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⋆⁺₊⋆ ❄ ⁺₊⋆ ❄ ₊⁺ ⋆
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣦⣤⣾⠟⠁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⢀⠀⠀⠀⢀⠀⠀⢻⡿⠃⠀⣀⠀⠀⠀⠀⠀⠘⢿⣆⠀⢀⣿⣿⣶⣶⣶⣶⡆⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣼⠀⠀⠀⠻⣷⣦⣼⣧⣤⣾⠏⠀⠀⠀⠀⠀⠀⠘⣿⣴⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀
⠀⠀⢠⣦⣤⣀⣸⣿⡀⢰⣿⠀⠀⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠿⢿⣿⠇⠀⠀⠀⠀
⠀⠀⠈⠉⠉⠉⠛⢻⣿⣿⣿⡀⠀⠀⡀⠀⠀⢠⣿⡄⢀⡀⠀⣶⡄⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠿⠟⠛⠛⠿⣷⣄⣸⡿⠒⢿⣾⣿⣷⡿⠃⠀⠹⣿⣴⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⡀⠀⠈⣿⡏⠀⠀⠀⣠⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⢠⣿⠀⢀⣶⠀⠀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⣿⡇⠀⢀⣼⡿⠃⠀⠀⠀⢀⣴⠇⠀⠀⢰⣿⠃⣠⣿⠟⠀⠀
⢀⣀⠀⠀⠀⠹⣿⣄⠀⠀⠀⣆⠀⠀⠀⠀⠙⢿⣿⣧⣴⣿⣏⣀⣀⣀⣀⣤⣾⣿⣤⣤⣶⣿⣿⣾⣿⣧⣀⠀⠀
⠘⠻⣷⣄⣀⠀⠈⢿⣷⣄⣀⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⢿⣿⠉⠉⠻⣿⣄⡈⠙⠿⣷⡄
⠀⠀⣸⣿⡿⠿⠿⣿⣿⡿⠛⠛⣿⡿⠋⠉⢀⣾⣿⣿⠉⠻⣿⣶⣄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣿⡆⠀⠈⠁
⠰⠿⠛⠁⠀⠀⣴⡿⠋⠀⠀⢰⢟⠁⠀⣠⣾⠋⠘⣿⠀⠀⠀⠙⢿⣷⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⣿⡆⠀⠀⠀⠈⣿⡿⢿⣧⣄⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠺⣶⣦⣤⣤⣴⣿⠟⣿⠇⠀⠀⣹⣇⠀⠀⠀⠀⠿⠃⠀⠹⣿⣿⣿⡿⠛⢛⣫⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡇⠀⠀⠀⣠⣼⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⡿⠟⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣷⣶⣿⡿⠋⣿⠁⠀⠀⠀⠛⠉⢹⣿⠛⠛⠀⠀⠀⠀⠀⠀⠻⡇⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢻⣿⡍⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢠⣿⠟⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠀⣀⢀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⡀⢀⢀⣀⡀⠀⠀⢤⠀⡤⣤⢠⡄⣠⢠⡤⣤⣠⣄⣠⠀⢄⠀
⠀⠀⠂⠃⠛⠛⠓⠃⠓⠚⠘⠛⠛⢚⠛⠚⠓⠘⠂⠓⠛⠃⠃⠀⠀⠒⠈⠛⠓⠐⠊⢙⠑⠚⠓⠛⢚⠓⠛⠋⠀
⡏⣏⠉⡍⠉⠉⠉⠉⠉⠁⠉⠈⠁⠉⠀⠁⠈⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠈⠀⠉⠈⠁⠉⠉⠉⠉⠈⠉⢹
⡗⡌⠥⠠⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⢸
⡗⡌⠤⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣾⣇⡀⢀⢔⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣚⡷⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣺⣞⣅⣆⠎⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠋⢲⣼⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣏⠤⣠⡀⠀⠀⠀⠀⠄⢌⠢⠀⠀⠀⠀⠈⣨⣿⠋⠁⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⠀⠨⣿⢶⠃⠁⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠈⣰⡿⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢿⢷⡀⠁⠠⠂⠀⢀⢄⡀⢠⣢⢀⣼⣿⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣳⡄⡌⡀⠀⠀⠀⢄⠏⠙⡟⣝⠁⠀⢄⠄⠤⠴⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⢻⢳⣵⢋⠀⠀⠀⠀⢠⣾⡏⠅⠒⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢰⠀⠀⢂⠈⠂⢊⠉⠀⡠⠀⠛⡩⣦⠀⠀⢠⡯⣿⣛⠄⠉⠉⠀⠐⠠⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰
⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠠⠣⠀⠀⢄⠀⠠⢀⠀⠉⠀⠀⠟⡛⠃⠀⣸⡾⢿⠠⠁⠀⢠⡴⠱⢁⠂⠂⡀⠂⠄⠀⡀⠀⠄⢂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰
⠆⠀⠀⠀⠀⠀⣀⢀⡀⣀⣤⡴⣾⣄⣀⣤⣀⣡⣄⣆⣄⣀⣄⣂⢃⢑⣆⣦⡤⠄⢈⡌⣦⠳⡋⡠⢤⣄⣀⣿⣀⣴⢍⣀⣀⣀⣐⣁⣰⣀⢎⣄⣮⣤⣀⡀⠀⢀⡀⠀⠀⠰
⠆⠀⠀⠀⠀⠘⠂⠄⠄⢰⡗⠳⣦⢷⠹⠳⠓⢶⠾⠻⠐⠖⠖⡳⠪⣭⡼⠟⠖⠒⢖⡸⡪⢃⠒⠲⠻⠦⡶⢸⢛⢐⠂⠛⠙⠓⠛⠟⠐⠟⢚⢝⢏⡫⠘⡍⠉⠙⠉⠀⠀⠰
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢠⠎⠀⠀⠀⠄⠖⠡⠡⠸⠃⠃⠀⢂⣞⠶⠢⣳⣥⣐⠀⠀⠐⠰⠃⢀⠁⠄⠁⡀⢠⠀⠀⢁⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠸⠀⠐⠡⠁⠀⠀⠀⣴⣿⡫⠃⠀⠰⣽⡻⡸⢀⠀⠀⠀⠀⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠈⠀⠈⢭⣷⠿⠋⢆⢄⢠⠛⢗⡹⣅⡀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠨⠀⠁⢃⡪⢂⢙⢾⣆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⢨
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⠇⠁⠈⠀⠀⠠⡱⠡⠃⠀⠀⢟⣆⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠀⣰⣶⠁⠀⠀⠀⠀⠂⡴⠀⠐⠀⠀⢠⠈⢯⣧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠣⡐⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠠⠊⡻⡷⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⢐⠎⡟⡁⠀⠆⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⢻⣷⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⡟⠃⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⣨⢳⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡽⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⠠⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸
⡇⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⢸
⣇⣎⣐⣄⣂⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣐⣈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣰⡟⠿⣶⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⠳⣿⢀⢠⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⠀⠀⣠⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⠀⠀⣿⡁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣄⣀⡇⢸⡇⠀⠀⢀⣤⣀⠀⢺⡟⠳⣦⣿⠀⠀⣿⣧⠾⢋⣿⠀⠀⠀⠀⠀⠀⢸⡏⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣟⠉⢛⣷⢸⣷⡀⠀⢸⠁⢿⡆⠀⠙⢳⣄⡙⠳⠘⣋⣠⡼⠟⠃⠀⣴⠾⣦⠀⠀⢸⡇⢸⡿⠟⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⣛⣿⣆⣤⠀⠙⠻⢦⣸⡄⢸⡇⠀⠀⠀⠈⣿⠁⠀⣿⠋⠀⠀⠀⠀⣿⠀⣿⣀⣴⠾⠇⠀⠀⢠⣦⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⣋⣡⡾⠟⠶⣦⣀⠀⠉⠷⠘⣷⡀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⢀⣿⡄⠿⠋⠀⢀⣤⡶⠶⢦⣬⣩⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠙⠁⠀⠀⢠⣬⡿⠛⢋⣀⠀⠈⠛⢷⣤⡾⠋⠈⠀⠙⠻⢦⣤⡶⠛⣭⡀⠀⠤⢾⣿⣅⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣧⣴⠟⠛⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠟⠛⠶⢤⣄⡉⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⡟⠶⢦⣄⣀⠀⢀⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⡀⠀⠀⢀⣠⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⡙⠛⠛⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠉⠛⣶⠞⢛⣡⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣠⡾⠛⢦⣤⣀⣠⡴⠟⠉⠁⠀⣤⡼⠟⠋⠙⠻⣶⠤⢤⣴⠟⠛⠙⠳⣦⣤⠀⠈⠛⢷⣦⡀⢀⣤⡴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⣳⣶⠾⠉⠉⠀⣀⣤⢾⠁⣿⡇⠀⠀⠀⠀⣿⠀⢀⣿⡄⠀⠀⠀⠘⣷⠙⣶⣄⠀⠈⠙⢫⣥⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣾⠋⠀⢀⡤⢸⡟⠉⠀⣼⣀⣿⠃⠀⠀⣠⣾⣟⠈⢈⡛⢷⣄⡀⠀⠀⢿⡀⣿⠉⠻⢷⣄⠀⠈⠙⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠓⠚⠛⡇⢸⡇⠀⠀⠈⠛⠉⠀⢸⡟⠋⣠⣿⠂⢸⣿⣧⡈⠛⣶⠀⠸⣧⣿⠇⠀⠀⢿⠈⣷⣤⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠈⠘⠿⠛⠁⣿⠀⠰⣿⡄⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠠⠰⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢉⣵⠀⠀⣶⡌⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⣿⡀⠀⣿⠝⠻⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⣤⣤⣤⣦⣶⣦⣤⣴⣷⢦⡴⣶⣶⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⢈⠉⠉⢀⣀⡉⣁⢁⡁⠉⠈⢉⡉⠉⢁⡉⡁⣈⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢟⡺⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠰⡄⠀⠀⢠⢄⣹⠸⣥⢤⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠀⠀
⠰⣏⡇⠧⡀⠙⡈⠑⢭⢊⡕⠋⢰⢲⢀⡇⠗⣲⠀⠀⠀⠀⠀⠀
⠰⠟⠋⣢⢬⠃⠧⣀⠼⠀⢆⣀⢼⠘⣡⡖⠒⠻⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠓⠋⠉⢲⠀⠀⠀⠀⢠⠞⠉⠒⠼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⢅⣒⠤⠚⡀⠀⠀⢀⡘⠢⣤⣖⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠺⣵⠒⢊⡡⢰⠉⠈⢱⢰⡉⠉⢶⢄⡙⠲⣢⠟⠀⠀⠀⠀⠀⠀
⠘⠤⢆⡏⠀⠚⢠⣖⣽⢸⣕⢢⠸⠼⠈⠂⡤⠽⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠁⠀⠀⠀⢁⡼⠸⢆⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠗⢺⣸⠗⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠳⠒⠒⠲⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠷⣄⡀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⢀⣤⠞⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠈⠙⠲⣤⡀⢸⡇⠀⠀⢸⠀⢀⣤⠞⠋⠀⠀⠈⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⢤⣀⠀⠀⠈⠻⢦⣀⠀⠀⠈⠙⢾⡇⠀⠀⣸⠖⠋⠀⠀⠀⣠⡶⠛⠁⠀⠀⣠⡤⠶⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠁⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⡏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣾⣤⡀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⢀⣤⣶⡀⠀⠀
⠀⣴⡟⠁⠈⠙⠳⢤⣀⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣀⡴⠞⠋⠀⠈⢷⡄⠀
⠐⡿⣤⡀⠀⠀⠀⠀⠉⠳⢦⣿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⡶⠞⠉⠀⠀⠀⠀⢀⣴⠿⠀
⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠐⠉⠁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠀⠃⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠛⣶⣤⡄⠀⠀⠀⠘⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠀⠀⠀⠀⢠⣤⡖⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣴⠶⠛⠉⠀⠀⠀⣀⣀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⣠⣀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀
⠀⣴⡖⠛⠁⠀⠀⠀⣀⣤⠶⠛⠉⠉⠛⠦⣄⡀⠀⠀⠀⠙⠳⣤⣀⢸⡇⠀⠀⢸⠀⣠⡴⠛⠁⠀⠀⠀⢀⣠⠴⠛⠁⠉⠛⠶⣤⣀⠀⠀⠀⠈⠛⢶⡤⠀
⠀⠈⢷⣄⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠉⠛⢧⠀⠀⠸⠛⠁⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣠⡿⠁⠀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⣀⠐⠁⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀
⠀⠀⣴⠟⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⣀⡆⠀⠀⢣⡀⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠻⣦⠀⠀
⠀⢾⣇⡀⠀⠀⠈⠙⠓⢦⣄⡀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⣀⣴⠞⢻⡇⠀⠀⢸⠙⠳⣤⣀⠀⠀⠀⠉⠛⢦⣤⡀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⢀⣽⡇⠀
⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠈⠉⠳⠞⠋⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠈⠙⠳⠞⠉⠀⠀⠀⢀⣠⠴⠞⠉⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣙⣻⠦⠀⠀⠀⠀⠀⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠶⣟⡋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡀⠀⠀⠈⠙⠲⢤⣄⠀⠀⠀⠀
⢀⣤⠶⠋⠁⠀⠀⠀⠀⣀⡤⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠈⣷⣦⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀
⠈⢻⣆⠀⠀⠀⣠⡴⠚⠉⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠙⠳⢦⣄⠀⠀⠀⣸⠏⠀
⠀⠀⠙⣷⠶⠋⠉⠀⠀⠀⠀⡏⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠇⠀⠀⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣿⠀⠀⠀⠀⠈⠛⢦⣼⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⢀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⠶⠟⠀⠀⠀⣀⣴⠞⠉⠀⠀⢀⣤⡎⠀⠀⢲⣄⡀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠿⠶⣥⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⣿⠁⠀⠀⢀⣠⠾⠋⢸⡇⠀⠀⢸⠈⠛⠦⣄⡀⠀⠀⠙⣷⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣤⡶⠋⠁⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠈⠙⢶⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀
⠀⠀⢠⠀⠀⠀⡈⢻⠟⡀⠀⠀⢰⡀⣸⣤⣤⠄⠀
⠠⣄⣸⣄⡇⠀⠙⢻⡞⠁⠀⠀⢠⡿⠷⠦⠄⠀⠀
⠀⠀⠼⠿⢷⣤⡆⢾⣧⠆⢱⣴⣏⠀⠀⢀⠀⠀⠀
⠀⠀⡄⠀⠈⠉⠳⣄⡇⢠⠞⠁⢀⡄⢀⣾⣰⠇⠀
⢧⣄⣙⣦⣼⣦⡤⢼⣿⣿⡒⠚⠛⠿⠛⢯⡙⠲⠄
⠞⠉⠹⠋⠀⣏⣠⠞⢷⠈⠻⣶⡤⠀⠀⠀⠉⠀⠀
⠀⠀⠀⠶⢤⣼⠻⠀⣸⡀⠀⠛⠙⣷⣖⣲⠆⠀⠀
⠀⠀⠶⢶⡟⠇⠀⠘⢹⡛⠀⠀⠀⠃⢹⠄⠀⠀⠀
⠀⠀⠀⠚⠀⠀⠀⢀⡼⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣰⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠤⠴⠤⠤⠠⠴⠠⠤⠄⠀⠂⠶⠢⠴⠦⠦⠴⠀
💘❄️🫧♡₊˚ʚ ᗢ₊˚✧ ﾟ.₊˚ʚ ᗢ₊˚✧ ﾟ.🫀
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🌲 🏠🌲 🌲 🌲
🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️🌫️
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⢤⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠷⡏⡀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⣴⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡟⡆⠀⠀⠀⠀⠀⣴⢤⣀⡇⠀⢻⣀⡶⢦⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⠟⠻⡇⣷⡀⠀⡏⢻⠀⠙⢦⡉⠻⡄⠞⣁⡴⠏⠀⣠⣦⠀⠀⣇⢸⣦⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢙⣷⢯⡄⠉⠻⢦⣧⢸⡆⠀⠀⠈⡏⠀⢾⠃⠀⠀⠀⡇⢸⣀⠶⠻⠈⠀⢴⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢯⠵⠚⠛⠳⣤⣀⠙⠈⢷⣄⠀⣀⡇⠀⢸⣄⠀⢀⣠⠗⠘⠁⣀⡴⠚⠛⠲⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡟⣉⣼⠶⢦⣀⠈⠛⠁⠀⠀⠀⠈⠛⠉⢀⣷⣦⣌⡙⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⢺⠋⠁⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⠓⠶⢤⣀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠺⣆⡀⢀⣠⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣀⡀⠀⠀⢉⣳⠶⠌⠁⣀⣴⢶⣄⡀⠀⢀⣠⡷⣄⡀⠙⠫⣵⣖⠉⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠙⢧⣭⡽⠒⠋⢁⣠⡆⢹⠉⠀⠀⠈⡏⠉⣿⠁⠀⠈⢹⡕⣤⡀⠉⠳⢖⣋⡽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡞⠉⢀⡄⣶⠋⠡⣇⣸⠀⠀⣀⡴⡃⠀⡛⢦⣀⠀⠈⣇⢸⠙⠲⣤⠈⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠉⣇⣿⠀⠀⠈⠁⠀⣿⣁⡴⡟⠀⣿⢦⣌⣳⠀⠹⠾⠃⠀⢸⣈⣷⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⢀⡇⠀⣿⡀⠈⠉⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢚⡅⠀⣭⡛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠉⣧⢀⣾⠉⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣀⣠⣄⣀⣀⣄⣀⣀⣀⡀⣀⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠉⠉⠉⢉⢉⢋⠉⡉⠉⠉⡋⠉⡉⡉⣉⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠀⠀⢸⣧⠀⢀⣾⣦⣤⣤⣄⠀⠀
⠀⠀⠀⠀⠀⢿⡇⠀⣶⠀⠀⠺⣦⣼⣧⣴⡿⠀⠀⠀⠀⠀⢻⣦⣾⣛⠉⠉⠉⠁⠀⠀
⠀⠀⢶⣶⣤⣼⣧⣰⣏⠀⠀⠀⠈⠹⣿⠋⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠻⠿⠂⠀⠀⠀
⠀⠀⠀⠀⢠⣬⣿⣿⣿⡀⢀⡄⢠⣤⣿⣤⡦⠀⢿⣄⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣇⠀⠙⣿⠋⠀⠀⣨⡿⠟⠛⠃⠀⠀⠀⢀⣶⠀⣠⡀⠀
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠙⢷⣤⣿⡆⢀⣴⠟⠀⠀⠀⣠⡟⠀⢀⣾⢃⣴⠟⠁⠀
⠰⣦⡀⠀⠘⢿⣄⠀⢰⣦⣀⣀⣀⣹⣿⣷⣿⣷⣤⣴⡶⢾⣿⣷⡾⢿⣿⡟⠿⣶⣄⠀
⠀⠈⣿⣷⣶⣶⣿⣿⠿⢿⣿⠟⠋⣹⣿⡟⠻⣿⣄⠀⠀⠀⠈⠙⠀⠀⠙⢿⣦⠀⠙⠁
⠰⠾⠋⠀⠀⣾⠟⠁⠀⣾⡁⢀⣴⠟⠸⣧⠀⠈⠻⣷⣶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣻⣿⣿⠀⠀⣿⠀⠀⠀⢸⡟⠻⣦⣄⣀⣠⣤⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠛⢻⣾⡟⠉⠃⠀⣠⣿⣄⠀⠀⠈⠁⠀⢸⣿⢿⣿⡷⠾⠃⠀⠀⠀
⠀⠀⠀⠀⢶⣶⣦⣶⡟⢿⠃⠀⠀⠚⠋⢻⡟⠗⠀⠀⠀⠀⠘⠿⠀⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⡿⠀⠈⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣴⠿⣿⡿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣰⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⢀⡀⠀⠀⠀
⠀⠀⠀⠚⠛⠛⠻⠛⠓⠃⠟⠻⠓⠐⠒⠒⠛⠁⠀⠀⠀⠛⠗⠝⠛⠛⠛⠻⠗⠓⠓⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⢦⣀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣠⠴⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢧⣀⠀⠈⠓⢦⣸⠀⠀⢸⣀⠴⠊⠁⠀⣠⠿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠹⡀⠀⠀⠈⠑⠦⡀⠀⠘⠂⠀⠈⠀⠀⣠⠔⠋⠀⠀⠀⢸⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣴⣄⡀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢀⡴⣆⠀
⢠⡞⠀⠀⠙⠲⢄⣀⣼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⣀⡴⠚⠉⠀⠈⣧
⠈⠙⠲⢄⡀⠀⠀⠈⠛⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠋⠁⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠉⠓⣦⡄⠀⠀⠀⠛⠦⣄⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠀⢠⡔⠋⠁⠀⠀⠀
⠀⠀⣀⡤⠖⠋⠁⠀⣀⡤⣄⡀⠀⠈⠙⠢⣄⡀⠀⢸⠀⠀⢸⠀⠀⢀⡤⠖⠉⠀⠀⣀⡤⣄⡀⠀⠈⠛⠲⢤⣀⠀
⠐⢿⡁⠀⣀⡤⠖⠋⠁⠀⠀⠉⠓⢦⣀⠀⠀⠉⠲⢼⡀⠀⢸⠶⠚⠁⠀⢀⣠⠴⠊⠁⠀⠀⠈⠑⠢⢄⡀⠀⢨⡟
⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠐⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀
⢀⣼⠋⠉⠓⠦⣄⡀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⣠⢴⠂⠀⢸⣤⣀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠙⣆
⠀⠉⠓⠦⣄⡀⠀⠉⠓⠦⠖⠋⠁⠀⢀⣠⠖⠋⠀⢸⠀⠀⢸⠀⠈⠓⠦⣄⠀⠀⠈⠓⠦⠖⠋⠁⠀⢀⣠⠔⠚⠉
⠀⠀⠀⠀⠀⣉⡷⠂⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠶⣾⡉⠀⠀⠀⠀
⠀⢀⣠⠔⠋⠁⠀⠀⣠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢠⡀⠀⠀⠉⠓⠦⣀⠀
⠸⣏⠀⠀⠀⣠⠴⠊⢻⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡏⠓⢦⣀⠀⠀⢀⡿
⠀⠘⢧⠖⠋⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠸⢦⡀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠈⠑⠦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⡇⠀⠀⠀⣀⡴⠚⠁⠀⡄⠀⢀⠀⠉⠲⢄⡀⠀⠀⠀⢹⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⡴⠚⠁⠀⣀⠴⢺⠀⠀⢸⠓⢤⡀⠀⠉⠳⣤⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡴⠊⠁⠀⢸⠀⠀⢸⠀⠀⠉⠳⢤⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢌⠙⠢⣀⡇⠀⣀⠤⠊⢙⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⡀⠀⠑⠢⣀⠁⠀⢁⡠⠊⠁⠀⡌⢩⠀⠀⠀⠀⠀
⢀⡞⠑⠢⢄⢰⠀⡇⠀⠀⠀⠈⡇⠀⠁⠀⠀⠀⠀⡇⢸⣀⠤⠊⠙⣄
⠀⠉⠂⢄⡀⠉⠀⢇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠇⠈⠁⡠⠔⠊⠀
⠀⡠⠔⠂⢁⡠⠤⣀⠈⠒⢄⡀⡇⠀⠀⡀⠔⠊⢀⠠⠤⣈⠑⠂⠤⡀
⠀⠱⠔⠊⠁⠀⠀⠀⠉⠢⢄⡈⠇⠀⠉⣀⠄⠊⠁⠀⠀⠀⠉⠒⠔⠁
⠀⡠⠤⣀⠀⠀⠀⠀⢀⡠⠐⠉⡀⠀⡈⠑⠤⣀⠀⠀⠀⠀⢀⡠⢤⠀
⠀⠓⠤⣀⠁⠂⠤⠂⠁⡠⠔⠉⡇⠀⠉⠒⠤⡀⠁⠢⠔⠊⢁⡠⠐⠃
⠀⢀⡠⠔⠉⢀⠀⡖⠉⠀⠀⠀⡇⠀⠀⠀⠀⠈⠑⡄⢀⠈⠓⠤⡀⠀
⠐⢇⢀⠤⠒⠹⠀⡇⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⡇⢸⠑⠢⣀⢈⠇
⠀⠈⠁⠀⠀⡄⢀⠇⠀⢀⠤⠊⡁⠀⠉⠢⢄⠀⠀⣇⢘⠀⠀⠀⠉⠀
⠀⠀⠀⠀⠀⠉⠁⠀⢎⢁⠤⠊⡇⠀⠉⠢⢄⢱⠂⠀⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀