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠛⠂
⠀⠀⠀⢀⣤⣴⣶⣿⡃⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠀⠀⠘⢶⣤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀⠀⠀⠀⠈⠙⠻⠿⢿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣄⣀⠀⠀⠈⢦⠀⠀⠀⠀⠛⠓⠀⠀⠀⢀⡞
⠀⢀⣤⣶⣶⣽⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣦⣌⡳⣦⣀⣀⣀⣀⣀⣤⡶⠋
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠀⢻⡀
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣦⣤⡀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣦⣀⣀⣀⣠⣶⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠉⠉⠉⠒⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⣀⣀⡀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠋⠈⠙⢦⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⢳⣤⠞⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠅⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢤⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⣿⠂⠀⠣⡀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠐⠦⠀⢰⠋⠀⢢⣌⣳⠀⣀⣬⡓⢤⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠸⣄⣰⣿⣯⠟⠺⢍⠈⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢰⠋⠀⠀⠀⠙⠋⠀⠘⡀⣠⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⠆⢉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠒⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠜⠀⠙⢦⡀⠀⠀⠷⠈⠁⢀⣠⠶⠋
⠀⠀⠀⠀⠀⣀⡤⠾⡀⠀⠹⡄⠀⠀⠀⠙⣆⠀⢀⣤⠊⠁
⢠⡶⠶⠚⠛⠀⠀⠀⠙⢆⠀⠙⢦⠀⠀⠀⠈⣿⠋⠁⢄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠳⡀⢠⠚⠁⣀⠄⠸⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠚⠛⠛⠛⠲⢦⣤
⢣⠀⠀⠀⠀⠀⠠⠎⠀⠀⠸⢀⡴⠒⠻⡄⠀⠠⠏⠀⠀⠀⠢⠈⠑⢢⠀⠀⠀⠀⠀⣀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆
⠈⣆⠀⠀⠀⠀⠀⠈⢂⠀⠀⠛⠀⠀⠀⠘⢆⡀⠀⠀⠀⠂⠀⠀⠠⡄⢃⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⣿⣆⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠡⠀⠀⠀⠈⠷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢹⠙⣦⡆⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠼⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⡇⠸⣧⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⢿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠸⠑⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣰⠋
⠀⠀⠸⡇⠀⣇⠀⠀⠀⠀⠀⠀⢀⡾⠁⡄⢷⠀⠀⠀⠇⠀⠀⠀⠀⢀⡮⠀⠀⠀⠀⠀⠑⠈⠶⣄⣀⠀⠀⠈⠐⢈⣀⡴⠞⠁
⠀⠀⠀⢻⡀⠸⡆⠀⠀⠀⠀⢀⡞⠀⠀⠀⣨⣇⡀⠀⠘⡀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣿⠛⠉⠁
⠀⠀⠀⠘⣇⠀⠹⡄⠀⠀⠀⡾⠀⠀⠀⠜⠁⠀⠉⠙⠦⢴⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢻⡀⠀⠘⢦⡀⢰⠁⠀⠀⡸⠀⡄⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⢀⠴⠒⠉⠋⠉⠀⠀⠀⠀⢀⠼⠃
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠉⢿⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⢬⠃⠀⠀⠀⠀⠀⠀⠀⣠⠆⠐⠁⠀⣁
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠙⠻⠶⠗⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠰⠡⠄⠀⠀⢤⠔⠊⠁⠀⠀⠀⡴⠋⢹
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣤⠶⠈⣧
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⠰⡄⠀⠀⠀⠀⣀⣀⠤⠤⠚⠀⠀⠉⠙⠒⠦⠤⣤⡤⠴⠖⢊⠝⠁⣠⠄⣹⠀⡀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢰⡆⠘⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⠔⠋⡁⢘⡇⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠶⠖⠛⠋⠉⠉⠣⠴⢃⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣨⠷⠒⠒⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⡙⢻⡋⢉⠋⢙⣏⠋⣹⡿⣻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠹⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⡿⠀⢀⣴⣶⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢹⣿⣷⣤⣬⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡄⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣏⠘⢿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠸⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠛⠛⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⣿⣿⣿⣷⡀⠀⢠⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⠛⠛⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⢀⣄⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⡄⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⣤⣤⢀⢄⡀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠗⠀⠐⠀⡄⠀⠀⠀⠀⢠⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠿⠟⠛⠁⠀⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠒⡄⠀⠀⠀⠀⠀⠀⠃⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⢀⠃⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢸⣶⣶⣶⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣴⣤⣤⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠤⠀⠀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢸⣇⠀⠀⠀⠀⣠⣾⡿⠛⠀⠀⠀⢿⣿⣄⠀⢀⣴⣶⠀⠀⢶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠙⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⠛⠋⠀⠛⠋⠀⠀⠀⠘⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣖⣋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠉⣿⠀⠀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢀⣠⣤⣶⣾⣿⣿⠿⠂⠀⠶⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠉⢳⣾⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⣀⣠⠤⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣈⣉⣁⣀⣀⣀⣠⣤⠤⠶⠒⠋⡍⣠⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⣹⣿⣟⠉⠀⠀⠠⣷⠀⠀⢣⡘⠃⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠉⢺⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣹⠆⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⠀⠀⠀⠀⣠⠀⠀⠀⠈⢀⣠⠔⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡇⠀⠀⠸⠁⠐⠒⠂⠉⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⢿⡍⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣵⣿⣽⣿⣿⣻⡄⢈⡛⢦⣤⣀⣀⣀⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣾⣿⣿⣿⣿⣿⣿⢾⣕⣿⡾⠛⠛⠛⢿⣯⣿⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢾⣿⣿⣿⢿⣿⣽⣾⣿⣮⢯⣿⣿⡀⠀⢠⣾⣽⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣫⣷⣿⣿⣿⢿⣻⣷⡿⣿⣯⣿⣿⣫⣟⣷⣴⣫⢷⣿⣿⣫⢻⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣽⣿⢟⣿⠟⠁⠈⣿⣞⢿⣟⣿⣿⣽⢿⣿⡿⣿⡿⢿⣿⡣⡳⡕⣙⢷⡝⢳⣦⡦⣤⣤⣤⡴⠶⠃⢀⣂⡜⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢯⣿⣟⣿⠞⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣾⡏⠹⣷⣜⣏⣌⢮⡻⣿⣽⣿⣿⣮⡿⠀⣀⡀⢪⠃⠬⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠒⠢⢤⡽⠁⠀⠀⠀⣰⣿⣧⡷⣿⠻⣿⣿⣿⣻⣽⡽⣯⣿⠀⠀⠈⠛⠿⣷⣷⣿⣾⣷⣿⣿⣽⣇⣠⠁⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⡴⢏⡀⠀⠀⣰⡁⠀⠀⣠⣾⡿⣳⣿⣽⣽⣷⣿⢶⢿⢿⢿⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣠⠋⡇⠀⠈⠑⠚⠷⢷⡖⣹⠏⣠⣼⣿⣿⣿⣟⣿⣾⣾⢟⣮⢻⡩⣧⣿⡳⣝⣿⡀
⠀⠀⠀⠀⡴⠁⠀⢿⣀⠀⢠⣀⡀⠀⠈⠉⠚⠻⠿⣿⣷⣿⣿⣯⣿⣿⣻⣻⡷⣝⢾⣽⣟⣿⢾⣧
⠀⠀⢀⠞⠀⠀⠀⠀⠈⠉⠀⠂⠭⢐⡀⠀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣝⠿⣻⣽⣞⢮⢞⣫⣣⣹⣽⣧
⠀⠀⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣾⣷⡝⣿⣟⣿⣝⣯⣿⣿⢿⡳⡻⡝⣛⡽⢌⢿⣇
⠀⠀⠘⠛⠿⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⢿⣟⣮⢾⡿⠟⠛⢿⣌⣳⣝⢾⣿⣌⣻⢮⡢⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣶⣦⣤⣀⣀⣼⣟⢯⣺⣿⣿⠟⠉⠀⠀⠀⠀⠹⣿⣟⢯⡾⣯⡳⡱⡿⡕⢿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣷⣿⣝⣿⣿⣿⣿⣷⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣾⣿⣽⣟⢾⣞⣮⢣⡻⣆
⠀⠀⠀⠀⠀⠀⡶⢻⣾⣯⢿⣻⣿⣿⣯⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡻⣿⡯⣱⡷⣻⣝⢧⡀
⠀⠀⠀⠀⠀⠀⠻⠂⣿⣻⣽⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣵⣿⣝⢯⣞⢿⢮⡳⣄⠀⢀⡤⢄⡤
⠀⠀⠀⠀⠀⠀⢸⡇⢻⣟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣎⡫⡱⡿⡵⠞⠁⣡⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠸⡇⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠉⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠳⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢢⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠛⠛⠛⠛⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠀⠀⠀⠠⠤⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣷⣶⣤⣸⣿⡇⠈⣀⠀⠀⠀⠀⢀⡀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠀⠀⠀⠀⠈⠁⠀⠸⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⡄⠀⠀⠀⠠⡤⠀⠀⠀⠀⣠⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠉⠁⠀⠁⠊⢀⡈⣧⠀⠀⠲⠤⠤⠴⠂⠀⢠⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠠⠆⠀⠀⠀⠈⠀⢸⣏⡄⠠⠈⣍⠀⡂⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠛⣿⣿⣧⡀⠀⠛⠀⠀⠀⠂⣸⠃⠙⠳⠷⠶⠗⠋⢹⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⢠⠥⢟⣯⣀⡴⠤⣤⣤⣴⢚⡿⠀⠀⣀⣀⣀⡴⢿⡼⣾⢩⣧⣄⣠⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⢾⡀⠀⠀⠀⠀⢸⡏⢹⠉⠉⠉⠉⠉⣉⣀⣀⣠⣯⡳⣬⡹⣷⡌⢦⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⡴⠚⠁⢀⡽⠓⠒⠶⠶⠾⠧⠼⡶⠒⢶⡋⠉⠁⠀⠀⡼⠳⣝⢦⡱⠈⠈⠈⡆⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⡶⢾⢷⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢙⣆⠀⢀⣞⠀⠀⡎⢳⡀⠀⠀⠀⢱⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠛⠛⢻⠀⣼⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠔⠁⠈⢣⡏⠀⠙⢦⡇⠀⠙⢦⡀⠀⠘⢧⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⡶⠿⠦⣭⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⠳⡄⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡲⣄⠀⠙⣆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣀⣀⣀⣘⡆⠀⠀⠀⠙⢆⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠸⡆⠀⠘⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠳⣦⢤⣌⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠐⠁⢠⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⢣⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡼⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢻⣄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⢀⡞⢁⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⡄⠀⠀⠀⠀⠈⠙⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⡛⠉⣹⢭⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢦⣀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠿⢿⣿⣷⣤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣀⣈⡙⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠐⠆⠀⠀⠀⠀⠀⡀⠠⠄⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡠⠁⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠐⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡀⠀⠲⡀⠀⠀⠀⠒⠒⢌⠀⠠⠀⠀⠀⠀⠁
⠀⠀⠐⠢⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠐⠀⠬⠦⠈⠀⠀⠀⠀⠑⡀⠀⡠⠐⠠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠈⠐⠂⢂⠀⠀⢠⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠔⠹
⠀⠀⠀⠀⠀⠀⠄⠒⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⢂⠰⠾⢇⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠉⠁⠀⠚⢋⠁⠉⠙⢶⠒⠂⠁⠀⠀⠀⠀⢀⠠⠄⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠁⢄⣀⢤⠐⠈⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠠⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠇⠀⡆⠀⠀⠀⠀⠀⡀⠄⠙⠈⠀⠀⡠⠃⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠈⠢⡌⠤⠑⠂⢺⣀⡅⠀⠀⠀⠀⡎⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰⠀⠀⠀⠀⡔⠳⠍⠐⡀⠀⢰⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠓⠂⠰⠤⠄⠄⠀⠈⠢⢄⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⠀⢀⡀⠀⠀⠸⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⢰⢆⠀⠀⠈⠳⣤⡤⢀⡀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢠⢼⡁⣄⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢙⠀⠑⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀⡠⠈⠁⠀⠀⠀⠒⠨⠍⣉⠂⠠⠄⠀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⡀⣀⡠⠀⠁⠀⠀⠀⠀⠀⡠⠦⠒⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡍⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠽⠀⠀⠀⠄⣀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠵⢤⡀⠀⠀⠀⠠⠀⢀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⠀⡆⡆⠀⢸⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⢠⢰⣻⣿⠀⠀⠀⠀⠀⢠⡄⢸⠀⡀⠀⠀⣠⣇⣿⣴⣷⣧⣴⢺⡇⣴⣼⣿⡖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣿⣤⣿⠸⡀⣾⣿⣿⣿⡇⠀⠀⢰⣦⣼⣧⣿⣶⡇⠀⠒⠾⢿⡟⠉⠻⣿⣟⣨⢻⣽⣿⣼⢣⠙⣿⡀
⠀⠀⠀⠀⠀⠀⣀⣧⣾⣿⣿⣿⣤⠇⢹⣿⣿⠙⠀⠀⠀⠘⠟⣿⣿⣿⡿⠆⣀⣀⣀⡜⠀⠀⠀⢹⡶⢺⣿⠦⣿⠇⣽⣦⢙⡇
⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⠗⡿⠀⠀⢿⠏⡀⢲⣣⣠⡜⠀⡘⣿⡏⠀⠀⠀⠆⢘⣧⠀⠒⠢⠀⣹⡏⢸⣧⣿⢾⣭⠻⣍⠁
⠀⠀⢠⣿⣿⣿⣾⣿⠿⠯⠻⠾⠃⠀⠀⢺⠀⠀⠸⣯⡿⠁⣀⠀⠻⡿⠧⢴⣶⣴⠃⠀⢀⣀⣄⣀⣸⠿⣾⣽⡟⢂⣿⠦⡇
⠀⠀⠿⠟⠋⣉⠁⠀⢀⣠⡄⠀⠀⠀⠀⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠋⠉⠛⠚⠋⠛⡈⢁⣸⠄⠈
⠀⠀⠀⠀⠀⠋⠀⠀⠤⠤⠧⠀⠴⢶⣄⡄⠀⠤⢤⡤⢤⡄⢠⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢤⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠁⠶⠺⠷⠶⠶⠾⠯⠀⢀⣀⣀⣀⡙⢓⣚⣦⠐⠛⣦⣀⣘⡧
⠀⠄⠀⠖⡀⣠⣤⡤⠄⡀⢠⣄⠀⠀⢀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣾⣿⣴⣄⠻⣧⣰⡴⡿⣦⡆⣬⣿⡀⣆⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢷⣿⣿⣿⣿⡿⠟⠻⣿⣷⣿⡇⠀⡀⣆⣄⢀⢸⣿⣷⠐⣼⣧⠀⠀⢀⢧⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠝⢻⣿⠛⠛⠛⢿⡆⠀⠅⡽⢻⣿⣾⣿⣿⡄⣥⣿⠀⠀⢰⢼⣷⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⠄⠉⠀⠀⢸⣭⣭⢍⣻⣿⣭⣤⣤⡖⠃⠺⠿⢿⣉⣉⣱⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠀⠀⠐⠘⠻⠗⠚⠟⠻⠟⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡹⠼⣖⣦⣤⣀⠀⢀⣀⢠⣤⣶⣷⣦⡀⠀⠀⠶⠶⠶⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠭⠈⡀⢶⣿⣿⣿⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢻⣛⡛⣉⠱⣄⢙⡛⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠙⠛⠢⡬⠴⣀⣺⣿⡧⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠄⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⢠⠠⣤⠀⠀⣤⡤⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠈⠛⠁⣤⣶⣦⣴⣶⡄⠘⠃⢀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣶⠀⠰⠀⠀⠀⠠⠀⠀⠀⢰⠟⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠂⠀⠀⠰
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣴⡶⠾⠟⠋⢶⡆⠀⣤⠀⠹⡟⠈⠛⠳⢶⣶⣿⣀⡀⣠⡄
⠀⠀⠀⠠⠀⠀⠀⢀⠀⢤⣤⣦⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠛⠛⢶⣤⡀
⠀⠀⠀⠀⣠⡶⠆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠚⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⢹
⠀⠀⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⠸⠿⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⣸
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢿⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⡷⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣿⡇⠀⣻⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⣿⣧⣠⠛⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⡿⣿⡇⠈⢷
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣸⣿⠀⢻⣷⡀⠸⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⣿⣿⠀⢸⣿⡇⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⢀⢸⣿⠀⠀⣿⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘
⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⣀⡾⢸⡿⠀⠀⣿⣿⣆⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣿⠇⣼⡇⠀⠀⢹⣿⣿⡆⠀⣴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠇⠀⣸⡏⠀⣿⠁⠀⠀⢸⣿⣿⣷⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⢠⣾⣿⠁⢰⣿⠀⠀⠀⠸⣿⣏⢻⣧⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣿⣿⠃⠀⣿⣿⠀⠀⠀⠀⠻⣿⡈⣿⣷⠀⠰⣧⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄
⠀⠀⠀⢸⡀⠀⠇⠀⠀⠀⠀⠀⠛⠁⢀⣾⣿⠏⠀⢠⣿⣿⠀⠀⠀⠀⠀⢸⣧⠸⣿⣆⠀⠘⣧⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠀⠀⢠⣿⣿⡟⠀⠀⣾⡏⣿⠀⠀⠀⠀⠀⠀⢻⡆⢹⣿⣆⠀⠉⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠘⣤⠀⠀⠀⠀⢀⡛⠀⠁⣿⣿⣿⠀⣀⠀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠘⣷⡀⢿⣿⣷
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠸⠃⠀⣰⣿⣿⣿⣴⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠈⣿⣿⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⠀⢀⣿⣿⣿⣿⡿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠘⣿⣧⡀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⣠⠈⢻⡏⠉⠉⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⣹⡿⢀⣀⠀⢀⣄⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠙⣿⣿⣶⣤⣽⣦⣤⣶⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣶⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⡄⢀⡘⠁⠀⠀⠈⠉⠉⠉⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠟⠀⠀⣀⣤⣤⣤⣤⣤⣀⠓⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣤⠞⠃⠈⠻⣶⡀
⠀⠀⠀⠀⠀⠀⡆⢀⣾⠏⠀⠀⠀⠀⠀⢻⡆⠈⠳⡀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⡼⠃⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠆⠀⡀⠀⠀⠀⠀⣿⠀⠀⠈⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢄⡀⠀⠠⠀⠰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠉⣀⣤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆⠀⠴⠉⠉⠁⠰⠶⠄⠀⠀⠀⠀⠀⠀⠰⠆⠀⠁⠀⠈⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠈⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣴⣤⣤⣴⣦⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠟⠁⠀⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡄
⠀⣰⣷⠀⠄⠠⠀⠀⠻⠶⠖⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡘⠅⢴⣶⣄
⠀⠈⠋⠀⠀⠀⠀⠃⠀⠀⠀⠈⠁⠀⠠⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⢼⣿⣻⣋⠉⣀⣀⣰⣀
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⠑⠦⠀⠈⠑⠦⠀⠀⠠⠶⠶⠚⠛⠛⠩⠽⠿⠟⠋⠽⠿⠿⠿⠿⠿⠿

⠀⠀⠠⡤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⢠⡌⠫⠤⣤⣤⠸⢧⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣛⢛⣉⡟⣫⣄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⢙⣏⣀⣀⣀⣀⣬⣥⣈⣏⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣛⣓⣲⣒⣶⣿⣿⣿⣾⣏⣉⣩⣽⣿⣿⠿⡿⠉
⠀⢸⣿⠿⠿⠟⠟⠟⠟⠿⠿⠿⠻⠻⠻⠶⠶⢤⡀⠀⠀⢿⠿⠿⠟⠟⠝⠝⠟⠯⠮⠮⠪⠫⠫⠫⠻⠳⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣶⡄⡀⠀⠀⠤⠈⠁⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣉⡀⠀⠒⢀⡀
⠘⢿⣧⣤⣤⣤⣤⣤⣴⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠿⡿⣿⣦⣤⣤⣿⣶⡆
⠰⠿⠿⠿⢿⣿⡟⠛⠛⠓⣼⣿⡄⠀⣀⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠊⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠙⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢀⢠
⠀⣠⣾⣿⣦⣤⣴⣾⣏⣷⡄⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⣤⣦⣦⡄⠘⢺
⠀⠻⢿⣿⢟⣻⣻⣏⣿⣛⡇⣀⣤⣄⢰⣿⣿⡆⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⡶⢤⣤⣋⣼⣿⣿⣿⣿⣉⣿
⢠⣶⣴⣿⣾⣿⣿⣿⣿⠿⣻⣿⣿⣿⣄⣠⣄⣀⠀⠀⠀⠦⣀⣩⣷⢶⢶⢶⢶⢾⢿⢿⢿⢿⢿⣿⣿⣿⣿
⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠋⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠉⠙⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⢤⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⣠⡖⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠙⢦⣬⣉⣛⣓⠓⢠⡀⠀⠀⡚⣒⣘⣡⠶⠛⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠶⠀⠀⠊⠉⠉⠋⠙⢧⠞⠙⠉⠉⠁⠈⠑⢶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⠀⢀⠞⢉⡑⣴⣜⣧⠐⡀⠢⡀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⢦⡀⠨⠢⢼⣤⣨⣴⢇⠀⣼⣦⣍⣠⠇⠔⠠⠠⢻⠃
⠀⠀⠀⠀⠀⠀⣀⣀⣠⢤⣴⣈⣷⣀⠀⠉⠶⣀⢁⠀⠉⠀⠈⠞⢏⡉⣈⡁⢀⡁⣴⠣⢺⣅⣄⠠⠠⠒⢂⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⠪⠽⣻⣙⠣⠔⠒⠼⠭⣭⣍⣉⡁⠀⣀⣭⣅⣬⣭⣴⣦⡗⢋⣡⣠⠤⠔⠊⠁
⠀⠀⠀⠀⢀⠄⠂⣀⠤⠶⠇⠀⠀⠈⠉⠑⠒⠂⠤⢤⡰⠿⠙⠎⠅⠙⢉⡠⠔⠾⠛⠋⠉⠁⠀⢲⣄⣁⠀⠐⠂⢀
⠀⠀⠀⠀⠀⢈⡠⠥⢚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠀⠀⠒⠁⠀⠀⠀⠀⠀⠈⢦⠄⣈⡉⠂⠀⡀
⠀⠀⠀⠠⠀⡤⢒⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⣈⡁⠀⠁
⠀⠀⠀⠀⢁⢰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠁
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠒⡆⠠⠤⠀⡀⠀⠄⢀⠀⠀⠀⠀⠂⠀⡀⠤⠔⠒⢉⡽⢁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⢙⡦⡀⠀⠉⠈⠙⠤⠤⡤⠴⠊⠁⠀⠀⡠⠴⠙⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣬⣴⡦⣐⣦⠤⠤⢀⣀⠀⡀⣀⣠⣤⣾⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⠿⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠯⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣤⠤⣤⠤⣤⣤⠤⣤⢤⣖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⠈⢳⣿⢃⠎⠀⢀⠀⠑⡄
⠀⣤⡤⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢧⠀⠳⠿⠃⢸⠁⢸⠀⠈⠶⠃⢀⡇⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢤⡄
⠈⢇⠀⠀⠀⠀⠀⠁⠐⠒⠒⠩⠵⠾⢷⣶⣤⣴⣫⣦⠄⢑⣶⣤⠶⠛⠰⠍⠛⠛⠒⠉⠉⠀⠀⠀⠀⠀⡇
⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠘⢄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠀⠀⠀⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⢀⣸⣻⣿⣟⢒⣤⣴⠒⣿⣏⣹⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣈⣉⣀⣀⣀⣀⣀⣉⣀⢈⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠺⠿⠿⠟⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠌⠀⠀⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣦⠀⠀⠀⢡⠟⠀⠀⠙⣿⣿⣿⣷⣄⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⢾⣿⣷⡊⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣄⠀⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠲⣤⣿⡿⡧⠀⠀⠀⢀⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⢰
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣦⣽⠿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣆⠀⡀⠀⠐⢡⣿⣦⡀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢰⣿⡆⢀⣹
⣼⠀⠀⠀⡆⠀⠀⠀⠀⠈⠉⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠟⠀⠀⠀⢠⣾⣿⣿⣿⣶⣤⡀⠉⠉⠉⠉⠉⠙⢿⣿⣿⢿⣿⣿⣿⣿⠶⣾⣿⡷⠈⣿
⣿⣃⠀⣸⣷⠀⢠⡀⠀⠀⠀⣾⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠉⣽⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠁⠀⣸⣿⣯⠀⠀⠐⣿⣿⣿⣺⣿
⣿⣏⠠⣾⣿⡄⢸⡇⠀⠀⠰⣾⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠻⠿⢿⣿⡿⠷⠆⠀⠀⠀⠀⠀⢾⣿⣿⠄⠀⣈⣻⣿⣟⣹⣿
⣿⣿⢤⣿⣿⣤⣿⣟⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠷⠀⣉⣿⣿⣿⣻⣿
⣿⣿⠶⣿⣿⣿⣿⣿⡀⠀⠻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⡀
⢀⡀⣇⡀⠀⡀⣧⠀⠀⡆⠀⠀⠀⠀⠀⠰
⢸⣗⣿⣿⠀⣧⣿⠀⣶⣗⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠙⠛⠿⣼⣿⣿⢠⣿⣿⢸⡆⣼⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠺⠿⠞⠒⡄
⠀⠀⠀⠈⠁⠈⠉⠙⠛⠛⠿⣧⣿⣼⣇⣷⢀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢋⡀⠀⠨⠀⠀⠆
⢠⠇⡀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣑⠀⢰⢻⠐⠤⡰
⢐⡛⢃⣼⢀⠒⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡔⡆⡠⠬⠁⢳⣢⠢⠺⣛⣋⠐
⢰⠇⢹⢶⠴⣴⡏⣶⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠀⣀⣈⣇⣤⣍⣴⣦⣷⢟⣿⣬⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢍⡉⠉⠉⠁⠠⠀⠀⠀⠈⠉⠛⠒⠦⠤⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠤⠀⠂⠠⣄⠉⠠⡌⡠⣤⡤⠤⡐⠒⣉⡽⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⣴⣶⣤⠈⡀⠀⣿⡑⣁⣤⡄⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠀⣾⣿⡯⠄⡅⢠⠇⠋⠻⡿⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠈⠳⣤⣀⡡⠔⠁⠈⠀⠓⠤⠴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠆⠆⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠠⡄⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⡌⡙⠤⣴⡴⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⠆⠈⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡆⢠⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⢻⣽⣯⠟⣶⣲⣶⣶⡶⡐⠶⠛⠉⣿⠙⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡋⣹⠀⢗⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣰⡁⢪⢤⣆⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⢀⠴⠒⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡤⠄
⡀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠔⠋⠁⠠⢿⣿⣿⠅⠀⠀⠀⠀⠀⢀⣠⣄⡀
⣿⣿⣷⣤⣧⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣧⣶⣦⣤⡆⣀⣿⡀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⣶⣦
⠿⠿⠿⠛⠟⠛⠋⠛⠋⠉⠋⠉⠉⠉⠁⠁⠛⠀⠉⠀⢀⠀⢠⡆⠀⢀⠀⠀⡀⠀⡄⢠⣸⣶⣠⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⣾⣧⣦⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠁⠈⠉⠉⠋⠉⠋⠙⠛⠛⠙⠛⠻⠟⠿⡿⡿
⣿⢿⣿⣿⣿⣅⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⡇⠈⣿⣿⣿⣿⣰⣿⡀⢠⡄⠀⠀⣿⠀⠀⠀⠀⢰⣿⡀
⡁⠀⢻⣿⣿⣿⣿⣿⣧⣼⣇⠀⣸⣿⡇⢠⡇⠀⣾⣿⣇⠀⣸⡆⠀⠀⣼⡀
⠀⠈⠽⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⡿⣿⣿⣰⣿⣿⣿⣥⣿⡧⠀⢰⣿⡦
⠀⠀⠀⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⠇⢠⣦⣾⣿⣷⡄⠀⣰⡆
⠀⠀⢒⣛⣿⡿⠀⠀⢿⣿⡿⠙⣿⠇⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣗⢠⣿⡇⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠙⠃⠀⠀⣼⣿⠇⠀⠻⠀⠀⠠⣿⣿⠋⣿⣿⠃⠀⠀⢼⣿⣿⡿⣿⣾⣿⣿⣂⣿⠀⣸⣿
⠀⠀⠀⢐⠉⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⢙⠉⠀⢹⠿⠀⠀⠀⠈⣹⣿⠁⢹⣿⠏⢿⣿⣿⣦⡟⣿⣷⣇⢀⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⢚⠃⠀⠘⠋⠀⠘⠈⣿⣿⠀⢻⣿⣿⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠈⠄⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠿⠿⠁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⢸⣿⠁⢀⠀⠀⠀⠐⠀⠱⢄
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢠⠛⠀⠀⠂⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠈⠢⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⡄⠀⠠⠀⠠⢀⣠⣤⣤⣤⣀⣀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠈⠢⢀⠀⠀⠀⠑⠄⣀⢁⡀⢴⡁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠐⠂⠀⠀⠢⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠛⠟⠛⠛⠛⠋⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠐⠀⠀⠀⠀⠠⠌⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣶⣶⡇⠀⠀⢄⡀⠀⠀⢀⣠⣾⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠁⢹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⢀⠂⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢻⣿⣿⣿⣿⣿⡆⠑⢄⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠙⣿⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢠⠘⠛⠛⠿⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠤⠈⠉⠉⠙⠃⠀⠀⠀⠀⢘⠦⣄⠀⡠⠊⠐⠣⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⢂⡠⠤⠶⠆⠀⠀⠀⠰⠀⠐⠀⠻⢄⠀⠀⠀⠀⠐⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠓⠀⠐⠁⠉⠐⡀⠀⠑⢄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠑⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠐⢀⠐⡆⣠⠆⠀⢲⡀⡶⠀⠀⠐⣶⠀⢀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢶⠀⠹⣇⠀⠀⣀⡼⣇⠸⣤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⠉⣉⠙⢿⡀⢹⠴⠚⠣⣄⠘⣄⣣⠀⠀⢹⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡞⠉⠀⠀⠙⣾⠀⡀⠀⣄⠀⢸⣃⣤⠖⠋⠉⠈⠀⠀⢀⡴⠛⢫⣋⠍⠏⣏⡛⠗⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢐⡧⠚⠁⠀⠘⣦⡏⠁⠈⡆⠀⠀⠀⠀⡴⣋⣤⣤⠀⠙⣷⠶⠶⠶⠾⠾⢷⠆⡇
⠀⠀⠀⠀⠀⠀⢰⠤⠴⠖⠷⠶⠿⠷⠾⠧⢤⠤⣿⣤⣾⣀⣴⣈⣓⣾⠓⣶⠾⣇⢹⠠⢸⠀⠀⣿⣿⢻⢹⡆⠀⢸⡶⡇
⠀⠀⠀⠀⠀⠀⠘⠚⠓⠛⠛⠛⠛⠓⠒⠒⠦⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠻⠚⠶⠼⢦⣄⣾⣈⢙⠉⠁⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣄⣀⣀⣄⣀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠋⠓⠒⢼⣍⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠲⠦⠤⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⢠⠴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⢀⣀⢀⠉⠉⠉⠙⠒⠒⠶⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡋⢳⣯⠭⡇⠀⠀⠀⠀⠀⠀⠀⠹⣟⠿⠿⠉⠩⠉⠍⠉⠙⢛⣺⡶⠦⣤⡀⠀⡅
⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⠶⣄⠀⢹⡉⡾⠴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡒⠂⠀⠂⠀⠂⠾⣍⣽⠁⠂⡌⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⡞⢩⠷⣤⣳⢷⡊⠀⢀⣤⠞⢻⢉⣯⣿⠃⠀⠠⠀⠀⣽⢷⣮⡀⡂⠐⠀⢾⡆⢄⣅⣠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⢷⠋⣰⢻⠻⣾⢇⡴⡇⢸⣤⠞⠛⡶⠃⠀⠀⠀⠀⠀⣳⠾⠃⢹⣭⣅⣁⣹⡗⠻⣤⡿⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠼⡞⠁⡞⠀⣏⣾⣠⠷⢯⣬⠽⠋⠀⠀⠀⢀⠀⠀⠀⣇⣤⡀⠀⣿⡏⠁⢽⡏⣁⣽⡉⡒⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠦⣧⢞⡁⠘⢿⠛⠛⠉⠉⠀⠀⠀⠀⡀⣹⡛⠻⡆⢸⠿⣼⠇⠀⣿⡧⠰⢾⡇⠦⢿⠀⣤⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⢾⡿⠛⢷⣮⣧⣶⣤⡦⠀⠀⠸⠀⠙⡹⢿⡴⠃⢸⠀⢿⠀⠀⡟⡇⠘⣸⡗⢐⢸⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠧⠤⠤⠤⠵⠿⠩⠤⠦⠤⠾⠤⠴⠥⠤⠧⠠⠼⠦⠼⠤⠤⠧⠯⠩⠽⠍⠍⠽⠭⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⣀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠄⣁⠀⠀⠀⠀⣀⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠉⠒⠤⣀⠀⣤⠀⠒⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠆⢸⡄⠄⡠⠔⠊⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⠀⠀⠀⠉⠃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠒⠀⠆⠀⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣠⣶⠿⠛⠋⠉⠛⠻⣶⣄⠀⠀⢀⣶⡾⠛⠋⠉⠙⠻⢿⣧⣈⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠻⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠞⠉⣿⡆⠀⠀⠀⠀⡄⢲⣦⠀⢠⣿⣿⣧⠀⢠⡐⣶⡄⠀⠀⠀⢀⣿⡷⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡴⠋⢀⠔⠙⢿⣦⡀⠀⠀⠿⣿⢟⣤⠟⠋⠉⠛⢧⣜⠿⠿⠃⠀⢀⣠⣾⠿⡀⠈⢧⣀
⠀⠀⠀⣀⣀⡷⠄⣏⠉⠛⠷⢤⣎⣀⠀⠀⠙⠻⠿⠶⠶⠾⠿⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠛⠁⠀⠑⡄⢈⣻⡵⠶⣆⣤
⠀⠀⠀⠘⡇⠉⠁⠒⠬⢍⣐⠒⠠⢄⣉⠒⠤⣀⠀⠀⠀⠀⠀⡗⢆⠀⠀⢠⠞⠇⠀⠀⠀⠀⠀⠀⡠⠤⠒⣋⡉⠤⠔⣚⣩⠷⣿⣤
⠀⠀⢸⣛⡳⠶⠒⠈⠙⢢⠀⠉⠓⠦⢄⡉⠲⢌⡙⢦⡀⠀⠀⠘⠢⠉⠎⠡⠊⠀⠀⠀⣠⠔⣂⡥⠖⢂⣉⠤⠖⠒⡝⠉⠉⠙⠳⢼⡀
⢀⠒⠉⠁⠀⠀⠀⠀⢀⠼⠦⢄⣀⠀⠀⠈⠓⢤⡙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⢀⠔⣋⠴⢊⣡⠴⠚⢉⣀⡤⠖⢋⣱⣄⠀⠀⠀⠀⠈⠑⠂
⡈⠀⠀⢀⣀⠤⠀⠚⠻⡳⠦⣤⣈⠙⠓⠦⣤⣀⠈⠓⢷⡄⠙⢦⠀⠀⠀⢀⣔⡥⠊⡡⠶⣉⣠⡴⠞⢋⣡⡴⠞⠋⡡⠊⠑⠂⠤⣀⡀
⡗⠊⠉⠉⠀⠀⠀⠀⢀⠇⠀⠀⠈⠙⠓⠦⢤⣈⣙⠓⠶⢬⣦⣈⣧⡀⣠⠟⣁⢐⣩⠽⢦⠈⢣⡴⠚⠋⠁⠀⠀⠀⠱⣀⠀⠀⠀⠀⠉⠑⠂
⡇⠀⢀⣀⢠⡤⢴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⣦⢸⡛⠒⠶⠶⠚⢿⠉⡤⠖⠋⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣱⠶⢤⣀⡀
⠸⡉⠉⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡧⠤⣀⣀⡤⢼⠀⣷⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢠⣾⣧⡀⠀⠀⠉⠙⣲
⠀⠑⣤⣤⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡧⣤⣄⣀⣤⣼⠀⢸⠀⠀⣤⡀⠀⠀⢸⣿⣿⣇⠀⢸⣿⣀⣽⡲⣤⣄⡰⠃
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⢸⡆⢀⣿⣿⣦⡀⠀⣿⣯⣿⠇⠀⠙⠛⠋⠀⡇⢸⡇
⠀⠀⠀⢸⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⡇⢸⡇⠸⠿⠋⠛⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⡇⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠸⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢛⣨⠇
⠀⠀⠀⠀⠳⠦⣭⣙⣛⠶⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠒⠶⠶⠶⠒⡇⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢚⣫⡥⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢷⡲⠬⣭⣛⡓⠶⠤⣤⣀⡀⢸⠀⣷⠲⠤⠤⠤⠴⡇⠀⣿⠀⣀⣠⡤⠶⢚⣩⣥⠖⢋⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣍⡲⢤⡀⠉⠙⠒⠲⠬⣭⣉⡀⣿⠀⠀⠀⠀⠀⡇⠀⢛⣋⣭⠴⠒⣋⡥⢞⣡⣖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠉⢏⣻⣿⣿⣶⣦⣤⣤⣀⣈⣉⣛⣦⣄⣀⣠⣤⣿⣚⣩⣥⣴⣦⣿⡷⣾⣉⠎⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠒⠋⡯⠤⠤⣙⣿⡔⠉⢙⡏⠉⠉⠉⠉⠉⠉⠉⠉⣟⠉⠙⣼⣟⡡⠤⠬⡏⠓⠢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⣠⡜⠀⠑⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠁⠘⣤⣀⡤⠃
⣿⡿⠿⣿⣿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⣧⣽⣿⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢻⣦⣀⠀⠀⠀⠻⣿⣿⣧⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣺⠏⠀⠀⠛⢿⣷⣄⠀⠀⠻⠟⠁⠈⣿⣆⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠋⠀⠀⠀⠀⠈⠉⠛⠷⣦⡀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⢈⣿⣟⡀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠸⣿⣿⠶⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣻⣿⣿⣿⣿⣿
⣤⣤⣦⣿⣶⣾⣾⣿⣷⣾⣶⣶⣶⣷⣶⣤⣴⣶⣤⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣨⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠁⠀⠀⠀⡉⠒⠤⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⠎⠀⠀⠀⠀⠑⢄⣇⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠖⠀⠀⠀⠐⠢⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⠄⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠘⡀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠀⠀⠸⣤⠀⠤⢀⣀⣀⣀⠤⠔⠒⠀⠁⠀⠀⠀⡠⠉⠒⡄
⠀⠀⠀⠀⠀⠀⣀⠤⠖⢻⡃⠀⢳⢄⠀⠈⠹⢀⠀⠅⡀⢠⣾⠉⠀⠀⠀⠀⠑⡐⡄⠠⠊⠀⠀⠀⢧⣄⣄⠗⢤
⠀⠀⠀⠀⡔⠙⣄⠀⠀⠀⢏⠀⠈⠷⣄⡤⠗⢺⠀⠀⣆⠏⠸⡇⠀⠀⠀⠀⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⢸⠀⠀⠘⡆⠀⠀⠈⢆⠀⠘⡀⠀⠀⠀⡇⢸⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠇
⠀⠀⠀⡟⠀⠀⠀⠸⡀⠀⠀⠈⢧⠀⢡⠀⠀⠀⢸⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⡅⠀⠀⠀⠈⢣⠀⣆⠀⠀⢸⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⠸⠀⠀⢸⠀⠀⠀⡤⠽⡀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣠⣴⡀⠀⠀⡆⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⡀⠀⠀⢠⠀⡰⠀⠀⢔⡒⢅⡦⢴⠖⡀⢐⣌⠁⠁⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⢸⣀⣷⢦⢝⠲⠝⡟⠁⡔⠞⠁⠘⠚⠀⢿⠷⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⠀⣸⠘⣆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠸⣠⠇⠀⠘⡶⠖⡀⠀⠀⠀⢐⣂⢄⣐⣨⣼⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡚⠉⠀⠀⠀⠘⡄⡷⠀⠀⠴⣚⡈⠘⡁⠄⠛⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⠬⠔⠒⠛⣅⠳⠀⠀⢸⠀⠈⠰⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠈⠑⠛⣿⢻⠀⠀⠀⢇⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⡠⠤⠤⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠠⠤⢙⣏⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢤⣤⣀⠑⠀⠑⢜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⡆⠐⠒⠢⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⢠⠼⡄⠀⠀⠅⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠈⢻⠀⠘⡆⠀⣆⡤⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⠉⠀⠒⠒⠠⠵⠄⠀⠀⠨⠸⡍⠀⠘⢸⡿⢂⠑⡆
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠈⠀⠈⠈⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⢀⣀⡀⠤⠒⠂⠉⠀⠀⠀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠐⣩⠄⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⡘⢆⣀⠤⡎⠀⡠⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣅⡀⠱⠌⣒⣉⣙⡞⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⡞⠀⠀⡀⡩⡀⠠⡤⡉⠄⠈⡄⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣈⡁⢸⡀⠓⠳⠞⢗⡵⠀⠀⠻⣁⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠒⠶⢶⠋⠀⠲⡀⠐⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢸⡠⣌⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢨⣧⣭⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠰⠶⠾⠕⠀⢀⣀⣡⡀⠀⢀⣀⣀⠠⢄⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠙⠓⠒⠒⠉⠽⠥⠤⠤⠤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⣀⠇⠀⠀⠀⢲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠂⣠⠒⠑⠲⠖⠚⢳⣀
⠀⠀⠀⠄⠀⠐⠁⠀⠈⠁⠒⠢⠤⣀⡀⠀⢘⠀⠀⠀⠀⠀⠃⠀⠀⢀⢈⠖⠀⠀⠀⡀⠀⠀⠀⠹⡈⠢
⢀⠈⠠⢀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠝⠋⠉⡇⠀⠀⠀⠈⠀⠀⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡰⠊
⡈⠀⠐⠫⠉⠉⠉⠐⡃⠒⠀⠰⠅⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣄
⡗⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠺⠠⢒⠠⠑⠅⢰⠀⠀⠀⠀⣀⡀⠔⣀⠙⢦⢤⣄⣀⣀⣀⣀⣀⣠⠼⡧⠄
⠑⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢸⡠⠔⢒⠩⠔⠂⠙⠒⠓⠊⠑⠄⡀⠀⠉⠉⠀⢀⡼
⠀⠐⠦⠍⠷⠂⠤⢀⣀⠐⠁⡰⠀⠈⠀⠠⠤⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢫⠉⠉⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣭⣠⡑⠄⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⡇⠀⢁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣈⢠⣰⠀⣌⠀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠢⡀⠀⢀⡜⠁⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠓⠌⣲⠿⠀⢀⠄⠀⠀⠀⠈⠣⡀⠰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣆⠞⢀⡼⠁⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⡄⣀⣸⠿⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠙⡶⠋⠀⣠⣟⣡⣀⣀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⢈⣳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠉⠉⠃⢀⣀⣀⠀⠀⠀⠀⠀⡀⠀⣠⡄⡄⠀⢄⡄⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⢀⣴⠟⠁⣼⡇⠀⠀⠀⣼⠇⠀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣠⣾⢀⣠⠄⠀⢀⣀⣌⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣾⠃⠀⣰⣿⢁⣤⣤⣼⣿⣤⠀⡩⣀⣀⠀⣠⡀⢀⣤⡄⣸⡿⠁⣤⠀⣘⢻⡉⣰⡏⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⣀⣤⣿⢳⡿⢃⣼⣿⣿⡏⡰⣿⡟⡹⢣⣿⡴⢫⡿⢁⡿⠁⣼⠏⣰⡏⣸⣿⠏⣾⢋⡼⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⢸⡏⠁⣼⣿⢾⣣⠏⢸⡏⢿⣣⠁⢿⣉⡔⠹⡿⠁⢿⣁⡼⣇⡴⣯⠜⢿⡼⣿⠏⡸⡏⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠘⠇⠀⢿⡟⠀⠁⠀⠀⠀⠀⣁⠀⣀⠀⣀⢀⣀⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⡯⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⣿⢢⣿⠸⣧⣼⣿⡇⠈⣧⠐⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⣴⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⢙⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⡞⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⠇⣿⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡏⠉⠀⠀⣀⣠⡿⠿
⠀⠀⠀⠀⠀⠀⠴⠶⢦⡀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⡇⠀⢸⣿⠏⠀⠀⠀⣶⡖⠀⠀⣶⠀⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢸⣿⣧⠀⠀⢸⣿⣿⡇⠀⢸⣿⠀⢰⣿⣄⣼⠇⣰⣦⣿⠰⢾⡇⢷⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢸⣿⣿⡇⠀⢸⣿⠀⢸⣿⣿⣿⠀⣿⣿⣿⢠⣼⣷⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⢸⣿⣿⡇⠀⢸⣿⠀⢸⣿⠏⢹⡆⠹⠃⣾⠈⠉⠇⠑⠃
⠀⢀⣴⣶⣶⣿⣄⠀⠀⣠⡀⠀⠀⠀⢿⣿⠀⠀⠈⠿⠿⠃⠀⠸⢿⣆⠀⠀⠀⠉⠓⠀⠀⠉
⠐⠛⠋⠉⠁⠀⢿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⠀⢀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠛⠛⠛⠻⠿⠟⢿⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣷⣶⣼⣿⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⣴⣾⣿⣿⣿⣾⣿⣶⣯⣴⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠠⠤⢤⣤⡀⢀⢤⡇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠇⠆⠀⠀⠉⠁⠀⠀⠈⢩⡇⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠈⠀⠠⢴⣿⡇⢸⡇⢹⠏⠉⠁⠀⠉⠙⢿⣿⣿⠃⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠷⠿⠀⠀⠀⢀⠀⠘⠀⠐⠀⠀⠈⢤⡀⢤⣿⣿⣿⣦⡀⢺⠀⠄⠀⠀⢀⠀⠀⣿⠏⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⡀⠀⠀⠀⠁⠀⢠⣇⠀⠀⠀⠲⢤⣶⣿⣿⣿⣿⣿⣿⣿⡆⠈⠀⠀⠙⠂⢀⣿⡇
⠀⠀⠀⠀⣰⠞⠉⠁⠀⠀⠀⠀⠀⣀⠀⠈⣽⠹⣷⡀⠀⠁⣸⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⠀⠤⠄⣠⠾⡿⣿⣶⣦⡀⠀⠀⠀⠀⠀⢀⣰⠆
⠀⠀⠀⠀⠅⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⢿⡿⣠⡿⣿⣦⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠁⠀⠴⠆⠈⠀⣠⢻⠡⣸⣿⣿⡆⠀⢀⣤⣶⡿⠃
⠀⠀⣆⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⢀⡞⠀⢰⢻⠀⢻⣿⡿⠉⢛⣛⠿⠿⡿⠀⠁⠁⠀⠀⠀⠀⠀⢠⢃⡿⢋⣵⢿⣛⣵⣾⣿⣿⡟
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣼⠀⣠⣿⡿⠁⡴⠤⠤⣄⣉⣑⠛⠒⠩⠄⠂⠀⠀⠄⠈⠘⠉⣫⣼⣿⣿⣿⣿⠟⠋⢹⣇⣠⣄
⠠⠀⠀⠀⠀⠀⡌⠠⠔⡒⠖⠂⠀⣠⠖⣽⠟⠋⠑⠘⠡⠞⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠤⢤⡀⠉⣽⣿⣿⣿⣿⠟⠛⠑⢶⠌⣾⣿⣿⣿
⠀⠙⠲⠀⣀⣸⠃⠲⠦⠤⠀⠀⠘⠃⣼⢃⠀⠀⠈⠀⠒⠀⠐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣼⣿⣿⣿⣿⣟⡀⠀⠁⣐⣼⣿⣿⣿⡏
⠀⠀⠀⠒⠛⠻⠙⠲⣄⠀⢀⠤⠐⡨⠁⠀⠀⠀⠀⠈⣄⠬⢥⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣾⣿⣿⣿⣿⡿⠏⢈⣿⣿⣿⣿⣿⣿⡟
⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⡤⠶⠶⠶⢭⣀⣀⡀⠀⠀⠀⠀⠀⢠⠏⣠⣿⣿⣿⣿⣿⠿⠗⠀⣴⣿⣿⣿⣿⣿⣿⠁
⡟⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⣠⣬⣿⣿⣿⡿⠁⠐⠒⠂⠠⢬⣍⣉⡓⠒⠲⠶⠋⣠⣿⠿⠟⠉⠁⠀⢠⣾⣔⣿⡿⠃
⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡫⠉⠉⠉⠙⠛⠧⠊⠀⠀⠀⢀⠂⠀⠀⠀⠍⠁⠓⠘⠛⠀⣀⣀⠀⠀⣰⡿⠁⢹⡌
⠀⡇⠀⠀⠀⣀⣀⡤⠖⠋⠀⡘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣿⣦⣀⠀⠀⠀⠐⡄⠀⠀⠀⠙⠁⠤⣀⡉⠁⠀⡸⠁
⠀⠈⠂⠒⠋⠉⠳⢶⣶⠶⢠⣇⣀⠀⠀⠀⠀⢀⠎⠀⢀⣼⣿⡿⠟⠛⠓⢦⡀⠀⠈⢄⠀⠀⠀⠐⠒⠚⠻⠷⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⠿⠛⠁⠀⠀⠀⠀⠋⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠓⠂⠀⠁

⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⣀⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢿⡿
⠀⢠⡝⢾⣿⣞⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣳⢿⣷
⠰⣾⡝⣿⣟⣫⠞⣠⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡻⣮⣻⣿
⠺⣿⣿⣻⣿⣷⣾⢿⡧⠀⠀⠀⠀⠀⢀⡸⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣶⣿⣿
⠷⣯⣙⣿⣿⣿⣶⣿⣶⠆⠀⠀⠀⣀⡶⣿⣿⡿⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⣿⣿⣿
⡷⣬⣉⣻⡿⠿⠛⣋⡴⠂⠀⣰⡆⣽⣷⣾⣷⣺⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣍⣛⠻⢿⣿
⣽⣿⣶⣼⣟⣿⡿⣿⠀⠀⣐⢾⣿⣽⡟⢿⣿⣾⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⣽⡿⣽⣿⣯
⡭⣿⡿⣿⣿⣰⡟⠁⠀⣐⢾⣿⣿⢯⡝⣻⡿⠿⢛⡭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⣿⣋⡄⠙⢶⣹⡿
⡙⣾⠻⣿⣯⡀⡑⠄⣸⣮⣃⣾⣼⣿⣷⣤⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠸⣿⡿⢋⣤⠀⢼⡿
⡀⢹⢹⣥⣟⠪⡷⠀⣌⡛⠿⣿⣙⣿⣽⣛⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⣘⣏⢻⣷⣾⣧⣽⣿⡷⣸⣿
⠈⠹⠀⠺⣿⣴⠷⠞⢻⣯⣿⣿⠿⣿⣏⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣅⣿⣿⣿⣼⣿⣻⣿⣷⢼⣏
⠀⠀⠀⢱⡧⣹⣂⠂⠄⠙⠀⣟⡿⣻⡁⢛⣇⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣽⣱⣿⡏⢭⣛⣛⡿⢿⡿⡉⢹⡟
⠀⠀⠀⠘⡇⠉⠦⠂⠀⠀⡀⡿⠁⢸⠖⣋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣽⣟⣯⡇⠀⡉⠉⡏⠈⠀⠽⠺⣯
⠀⠠⠀⢸⡇⠀⠀⠀⣆⠀⠉⣇⠙⠺⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣽⡛⠏⠁⠀⠶⠀⣇⡄⠀⠀⠘⡧
⠀⠀⠀⢸⡇⠐⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⠀⠀⠈⢹⢺⡏⠀⠀⠀⢸⡇
⠀⢀⠀⢸⡇⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠉⠀⡇⠀⠀⠀⣸⡇
⣤⣾⣿⣾⣷⣾⣶⣴⣶⣦⣤⣧⣀⣠⣤⣼⣧⣤⣤⣀⣠⣤⣤⣤⣶⣤⣶⣷⣦⣤⣴⣾⣿⣷⣶⣷⣾⣶⣶⣧⣦⣰⣴⣧⣤⣴⣤⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣭⣥⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⣶⣿⣿⠿⣶⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣦⣀⠀⠀⠀⠀⠐⢋⡭⢷⠀⠀⠐⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡹⢃⠻⠂⠀⠀⠀⠀⣀⣀⣸⣀⠀⢠⣴⣴⠞⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠈⠁⠀⠀⠀⠀⠀⠈⠙⢻⣿⣶⣶⠟⢂⣜⣶⡴⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⣀⣀⡆⠀⠀⠀⠀⡴⣶⢿⢿⣿⣿⡿⠀⠂⠀⠀⠶⠦⡄⠀⠀⠀⣄⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣅⣨⣿⡏⠀⠀⠀⣤⣤⣀⣸⢺⣿⣿⣶⡀⠀⠀⠀⠀⢀⣀⡀⢀⣾⣿⣐⣨⣿⣇
⠀⠀⠀⠀⠀⠀⢲⠀⠀⢿⣿⣿⣿⡇⡄⠀⢠⣶⣴⣤⣼⢸⣿⣿⠀⠀⠈⠀⠀⣤⣤⠄⠀⠘⢿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⡼⠛⢯⣠⣆⠘⢿⣿⣿⠃⡋⠀⠘⠛⠛⠛⠛⢸⣿⣿⠀⠀⠀⡀⠀⠁⠀⡴⣧⠀⠀⠉⡛⠉⠉⣴⡴⣆
⠀⠀⠀⢀⡟⠶⣅⣁⣿⣀⣀⡹⠇⢠⠟⠳⠘⠓⠚⠒⠖⠘⠿⡷⠒⠒⢺⠗⠒⠀⣴⣀⣁⠀⠀⠀⠙⢦⠚⠛⡂⣐⣧
⠀⠀⣠⣶⣷⣴⠋⠉⠙⣤⠀⠀⠀⢨⠗⢺⠀⢴⣶⣶⠀⠀⢀⡀⠀⣀⣤⣤⡀⠀⠉⢿⡋⣀⡀⠶⠶⢾⠶⠶⣿⣟⠉⢅
⠀⠀⣿⣿⣿⠋⠙⠛⠛⡿⠒⠒⠐⢿⡶⣾⠀⠀⣿⠇⠀⠀⣾⣯⡿⣿⣿⣿⠁⠀⠾⣿⣿⡟⠈⠀⠀⣸⠀⢸⣿⣷⣶⡾
⠀⠀⠸⣿⣿⣆⡀⠀⠀⢧⣄⣀⣠⣼⣿⣞⠀⠀⠉⠁⠀⢹⣿⣯⡏⠉⠉⠉⠀⠀⢀⣿⣿⣿⣶⠀⠀⠞⠀⠈⢛⣿⡿
⠀⠀⠀⢽⣿⣿⡿⣿⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⣻⣝⣿⡿⠀⠀⣆⠀⢠⣾⣿⠇
⠀⠀⠀⠈⡈⣿⠦⣞⠀⢈⠀⠈⠛⣟⣫⠅⠀⠀⠸⠿⠿⠿⢹⣏⣿⣿⣿⡟⠀⠀⠀⠛⢟⣿⠀⠀⠀⠈⠻⣿⡋⢛
⠀⠀⠀⠀⠉⡧⣤⡏⠀⠠⠀⠰⠺⣅⣨⡇⠀⠀⢠⣤⣤⣠⢸⡗⣀⣀⣀⡀⠀⠀⠀⢲⡶⢿⠄⠀⠀⢰⡶⡿⣷⣶
⠀⠀⠀⠀⢹⣧⣤⠗⠆⠐⠀⠰⢾⡋⢹⠀⠀⠀⠠⣿⣿⣿⣼⡇⣿⣿⣿⡇⠀⠀⠀⢸⣦⣄⡄⠀⠀⢸⣇⣠⣼⣗
⠀⠀⠀⠀⠸⣅⣨⠷⠂⠐⠀⠤⣔⠉⠓⠀⠀⠀⠀⠛⠛⠛⠓⠓⠛⠛⠛⠁⠀⠀⠀⠀⠫⣿⠁⠀⠀⠈⠙⣿⠅⠉
⠀⠀⠀⠀⠀⢉⣹⠴⠄⠀⢀⣤⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⠀⠀⠀⡟⠟⢷⡇
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠾⠄⠀⠀⢧⣴⡼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⢰⠄⠰⣓⠂⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⡆⠘⣯⠅⠀⠀⠘⠁⠙⠚⠁⠀⠀⢯⣀⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢳⡈⠋⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠸⣤⠞⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢇⡀⠙⠋⠀⢀⡴⣾⠟⠒⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠠⠀⠀⠀⠴⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⡀⠁⢀⡀⠀⣾⠸⡇⠀⠀⢀⠀⠀⠀⠀⠐⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠀⠀⠀⠁⠀⠘⢦⣉⣒⡶⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠁⢀⣦⡀⠁⠀⠀⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⣆⡆⠀⠀⣼⡤⠀⠁⠀⠀⠀⠀⠀⠤⠀⣰⢿⣦⠀⠀⣀⡀⠀⠀⠀⠈⠟⠁⠀⠰⠂⠀⠉⣻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡈⠀⢀⠀⠘⠀⣠⣿⣄⠀⠂⠀⠀⠀⢰⠇⢹⡘⣇⠘⠃⢹⠀⠀⠉⠀⢠⣄⠀⠀⠀⠀⠈⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⡀⠀⢀⡼⠃⣼⠸⡆⠰⠆⠀⣰⠋⢀⡞⠀⠈⢁⡴⠋⠀⠆⠀⡴⠻⡏⢷⠀⠀⠀⠀⠓⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⢹⡆⠀⢁⡴⠋⠀⢰⡇⠀⢹⣄⣠⠞⠁⠀⣾⣁⡠⢀⡞⣠⠶⡄⢠⠾⣇⢀⡟⠈⠳⣄⠛⠀⢘⣿⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠄⠀⠈⢀⡄⠀⠈⢳⣴⠋⠈⠻⡄⠀⠈⠋⠉⠀⠸⡇⢻⡀⠡⡀⠀⠙⣾⠁⠀⣤⠈⠃⠀⢨⣄⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠄⠀⢀⠾⡿⣆⠀⠀⠉⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠹⣄⢳⡀⠙⠀⠀⠀⠀⡴⣿⢧⠀⠀⠛⠚⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⢦⠀⠀⢠⣷⡀⠀⠀⢀⣤⣀⣀⣀⣀⡀⠹⢸⠇⢀⣿⡀⠀⢀⡴⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠆⣠⢞⣟⢦⡀⠐⢫⣯⡓⠀⢀⡾⡴⠀⠀⢠⢠⣿⣆⠋⠀⢋⣿⡙⠀⢀⡾⣿⠳⡄⠰⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⠀⡴⢛⣟⠢⡀⠐⣫⣯⡛⢀⣞⡁⠙⠓⠒⠋⡼⣻⣘⣦⠐⢫⣿⣝⠂⢠⠞⣿⡳⡄⠘⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡴⢛⣟⠳⡄⠜⣩⣯⡙⠆⢉⣉⣙⠛⠒⠞⠛⢋⣉⡀⠰⣫⣿⣝⠆⡠⢞⣿⡛⢦⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣫⣏⠳⢦⢚⣵⣷⣍⠂⠰⠆⣄⠰⠶⠶⠀⣀⠰⠆⠘⣡⣿⣌⠃⡴⢋⣿⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠑⠀⢋⣴⣷⣌⠓⠈⣼⣿⣄⢉⡉⣴⣿⣆⠁⢚⣡⣿⣮⡓⠀⠋⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⡷⣌⠓⢈⡴⡿⣆⠐⢀⡴⣿⢦⠀⠋⡴⣿⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠾⡿⢮⠀⠈⡼⡿⠦⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢀⠔⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣾⣧⠀⣴⠂⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣷⠉⣻⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢠⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠷⠀⠀⠐⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠸⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠙⠛⠋⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠛⠛⠛⡉⠉⠁⠀⠀⣀⣀⣤⣴⣶⣿⣡⠀⠀⠀⣰⠀⡀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⢠⡄⠀⣠⠀⠀⠀⠀⣠⠀⣠⣤⣤⣷⣴⣶⣾⣿⣿⣿⣿⣿⡟⠡⣿⡄⡂⠀⣿⡂⠠⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⢀⣸⡄⡠⠲⢾⡇⡀⠀⢀⡷⢤⡴⠒⠛⡦⠌⣿⣿⡿⠻⠙⠟⠛⡿⢏⢁⠀⠘⠿⠇⣈⢰⣿⣇⠲⠇⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡿⠛⠋⠀⣠⠚⠉⠒⠣⠀⠂⠀⢠⣆⢁⠔⠀⠀⠀⠀⢄⠈⢰⡆⠀⠁⠋⠳⠴⢄⣆⡀⠁⠉⠑⣄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠾⠋⢀⠤⠀⠀⢊⠉⠁⣷⢠⠀⢢⠤⠀⠀⠀⠀⡀⠠⠒⠉⠀⢠⡆⣼⣇⠀⠐⠂⠀⠠⠐⠩⠙⡄⠀⠀⡇
⠀⠀⡀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠡⠿⠜⠂⢀⡀⠀⠀⠀⢰⡇⣀⣐⡀⠀⣼⣧⡿⠿⠖⠒⢂⠀⠀⠀⠠⠀⡇⠀⠀⠇
⠀⠀⠇⠠⠄⠀⠠⠄⠁⠒⠂⠀⠶⣿⣿⣽⣷⠀⠀⠉⠁⠀⠚⠃⠼⣷⡐⢉⡁⠨⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠈⠀⠈⠠⠆⠀⠆⢴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠂⠀⠠⠤⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠣⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠿⠛⠛⠛⠻⣦⣤⣤⠴⠶⠶⠶⠶⠿⠛⠛⠿⠷⠶⢦⣄⢀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠉⠉⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢀⡴⣦⣤⣴⠟⠋⠉⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⣀⣠⣿⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠰⣟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠻⢧⣄⡀
⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠋⠉⠳⣤⡀⠈⠻⣦
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⢹⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡶⠾⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣋⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤⡀⠀⠀⠀⠀⢸⣧⠀⠙⣧
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣴⡟⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣷⡄⠀⠀⠀⠀⣿⠀⢀⣸
⠈⢿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠄⠀⠀⠀⠀⡼⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⡟⠛⠉
⠀⢠⡟⠁⠙⢷⡀⠀⠀⢰⣶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠘⣧⠀⣤⡈⠿⢆⡀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠈⢿⡟⠛
⠀⠀⠙⢷⣬⠇⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢘⣷⣄⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⡀⣀⣠⡾⠛⠃⠀⠀⠸⣧⣰
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠷⠶⠾⠛⠉⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣦⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣻⣿⣶⠶⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⡛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⢾⣿⡿⠋⠁⠙⠶⣤⣤⣀⡀⠀⢀⣤⡾⠉⠙⠛⣿⣷⠶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠻⢧⣄⠀⠀⠀⠀⣠⣼⠟⠛⢿⣏⡀⠀⠀⢀⣼⠟⠁⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⠉⠀⠀⠀⠀⠈⠻⢶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀
⠀⠀⠀⠀⠀⠀⠰⣿⣉⠀⠀⠀⠀⢀⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⠀⢈⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠈⠉⣹⡟⠛⠷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⢿⡉⠉⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⢸⣧⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⠀⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠀⠀⢸⣟⠀⣀⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣦⣤⣄⣀⣀⣀⡀⣀⣴⠿⣦⡀⠀⢀⣀⣀⣠⣤⣤⡶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠉⠉⠉⠛⠛⠉⠁⠀⠈⠛⠛⠛⠉⠉⠉⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣶⠶⣶⣶⡶⠶⠶⠶⠶⠶⠶⢶⡆⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢹⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠛⠛⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠛⠛⠛⠉⢻⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣛⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣷⣴⣶⣾⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡗⢀⡀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣤⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⣟⣿⢿⠟⠉⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢈⡟⡄⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⢿⣿⠇⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠉⠀⠀⣸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠽⠯⠛⠁⠀⠀⢀⠢⠀⠀⣀⣀⣀⡀⠀⢀⡀⠀⠂⢄⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠛⠛⠒⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⡾⠃⠀⠀⠲⠶⠶⠂⠒⠀⢲⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢰⡞⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡽⣀⣀⣸⠇⣇⣀⣀⡿⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠓⠓⠀⠀⠘⠃⠃⠀⠈⠚⠚⠋⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠟⠋⠉⠉⠛⠛⢿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⠀⠀⠀⣀⠀⠀⠀⢻⣄⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠉⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢀⣶⡶⣤⣾⡿⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⡡⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡆⠀⠀⢰⠲⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣄⠀⢸⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠀⠭⠄⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣤⣦⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢫⡶⢶⣶⡄⣻⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣵⢋⣤⣾⣿⣿⠋⠀⢻⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢃⣴⣾⣿⣿⡿⠆⠀⢸⡟⠀⠈⡇⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡷⠆⠀⣸⡇⠀⠀⠻⣸⡀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣾⣿⡇⠀⠀⣿⡖⠀⠀⣿⠉⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⣿⡏⠀⠀⣿⠀⠀⠐⠀⢀⣀⡰⡿⣿⣷⡆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡉⣿⣿⣆⠀⢰⣿⣇⠀⠀⣿⡀⠀⠀⠀⢀⠛⠛⠉⠉⠩⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⣯⡄⢸⣿⠏⠀⠀⣿⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⡿⠀⢸⣿⡇⠀⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⣿⣿⣷⡇⢸⣿⠇⠀⠀⣿⠀⠀⠀⢸⠙⢶⡄⠀⠐⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠌⠻⠂⠀⠀⠙⠀⠀⠀⠸⠦⠈⠋⠀⠆⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡇⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⡇⢠⣜⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠃⠀⠀⢀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡿⠀⢀⢔⠕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣼⣶⣿⣿⣶⣤⠘⢷⣦⠴⢧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠙⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠈⠂⢸⣿⣟⢻⣿⣻⠟⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡀⠀⡇⠀⠀⠀⢸⢿⣿⣷⣌⣰⢶⠝⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⢀⡈⣶⠀⠀⠀⠀⠘⣮⣤⣋⣛⣉⣶⡀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠿⠉⠁⠘⠀⠀⠀⠀⠀⠘⣯⡹⡉⢍⠀⠳⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠳⣟⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠙⣿⠷⠔⠋⠰⣝⠂⠀⠀⠀⠀⠀⠹⡾⡀
⠀⠀⠀⠀⠀⠐⢄⠀⣿⣈⡀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣎⠠⠼⢿⡀⢻⡴⣆⠀⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⣀⡀⠀⠉⣿⣿⡧⠀⠀⠒⠀⠞⢾⣿⠛⣿⠏⠀⠀⢄⡙⠿⢇⡟⠀⠀⠀⠃⠘⣇⣤⢜⣂
⠀⠀⢀⠼⠫⠁⠟⠶⠽⡯⠁⠀⠀⠀⠀⠀⢸⡿⠴⢹⠀⠀⠀⠄⠙⢦⠀⠁⠰⠧⠿⠚⢹⠟⡠⠚⠛⢠

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣀⢀⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⠁⠀⠀⣶⡤⠽⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢹⣿⡄⠀⠀⠀⠀⢠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⣧⠄⠀⢸⣿⣷⣺⣷⣶⠄⠀⠀⢰⣧⠀⠀⠀⠀⠐⢤⣥⣤⣤⡤⢴⢾⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣾⣷⣾⣿⣿⣽⣿⣿⣦⣴⣂⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣰⣴⣬⣧⠀⠀⣠⣤⣀⡀⣀⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠐⠒⠲⣾⠫⣴⣶⣿⡏⠐⠲⣞⢠⡫⠁⠙⢷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⡀⠀⠀⠀⠌⢸⡿⠋⠉⠉⠀⠱⣸⣆⡁⠀⢈⠋⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠃⠀⣼⠿⠶⢀⢞⠁⡀⠀⠀⠀⢠⣿⣿⡇⠤⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣨⢴⡞⠉⠁⠀⢋⠂⡸⠃⠀⠙⣦⠀⠀⠸⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠂⠜⠀⣿⠇⡀⠀⠀⣸⣴⣥⠄⡠⢶⡻⡧⠀⢠⣴⠎
⠀⠀⠀⠀⠀⠀⣇⡘⠀⢰⣿⢋⣀⠀⣤⡿⣿⠁⠊⠀⠈⠉⠀⢦⡀⠷⠸⡀
⠀⠀⠀⠀⠀⠘⠿⠇⠀⣼⠟⠋⡀⠀⠈⠻⣾⣆⠀⠀⢰⡷⠁⠀⢷⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣤⣾⡄⠠⠀⡠⠂⠁⠀⢀⢸⣥⡀⠀⠈⠻⣄⠀⠀⠙⠳⣤⣀⡀⢄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⠿⣿⣣⣾⡁⠀⠀⠀⣼⡿⠉⠻⢗⢦⣄⣀⠉⠒⠠⠤⢄⣉⠳⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠉⠉⠉⢹⣷⣭⡴⠊⠀⠀⢰⠋⠀⠈⣿⡄⠀⠀⠀⠈⠉⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠽⣿⡸⣿⣄⣠⢶⣯⣤⡴⠤⢉⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⢡⠉⠻⢿⠘⠁⢉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⡶⣞⠁⠀⠀⠀⠀⠀⠈⢧⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡼⢇⡟⠀⠀⠀⠀⠀⠀⠀⣾⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⡾⢇⡼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣷⡤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃⠀⠀⣀⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣶⡏⡏⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠁⡁⠀⣀⣀⡄⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠛⠛⠛⠋⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠛⠛⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠤⠶⠖⠋

⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣦⣾⣿⣏⠉⢹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⡀
⣾⢃⡶⠀⠀⠀⣠⣤⣤⣴⡾⠺⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠃⢸⣿⠀⠀⠀⠀⠉⠙⠋⢻⣶⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢻⣧⣤⣀⣀⡀
⠀⣸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠋⠁⠈⠙⢿⣿⣶⣤⣶⣶⣴⣶⣾⣿⣟⠋⠉
⣴⣿⠃⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀
⡿⠙⠿⠃⠀⠀⠀⠀⠠⣧⣿⣯⣀⠹⢯⠀⢹⣿⣿⣷⣔⢛⣿⣳⡿⣿⣿⣿⡿⠋⠙⣻⣏⢿⣿⠀⠀⠀⠀⢸⣟
⡃⠀⢰⠀⠀⠀⠀⠀⠀⠇⠘⣛⣿⣿⣿⣿⡷⣿⣷⣟⡏⠙⣿⣿⣵⣿⣿⢿⡻⣷⣿⢿⣾⣹⡏⠀⠀⠀⠀⠈⢿⣦
⡗⠀⢾⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣬⣀⡀⢻⣿⣿⣶⣿⣿⣿⣏⣤⣾⣿⢫⣁⣾⣧⠽⣇⠀⠀⠀⠀⠀⠀⢻⣷
⠁⣰⣾⠀⠀⠀⠀⠀⠀⠠⢿⠓⣳⣸⣥⣮⣿⡿⠿⢻⣿⣿⣏⣒⡻⠿⣿⣿⣖⣺⣟⣺⣗⡓⣿⠆⠀⠀⠀⠀⠀⠈⢿
⢀⣿⣿⠀⣤⠀⠀⠀⠺⣷⣿⠟⠛⣽⣿⠉⢴⡶⠃⠘⢛⣿⣿⣿⣥⣤⠀⡉⠙⣿⣿⣿⣿⣷⣿⣶
⣸⣿⡇⣾⣿⠀⠀⠀⠀⠙⠻⢿⡻⣿⣷⡶⡮⠱⣾⣿⣿⣿⣿⡿⠿⠟⠃⢹⡋⢉⣁⣙⣾⠿⠛⠉⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⡄⠀⠉⢻⣿⣯⣿⣿⣿⣿⣿⣟⠁⠀⣀⣶⢶⣶⣾⣻⣿⠍⢡⣶⡄⠀⠀⠀⠀⠀⠀⢸⡄
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠛⠃⡤⠀⢸⡏⠻⣿⣿⣿⡿⠛⣿⣿⢛⣿⣩⣽⠏⣾⣿⡏⠠⠤⢉⠀⠀⠀⠀⠀⠀⠐⣿⣧
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠰⠄⠀⢠⢸⡇⢀⣼⣷⣿⣷⣾⢸⠉⢸⣿⣿⣿⡿⠋⣿⡃⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠖⣈⡃⠿⢿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⠃⠀⣿⠿⣿⠇⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⢀⣀⠀⠀⠀⠀⠠⠀⠀⣿⡿⠀⢸⣿⣿⡏⢿⣿⣄⣿⡟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣧⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⣰⠀⢸⣿⣿⡇⢸⣿⡿⢛⣶⣶⡖⠀⠀⠟⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠸⢿⣿⡇⠸⡇⠀⠈⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⢿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⡧⣀⢳⡜⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣉⣙⣿⣿⣿⣿⣌⡲⣯⡳⣄⠙⠛⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⠟⠟⡁⠀⠑⠑⠄⠙⢿⣿⣕⣿⣿⣌⠑⠴⠿⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣭⣉⣉⣠⣴⣿⣧⣷⠶⠛⢶⣤⣀⡈⡙⠛⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣷⣤⣭⣻⣿⣿⣷⣶⣷⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣠⠖⠚⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠒⢦⡀
⠀⠀⠀⠀⠀⣠⠃⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⡀
⠀⠀⠀⠀⠀⢿⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣆⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⢧⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣆⠀⠀⠀⠀⣼⣿⣿⣿⠟⠋⠉⠁⠀⠈⠉⠙⠻⣿⣿⣿⣆⠀⠀⠀⣸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣼⣿⣿⣏⠀⠀⣀⣠⣤⣤⣤⣄⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠆⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⡛⠱⠦⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣴⠋⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢦⠀⠈⠳⡄
⠀⠀⠀⠀⠀⣴⠃⠀⠀⡜⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⣆
⠀⠀⠀⠀⡰⠃⠀⠀⣴⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢣⠀⠀⠙⣦
⠀⠀⠀⣸⠃⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢆
⠀⠀⣰⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠁⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇
⠀⢠⡍⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣄
⠀⡜⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢩⡄
⡘⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣡
⢷⣤⣀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠴⠶⠶⠾⠉
⠀⡘⠁⠈⠉⠋⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢡⡄⠀⠀⠀⠰⡆
⢀⡇⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢣⠀⠀⠀⠀⢇
⠘⠇⠀⠀⠀⣴⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠘⣄⠀⠀⠀⢸
⡄⠀⠀⠀⢀⠏⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢻⡀⠀⠀⠸
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠐⠁⢠⡄
⣿⠀⢶⡶⠈⠀⠀⠀⠀⠀⠀⠉⠉⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⣸⠇
⡟⠀⢺⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣄
⠀⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠟⠉⠉⠉⠉⣿⠀⢸⠉⠉⠉⠉⠫⡤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠊⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⠲⠶⠶⠶⠶⠶⠦⢄⣉⠿⠀⠻⣏⣡⠶⠶⠶⠶⠶⠶⠶⢙⡇
⣤⣦⣤⣤⣤⣶⣤⣤⣤⣤⣤⣴⣦⣤⣦⣤⣾⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣶⣶⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤
⣿⣿⣿⣿⠛⠉⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⢠⣤⣀⢀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⣄⠀⠀⠙⠀⠀⠀⠀⣠⠴⡞⠙⠻⠁⠀⠀⠀⠺⠿⣶⡌⠉⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠈⠃⠀⠀⣴⠉⠙⢦⡄⡠⠃⠀⠀⠀⢀⡤⠴⠲⡄⠘⠟⠀⠀⠀⠈⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⣠⠛⢧⡀⠀⠻⡀⠀⠀⠀⠴⠩⠾⢇⣴⠃⠀⠀⠀⠀⠀⠰⣄⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⢠⠞⠁⡰⠋⠙⠶⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠒⠢⠄⠀⠀⠀⢠⣌⢷⡀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠦⣤⣤⡀⠀⠀⠀⠀⠀⢤⡙⣷⣷⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠆⡜⠈⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⢻⡀⠀⠀⠀⠰⣄⣻⣟⠧⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡸⢠⡇⢠⠃⠈⡗⠒⠲⠶⠖⠶⠒⠂⠏⠁⡼⠀⢸⠁⠀⠀⠀⠰⣼⣿⡙⠆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⢸⠃⠦⠄⣠⣀⢀⡜⠀⢀⡃⠀⣸⢀⡼⠁⠀⠁⢠⠀⠀⠀⠀⡨⢔⣒⣚⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣷⠀⢠⠃⠀⢸⠁⠀⡝⠁⢠⢋⡼⠁⠀⠀⣠⠃⠀⠀⠀⠀⠰⣍⣀⠀⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢻⣀⠆⠀⢀⠇⠀⣰⠁⢀⡶⠋⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠤⠤⠞⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣄⠀⠙⢦⣀⣌⢀⣀⡧⠖⠉⠀⠀⠀⠠⠊⠀⠀⠀⠀⠐⢦⣤⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠸⡀⠀⠀⠈⠉⠉⠁⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⠲⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢤⣀⣀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠯⣉⠢⣄⡹⠦⢌⣉⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠚⠉⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⡒⢌⡿⠋⠀⢰⢀⣬⡻⠉⣉⠝⢋⠙⠿⠿⢿⣿⣿⣿⠇⠀⠀⠘⣆⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠠⣌⡾⠀⠀⠀⠘⣟⣮⡷⠊⠀⢠⡯⠩⣭⠁⢀⣽⣿⣿⡀⠀⠀⠀⠘⣦⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣧⠀⠀⠀⠀⠙⠋⠀⠀⠀⢘⣂⣐⠀⠴⠛⢻⣿⣿⣿⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣆⠀⠀⠀⣉⡀⠀⠀⠀⠀⣿⣥⣤⣤⠃⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⠀⠠⠄⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣀⣾⣷⣄⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠿⠀⠀⠀⠹⣿⠟⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠙⠄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠈
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣤⢠⡶⣿⢠⡀⣇⣼⣠⣷⣀⢠⣦⣿⣄⣾⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿
⢠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠆⠿⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠑⣿⢊⡀
⠘⠿⠻⠻⣿⣿⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣻⣭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠭⣉⢹⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⣄⣰⡒⣿⡤⠄
⠀⠀⣠⡀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢺⣇⠠⣤⠤⠽⣿⠟⣋
⠠⢰⣿⣧⣴⣾⣶⣿⣾⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠐⢨⣽⡥⠄⠈⠳⠶⣿⡟⣃
⠀⣽⣿⣷⣿⣿⣿⡟⣁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⠄⠀⠙⠪⣽⣗⣒⠀⠒⢶⣾⡟⢋
⠀⣿⣿⣿⣿⣿⣿⠟⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢍⣽⣮⡄⠨⣹⣿⢯⠡⠄⡨⢿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠎
⠀⠀⠀⠀⠀⠡⠐⠠⢀⣀⡄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠬⠀⠠⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡕⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⣨⣴⠶⢤⣄⡀⠀⠀⣀⣤⠴⢶⣤⡄⢄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡢⠊
⠀⠀⠀⠀⢀⣀⣀⢀⣿⠋⠀⠀⠀⠈⠻⡄⣼⠋⠀⠀⠀⠈⠹⣇⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠜
⠀⠀⠀⠀⠻⠋⢛⢿⡇⠀⠀⠰⣼⡇⠀⣿⣇⠀⣮⣿⠀⠀⠀⣿⡛⠋⠿⠂⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠔⡵⠁
⠀⠀⠀⠀⣀⡴⠃⠌⠻⣄⡀⠀⠀⣀⠼⠛⠻⢦⣀⠀⠀⣀⣴⢏⠙⣄⢀⠀⠀⠀⠀⡇⠀⠈⢢⡀⡠⡢⠊
⠀⠀⢠⠊⡝⢀⠊⠀⠀⠈⠙⠛⠛⢡⡀⠀⠀⣠⠙⠛⠛⠉⠀⠀⠂⠈⢆⠈⠉⠁⡨⠷⡀⠀⠀⠙⢾
⠀⡰⠁⡜⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡆⠀⠀⡇⠀⠈⠢⡀⠀⠀⠁
⡰⠁⢰⠁⡄⠀⠀⠀⠀⠀⠀⠀⠒⠂⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⣦⡀⠀⠈⠐⠄
⡇⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠇⠝⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⢀⢾⡀⠈⠐⢄⡀
⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⢱⢦⣀⠜
⢃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠂⠈⠉
⠈⢾⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠈⢧⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠇
⠀⠀⠈⢣⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣡⠋
⠀⠀⠀⠀⠉⣪⣗⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣮⣞⠁
⠀⠀⠀⠀⠸⣀⠰⡞⣛⢿⡗⠶⠶⠶⠶⠶⠶⠶⠶⠶⢺⡟⠛⣳⠆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠣⠤⠌⠑⠒⠁⠀⠀⠀⠀⠀⠈⠒⠊⠣⠤⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢶⣒⠻⢯⡙⠿⣍⡉⠻⣍⠻⡗⢶⢲⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣉⠛⠳⠦⣍⣛⠾⣝⡒⠭⣓⠬⣙⠢⣈⠣⡙⠌⠊⠇⠳⢣⢟⡷⢲⣄⡀
⠀⠀⠀⠀⣀⣴⡟⠉⠒⡍⠉⠉⡏⠑⠢⠭⣙⠲⠬⣕⡢⢅⡂⠁⠀⠁⠀⢀⠤⠒⠦⣄⠈⠚⠡⢒⣋⣷⣄⡀
⠀⠀⢠⣞⡭⢍⣀⡠⠒⠮⡀⠘⠀⠠⠓⠀⣸⡿⣿⣷⣬⡑⠂⠁⠀⡠⢴⠃⠀⠀⠀⠈⣆⢀⡼⢳⣒⢒⣚⣛⣦
⠀⣰⣿⣷⣾⡿⢿⣷⣦⠰⣋⡵⠴⢚⡶⠚⠁⠀⣹⣿⠀⠈⢒⣾⠭⣁⡸⠧⠖⠓⣦⣤⣿⡏⠀⣾⡟⠳⣽⢶⠊⢳⡀
⢰⣿⣿⣿⡿⣤⣶⣤⣍⡛⠧⣤⣶⣯⣀⠀⠀⢀⣼⡿⠃⣠⠏⠉⢢⠈⠑⠲⣿⣛⠟⠋⠃⠀⠀⣼⡇⠀⣨⣿⣷⣿⣷
⣿⣿⣿⣿⣿⡝⣿⣿⣾⣻⣷⣌⡙⠻⢿⣷⢠⡞⠃⣀⣾⣿⣿⣷⣯⣤⣴⣶⣶⣿⣷⣄⣀⣴⣾⣿⣿⣟⣿⣯⣿⣿⣿
⣿⣿⣾⣯⡽⠼⣿⣟⣿⣿⣿⣿⣿⣛⠦⣌⠙⠻⢿⣿⣿⣶⣾⣭⣿⠿⠿⣛⣛⣿⣭⣭⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⢻⣷⣿⣿⣽⣿⣽⣿⣻⣫⡟⣿⣿⣷⣦⡈⠻⣿⡶⢯⣽⠋⣟⣀⠐⠺⠿⠥⠶⢽⣧⢿⣻⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⣤⢌⡺⣽⡦⣌⡉⠛⠳⢾⣼⣿⣿⣛⣿⣿⣷⡿⢿⣿⣽⣟⣿⣿⣿⠃
⠀⠀⠹⣷⣽⣻⣿⣿⣿⣿⣿⡿⣿⣯⣟⡿⢟⡿⣿⣿⣿⡷⠟⠃⠀⠀⠀⡙⣿⣿⣿⡿⢿⣻⣯⣽⣶⠮⠽⢿⡿⠁
⠀⠀⠀⠈⠛⢿⣿⡿⢿⢻⣛⣻⢷⣺⢝⣯⣷⡾⠟⠋⠁⢀⠀⠀⠀⠂⠀⠀⣿⣯⣶⣿⠿⢿⣒⣛⣫⣭⠟⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣯⣟⣯⣿⣿⣟⡋⠁⠀⠀⠀⢀⠀⠀⠀⠌⢀⡴⣻⢿⣻⡽⣖⡻⣽⡷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣵⣶⣒⣀⣶⡖⠀⠀⢐⣴⣿⣿⣷⣯⠷⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠏⠤⠂⠒⠐⠂⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠐⠚⠙⠣⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⣀⡀⠤⠄⢛⣲⣒⠂⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⡀⣤⠀⠈⠒⠂⢑⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⢀⡀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⡀⠀⠀⣤⠀⠀⠀⡀⠗⠠⡤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⢇⣀⣀⠸⡄⠀⠐⠀⠀⢂⡇⠂⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢈⡓⠇⠀⠈⠒⠒⠁⠈⠧⠐⠂⠁⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⡀⢀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠇⡌⠰⠀⠀⠀⠨⠁⠂⠤⠤⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣷⢼⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣿⠇⠀⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⣄⠠⠃⣜⡩⠒⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⢉⡈⠁⠀⠈⠀⢀⠔⠁⠀⠔⠀⠀⠀⠀⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⡀⠘⡄⠀⠀⠠⡔⠁⠀⠀⡀⠨⢄⠀⢠⡀⠀⢀⠀⡠⡞⡉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠔⠈⠡⢴⣣⣠⠪⢄⣱⠂⠠⠦⣀⡀⣼⠀⡼⢡⠠⢾⠶⡱⠾⡖⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⢀⠀⠀⢀⣀⠈⠉⠒⠺⠒⢒⡒⠰⣀⠘⢣⡅⣟⠉⡆⠈⠀⠀⢻⠁⠚⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠐⠂⠀⠀⠈⠉⠫⠈⢻⡆⠁⠀⠀⠀⠀⠀⠀⠁⠤⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠒⠤⠄⣐⣀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠉⠉⠁⢉⠹⡙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠓⡌⠂⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠉⠙⢍⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠑⠄⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢀⠀⠀⠀⣼⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⣤⣤⣄⣝⣄⣀⣼⣧⣐⣿⣿⣶⠒⠂⠐⠒⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠱⠒⠂⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠠⠀⠐⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⢀⣴⣾⣿⣿⣿⣟⣿⣿⣿⣿⣶⣤⡈⢀⠬⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣿⠏⣴⣿⣿⣿⡟⢿⣿⣿⠣⡰⢛⢻⣿⣿⣿⣆⢻⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣾⡋⠙⢷⣿⣇⣿⣿⣿⣿⣿⡜⢿⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣤⠀⢸⣿⣿⣿⣿⣯⣻⡟⢠⣾⡿⣫⣿⣿⣿⣿⣿⠇⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠿⠆⡜⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⠀⢸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⣿⡘⣿⡿⠿⣛⡛⠉⠉⠭⠙⠛⠻⢿⣿⡿⢣⣏⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡞⡋⠉⠛⠂⠀⠓⠈⠁⠀⠲⠶⠦⠤⠝⠒⠉⠔⠫⠚⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠉⠿⣿⣷⢤⣄⡀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣤⣶⣿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠉⠻⣥⣌⣉⣛⡒⠒⠒⠀⠀⠐⠒⠓⢛⣉⣭⣿⠟⠁⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣦⠀⠀⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢻⣿⢻⡿⠟⠂⠙⠓⠊⠁⠈⠀⠸⣿⣿⣿⣿⡟⠀⠀⠌
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠘⣄⠀⠘⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢣⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀⢸⠏
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠛⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠋⠁⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠤⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣁⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠉⠒⢄⣀⠀⢀⡁⠠⠂⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠠⠄⢰⡄⠄⣀⠤⠒⠉⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠈⠉⠻⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠤⠀⠄⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⠀⣠⣶⡿⠿⠛⠻⠷⣦⣄⡀⠀⠀⠀⣤⣶⠿⠛⠛⠻⢿⣶⣔⠐⣢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢈⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⣷⡀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⣠⠟⢿⣇⠀⠀⠀⠀⠀⣀⣄⠀⠀⢸⣿⣿⡆⠀⠀⣠⣄⠀⠀⠀⠀⠀⣼⣿⡉⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠜⣿⣄⠀⠀⠀⢸⣦⣿⡇⣠⣿⠿⠿⣷⡄⢸⣶⣿⡇⠀⠀⠀⣰⣿⠃⠹⣄
⠀⠀⠀⠀⠀⣄⠀⣿⠲⢾⣟⠀⣠⠃⠀⠈⠻⢷⣦⣤⣤⣭⣽⡾⠉⠀⠀⠀⠀⠙⢷⣯⣭⣤⣤⣶⡾⠟⠉⢢⠀⠘⢷⢤⣀⡀⢀
⠀⠀⠀⠰⡖⠿⢥⣟⣢⠤⢤⣉⣙⠒⠦⢤⣀⠀⠈⠉⠉⠉⠁⢱⣄⠀⠀⠀⠀⣠⡆⠉⠉⠉⠉⠁⠀⠀⢀⣀⡵⠴⠚⣋⣩⠷⣿⣠⡀
⠀⠀⢠⣤⣷⣀⣀⠠⠬⣉⠒⠠⢌⡉⠑⠢⢌⡑⠢⣄⠀⠀⠀⠈⢄⠑⢄⡠⠊⡰⠀⠀⠀⠀⢀⡠⠔⣊⡩⠤⠒⢊⣉⢭⠴⠒⠯⣼⢻⡇
⠀⣀⠸⠖⠊⠉⠀⠀⠀⢨⡆⠀⠀⠈⠙⠲⢄⡉⠳⣌⠳⣄⠀⠀⠀⠉⠋⠃⠉⠀⠀⢀⡴⢚⡡⠖⢋⣡⠴⠒⠋⣁⡤⢾⠀⠀⠀⠀⠉⠓⠤⣀
⢰⠁⠀⠀⠀⠀⠀⣀⣴⣎⡉⠙⠲⢤⣄⡀⠀⠈⠓⢬⣳⡈⠳⣄⠀⠀⠀⠀⠀⢀⠔⣡⠖⢉⠤⠚⠉⣀⡤⠖⠋⣁⡤⠞⣳⣤⣀⠀⠀⠀⠀⠀⠹
⣄⢀⡠⠤⠒⠊⠁⠀⠈⢫⠉⠓⠲⢤⣀⡉⠙⠲⢤⣄⣈⠻⢆⠈⢧⠀⠀⢀⣴⠗⢊⡠⢆⠙⢦⡖⠋⣁⡤⠖⠋⠁⠀⢸⠁⠀⠀⠉⠒⠤⣄⡀
⡏⠀⠀⠀⠀⠀⠀⣀⡤⠋⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣉⡙⠲⣷⣖⡓⠀⠞⣡⣴⡥⠖⢋⣳⣠⡽⠏⠁⠀⠀⠀⠀⠀⠘⠢⣄⡀⠀⠀⠀⠀⠈⠙
⢣⣠⡤⠴⠔⠒⠛⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⣿⠈⠉⠉⠉⠁⣿⠰⡏⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠓⠲⠤⣄⣀⣰
⠘⡆⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠒⠒⠲⠖⠒⢿⠀⣷⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⢰⣿⠿⢄⡀⠀⠀⠀⢨⠇
⠀⠈⠲⢶⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠒⠶⠶⠴⠶⢾⠀⣿⠀⠀⣷⣄⠀⠀⠸⣿⡿⣷⡄⠸⣿⣦⣶⡏⣷⠦⡔⠃
⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⢸⠀⢸⡄⢸⣿⣿⣷⣄⠀⢻⣷⠿⠃⠀⠈⠉⠉⠀⢹⠀⣷
⠀⠀⠀⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⢸⠀⢸⡇⠘⠟⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿
⠀⠀⠀⠀⡇⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⠀⠀⢸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⣛⣥⠿
⠀⠀⠀⠀⠛⠲⠦⣭⣙⣛⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠋⠓⠒⠒⠒⠚⡇⢸⡇⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⣛⣩⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠻⣗⠲⠬⣍⣙⡓⠶⠤⣤⣀⣀⣿⢸⡗⠒⠲⠴⠖⠺⡇⠈⣇⢀⣀⣤⠴⠞⣋⡭⣴⠞⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣮⣑⠦⣄⡀⠉⠙⠓⠶⠤⣍⣁⢘⡇⠀⠀⠀⠀⠀⡇⠀⢛⣉⡥⠶⠚⣉⡥⢚⣥⣶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⢹⣉⣶⢿⣷⣶⣤⣤⣤⣀⣈⣉⣳⣤⣄⣀⣠⣴⣷⣪⣭⣤⣴⣶⣯⠷⣮⣉⠎⠁⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠖⠊⣹⠤⠠⢌⣻⣧⠋⠉⣻⠉⠉⠉⠉⠉⠉⠉⠉⠙⡏⠉⠑⣼⣗⡡⠄⠤⣏⠑⠢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣀⡠⠋⠘⠲⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠃⠹⢄⣀⡤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠤⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠀⠈⠉⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⠔⠁⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⣀⠒⠶⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⢶⡄⣀⡀⠀⠀⠤⠤⣤⡉⠀⣀⣀⠀⠀⠀⠀⠘
⠀⠀⠉⢄⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠑⡦⢀⡀⠑⢀⡀⠠⠄⠀⠀⠀⠑⢄⠀⠀⠀⠀⣀⠀⠀⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⡄⢰⠁⠀⠈⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠊⠉⠑⢦⠀⠀⠀⠁⠒⠒⢃⠀⠂⠀⣄⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⠀⠀⠴⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠤⠀⣤⣾⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠉⠉⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣈⣡⣤⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠋⠀⠀⠀⠈⣙⣡⠀⠀⠈⠻⡝⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢀⠀⠀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠁⠀⠣⡄⣀⣀⣀⠐⠊⠁⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠤⡀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢩⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠆⠀⡃⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡅⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠠⠋⠀⢀⠃⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢛⡀⢸⠀⠀⠀⠀⠀⠀⣀⡤⠒⠀⠉⠀⠀⠀⣠⠊⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢇⠀⠑⣤⡌⠭⠹⠒⠂⣇⠀⡃⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⣢⠀⠀⠀⢠⠀⡡⢷⣐⠂⢄⠀⠀⠈⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⡇⠀⠉⠀⢸⣤⣄⣠⡅⠀⠀⢠⡎⠑⣄⡀⠀⠀⠀⠀⣠⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⢻⡄⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠀⠀⠀⠙⠳⣤⣠⡾⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠀⠂⠀⠀⠀⣀⣀⡀⠀⣇⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠙⠛⢠⣤⣄⣀⣀⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠄⠀⠀⣠⣾⠶⣄⠀⠀⠀⠈⠀⠸⣯⣍⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠢⠀⠡⠀⠀⠀⢃⠉⢶⠍⠢⢄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⢺⠄⠀⠀⢈⠀⠂⠀⠤⢤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠐⢢⡤⠒⠁⠀⠀⠀⠀⠀⠉⠀⠒⠠⠤⢁⣐⠂⠀⠠⠤⠤⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⢀⠤⡴⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉⣉⠝⠋⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣀⠀⠀⠀⠉⠁⠐⠒⠂⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈⠙⠻⠶⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡀⠀⠀⠀⠘⠋⢄⠀⠀⠀⠢⠤⠀⠀⠀⣀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠶⠄⣀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠉⠉⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠤⣤⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢌⢀⠴⠃⠀⠀⠑⢆⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠈⠃⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠶⠶⣖⠀⠱⣄⠀⠹⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠂⠀⡋⢀⣶⢬⣆⡠⢼⣕⠦⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣀⠄⠀⠳⢼⠿⠋⠉⠐⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⠐⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠈⢦⡀⠀⠐⠤⣣⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠐⢄⠜⠈⠳⣄⠀⠈⠒⠀⢀⠤⠚⠁
⠀⣀⣀⣀⠰⠚⠳⡀⠈⢦⠀⠀⠈⠣⣄⡴⠊
⡞⠉⠁⠀⠀⠀⠀⠘⡄⠈⠳⡀⠀⡠⠋⠀⣈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣄⡀
⢇⠀⠀⠀⠀⢠⠂⠀⠸⢀⡤⠽⣄⠀⢀⠇⠀⠠⠉⠑⠠⡀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠉⠢⡄
⢸⡄⠀⠀⠀⠀⠐⠀⠀⠓⠀⠀⠈⢆⡘⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠨⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⡿⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢷⠹⣧⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠸⡄⢹⡀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠏
⠀⠀⢣⠀⣧⠀⠀⠀⠀⠀⢠⠞⡉⢷⠀⠀⢠⠀⠀⠀⠀⣸⠃⠀⠀⠀⠁⠹⢦⣀⠀⠀⠀⠀⢊⣠⠔⠁
⠀⠀⠘⡆⠘⡄⠀⠀⠀⢠⠏⠀⠀⡠⢇⣀⠀⢂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉
⠀⠀⠀⢻⠀⠘⣄⠀⠀⡏⠀⠀⡜⡀⠀⠈⠙⠲⢦⠀⠀⠀⠀⠀⢀⣀⡠⠎⠀⠀⠀⢀⡎
⠀⠀⠀⠸⡇⠀⠈⠳⣴⠀⠀⢰⠁⠃⠀⠀⠀⠀⠀⠉⠒⠤⠀⠈⠀⠀⠀⠀⠀⡀⠠⠊⠇
⠀⠀⠀⠀⣿⠀⠀⠀⠘⠲⢦⡴⢤⣀⡀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⢀⠴⠒⠁⠀⢀⠔⢳
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣐⣡⡴⠙⡆
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠉⠢⡀⠀⢀⡠⠤⠄⠒⠋⠀⠀⠉⠓⠲⠶⠶⠖⢛⡍⢉⡤⢂⠏⠀⠀⠀⠒⠒⠒⠒⠶⠶⠦⣤
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠼⡗⣁⢀⠰⠆⠒⠒⠒⠒⠒⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣣⡤⠤⠤⠤⠤⠤⠔⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋

⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠳⣄⠀⠀⠀⢿⠦⠤⠤⠒⠒⠒⠒⠶⠤⠒⢒⣺⠃⠀⠀⠀⡠⠊⠉⠳⣄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⢳⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⠀⣴⢻⡇⠀⠀⢠⠋⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢠⡏⣀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⡇⢺⠷⢤⠀⠀⢀⣰⣾⡅⢸⡇⠀⠀⢸⠀⠀⠀⠀⠘⢶⣄⠹⡄
⠀⠀⠀⢀⡆⠍⠀⠐⠆⠐⣏⣠⠄⠸⢆⠀⠀⡇⠈⠉⢁⠱⣀⠞⡍⣉⠀⢻⠀⠀⢀⠞⡀⢀⠀⠳⠤⠜⠀⠉⠱⡄
⠀⠀⠀⡼⠀⠀⠆⠀⠀⠀⠀⢀⡀⠀⠘⠦⣼⢀⠀⠀⠀⠀⠉⠀⠀⠀⡀⡄⢇⣠⠋⠀⠑⠈⠋⠀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⢰⠃⠀⡄⠀⣀⢼⠁⠀⠈⠀⠀⠀⠀⡇⠀⠘⠀⢄⠀⠀⠠⡄⠠⠁⠇⠘⠀⠀⠀⠀⢀⠂⠀⠀⠠⠄⠐⠀⡀⢧
⠀⠀⡏⢠⠛⡇⠀⠀⢸⢰⠆⠁⢀⠃⠀⠀⡆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⣘⡀⠘⠀⠀⠁⠀⠀⠚⠈⢁⠘⡆
⠀⢰⣠⠏⡆⠀⠀⠀⠈⢰⢠⠀⠼⠀⠀⠀⡧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⠀⢐⠈⠒⠀⢀⠀⣀⠀⠃⠀⡀⠀⠀⠈⠀⢻
⠀⠘⠁⠀⠀⡃⢀⢃⠀⠉⢸⠀⢳⠀⡄⡆⢱⠄⢀⠀⢠⠀⠀⠀⠀⠁⠁⡄⡾⢠⠀⢆⠈⡆⣹⠀⣈⠀⠡⡀⠀⠀⠀⠰⡄
⠀⡇⠀⢸⠀⠈⠁⡌⢠⢃⡞⠋⠈⠂⠀⠈⢹⢀⡘⡇⠘⠄⠀⠀⠀⡴⠀⣼⡷⠞⠈⠈⠃⠀⠈⡆⢸⠀⠀⠈⠀⠀⠀⠀⢧
⢠⠀⠀⠀⠀⠀⢀⠇⡜⠉⠀⠀⠀⠀⠀⠀⠘⡄⠀⢈⠀⠰⠄⠃⠐⠃⠨⢰⠀⠀⠀⠀⠀⠀⠀⠈⠉⡄⢠⠀⠀⠀⠀⠀⢸
⢸⠀⢠⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠁⠀⠀⠀⠀⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘
⢰⠀⠘⠀⠈⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠲⠀⠀⢠⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠀⠘
⢈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠀⠀⠐⡀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⡆⠀⡇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢈⠊⣧⠠⣁⠰⡄⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡁
⡇⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢠⠆⠺⠬⠤⠾⠷⠧⠦⠇⠼⠼⠤⠄⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⢧⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⢀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡰⡿⣀⣀⣸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢯⢩⠁⡉⠉⠉⠉⠉⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠘⣈⣠⠀⠀⠀⢀⡄⢂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠁⠒⢲⢉⠟⠒⠒⠛⠛⠋⠉⠉⠉⠛⡑⠉⠉⠉⠙⡩⠽⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠀⠀⢺⣼⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⠶⠤⢬⠤⠤⣤⣤⣤⣤⣤⣤⣬⣦⡧⠤⠤⣤⢌⣷⣀⣄⣠⣄⣈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⢀⡴⠃⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠉⠉⢬⡅⠀⠀⢈⡀⠂⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠁⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠐⠤⠊⠉⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠈⠳⢄⠀⠀⢀⡄⠃⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⢀⣀⠀⠀⠀⠀⠀⠀⣤⠭⠰⠀⠀⠀⠀⠱⡀⠑
⠀⠀⠀⠀⠀⠀⠀⢠⠉⣇⠀⠀⠉⡶⠂⠀⠀⢰⡏⠀⠀⠀⠀⠠⠤⠴⠁⢀⣀⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⢹⠀⠀⠊⠀⠀⠀⢠⡟⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣠⢤⡤⠀⠀⠠⣼
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⣠⠞⢹⠉⠂⠀⠀⠄⠀⠀⢠⣤⠀⠀⠀⠰⢾
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⣀⡤⠤⠤⣤⣀⡀⢀⣸⠆⢆⠀⠀⠀⠀⢀⠀⠈⠚⠂⠈⠈
⠀⠀⠀⠀⢠⡇⠐⠉⠀⠀⠀⠀⠀⠉⠻⢯⣽⠀⠈⢳⣄⠀⠀⠀⠙⠶⠤⠤⠞
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠙⢧⣄⡀⠀⠀⠀⣀⡴⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⠉⣩⠏⠉⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢿⣄⣤⣶⠟⠛⢹⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡟⠲⣄⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢀⡼⠛⠉⠀⠀⠀⠸⣤⣄⠀⠀⠀⠀⢈⠀⠲⣄⠀⠀⢸⡟⠀⠈⠂⠀⣀⠤⠔⠛⠒⠂⠠⡀
⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢠⠀⣄⣠⠖⠋⠉⠙⣆⠈⠳⣄⠘⠁⠄⠀⠀⣋⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠈⠃⠀⠀⠀⠀⢁⣒⠁⠠⠤⠀⠀⠀⠀⠀⠳
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⢀⡤⠠⠐⠒⠂⠀⣀⣀⣠
⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⢸⡏⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢈⡋⠉⠉⠙⠦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⠤⣤⣀⣀⡀⣀⡷
⠀⣾⠀⠀⠀⣀⠠⠚⠁⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠸⢃⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠒⠶⠤⠴⠶⠖⠋⠁
⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⢦⡀⠀⠀⠀⠀⠀⢀⣠⡞⠁
⠀⠀⢄⠀⠀⠀⠀⠶⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⣀⠄⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠐⡆⢄⡘⠀⢄⠀⢆⢼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠀⡇⠃⠀⡀⢥⠈⠈⢀⡰⠖⠂⠀⠀⠀⠀⠀⠈⢀⠀⢹⡰⠃⠀⢼⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡇⢣⠀⠨⠀⢡⡀⢀⠠⠖⣀⡤⠕⠋⠠⣴⢆⡢⡄⠸⠀⠈⠲⢽⡞
⠀⠀⠀⠀⠀⠀⡇⠘⣶⠀⢰⠁⢀⣡⠀⠁⠋⠅⠀⠀⠴⡥⠄⠀⠀⠒⠏⢠⢙⣟⣦⢀⠀⢀⠈⣧⠄⡄
⠀⠀⠀⠀⠀⠀⠘⢄⡟⢡⡸⠀⠀⡏⢣⠀⠀⢀⡤⠚⠉⠀⠀⡀⠴⢴⣦⣠⡇⠃⢸⡘⡎⠸⠂⠸⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠇⠢⣠⠞⠁⢣⡀⠈⠀⠀⠀⠀⠀⠀⠀⠚⢀⠙⡛⣿⣯⢽⣦⣼⣠⣀⡟⡄
⠀⠀⠀⠀⠀⠀⠉⠹⡔⠇⠀⢸⣾⠀⠀⣹⡿⠀⠀⡞⠀⠀⠀⠀⠂⡀⠈⡦⠁⠇⢸⡅⡄⠈⠀⣸⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⢠⣿⡿⠀⢰⠇⡇⠀⠀⡀⠀⠀⠀⠀⠀⢃⠀⢣⢠⢆⡆⢱⠁⢀⡟⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣽⡇⠀⠘⣿⡅⠀⠀⡇⠀⠀⠀⠀⠀⠘⡸⠸⣿⠀⣧⣼⢀⣾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⠈⢦⡀⢹⡇⠀⠐⠂⠀⠀⠒⣛⣻⣜⣧⡇⢻⡀⢸⣹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣄⠀⣷⢈⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⣿⡏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⣄⣉⣉⠉⠉⠉⠉⠉⠍⢩⡄⢬⣵⣶⣶⣾⣾⣿⡇⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡼⠟⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢐⠉⢸⡀⡤⠤⡔⠁⠙⡄⠀⠀⠀⠀⠀⠠⠀⡀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠜⢆⠀⢸⠀⠀⢻⣤⢼⡀⠀⠀⠀⠀⠀⠀⠈⠀⡖⠛⠤⣓⡖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠈⠦⡤⠎⢀⠑⢍⡢⢄⠀⠀⠀⠀⠀⠀⢸⠀⢞⢣⡙⢄⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⡦⠀⠀⡸⠀⡀⠠⡎⠻⣀⠳⣄⠉⠢⡈⠲⡀⠀⠀⣀⡤⠃⣈⣦⡹⠚⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣔⣊⠁⠀⠘⡿⢾⡳⡀⢱⠀⠈⠣⣮⣑⡲⠞⣰⠃⡠⠚⠁⢷⡞⠴⣁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⢤⡤⢄⡀⠻⠿⢃⡱⡀⢇⢸⣉⠀⠀⠀⣴⠵⠋⠀⢀⣠⠄⠃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠑⢆⣳⡌⠋⠀⣀⡴⠚⠁⣀⠴⢊⣡⠃⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣈⡹⠖⠊⣁⢠⠖⠉⠀⡉⠤⠤⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣠⢶⠋⠀⡜⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠁⡌⠀⢀⠁⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⢸⠀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠅⠀⢸⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠓⠒⢺⠀⠀⢀⡠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⣨⠀⠀⠈⠒⠈⠁⠀⡇⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡧⣪⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⢲⣶⠂⠈⠁⠸⣉⠗⠙⠚⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡄⠀⠀⠀⠀⠀⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡰⡀⠀⠀⠀⠀⢧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠲⡖⠂⣃⣴⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠤⠄⠒⠊⠉⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣷⣶⣶⣿⣿⣿⣷⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣟⡛⢉⣁⣀⠀⢠⣤⣤⢬⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣯⣬⣿⣿⢛⣿⣴⣿⣿⣉⣾⣿⣧⣤⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡋⣝⣿⣾⣿⣏⣄⠿⢿⣿⡟⣷⣄⣹⠛⠿⢿⡇⠀⠀⠀⠀⠀⠀⡞⠛⠋⠻⣿⡟⠛⠂
⣿⣿⣟⢛⣿⣄⣸⣿⡿⢿⣿⣿⣿⣿⡛⠛⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣄
⣿⣿⣿⣷⡟⠍⢛⣿⣷⣬⣥⣿⣁⡉⣿⠿⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣀⣀⣄⣀⣀⣀⡏⠀⠀⠀⠀⣶
⣿⣯⡉⢟⣿⣿⣿⣇⣰⣾⣄⣹⡿⢿⢛⢶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣉⣷⣆⢉⣭⠉
⣿⣿⢿⣿⣯⣬⣼⣏⢹⣻⣿⣿⡷⢾⣿⣟⠻⣿⣿⣇⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤
⣿⣷⣦⣭⣽⡇⢸⣿⠛⣙⣿⣯⣥⣾⣷⣦⢼⣿⣿⣷⠀⠠⠠⣿⡏⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀
⣿⣿⣷⣜⣿⣿⣿⠛⣿⣿⠟⢣⣥⣿⣴⣯⣶⣿⣿⣿⠀⠀⢠⣿⡇⣸⣷⢸⣿⣿⣿⣿⣿⣷⣶⣾⡇⠐⡒
⣿⡿⠛⠉⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠉⠈⠻⢿⣿⣿⠄⠀⠈⠉⠱⠉⠉⠖⢿⠏⠉⠉⠁⠉⠉⠉⠉⠀⠈
⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠚⠛⠛⠛⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡂⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠉⠰⠄⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⠂⠢⠤⢀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠱⣀⣀⠀⠀⠠⠤⠤⠤⠄⠈⠒⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⠀⠀⣀⡀⢰⣶⡆⢠⣄⣀⣤⠀⠀⣼⠓⠒⠒⡞⣷⡀⠰⢤⣴⡄⢰⣦⠀⢀⢀⣀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⠆⢠⠏⠲⠟⠀⢥⣾⡁⣸⣟⠧⢸⣇⣼⣀⡀⠿⠙⣷⡿⢋⡉⢿⣾⣍⣧⣜⡏⣹⣧⠀⣠⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡴⣆⣤⣄⣤⡄⢤⣤⢼⣿⣸⣿⠈⠳⡏⠻⡟⢩⡌⢠⣸⡷⠻⣇⠘⠛⠀⠈⠙⠿⢿⣽⣿⣿⣏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣉⣛⠿⠉⢿⣯⣿⣿⡏⠀⠻⠿⠟⢓⠋⢠⣦⡏⢻⡇⠹⠟⠀⠄⠀⠀⠀⣐⡀⠀⠀⡤⣄⣈⢙⣫⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣸⣿⣧⣽⣧⢿⡏⢘⠿⣿⣟⡙⢾⣷⢯⣽⣧⠈⣧⠁⢲⡇⢤⣖⠈⣽⢛⣿⣯⣿⠀⢹⣿⢛⢿⣦⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⣿⣧⣬⣇⣸⣯⣿⣤⣤⣿⣿⣷⣿⣷⣖⠛⠛⢻⣿⣿⣿⣴⣇⣿⣾⣿⣾⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠛⠲⠿⠿⢿⣿⣿⣿⡿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⠟⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠁⠀⠀⠉⠙⠻⣿⣿⣟⣩⣤⣠⣴⠲⢲⣄⢀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡶⠿⠖⠛⠋⠉⠁⠀⠀⠀⠈⠉⣽⠒⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⠈⠝⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⣰⠆⠀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⡋⠹⠉⠻⠃⣤⡐⠿⠛⠷⢤⣄⣀⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⠖⠉⠀⠀⠀⠀⢰⠇⣼⠀⠀⢸⠀⣇⠀⠀⠀⠀⠈⠉⠻⢷⣶⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⣠⡟⠀⣿⠀⠀⠈⣧⠈⢣⡄⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠿⣤⣴⣿⣀⣀⡀⣻⣧⣀⣿⠶⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠐⠂⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠄
⠀⠀⡠⠠⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⢤⠀⠀⠀⠀⠤⠄⣐⠈⢀⡀⠀⠀⠀⠐
⠀⠀⠱⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠖⠄⢀⡐⣀⠀⠀⠀⠀⠀⠲⡀⠀⠀⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠨⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀⠀⠀⠢⣀⣈⡄⠀⡀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⡐⡇
⠀⠀⠀⠀⠀⠀⠀⣀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀⢀⣸⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢤⠁
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠤⠄⠀⣀⡤⠤⠦⣄⣀⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠰⠀⢁⠀⠀⠀⠀⠀⠀⠄⠂⠁⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠖⣆⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌⠀⠁⠀⠀⠀⠀⠀⣀⠄⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢈⠀⡠⠔⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡁⠸⠀⠀⡀⠀⠀⠀⡤⠒⠈⠁⠀⠀⡠⠃⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠲⡄⠀⠑⠂⠩⠀⡄⢀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠔⠛⠧⠀⡄⠀⠀⠆⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢃⠀⠀⠀⠑⠂⠰⠧⣤⣠⠂⠀⠈⠢⣀⠀⢀⠔⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠄⠀⡀⢀⠀⠀⢈⠀⠈⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠋⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⠉⠙⣛⣀⡀⠀⠈⠛⢃⣀⢀⣀⣀⣀⣀⣠⡴⠞⠉⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢩⢼⡓⣀⠀⠀⠈⠀⠘⠫⠈⢉⠉⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⢄⢹⡂⠑⠤⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠤⡀⠀⢀⠌⠓⠀⠀⠂⠩⠀⣀⠚⠡⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣄⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⢀⣄⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠈⡡⠛⠀⠀⠀⠀⠀⠀⠀⠔⠁⢈⡀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠉⠙⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠁⠐⠠⠄⢀⠀⢀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⢊⠳⣀⠀⠀⠀⠁⠀⠀⠀⠁⠒⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⢀⡠⠴⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣴⡿⠋⠀⠉⠉⠛⠷⠀⠀⢠⠒⠉⠀⠀⠈⠛⢷⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣤⣼⡟⠀⠀⠀⢀⣀⡀⠀⢡⢠⠃⠀⡀⣄⡀⠀⠀⠈⣿⣤⣴⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢈⠝⢻⡇⠀⠀⠀⠻⣾⠇⠀⢸⣹⠀⠀⠷⡿⠇⠀⠀⠀⣿⣏⠁⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠠⠊⢿⣦⡀⠀⠀⠀⠀⠐⠃⠈⠑⢤⡀⠀⠀⠀⣀⣼⢏⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡱⠁⡰⠁⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⢀⠛⠻⠟⠛⠋⠁⠀⠡⡀⠹⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡰⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠹⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡇
⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢀⠇
⠀⠀⠀⠀⠀⠀⠘⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠙⣝⣴⢷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⡿⣞⣩⠉⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠙⠒⠒⠘⠓⠉⠉⠋⠉⠉⠉⠉⠉⠉⠙⠉⠑⠚⠁⠒⠚⠋⠓⠚

⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡆
⣴⣶⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣆⠀⠀⠀⠀⠀⢠⣶⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⡀
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⢻⣿⣿⢿⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧
⠛⣿⣿⣿⠛⠀⣰⣷⡀⠀⠀⣰⣗⡀⢛⣿⣿⣿⣿⠃⠀⠀⠀⠘⠃⢺⣿⣿⠘⢧⣾⣦⡶⣴⣷⡼⣻⣿⣿⣿⡟
⠀⣿⣿⣿⠀⠰⢻⣿⠻⠀⢼⣿⣿⡷⠈⢹⣿⣿⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢨⣿⣿⠀⢹⣿⠁⠉⣿⣿⡏⠁
⠀⣿⣿⣿⠀⠀⢸⣿⠀⠀⠈⣽⣿⠁⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⣿⡏⠀⢸⣿⠀⠀⣿⣿⡇
⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠁⠀⠈⠉⠀⠀⠈⠈⠁
⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⠀⠀⣠⣤⡀
⠀⣀⣻⣟⡀⠀⠀⠀⠀⢀⣘⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣟⣀⠀⢀⣙⣿⣁
⢠⣿⣿⣿⣿⡀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⢠⣶⣤⣴⣦⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⣾⣿⣿⣿⡆
⡾⣿⣿⣿⣿⣧⢠⣄⠰⠏⣿⣿⣿⠹⡆⣤⡄⠀⠸⣿⣿⣿⡿⠀⠀⣤⡄⡾⠁⣿⣿⡇⢿⣿⣿⣿⣿⣿⣠⣤
⠐⢻⣿⣿⠛⠘⣿⣿⣆⠀⣿⣿⣿⠀⢹⣿⣷⡄⠀⠈⠛⠋⠀⠀⣰⣿⡿⠁⠀⣿⣿⡇⠀⠛⣿⣿⡟⠃⢻⣿⣷
⠀⢸⣿⣿⠀⠀⣿⣿⠈⠀⣿⣿⣿⠀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠁⣿⡟⠀⠀⣿⣿⡇⠀⠀⣿⣿⡇⠀⢻⣿⠟
⠀⠘⠛⠛⠀⠀⠛⠛⠀⠀⠛⠛⠛⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠛⠛⠃⠀⠀⠛⠛⠃⠀⠘⠛⠁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢿⡿⠂⠀⠀⠀⠀⠀⠸⣿⠗⠀⠀⠀⠀⢿⣿⠇⠀⠀⠸⣿⠇⠀⠀⠀⠀⢿⡿⠂⠀⠀⠀⠀⠀⠸⣿⡿
⠀⣾⣿⣿⣿⡄⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡆⢰⣿⣿⣿⡆⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣆
⣸⠏⣿⣿⡟⣧⠀⣀⢀⣿⣿⣿⣿⣿⡀⢰⡏⣿⣿⡏⣷⣿⣿⣿⣿⣿⡀⣸⠏⣿⣿⡏⣷⠀⣀⠀⣾⣿⣿⣿⣿
⠉⠀⣿⣿⡇⠘⣮⣿⡞⢽⣿⣿⣿⡏⠁⠈⠀⣿⣿⡇⠈⢽⣿⣿⣿⡏⠁⠉⠀⣿⣿⡇⠈⢯⣿⡽⢹⣿⣿⣿⡯
⠀⠀⣿⣿⡇⠀⣾⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⣾⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇
⠀⠀⣿⢿⠇⠀⢸⣿⠀⠀⢸⢿⡇⠀⠀⠀⠀⣿⢿⡇⠀⠀⢿⢿⡇⠀⠀⠀⠀⣿⢿⡇⠀⢸⣿⡇⠀⢸⡿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠐⢦⡄⠒⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠲⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠄⠐⠒⢦⡀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⣉⠀⠀⣠⣤⣀⡴⠶⠶⠊⠁⢀⠀⢀⣤⡄⠀⠙⠆⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢘⣏⠀⠉⠀⠀⢤⡴⠟⠉⠓⠚⠛⠁⠀⠀⣦⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠷⠆⠀⣀⠴⠶⠚⠛⠳⢶⡀⠀⠀⠀⢈⠇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠲⠆⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠃⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⠆⢠⣾⣿⣦⠀⠀⠀⡸⠃⠀⠀⢠⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠛⠳⠄⠙⠛⠁⣀⣴⠞⠁⠀⠀⠀⠀⠵⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⡶⠂⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⡖⠒⠂⠉⠀⠀⢠⡜⠀⠀⠀⣰⠟⢀⣤⡀⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠈⠁⠀⠀⢀⡼⠃⠀⣀⣀⣈⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⡀⠀⠀⣤⠟⠁⠰⠛⠉⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢲⣄⠀⠘⠄⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠦⠂⠤⣈⠙⠿⠶⠶⠶⠤⣠⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⢀⣠⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢸⡇⠀⣀⣀⠤⠤⠤⠐⠒⠂⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢈⣿⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡄⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢹⣦⣠⡤⠖⠒⠒⠀⠒⠒⠒⠂⠀⠀⠀⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀⠀⠀⣠⡔⠉⢠⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠀⠀⠀⠉⠳⣆⣘⠀⠀⠀⠋⢿⣄⡀⣀⡀⠀⡀⢀⣀⠀⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡀⠀⠀⠀⠀⠻⡇⠀⢀⣶⡶⠉⠋⠛⣧⡀⠀⠉⠙⠃⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⣀⠀⠀⠀⢸⠀⢠⡅⠀⠀⣤⠄⠈⠛⠛⠒⠛⠛⠂⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡴⠀⡀⠀⡟⠉⠀⡇⠀⠀⠀⠀⠀⣴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡃⠀⡇⠀⠀⢳⡀⠀⠀⣀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠠⠗⠛⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠘⣿⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣸⣷⣠⠔⠶⠖⠀⠖⠊⠉⠉⠉⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⣠⣄⡀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣧⠞⠀⠀⠀⠀⠃⠀⢸⠀⠀⠈⢻⡀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⠟⢿⣧⣤⠤⠀⠒⠛⢳⡿⣦⣤⣤⡿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢹⡏⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⠄⠀⠤⠀⠀⠚⠛⠛⠛⠀⣰⣿⣄⡀⠀⠈⢁⡀⣀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠶⠶⠶⠶⠂⠈⠉⠉⠉⠀⠉⢶⣈⣉⠉⠉⠉⠉⠉⠁⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⡿⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡌⢁⣀⣉⣿⡀⣠⣮⢀⢈⣷⡌⣁⣴⣼⠛⣰⣆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠎⠸⣇⠀⠀⠸⠀⠀⢰⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⢀⡾⠋⠀⠀⣿⠖⢀⡐⠀⠐⢁⣢⠟⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢸⣏⡁⢠⡞⡁⢿⡟⢣⢆⢲⣄⣼⠿⠃⠀⡴⠂⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⢣⣟⣼⢃⣿⣯⢜⣿⣾⣸⣿⡽⣇⠼⣁⠰⣀⠀⣨⣷⣨⣁⠀⣠⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣴⣆⠰⣾⣿⠿⢋⣿⡟⢨⣎⣿⣽⣾⡷⢋⡆⠆⠂⠉⣄⠿⠙⢉⠄⠀⡽⢛⡓
⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⣾⣽⡟⣆⣿⢻⢸⣿⡏⣧⣼⣯⣾⡿⡏⢿⠃⢽⣆⢠⠆⡹⢴⡺⣡⠄⡼⠓⡿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⢿⣷⣹⢿⣻⣸⣿⣄⣿⣷⣿⢿⣃⠙⣬⣦⢾⡁⣸⢡⣿⢗⣯⠋⣴⣳⣻⣛⡶⡴⢉⡄
⠀⠀⠀⠀⠀⠐⠀⣀⠀⡘⢿⣘⣷⡟⢻⣿⣯⣸⡿⢏⢮⣿⣼⡃⣠⠉⢿⣿⣼⠉⢾⢳⢹⣏⣰⡏⣰⠿⡿⠁⣴⣼⣧
⠀⠀⠀⠀⠀⠢⣶⡿⣤⠙⠄⣿⣼⣰⠟⠑⠈⣿⣷⣿⣽⡋⣿⣽⠛⢢⣼⡿⣡⡄⡚⢠⣾⠡⣾⣻⣏⣼⠷⣿⡭⢆⣶
⠀⠀⠀⠀⠈⠢⣉⣙⡾⣗⢦⡈⢿⣃⢷⣴⣻⣷⠉⣮⢿⣦⣿⢣⡵⡟⣹⠷⣄⢸⣿⡿⣯⣾⣿⣿⣭⠞⡻⣿⢶⢯⣿⡆
⠀⠀⠀⠀⠀⠢⣌⠫⣉⣛⠳⣽⣿⣿⣌⠻⣽⣧⣾⠁⠻⣿⣿⠏⣼⡔⣽⣰⠋⢻⣿⠋⢹⢹⡡⢾⢇⡼⢡⡿⠋⣼⡿⠁
⠀⠀⠀⠀⠀⢀⠀⡀⠽⠾⣟⣻⡿⣿⣿⡄⣿⠏⠈⢳⣇⣽⣏⡾⡟⢀⣿⣫⢦⣦⣿⣦⠈⣸⢁⣾⢪⢟⠁⣀⣴⣫⠔
⠀⠀⠀⠀⠀⠀⠰⣞⣦⢦⠀⣻⢯⣛⢿⣿⡟⠛⡙⣦⠹⣿⡟⢰⣷⢟⡿⢻⣾⠉⣿⣿⢳⣿⠋⢄⣞⣵⠊⣽⠿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣤⣿⡴⢻⣿⣿⣧⠞⠓⢾⣴⣿⣧⣾⡿⣠⣿⣿⠏⠰⣿⠘⣿⣿⣰⢞⡽⢹⢏⣴⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⣷⡟⣳⣿⢿⣿⣇⠰⣶⡄⣿⣿⡿⡿⢄⣹⡟⣻⡂⢄⣿⣰⠍⣿⣫⣿⢃⡿⢻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁⢸⣿⣥⢳⣍⢿⣿⣿⣹⣟⢠⣿⢿⣿⣧⣼⣿⢻⣄⣻⢇⣷⢋⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⢸⣿⣡⡾⠛⢆⣿⣿⣇⣮⡾⣿⣿⢟⣧⡞⣿⣌⣿⣿⢟⣽⡿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠈⣿⣿⣿⠋⢹⣿⡷⣿⣿⠞⣿⡿⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⣿⣿⡇⠀⢨⣿⣷⠏⠁⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠻⠏⠉⠀⠀⠀⠀⢀⠲⣿⣷⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⡠⣆⡄⠀⠁⠀⢦⡄⠈⠙⠛⠳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⣀⠠⠤⢂⡰⣣⣮⢷⣩⡥⠤⠄⠈⠁⠒⠰⠶⠆⢉⢆⡀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⢖⣯⣵⣏⣇⣿⣾⢿⡟⣢⠁⡔⠀⠠⠐⠀⠀⡄⠘⠬⢵⢋⡴⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⢀⣤⣄⣁⡉⢋⢽⣿⣿⣟⣫⣿⠻⣧⠀⠓⡠⢉⠧⢦⣧⠀⠠⣀⣤⠋⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠯⡷⡿⣿⡇⣹⣺⡯⣬⡯⢿⣿⡦⠍⣰⡆⢣⣈⠙⠂⠁⠅⢀⠜⠉⠡⠄⢠⡴⠶⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢷⣾⣿⣿⣿⢿⢉⣿⡞⠕⢡⣧⠴⠊⠹⡙⠀⢹⡖⢲⣔⣶⡂⠀⠀⠐⣦⠛⣃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡽⣷⣯⣿⣽⣐⣿⠛⡢⠺⠋⣉⣁⡀⡙⢤⣹⠘⡉⢦⣼⣯⡶⠈⢆⣼⠋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⣻⣹⣿⣿⣟⣷⡿⣴⢏⣠⠖⠋⠉⠀⠈⠉⢷⣟⢀⡷⠳⣼⠟⡉⣓⣾⡋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⡫⢷⡧⣯⡝⣿⣯⣿⣿⣿⠀⢀⠀⠀⠀⠀⠈⣿⡿⡻⢄⣹⠞⣱⣼⠷⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣻⣿⣭⣗⣯⣏⣷⡫⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣿⢰⡴⣌⢹⡼⣤⣏⡱⠊⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣿⡿⢯⣻⡟⣯⡝⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣦⠙⣾⣉⢻⡤⠆⢸⣶⡒⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⠚⠋⣳⣿⡐⣿⠁⠀⠀⠀⠀⠀⠀⠶⠟⠋⣰⢋⣴⣇⠛⣾⡅⡂⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣦⣀⢸⢸⣿⠀⠀⠀⠀⠀⢑⠄⠀⢠⣾⣿⣦⣹⢯⢟⢻⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠛⠌⠛⣾⢿⡄⠀⠀⠀⠠⠀⠀⠀⠀⢰⣽⣿⣿⣧⣃⢜⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢾⠑⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢻⢏⡴⢊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂⢻⡿⣦⡀⠀⠀⠀⠀⢀⣆⠀⢈⡠⢻⣟⣉⠭⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⡜⠄⣿⠛⠲⣶⠲⣺⠟⢳⣿⣠⣂⣏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⣱⠋⢉⠽⣿⣗⡉⠙⢣⡤⠔⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢰⠋⠀⣜⠀⠉⢣⡀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠐⠊⠉⠓⠰⠖⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠃⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣴⠟⠛⠛⠛⠛⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣰⡏⠀⠀⣀⣀⡀⠀⢀⣈⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡼⣿⡧⠀⠀⠤⢔⠀⠀⣭⠌⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡏⠃⠀⠀⠀⠀⢀⠀⢉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠂⢤⡤⠤⣤⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠈⠀⠀⠀⠠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢧⡀⠀⠄⣤⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣻⣯⣿⣺⡿⣶⣢⣤⡉⣿⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣯⣿⠻⣾⣭⡿⣷⣟⠛⣿⣿⣾⣿⣿⣿⣿⣝⣷⠦⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢛⣿⣟⣻⠿⢿⣟⣯⣿⣷⠾⣿⣿⣉⣿⣧⡬⢿⣿⣻⣿⣬⣿⣟⣻⣟⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣩⡟⢿⣶⣏⡽⡷⠋⢕⡠⠤⠐⢈⢦⡿⣷⡶⢿⣯⣙⣿⣦⢿⣯⠿⣷⣻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣏⣹⠿⣿⣿⣭⡟⣻⠶⣵⣩⣜⣭⢤⣤⣤⣷⣿⣷⡞⢿⣯⣽⣿⣷⢻⣷⣛⣿⣯⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣨⡟⢻⣿⣦⣞⣹⣟⡿⢿⣾⣿⡿⠟⠛⠿⠿⠿⠧⠼⠿⠿⠛⠓⠚⠻⣿⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⡋⣿⠿⣾⣧⣼⠛⢿⣿⣷⣯⣾⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣾⠷⣿⣳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣻⣿⢦⣿⣯⣿⠟⣿⣷⣿⣹⣏⣿⠞⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠌⠙⣭⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣯⣹⣶⢻⣏⣿⣿⠿⣿⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣷⡼⢿⡛⣧⣽⣷⡞⣿⣿⣽⣿⣷⣶⣶⣶⢶⣟⣿⡛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣹⡾⢿⣹⡷⢾⣟⣹⣿⡼⢿⣉⣿⣶⢿⣏⣻⡙⣿⣹⡟⣿⢶⣤⣤⣤⣤⣶⣖⣾⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣡⠿⣾⣹⢷⣟⣿⣯⣿⣾⢿⣿⣿⣟⣿⠿⢯⣿⢻⡿⣷⡿⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⡽⢾⢭⣿⣾⣿⣿⣿⣿⣿⣏⢸⣿⣿⡇⢾⣿⢼⣿⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠀⠟⢻⠹⢍⠀⠀⠀⠈⠀⠀⠀⠘⠛⠒⠋⠙⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡇⠅⠀⠑⠀⠀⠀⠀⠀⠀⢠⢘⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⢂⡌⢻⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡔⢀⣴⣿⣿⠿⣯⠉⠋⡀⠈⠛⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⣰⣾⢳⡎⣣⣸⣿⡿⢿⡷⠾⢿⣅⣀⠘⢷⠉⢸⡁⠀⣠⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⣋⠋⣉⣢⣦⣾⣟⠻⣯⣾⣻⣤⣡⡀⣈⣀⡀⠛⠉⢉⣷⣏⣿⣿⣿⣷⠿⠊⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢋⠼⣡⣼⣏⣡⣶⣟⠁⣼⣿⣧⣄⣨⣽⡓⢉⣬⡄⢓⠙⠓⡀⠉⢻⣖⠛⠋⢥⠀⠈⠥⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⣿⣿⣿⣿⣿⣿⣿⡶⣿⣿⣿⡛⣉⠟⣿⡛⡛⣿⣏⠀⣶⡤⣆⠉⣦⠈⠘⠉⠤⣏⣽⢀⣽⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⠠⡓⢈⣯⣤⣾⣷⣿⣻⣿⣾⣿⣿⠿⠾⣯⡴⢿⣷⣿⢿⣾⣿⣷⣹⣾⡦⠇⠀⠀⠀⠁⢿⡚⠡⠠⠴⡆
⠀⠀⠀⠀⠀⠀⢰⣯⣁⣾⣿⠇⣹⣿⣿⣏⢱⣿⠿⠏⢠⣽⣯⡴⢶⣦⣶⣢⣄⠀⠈⣥⡀⠈⠀⢙⠿⡆⠀⠀⣤⣄⣮⣹⠶⢄⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⣿⢱⣿⣿⣏⡟⠙⣿⣷⣧⣾⣿⣧⣴⣹⣏⡀⠠⡍⢉⣴⣿⠀⢀⡶⠀⢛⣿⣷⢧⣞⠿⠏⢥⣤⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣶⢷⢾⣿⣿⠋⡛⢿⣷⣷⣿⣿⣛⣻⣿⣻⣿⣿⣷⣴⣷⣾⣿⡟⠛⢾⣿⣞⣿⣥⣿⣷⣿⣿⡇⣾⡷⠓⠉⠁
⠀⠀⠀⠀⠀⣤⣴⣿⣿⢿⡼⢿⣿⣿⣷⣠⣿⡹⣿⣷⡮⡤⢾⣿⣼⣜⠙⢛⣿⡿⣻⣿⠁⣞⣯⠟⠿⠧⠻⢿⣿⠁⠀⢈⣽⡀⡀
⠀⠀⠀⠀⠀⠈⠁⠼⠿⣿⣧⣿⣼⣿⣿⣷⣿⣿⣿⣭⣭⣷⣾⣿⣿⣀⣙⢿⣿⡏⣹⣷⡆⠳⡶⢶⡶⠖⠀⠀⠀⢶⣴⠦⣂⡂⡨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⡉⠀⠀⣨⢻⣿⣿⠿⠫⠋⠉⠛⢿⣿⣿⣅⠑⢷⠟⢿⣿⠶⣶⢈⡁⢻⠛⠁⠀⠀⣤⢀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠁⠉⠀⠈⠛⢷⣿⣿⡾⣾⠖⠀⠀⠀⣿⣿⡙⣎⠾⡆⠈⠁⠓⠛⣼⣿⣿⠁⠀⢀⡀⡀⣀⡤⢌⠀⣀
⠀⠀⠀⣠⣄⠀⣀⡤⢄⡉⠀⣁⠈⣀⣁⡀⠸⢶⣰⠀⠁⣀⣂⡂⠀⣿⣿⠇⠈⠠⣇⠠⠾⠦⣀⣀⠠⡤⠶⡐⢟⠿⡚⠛⠿⠚⠛⠊⠤
⠀⠀⠤⣬⠀⢾⣷⢟⣰⡎⢳⡉⣼⢫⡯⡙⣦⠰⢀⣴⠲⢤⣀⣄⢰⣷⣿⡀⢠⠇⣻⠀⡀⠀⠈⣀⣠⡀⠀⠈⠀⠁⠀⠀⠄⠨⠀⠡
⠀⠀⠀⠂⢢⠙⠛⠛⢛⣟⠿⡃⠹⠛⣿⠻⣯⡇⠼⢿⢶⡾⠇⢩⣿⢋⡿⠀⣼⡌⢹⣆⠨⢇⠾⣯⣵⣄⣹⢀⣾⣍⢲⡀⢄⣄⠀⠁
⠀⠀⠀⠀⠈⠒⠀⠉⠁⠈⣀⣀⠚⠉⠁⢁⣚⣀⣠⣴⣾⣿⣿⣿⣿⠾⢁⠼⠿⠷⣦⣙⡗⠾⠶⢮⣬⣬⣉⣙⣡⣏⡙⠷⠿⠶⣧⠰⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠐⠒⣟⡙⢛⡋⠙⠛⢻⡿⠏⣿⠟⢛⡉⠀⠋⠁⠀⠀⠀⡀⠀⠀⠀⠉⠛⠳⠾⠙⠒⠒⠆⠉⢉⠉⡉⠓⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⠃⠶⠤⠤⠀⢤⣬⠻⠿⠓⠀⠂⠤⠤⣀⡤⠒⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘