Pony Fist Bump Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⢳⠀⢀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⢻⣿⣿⣯⣉⠀⠉⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢦⡀⠀⣿⡟⢮⣝⠻⣦⡆⠀⠀⣤⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡇⠀⠉⠙⣿⡇⠀⠙⢷⣌⠻⣆⠀⠘⣷⣄⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠋⠀⠉⠳⣄⣠⣴⣾⣯⣍⡙⠛⠻⢿⣷⡶⣤⣿⡇⠀⠀⠀⠻⣆⠹⣧⠀⢻⣿⡄⠚⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⡀⠀⠀⠙⢿⣿⠈⢻⣏⠉⠳⣤⡀⠈⠻⢦⡉⠋⣦⠀⠀⠀⢹⣇⢻⡆⢸⡇⢿⡄⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⢧⠀⠀⠀⠀⠙⢧⡀⢻⣆⠀⠈⢷⡄⠀⠀⢻⣄⠘⣧⡀⠀⣀⣿⣾⣷⣼⣧⣼⣷⣶⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠸⡀⠀⠀⠀⠀⠈⢿⡄⢻⡆⠀⠈⣷⠀⠀⠀⣻⣤⣴⣿⣿⣿⣿⡟⠋⠉⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠀⢳⡀⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⣹⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠓⢄⣤⣶⣿⣿⣿⠁⣹⣷⡿⠟⠉⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠈⠻⣿⣿⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣤⣶⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⡀⠀⠀⠠⣶⣿⣿⣿⣿⠘⢿⣿⣿⣿⣿⣆⠀⠀⣸⡟⣠⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠻⣿⣿⣿⡟⠀⠈⠻⣿⣿⣿⣿⣧⣼⣿⠞⠁⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⡿⠿⣿⣿⡉⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢙⡿⠁⠀⠀⠀⠈⠉⠙⣿⠹⠋⠁⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀ ⢹⣿⣿⣿⠄⠀⢸⡟⣧⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠟⠁⠀⠀⠀⠀⠙⠁⣰⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀ ⠀⠻⣿⡿⠀⠀⠈⣧⠹⣧⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠴⠒⢒⣶⠏⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠊⠿⣿⣦⡀⠀⠠⡤⠤⠤⠤⠤⠴⠖⢲⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠷⣄⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠘⣏⣿⠀⢰⡈⠉⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠙⠂⠀⠀⣠⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⢠⡷⣿⡆⠈⢿⣶⣄⡀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⢧⡀⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠹⣇⠀⠀⠻⣿⣿⣷⣾⣽⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠙⣦⡀⠀⠈⠛⢷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣠⡤⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞⢷⡈⢷⡀⠀⠈⠀⠈⠙⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⢳⡄⠹⣆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠹⣦⡈⢷⣄⠀⠀⢀⣼⣿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣞⣷⣄⠙⢧⣠⣼⣿⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠐⠒⠒⠚⠛⠓⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟥⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛🟥⬛⬛🟧🟧🟧🟨🟨🟨🟩🟩🟩🟦⬛🟦⬛⬜ ⬛🟥🟥🟥🟧⬛🟧🟨⬛🟨🟩⬛🟩🟦⬛🟦⬛⬜ ⬛🟥⬛🟥🟧⬛⬛🟨⬛🟨🟩⬛🟩🟦🟦🟦⬛⬛ ⬛🟥🟥🟥🟧⬛⬛🟨🟨🟨🟩⬛🟩⬛⬛🟦🟪⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟦⬛🟦⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⣿⢗⠦⣄⠈⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡤⢄⠀⠀⣀⢤⣶⣿⣁⠉⢻⠀⠙⣌⢣⠀⢷⡸⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢀⠀⠑⢿⡙⣗⠢⢌⠙⢯⡛⢢⠀⠈⣇⢧⢸⢱⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⢠⠘⡀⠀⠈⠳⡜⣆⠈⢧⠀⠙⡌⣣⣤⣼⡿⠾⣶⣷⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠸⡀⢣⠀⠀⢀⣷⢸⡀⣸⣤⢶⣿⣿⣿⣿⣷⡀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣀⣵⣾⣿⣿⣴⣿⡉⠀⢀⣽⣿⡟⢿⣿⣿⣄⠈⢻⢏⠲⡀⠀⠀⠀⠀ ⢀⣠⣾⣿⣿⠿⠿⣿⣿⣿⣿⣆⠈⠻⣿⡇⠀⠻⠿⣿⢶⠿⠃⠀⠹⡄⠀⠀⠀ ⢻⣿⡏⠁⣿⡆⠀⠙⢿⣿⣿⣿⣷⣠⠞⠀⠀⠐⠂⡜⢄⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠛⠃⠀⢸⠹⣄⡀⠀⠉⠛⠛⠋⠁⠀⠀⢀⣩⠟⠁⠈⠢⡀⠀⠀⠀⠘⢆⠀ ⠀⠀⠀⠀⠈⣦⠟⠿⣤⣀⣠⠀⠀⠀⠒⡖⠉⠀⠀⠀⠀⢀⡬⠢⣀⠀⠀⢈⠇ ⠀⠀⠀⠀⠀⣿⡆⢳⣄⠀⠙⣇⠀⠀⠀⠱⡀⢀⡠⠔⠊⠁⠀⠀⠀⣀⠔⠋⠀ ⠀⠀⠀⠀⠀⣏⢧⠀⠙⢿⡺⠾⠆⠀⠀⠀⠈⠣⡀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣯⢦⠣⡀⠀⠙⠳⢶⡄⠀⠀⠀⠀⠙⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣯⣧⡙⢄⠀⠀⢸⡇⠀⠰⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣿⣎⣳⣤⣿⡇⢀⣀⣣⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⢀⢠⠴⠖⠉⠉⠉⠢⡀⢢⠉⠃⠶⣤⣀⢤⣄⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠋⠒⠒⠀⠤⣀⠀⠀⠱⡈⡄⠀⠀⢠⡟⠁⠘⣦⠀⢰⢠⢊⠕⣵⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⠇⠀⠀⠀⠐⠂⠠⠄⡈⠂⣄⡥⠓⠀⠀⠜⠀⠀⠁⠸⡄⢸⢁⠆⠀⠀⢠⠟⠁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠁⠀⡠⠄⠲⠤⣄⡀⠀⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡟⣎⠘⠀⠀⠠⡏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⢸⠁⠀⠀⠀⣟⣭⠲⠃⠀⣴⠶⢦⡀⠀⠀⠀⠀⠁⣸⠁⢸⡆⠀⠀⠘⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⢸⠀⠀⠀⢤⡾⣌⠀⠀⢸⣓⡰⢦⡙⢦⠤⠀⠀⠐⡇⠀⢀⡃⠀⠀⠀⠀⠰⡿⠔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡄⠈⣆⠀⠚⠋⣷⣸⠀⠀⢸⣿⣇⠀⣷⢈⠛⠯⠔⢰⠃⠀⢸⡿⠙⡆⠀⢀⠏⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⢄⠈⢆⠀⠀⣹⠟⠀⠀⠀⠻⣿⣿⣼⢺⡒⠀⢀⡞⠀⢀⢧⡁⠀⠇⣠⢤⡀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⠑⣌⢧⡐⣠⠀⠀⠀⠀⠁⠀⢁⠀⣠⠎⠀⢀⠎⢎⡏⠀⡶⠁⢀⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⡈⠳⣍⠓⠒⠀⠠⣦⢴⡏⢁⡴⠃⠀⢀⠎⡜⢸⠁⠀⠁⢀⡾⠋⠂⠀⣀⡀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣄⠈⢢⡀⠀⠀⢹⢸⣧⠏⠀⠀⡰⠃⡜⠀⣏⠇⠀⠴⢫⣀⣴⡿⠛⠉⠀⠀⠀⠈⠉⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠄⣀⠀⠱⣣⠀⠱⡀⠀⣾⢸⡏⠀⢀⠞⠀⡜⠀⣸⠁⠀⠀⡠⠜⠛⠻⣄⠒⠒⠒⠢⢄⡀⠀⠀⠀⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢡⡶⠒⠵⢀⠿⡆⠀⢣⢠⡿⢌⠀⠀⡎⠀⡸⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⡎⠿⠳⣦⡀⠀⠈⠢⡀⠀⠀⢩⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⡈⠳⠆⠀⠞⠁⡇⠀⢸⡞⠀⢸⡀⢸⠀⢠⠃⢀⡏⡀⠀⠀⠀⠀⠀⠀⡄⠹⣼⠆⠈⢓⡄⠀⠀⠐⡄⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠶⣤⡄⠀⢀⣧⠶⡏⠀⠀⢰⣧⢸⠀⢸⠀⢸⠁⡇⠀⠀⠀⣠⠀⠀⠀⠘⣶⢀⡀⠈⣶⠀⠀⠀⢱⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⣾⡀⢸⠀⠸⣼⣝⣞⡆⠁⠘⠄⠀⠀⠘⠁⠀⣿⠀⠙⠀⠀⠀⢸⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠋⠳⣄⣣⠀⠙⠺⢣⡯⠀⠀⠈⠒⡄⠀⠀⠀⡟⠀⣿⠀⠀⠀⡘⠀⢠⠃⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡀⢠⡇⠀⠀⠀⠙⢃⡆⠴⡏⠁⠀⠀⠀⢰⠀⠀⠀⠀⣧⡰⠆⠀⠀⡰⠁⡠⠃⢰⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢰⡆⠀⠀⠀⢈⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⠀⠀⡰⢁⠔⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⠀⣜⠃⠘⣃⡀⠀⠀⣄⣵⠀⠀⠀⠀⣸⠀⢀⠜⡰⠁⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠶⠞⠃⠀⠀⠈⠁⠀⠉⠀⠐⢦⣤⢰⠞⠁⠀⠎⡌⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⢸⠀⠻⣥⣀⣀⣀⢀⡀⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣢⣸⡈⢄⠀⠀⠉⠀⢀⡀⠀⡀⠈⣉⠓⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠀⠀⠛⠈⠁⠀⠀⠀⠉⠫⡎⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠀⠀⠄⠉⠉⠉⠉⠁⠀⠐⠀⠆⠄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠂⠛⡂⠋⠀⠀⠀⢸⠀⠌⠀⠀⢀⠠⠄⠀⠈⠀⠀⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠳⡠⠄⠠⠴⢼⣀⠀⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀ ⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣥⠀⢀⡠⡆⠉⠓⠢⠆⠀⠀⠀⠓⠀ ⠀⠀⠀⢀⡾⠰⠄⠐⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠘⠳⠓⣁⡴⠀⠀⠀⠀⠉⡄⠀⢸⡇ ⣀⠀⠀⢠⡇⠀⠑⡀⠀⠀⠀⠀⢀⡔⡩⡐⡒⢷⠀⠀⠀⣧⣺⢦⡄⡀⠀⠀⢳⠀⠸⠇ ⠀⠈⠢⢈⠇⠀⠀⠏⠀⠠⣈⣩⠋⠐⡂⠀⣼⣞⠀⠀⠘⣧⣿⡀⠁⠂⠀⠀⡆⠀⠶⠀ ⣄⠀⠀⠸⠶⡀⠀⢸⡀⠁⠈⢁⣄⠇⢿⣿⣿⡟⠀⠀⠀⠹⡏⡀⠀⠀⠀⠆⢁⡼⠁⠀ ⠈⠅⢀⡀⠖⡡⡀⠀⠻⣆⠀⠀⠉⠏⠚⠛⠋⠁⠀⠀⠀⠀⢀⡣⠀⢀⡖⣠⠜⠀⠀⠀ ⠀⠨⡁⠁⠸⡵⠁⡀⠀⠘⢶⡄⠠⠀⣀⡀⠀⠀⠀⠀⠨⠖⠃⣀⡔⢙⡤⠊⠀⠀⠀⠀ ⠀⠀⠡⡄⡀⢹⡀⠀⢄⠀⠀⠛⣦⠀⠀⠐⠖⠀⠀⠀⢀⣠⠖⡡⡤⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⢔⢧⠀⠀⠡⡀⠀⠈⢗⡄⠀⠟⠀⠠⡴⠓⢡⠞⠁⢠⠐⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡄⠠⠀⠈⠀⠀⠀⠱⡤⣀⢠⠂⠀⢀⢚⠀⠂⠀⠈⡇⠀⠁⠀⠀⠀ ⠀⠈⠂⠀⠀⠀⠀⢐⠀⢡⠀⠀⢂⠀⠀⢳⠹⡏⠀⠀⢸⠀⠓⠶⠶⠚⠁⠴⠃⠀⠀⠀ ⠀⢠⡀⠀⠀⠀⠀⠀⢧⠀⠆⠀⠀⠆⠀⢸⡇⠀⠑⠠⠘⣀⣀⠀⠠⠄⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠡⠂⡄⢀⠠⢰⠀⠸⠀⠀⢸⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣠⣄⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢟⠥⡖⠉⠁⠀⠔⠉⠢⡴⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠞⢁⠎⠀⠀⡴⠀⠄⠂⠈⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⣠⡜⠳⡸⠤⠀⠠⣤⢂⠌⠀⡀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣠⣉⡇⠀⠐⠂⣩⣏⠋⢸⠦⠊⣐⡡⡰⠊⡡⢊⠠⢐⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⢏⣀⡄⠀⠀⠛⠁⢀⠜⢰⠚⢁⠮⡤⠞⠈⣠⠔⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠓⠒⡲⠈⡠⡎⠀⣾⢐⠏⡴⢥⠐⠚⠛⣢⢍⡒⢄⠀⠀⠀⠀ ⡠⠒⠉⠉⠉⠉⠐⡤⠁⢀⠏⡀⣠⡿⠃⣀⠴⢷⡒⢈⢁⠑⡐⢻⡝⢇⠀⠀⠀ ⠑⠠⠄⠤⠊⡁⠀⡇⠀⠘⡔⠋⠁⠠⠤⣎⠐⠏⠘⡄⢂⢂⢠⠃⣽⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠒⠳⡀⠀⠀⡀⠀⢀⡔⠁⢰⠀⠀⢰⡌⠐⢸⠀⡟⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⢋⠀⠳⠀⠈⠆⠀⢸⡇⢠⢸⠀⣇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⢠⠁⠀⡇⠀⠘⡀⠀⢣⢸⡬⠀⢛⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡌⠀⠀⡇⠀⠀⡇⠀⠘⢿⠙⣞⣈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠸⣀⡀⢤⠁⠀⠀⡇⠀⠀⠀⠁⠀⠙⠃⠛⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠊⠠⠤⠐⠃⠀⠀⠑⡒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠓⠢⣀⣀⣀⣀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠞⢻⠁⠀⠀⢠⠞⠁⢀⡤⠟⠛⢢⣴⢁⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠁⠀⢸⠀⠀⢠⡏⣠⠞⠉⠀⠀⠀⢰⡇⡾⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠛⢿⡇⠀⠀⠘⡆⠀⣸⡴⠃⠀⠀⠀⣀⣀⠾⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢮⠳⣄⠀⠀⢱⡀⣿⠃⠀⢀⡴⢾⢍⠀⠀⠀⠗⠀⣼⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠘⣦⣈⣙⣲⠶⠒⣿⣤⣾⠃⠰⣿⣟⠟⠓⠀⠀⠘⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⡼⠁⣰⣿⣿⣄⣴⡏⢹⣏⡇⠀⢬⣽⣾⡲⣶⣄⠀⠘⣌⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⢠⣿⡋⠿⠞⠁⢧⡸⡏⠁⠀⠏⢠⣇⢸⡿⣿⡷⡄⢹⣆⠀⢱⣄⠀⠀⠀⠀⠀⣠⠴⠒⠋⠓⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⡾⣼⣾⣿⣷⣤⡈⠓⠓⠀⠀⠀⠈⣯⣿⣿⡿⠃⠁⠀⢻⢧⣀⣿⠀⠀⠀⢠⡜⢁⡤⠞⠛⠛⠓⢄⡈⢣⡀⠀⠀⠀⠀⠀⠀ ⠘⣿⢰⡇⣿⡇⣽⣽⣿⣿⣀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⢸⣼⠟⠁⠀⠀⠀⡼⢠⠏⠀⠀⢀⣀⠀⠀⠙⢦⡱⣄⠀⠀⢰⣦⡀ ⠀⠹⣼⡁⢻⠧⣘⡿⣿⣏⠁⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⢸⠃⡞⠀⡠⠞⠉⠈⠙⠲⣄⡀⠈⠚⠦⢤⠼⣿⡇ ⠀⠀⠙⠇⠸⡇⠀⠀⠀⠻⣅⣀⣤⣀⣾⡿⣿⠀⠀⠀⠀⢀⠾⡇⢸⠀⠀⠀⠀⢸⡀⡇⣰⠁⢀⡤⠖⠒⠒⢮⣝⡢⠤⠤⠼⠚⣽⠇ ⠀⠀⠀⠀⢰⠿⣆⡀⠀⠀⠀⠙⢿⣿⣿⢈⡿⠀⠀⢠⣾⠉⣸⠁⡾⠀⠀⠀⢀⣀⣷⣷⣿⠰⠋⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀ ⠀⠀⠀⢀⡇⠀⢨⡟⠓⠤⣤⣀⣀⣈⣛⣋⡀⠀⠀⠀⢿⡴⣣⠞⠁⠀⣠⠖⠋⠁⠀⢀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⠁⠀⠸⡇⠀⢸⠇⠀⠉⢹⠉⠉⠀⠀⠀⠀⠈⢿⠁⠀⣠⣾⣁⣀⣠⠤⢤⡏⣴⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⢧⠀⢸⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠳⠿⣓⣲⠞⠋⠀⠀⠀⢻⡻⠟⠓⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠈⢧⡘⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⢦⠀⠀⠀⠀⠀⢷⠀⠀⠀⣧⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠶⢽⡾⠦⠤⣴⣇⠀⠀⠀⠀⠀⣀⡴⢛⡵⠋⢳⠐⢷⠀⠀⠀⠀⣈⣇⠀⠀⠃⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢛⡟⢹⣏⠙⠒⠒⠒⠛⢉⡴⠋⠀⠀⠘⡇⠈⡇⢀⣤⢞⡽⠋⠀⠀⢀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠦⠯⠴⡯⢿⡉⠒⠒⠒⠋⠁⡀⠀⠀⠀⠀⣧⣀⣇⡿⣾⡏⠀⠀⠀⣠⠏⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸⢫⣧⡴⡏⠙⠓⠒⠚⢹⠂⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢀⣷⣤⠤⣖⠋⠙⠢⣤⣀⡼⠁⠀⠀⣶⣴⡿⠛⠁⠀⣧⣄⠀⠀⠀⣼⣴⠀⠀⢀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢿⣻⣿⠯⠿⠦⣤⣄⡾⠀⠀⠀⢸⠁⠀⠹⣆⡀⠀⠀⢸⠀⠀⠀⣿⢱⠀⢡⡀⣷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⣯⣷⣦⠖⢋⡞⠀⠀⠀⢠⡏⠀⠀⢀⡞⠀⠀⠀⡏⠀⠀⠀⠻⣯⠤⠟⠚⣡⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡞⠀⠀⠀⠀⡾⠀⠀⢀⡞⠀⠀⠀⢸⠇⠀⠀⠀⠀⠙⠶⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⢀⠘⠓⠀⣤⠚⡇⠀⠀⣸⠁⠀⠀⠀⢰⡇⠀⢀⡞⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⠈⣿⠂⢀⡟⢰⠇⠀⠀⡏⠀⠀⠀⠀⠈⡇⢀⡞⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠓⠾⢭⣁⣀⠎⠀⠀⢸⠃⠀⠀⠀⠀⠀⣧⢞⡄⢀⠀⡀⢰⡶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢻⡖⠃⢮⣷⣿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⢷⠤⠤⠬⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⢀⠀⠀⠤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠤⠄⢠⣀⣠⠖⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠒⠠⠤⠒⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠓⠀⠁⠗⠚⠀⠀⠐⠀⠀⠀⠀⣰⢋⣀⣀⣀⠀⠀⣀⢠⡎⠉⠲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠉⠑⠪⡟⢀⠄⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡄⠀⠀⠸⡆⠀ ⠀⠀⠀⠀⣀⣀⡤⠶⠛⣁⡤⠤⠖⠒⣲⠂⠀⠀⢀⣠⢼⡀⠀⣧⠀⠀⠀⢹⠀ ⢹⠋⠉⠉⠁⢀⡠⠖⣋⣁⣀⠄⠀⡼⠁⢀⡠⢞⡉⠀⠀⢳⠀⡇⢳⡄⠀⢸⡇ ⡎⠀⠀⣠⠖⡏⣲⠞⢋⣿⡆⠀⢰⢃⡴⠋⠀⣠⠽⢶⡤⠄⠃⠈⠀⠁⠀⢼⠁ ⠃⢀⡞⠁⠰⡷⠁⣾⢿⣿⡇⠀⣿⠞⠀⠀⠞⠁⠀⠀⠹⣦⡄⠀⠀⠀⢀⡏⠀ ⣠⠋⠀⠀⠀⡇⠀⠻⣂⡨⠃⠀⠋⠀⠀⠈⠘⣿⡄⠀⠀⢷⠤⠀⠀⠀⡎⡇⠀ ⠁⠀⠀⠀⢠⠷⡄⠀⠀⣀⠤⣄⣀⠀⠀⢸⣾⣿⡇⠀⠀⠾⠂⠀⠀⢀⡇⡇⠀ ⠀⠀⠀⠀⡾⠐⠈⠙⠉⠁⠸⠄⠠⠉⠀⢸⣻⡩⠃⠀⡀⠂⠀⠀⠀⢸⢹⠁⠀ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠈⠉⠉⠩⠤⠦⠀⠀⣠⢇⡏⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡿⠛⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠘⠧⢄⠀⠼⠂⠀⠀⠀⠀⢀⡰⠋⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠙⢳⡦⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡀⠳⣄⡀⠀⠀⠀⠀⠀⣇⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⣯⡛⠓⠛⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠦⠤⠤⣀⣀⡴⠋⠀⣰⠀⣸⠃⠙⠦⣄⡀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠉⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠿⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⣀⣀⣀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠛⠋⠉⠉⠉⠙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣤⣤⣤⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣤⣄⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⣰⡿⠀⠀⠀⣠⣶⣿⡟⠉⢹⡇⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⢸⣿⠀⠀⠀ ⠀⠀⢠⣿⠁⠀⣠⡾⢻⣿⡏⡷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⡿⠀⠀⠀ ⠀⠀⣾⡇⠀⣼⡟⠁⣾⣿⣿⠃⠀⣸⠃⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠉⠛⠶⣄⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠘⣿⡃⠀⠀⠀ ⠀⢸⣿⠀⣼⡿⠁⢠⣿⠙⠁⠀⢠⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⣧⡴⠟⠁⢀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀ ⠀⣿⡏⢰⣿⠇⠀⣸⡏⠀⠀⢀⡞⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣧⠀⢻⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀ ⢠⣿⠇⣼⣿⡶⣟⣿⣧⣤⠤⠊⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⣿⡿⣇⣀⠏⠀⣿⣤⡶⠖⠀⠀⢦⠀⠀⠀⠀⠀⢻⡇⠀⠀ ⢸⣿⠀⣿⣿⣇⡇⠀⠀⣀⠀⠀⣀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠉⠀⡴⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⣸⡇⠀⠀ ⣸⡟⢰⣿⡏⢿⣷⡀⠀⠈⠀⢀⣿⡄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣄⠀⠀⣿⠁⠀⠀ ⣿⡇⢸⣿⠀⠀⠛⢿⡳⠶⠖⠋⠀⣇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣠⣴⢿⣍⠻⠀⠀⠀⠀⠀⢠⠞⣹⣿⠈⣿⢷⣴⡟⠀⠀⠀ ⣿⡇⢸⣿⠀⠀⠀⠈⢳⡄⠀⠀⠋⣿⠀⠀⠀⠀⠈⠙⠒⠶⠖⠚⠋⢹⠟⠓⠛⠀⠀⠀⠀⢠⠔⢋⣦⣿⣿⠀⣿⡇⠈⠀⠀⠀⠀ ⣿⠁⢸⡟⠀⠀⠀⠀⠀⢻⣄⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠀⢿⣷⠀⠀⠀⠀⠀ ⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣶⢧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⡿⠀⢸⡿⣧⡀⠀⠀⠀ ⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡏⣿⠛⠛⠳⠿⣿⠿⠿⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⡇⠀⢸⣇⠈⠳⣤⣀⠀ ⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⣿⢀⣠⣤⣦⣧⣄⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⢸⣿⠀⠀⠈⠙⣿ ⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⢇⣿⣿⠟⠋⠉⠓⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⣿⣇⠀⠀⠀⣿ ⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⣾⡿⠁⠀⠀⠀⢀⣴⠞⠛⠛⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣿⡇⠀⠀⣿⢻⡄⠀⠀⣿ ⣿⠀⣿⡇⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠙⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢹⣿⠀⠀⢿⡄⠻⣄⠀⣿ ⣿⠀⣿⡇⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣦⠀⠀⡇⣿⠀⢸⣿⠀⠀⠸⣧⠀⠙⢷⣿ ⣿⠀⢻⡇⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⡀⢸⣿⠀⠀⠀⢻⡆⠀⢸⣿ ⣿⠀⢸⡇⠀⠀⣾⣻⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣷⢤⣄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢸⢽⣇⠀⣿⡇⠀⠀⠀⠻⣦⣸⡿ ⣿⣦⣼⣧⣤⣴⣿⣇⣀⣀⣀⣀⣀⣿⣁⠀⠀⠀⠀⠀⠀⣸⣆⣙⣻⣶⣤⣤⣤⣾⣋⣀⣀⣀⣸⣿⣿⣶⣿⣷⣤⣤⣤⣤⣬⣿⡇
⠀⠀⢀⣀⣀⣀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⢿⡟⡓⠌⠃⠀⡁⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⣎⣅⠓⠉⢟⣿⣟⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠷⠉⠹⣵⠀⢋⡿⣙⣰⠀⠀⠀⠀⡀⠄⠒⠒⠢⢄⠀⠀⠀ ⠀⠀⠀⠪⢠⡀⣰⣟⠏⣇⠀⠀⣀⣀⣀⡀⠀⠀⢊⠣⡀⠀ ⠀⠀⠀⠀⠀⡰⠁⡈⠀⢦⠀⠠⢿⠁⠈⠙⢄⠀⠁⡄⣷⠀ ⠀⠀⠀⠀⠀⢀⡀⠙⠦⠊⠀⠟⠚⠀⠀⠀⠈⣴⠀⠀⡇⡆ ⠀⠀⠀⠀⠀⠀⢂⠃⡒⠒⢗⢄⠐⢆⠀⠀⠀⣿⠆⢠⡠⠃ ⠀⠀⠀⠀⠀⢀⠂⢀⠐⠀⠀⢡⠀⠈⢂⠀⢀⣿⣠⠞⠁⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠇⠀⠰⠀⠀⠈⡆⠸⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠓⠀⠒⠈⠀⠁⠀⠈⠓⠐⠂⠁⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡚⠉⠉⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠑⠇⠀⠀⣇⠔⠉⠸⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡲⠖⢀⢀⠛⠂⢄⡐⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⢰⡾⢒⡄⠀⠁⢀⡀⢀⡅⡰⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⣂⡇⣴⡷⠀⢰⣉⢽⡆⠛⣡⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⡞⣛⠁⠂⠘⠿⠿⠤⢤⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠊⠐⡢⠄⡀⠀⠀⠀⠡⣹⢃⠄⢀⠝⠁⡠⠊⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠀⡅⠀⠀⠁⠂⠄⡀⢈⠗⠒⠒⠲⡉⠀⠠⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠒⠚⠀⠤⠤⠀⢀⣀⣠⠁⠀⠀⣔⠉⡠⠀⢪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⢹⡑⣒⢿⠊⠁⠉⠐⢄⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡠⠤⡇⠀⠀⠀⠀⠈⡶⠒⠼⣀⠐⠀⠀⠂⠉⠀⠀⡱⡤⡰⠄ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⠀⡆⠀⠀⡇⠀⠀⠀⢣⠀⡖⢂⠈⡄⠘⠤⠁⠐⢀ ⠀⠀⠀⠀⣀⠠⠌⠂⠤⠀⢣⣀⠃⠀⠀⡧⢀⡀⠔⡃⠀⠡⡜⠀⠈⠀⠈⡺⠈⠁ ⠀⠀⢰⠭⡀⠀⠀⣀⠤⠐⠒⡝⠀⠀⠀⠧⢀⠀⠀⠈⠑⢎⠈⠒⠀⠀⠊⠀⠀⠀ ⠀⠀⠀⠈⠐⠒⠈⠀⠀⠀⠘⠤⠤⠤⠜⠀⠀⠑⢄⣐⣈⠔⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢨⠀⠀⠀⠀⠈⠉⠐⠬⣙⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢷⣦⣄⣸⢋⡩⢙⠻⣿⣿⣿⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀ ⣷⣄⡀⢀⣠⣶⣿⣯⣽⠶⠶⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⢍⠃⡎⠀⠀⠑⠮⡻⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⢀⣴⣾ ⣿⣿⣷⣿⡉⠉⠀⠀⢀⣠⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⡜⡸⠀⠀⠀⠀⠀⠘⢎⢣⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⣠⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⣤⣶⠿⠋⠁⠀⠀⠀⠀⢠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣫⣤⣶⣶⣤⣍⡓⢧⡀⠀⠀⠈⢣⡀⠈⢣⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⣮⠈⠑⠿⡦⣄⣠⠤⠄⠀⠀⢀⠏⣼⣿⣿⠉⠉⠉⠛⣿⣶⣝⢦⡀⠀⠘⣧⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣣⠀⢠⠿⠑⢝⠦⣠⢤⣤⣼⢰⣿⣿⢸⠀⠀⠀⠀⠁⠙⢿⣷⡙⢆⠀⢸⡆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡎⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠴⢒⢟⣿⡷⠳⡟⠁⠀⠀⣷⠮⡻⣿⡿⢿⣿⡟⠀⡆⠀⠀⠀⣇⠀⠈⢻⣿⡎⢆⢸⡇⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿ ⠏⠀⠀⣀⣠⣤⣶⣶⣿⣿⡿⠉⠀⠀⡞⣿⡟⠀⠱⡵⡄⢀⣰⡝⠀⠈⠪⣻⠘⣿⣧⠀⠹⡀⠀⠀⠈⢆⠀⠀⢻⣿⡌⢾⠇⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣶⠿⠛⠋⠉⠉⣽⡿⠋⠀⠀⠀⢠⢳⣿⣧⠀⢀⢼⣎⢟⠊⠀⠀⠀⠐⣻⣆⢻⣿⡤⠊⠙⢄⠀⠀⠈⢧⠀⠀⢻⣷⠸⡀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⢸⢹⣿⡏⢠⡇⢸⣿⣯⣧⡀⠀⠀⠀⣿⣿⣄⢿⣿⡄⠀⠀⣹⠀⠀⠈⡆⠀⣸⣿⡇⡇⢰⠁⡇⠀⠀⠀⠀⠀⠀⢠⢠⣿⠿⠿⠟⠛⠛⠛⠋⠉ ⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⢀⣠⣾⣿⢸⣿⡇⠈⡇⣾⣿⡍⠀⠀⠀⠀⠀⢿⠟⠈⢆⢻⣿⣄⡔⠁⠀⣠⣼⡷⣯⢸⣿⡇⡇⢸⢠⠃⠀⠀⠀⠀⠀⠀⡞⡞⢿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠃⠀⠀⣀⣴⣿⣿⠋⠈⣹⣿⣧⠀⣹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡙⢿⣷⣄⡸⠟⢈⢆⢈⣽⣿⢣⠇⢸⢸⠀⠀⠀⠀⠀⠀⢠⢠⡁⠈⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠁⠀⣠⣾⡿⢿⣿⠃⠀⠀⡏⣿⣿⣶⣿⢯⡏⠙⢷⡄⠀⠀⠀⠀⡀⠀⠀⠀⣩⣶⣙⠿⣿⣷⣶⣾⣿⡿⢣⠎⠀⡀⠈⠀⠀⠀⠀⠀⠀⡎⡏⣷⣄⠘⣿⡀⠀⠀⠀⠀⠀ ⠀⢰⣿⠃⣠⣾⡿⠋⠀⣾⡟⠀⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠘⢷⡀⠀⠀⣿⠀⣠⣴⣿⣿⣿⣿⠓⢲⣬⣉⡭⠥⠒⠁⠀⠀⡇⡆⠀⠀⠀⠀⠀⣰⡸⠀⢿⡿⣦⣿⡇⠀⠀⠀⠀⠀ ⢀⣿⢧⣾⡿⠋⠀⠀⣰⣿⠀⠀⠀⠀⠀⠈⠓⠊⠙⡟⣿⣷⣄⣸⡇⠀⠀⣿⣿⠋⠀⢻⡻⣿⣿⣷⣾⣿⣿⡗⡃⠀⠀⠀⢠⢧⠃⠀⠀⠀⠀⢀⢣⠃⠀⢸⡇⠙⣿⡇⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣴⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⠀⠀⠀⠈⢷⡀⠀⠳⡟⣿⣿⣿⣿⡟⣳⠃⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⡞⣯⠀⠀⢸⣿⣦⣼⣧⣤⣄⣀⣀⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠻⣽⣿⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⠈⠓⠭⠯⠭⠞⠁⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⡜⡜⣼⣆⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⡆⠀⠘⢿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣰⡝⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⡾⣿⡇⠀⠸⠀⠀⡴⣪⠕⠁⢀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠁⠀⠀⠀⣰⠟⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣠⠤⠴⠿⣀⣿⠀⠀⠀⠀⠀⢇⢇⠀⠐⠚⠀⢠⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⣼⢹⠀⠀⢰⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠟⣿⣷⢡⠒⠒⠐⠒⠒⠠⣝⠢⣄⠀⠀⠈⠪⣗⣀⣀⣲⠝⠰⠛⣧⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⢀⣎⣾⠀⠀⣾⡇⠀⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠋⠀⠀⢸⡇⡎⠀⠀⠀⠀⠀⠀⠀⠙⢦⠱⡄⠀⠀⠀⠀⠀⣽⣿⢶⡼⠧⠤⠤⠐⡲⠝⠚⠁⠀⠀⠀⠀⠀⠀⠀⡠⢪⠎⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿ ⡿⠟⠁⠀⠀⠀⠀⢸⣇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡸⡄⠀⠀⠀⣼⣿⡇⠈⠳⣦⠞⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣴⠁⠀⣿⡆⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣸⣿⣿⠃⢀⠴⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⣾⣿⣷⡀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠇⠀⢰⣿⣿⣿⠔⢉⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⣿⣿⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠳⡳⡀⠀⠀⠀⠀⠀⠀⠀⠸⣴⡤⠾⢛⡯⡺⢣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣝⣄⠀⠀⠀⠀⠀⠀⠀⠘⠺⠉⠀⡴⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⣀⣤⡴⠞⠛⠋⠉⢡⡾⠯⠥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣀⡀⠤⠀⠒⠒⠒⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣮⣲⣄⠀⠀⠀⠀⠀⢠⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⢿⣿⣿⣿⣿⣿⣿⡿⢛⣡⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡶⠤⢄⣀⠀⠀⠀⠀⠀⢷⠛⠷⣖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠉⠉⠉⠉⠉⠉⠒⠢⢤⣀⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠈⠙⢦⡀⢀⡴⠛⡷⠖⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⡽⠋⠀⠀⢻⣄⡠⠞⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⢸⠀⠀⢸⠀⠀⠀⡞⠁⠀⠀⠀⠀⢷⠀⠀⠀⠀⡟⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷ ⢸⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⣧⡀⠤⠊⠀⢠⠃⠀⠀⠀⠀⠀⡄⢀⡞⡴⠁⠈⠉⠑⠒⢲⠒⠶⠶⠶⠒⠒⠚⠉⢧⠀ ⢸⡄⠀⠈⡇⢀⡇⢠⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡴⠃⠀⠀⠀⠀⠀⢰⢁⣼⠟⠁⠀⢀⡀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⢸⡇⠀⠀⢣⢸⣠⡏⠀⠀⠀⠀⠀⠀⠀⠚⠓⠉⠀⠀⠀⠀⠀⠀⢠⣧⠞⠛⢀⣴⡾⠷⠒⠲⣶⣶⣾⣖⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠘⣎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⢠⢿⠁⠀⠀⠀⠀⠘⡟⣇⠙⡄⣤⠀⠀⠀⠀⠀⠀ ⠀⠹⣧⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠸⡌⣆⠀⠀⠀⠀⢠⠇⣿⠀⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣷⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⠈⠲⠤⣤⣴⣋⡰⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠦⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⣿⣁⣀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠉⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⢣⠀⠀⠀⠀⠀⠀⠚⠁⢀⣼⠟⠋⠁⠉⠁⠀⢀⡤⠒⠋⠁⢠⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠐⠚⠿⣿⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢃⠀⢀⡼⢁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⠈⡧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⣆⠈⢶⣿⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⢇⠀⠉⠙⠒⠒⠒⠲⡶⠶⠒⠒⠉⠱⣄⠈⢀⡼⠋⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠘⢷⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣄⡀⠀⠀⠻⣦⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⡯⠍⠀⠀⠈⠉⠓⠢⣄⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢉⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣣⡴⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠃⠀⢠⠀⣧⡀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⢹⠁⠀⠀⠀⠀⣠⠄⣠⠞⠉⠀⠀⠀⠀⣸⠀⡏⢹⠀⠀⣠⢤⡴⠋⢀⡎⠀⣠⠴⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⢀⡴⠞⣿⢞⣵⣖⠓⠲⣎⣀⠔⠁⣠⣁⡎⡰⠋⢀⠎⠀⢀⣎⡴⠋⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣀⡤⣶⣩⡇⠐⣿⣿⠋⢻⣧⠀⠹⠷⠀⢰⡿⣿⠎⠀⢀⣞⣤⣤⡟⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠀⠀⣿⣿⠁⠀⣿⣿⣧⣴⣿⠀⠀⠀⠀⡼⢀⡇⠀⢀⣾⠋⢀⠏⠀⢀⣴⣋⡀⢀⣠⡤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡛⠁⠀⠀⠈⠿⣿⡿⠃⠀⠀⣠⠞⠁⣸⣷⢶⠋⣹⠀⣼⠖⢳⡎⠀⠀⠀⣀⠼⠛⠛⠳⣦⡀⠉⠳⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣤⡊⠀⠀⠀⠀⠀⢀⡶⠟⢷⠆⣰⣿⣿⡜⣠⠇⠀⠁⢀⣞⡠⠔⠊⠉⠀⠀⠀⠀⠀⠈⠻⣟⢶⢬⣳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠊⢉⡏⠀⢠⢏⣼⣿⡿⣿⠼⠟⠀⠀⠰⡏⠉⢙⡖⠢⢤⡀⠀⠀⠀⠀⠀⠀⢹⣆⢧⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠃⡏⠀⠀⠀⣀⣠⣧⠖⡏⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣿⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣿⡟⢻⡇⢀⠇⠀⠀⠉⠁⠀⣿⠀⢳⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⢹⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢿⠁⠸⡄⢸⠀⠀⠀⠀⠀⡐⠸⠀⡟⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⢸⡇⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢌⡀⠀⠹⣾⠀⡄⠀⢀⡴⠃⠀⢠⠃⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⢺⠈⠃⢹⣾⡉⠹⡀⠀⠸⠲⡀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢸⣿⡸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠇⢣⠀⢣⠀⠀⠀⢳⠀⠀⠀⠀⠋⢸⠀⡄⠀⠀⢸⣿⢿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢸⢸⠀⠸⡆⠀⠀⠈⡇⠀⠀⠀⠀⢸⡇⣿⡄⠀⢸⣿⡄⠻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡎⠀⠀⠀⢸⣠⠀⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⢷⣾⠙⣄⠘⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡇⠀⠀⠀⢸⡿⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⡄⠈⠳⣿⡿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣼⠀⠀⠀⠀⢸⠃⠀⡼⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠂⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⢶⠃⠀⠀⠀⠀⣸⠋⢹⣃⡀⠀⢀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣿⢿⣫⣧⡑⡌⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣇⣿⢈⠁⢳⠱⠘⣀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠑⠒⠂⢠⠶⠶⣖⡒⣮⣿⢩⣽⠉⢉⢯⣹⡝⡠⠄⠀⣤⣤⣀⣀⣀⠤⠤⡀ ⡨⠶⠀⠀⠘⠒⢤⠄⠈⢷⢿⣿⣿⠀⢸⣿⣿⡟⡠⠊⢁⣀⠨⠕⠀⠀⣀⠔⠁ ⠙⠢⠤⣀⠀⠀⠥⠤⡄⠀⠺⣑⡤⠷⠧⣴⡿⠓⢁⣄⣈⣱⠀⠀⠀⠀⣈⠅⠀ ⠀⠀⠸⠤⠔⣖⣁⣠⠉⢉⠒⡛⠇⠀⠀⡝⡗⡙⣿⢃⡀⠰⡄⣈⣙⡍⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣒⣧⣻⣄⣴⣧⣧⡈⡸⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣒⢧⡈⡳⢋⣸⡿⡫⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡿⣯⣘⣿⣟⣹⢶⣾⠑⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠿⡘⠐⠘⠀⢿⣌⢿⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⡊⠔⡇⠀⠀⠀⢸⣜⣌⡊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠞⠒⠛⠒⢺⢴⡿⣶⢾⢺⡏⡧⠩⠦⠵⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠃⠃⠬⠔⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠳⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⡝⢧⠉⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣽⠀⠀⠀⠀⠀⠀⡇⡇⠀ ⠀⠀⢀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣇⠀⠀⠀⡃⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡧⣇⠀ ⠀⠀⣸⠀⣠⠔⠋⠉⠉⠉⠑⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠀⠀⠀⡇⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⡇⣷⠀ ⠀⠀⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⡤⠀⠀⠀⢻⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣧⣿⠀ ⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⡀⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⢸⡇⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣿⣿⠀ ⢀⡟⠀⢀⣀⣤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⢰⡟⢀⣼⡴⠚⠋⢻⡄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡷⡿⠀ ⣼⡥⠞⠉⠀⠀⢀⣠⡴⠶⠒⠛⠛⢲⣤⡀⠀⠀⢻⡁⢠⠀⢠⣯⡴⠋⠁⠀⠀⠀⠀⠹⠄⠀⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⣿⡀ ⠏⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⡶⠋⠀⠈⠓⢤⡀⢳⡏⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡄⠀⠀⠀⠀⠀⠀⢸⡆⠉⠉⠁ ⠀⠀⣰⡿⠃⠀⠀⢀⣴⠞⢁⡞⠁⢀⡤⠂⠀⠀⠙⢾⡷⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠿⡄⠀⠀ ⢀⣾⠟⠀⠀⠀⣴⡿⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢷⠀⠀ ⠈⠏⠀⠀⢠⣾⠟⠀⠀⣼⠁⣀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣖⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠘⣇⠸ ⠀⠀⠀⣰⣫⠏⠀⠀⠀⣿⣤⡿⠋⠐⠚⢿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⣿⣿⡆⠙⢿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⡀⠀⢹⡄ ⠀⠀⢰⢿⡏⠀⠀⠀⢀⣧⣾⠁⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⢀⣿⣿⣿⠀⠈⢻⣟⠛⠃⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⠀⠈⣧ ⠀⢀⡏⡼⠁⠀⠀⠈⠉⣹⡏⠀⢸⣦⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⣾⣿⣿⣿⡀⠀⠈⢿⡦⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸ ⠀⠸⢀⠇⠀⠀⠀⠀⠀⣿⡙⠀⢸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⡿⣿⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠸ ⡄⠀⢨⡄⠀⠀⠀⠀⠀⣸⠇⠀⠘⣍⠈⢀⡇⣀⣠⠤⣤⡀⠀⠀⠘⣯⠃⠈⠀⣹⠏⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣄⡇⠀⠀⠀⠀⣰⢏⡠⠴⠄⠉⠉⠋⢸⡁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣉⡉⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠁⠀⠀⢀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠘⡉⠳⣤⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠃⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠘⣿⠟⠁⠀⠀⠀⠀⣰⠃⠀⢀⠄⠀⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣻⠖⢶⣶⣾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣀⡾⠃⠀⠀⣾⠃⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢧⡀⠀⢀⣀⣴⠟⠀⠀⠘⣿⡇⠸⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣶⡿⠋⠀⢀⡾⡛⠀⣼⢡⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠬⠓⢚⣩⠞⠁⠀⠀⠀⠀⢿⣇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⢻⡟⠋⠀⠀⣠⠞⡱⠁⣼⠃⢸⠀
⣿⣿⡿⣿⢿⣟⡿⣿⣻⢿⣟⡿⣿⣻⢿⣻⢿⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⡿⣿⢿⣻⢿⣻⢿⣟⡿⣿⣻⢿⣟⡿⣟⡿⣟⣿⣻⡿⣟⡿⣿⢿⡿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠠⠀⠄⡀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂ ⣿⢷⣻⣽⣟⡾⣟⣷⣻⣟⡾⣟⣷⣻⢯⣟⡿⣞⡿⣽⣳⢿⣯⣟⡾⣿⣽⣻⣽⢯⣟⣯⣿⣻⢾⣻⣷⣻⣟⣾⣟⣯⢿⣯⢷⣟⡿⣽⣻⣽⣯⢿⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣐⣀⡤⠀⠄⠡⠉⡐⠠⣈⣁⣄⣁⣡⣈⣁⣂⠄⠚⠒⠶⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⣿⣟⣯⢿⣽⣻⣽⢾⡷⣯⢿⣻⣾⡽⣿⣽⣻⢯⣟⣯⢿⣻⢾⣽⣻⢷⣯⢷⣻⣯⣟⡾⣷⣻⢿⣽⡾⣷⢯⣷⢯⣿⣻⢾⣻⣞⡿⣯⡷⣟⡾⣟⣾⣽⣿⠀⠀⠀⢀⣠⣤⠶⢛⣋⣡⣴⣾⣾⣿⢿⡿⣿⣟⡿⣿⣻⢿⣻⢿⡿⣿⢿⣿⢿⣷⣶⣮⣭⣭⣁⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⣿⡾⣽⣻⡾⣽⡾⣯⢿⣽⣻⢷⣯⣟⡷⣯⣟⣯⣟⣾⢿⣽⣻⢾⡽⣟⣾⣟⣷⣻⣞⣿⣳⣟⡿⣾⡽⣯⡿⣽⣯⢷⣟⡿⣽⣾⣻⢷⣟⣯⣟⡿⣾⣳⣿⢀⡤⠖⣋⣡⣤⣶⡿⣟⡿⢯⣷⣛⡾⣏⣿⢳⡾⣽⣳⢯⣟⣭⣷⣿⣾⠿⠾⠿⢾⠷⣿⠿⠿⣿⣿⣿⣶⣥⣒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣽⢯⣷⣟⣯⢿⡽⣯⡷⣟⡿⣾⣽⣻⢷⣻⡾⣽⢾⣻⣞⣯⢿⣻⢯⣷⣟⣾⣽⢾⣳⡿⣽⣻⢷⡿⣽⣻⢷⣯⡿⣾⢿⣽⢾⣽⣻⣾⣻⣞⣿⣷⠟⢛⣩⣴⠿⣛⠿⡹⢷⢻⡽⣛⡿⣼⣏⣷⣻⢞⣯⣽⣳⢯⣟⣞⣧⢿⣹⢯⡿⣷⣶⣤⣀⡀⢠⣀⠀⠀⠀⠈⠉⣭⢟⣍⡛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄ ⣿⣽⣻⢾⣽⢾⣻⣽⢷⣻⢯⣿⣳⢯⣟⣯⡷⣟⣯⣿⣳⣯⣟⣯⣟⡿⣾⣽⣞⣯⡿⣯⡿⠿⢿⣿⣿⡽⣯⡿⣾⡽⣯⢿⣞⣯⣟⣷⢯⣷⡿⢋⣠⣴⠟⣯⢘⢧⡙⢮⡱⢋⠶⡱⣍⠶⣱⠪⣕⣋⡛⡞⢧⡟⣯⢾⣽⣺⢏⣯⢿⣹⠷⣯⣻⢟⣿⣦⣍⣙⠂⢤⣄⠀⠀⠀⠀⠉⠛⠲⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣈ ⣿⣳⣟⡿⣾⣻⣽⢾⣻⢯⣟⣷⣻⢯⣟⣾⣽⣻⢷⣯⢷⡿⣞⡿⣞⣿⣳⣟⣾⣽⣿⠏⣡⠔⠦⣈⠛⣿⣿⡽⣷⣻⣽⣯⣟⡾⣿⣾⠟⢡⡴⠚⠛⠛⠛⠶⢯⣦⣙⢦⡹⢍⡞⡱⢎⡵⢣⡹⢔⡎⡱⣍⠶⣉⢖⡣⢎⡭⣛⠞⡿⡽⣟⣷⣫⣟⡾⣝⣿⣻⢿⣦⣍⠙⢦⣀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠ ⣿⣳⣯⣟⣷⢯⣟⣯⣟⣯⢿⣞⣯⣿⣻⣞⣷⣻⣟⡾⣿⣽⣻⣽⣟⣷⣻⣟⣾⡿⠁⡴⠃⠀⠀⠈⠳⣀⠛⣿⣿⡽⣾⣳⣯⡿⢋⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣕⣮⢱⢣⢎⠧⡹⡜⣜⡱⢎⡵⡩⢖⡙⣎⠶⣡⢛⡴⡹⣌⢧⡛⡽⢻⠿⣶⣯⢿⣹⣟⣷⣦⣙⠲⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⣿⢷⣻⡾⣽⣯⣟⣾⡽⣯⢿⣽⣾⣳⣟⣾⣽⣳⣯⢿⣳⣯⢷⣻⢾⡽⣷⣯⣿⠁⡼⠁⠀⠀⠀⠀⠀⠈⠳⣌⠹⢿⣷⠟⢉⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢯⡜⢮⡱⢓⡼⢌⡳⣒⡝⣪⠕⣎⠞⣡⢏⡴⢓⡬⣒⠭⣜⠣⡝⢦⡙⣯⠳⡿⣾⣽⣻⣷⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠻⠷⠻⡷⣿⣾⣽⣿⣽⣿⣞⣷⣟⣾⣳⣯⣷⣟⣿⣻⣾⣻⣯⣿⠿⣷⣿⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⢻⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⡳⡜⢎⡵⢪⡜⣱⢚⡬⣙⠖⢮⢜⡣⡜⣥⢋⠶⡹⡜⣢⠷⣭⣻⢶⣇⢮⡙⡞⡿⣷⣌⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⡉⠉⠋⠙⠉⠋⠛⠛⠛⠛⠳⠷⠾⠿⠼⣏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣼⢰⢣⠞⡱⢎⠶⣩⠞⡱⢎⡱⡹⡔⡫⢞⣡⠳⢥⢛⡬⣹⢳⣍⠻⢷⣝⡲⣍⠟⣷⡌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧ ⠠⠌⠐⠀⡀⢠⠤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣇⢯⡱⢋⢮⡱⢎⡵⢋⠶⡱⢭⡱⢣⢎⡝⢮⡱⢎⡱⢎⡽⣷⡄⠉⠙⠷⣯⣲⠹⣦⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⢿ ⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⢏⢦⡓⡭⢲⡍⣞⡱⢣⣍⠳⣎⡜⣣⢜⡣⡝⢎⡖⢭⢿⡔⢦⠀⠫⣝⠷⣭⣳⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢯ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⠛⠛⠓⠒⠲⠬⢭⣝⣒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣆⠳⣍⠳⡜⢦⡙⢧⠜⡳⣌⠞⣡⢎⡵⣊⢗⡸⢣⢞⣻⣌⢷⡀⠈⠳⢮⡷⠿⠹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⠤⠤⠤⠤⣸⢸⡁⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢭⣙⡲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣌⢳⡙⢦⡙⢮⢍⡳⣌⠻⣔⢫⠴⣩⢎⠵⣋⢦⢣⢻⣎⢷⠀⠀⠀⠉⠳⣄⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣛⠶⣄⡀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠻⣧⣙⢦⡙⣎⢮⠱⣌⠳⣌⠧⣛⠴⣊⠷⣩⠖⣭⢒⣻⣎⢷⡀⠀⠀⠀⠈⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⢶⡤⣤⡴⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣝⡶⣄⡀⠀⠀⠀⠹⡟⢦⣄⡀⠀⠈⢻⣦⢙⡖⣊⠷⣌⠳⣌⠳⣍⢞⣡⢛⡴⢋⠶⣩⠖⣻⡌⢷⡀⠀⠀⠀⠉⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣳⡝⣾⡱⣏⢾⣱⢏⣾⢻⣏⣿⢯⣿⣿⣿⣻⢟⡿⣳⡶⣶⢶⡶⣶⣴⡇⢸⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣧⡟⢦⡀⠀⠀⠙⣷⡜⠿⣶⣄⡀⠙⣮⣜⡱⣚⢬⠳⣌⠳⡜⣎⠲⣍⠶⣩⠞⣡⠞⡥⢿⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⢘⡧⣟⠶⣽⡹⢮⡽⣞⡵⣏⡞⣿⡳⣞⣿⣷⢫⡟⣼⣹⢳⡝⣮⡝⣷⢺⣷⠘⡇⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⡇⠙⠲⣙⢳⣄⠀⠘⢿⡄⠈⢻⣿⣓⣮⣷⣕⢣⢎⡳⣌⠳⣍⠶⣙⢬⡚⣥⢚⡥⡛⡼⣙⢷⡘⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀ ⠠⣟⢾⣹⣖⡻⣝⢾⣱⢟⣼⣛⠶⣝⣿⠘⣿⣷⢻⡜⣧⢻⡜⣧⢻⣜⡻⣽⣇⠹⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡿⠋⠀⠀⠀⠈⠳⣮⡳⣄⠘⣿⡄⠘⠿⠿⣶⣮⣙⠿⣮⣵⣊⠷⣌⢳⣉⠶⣩⠲⡍⢶⡙⡴⣩⠞⣷⡙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀ ⠀⡿⣎⠷⣮⣝⡞⣯⢞⣽⢲⣏⢿⣺⣏⠢⢹⣯⢷⡹⣎⠿⣜⢧⡻⣜⣳⢭⣿⡄⢳⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠁⠀⠀⠀⠰⡄⠀⠀⠀⠹⢯⣷⡿⣿⡀⠀⠀⠀⠁⠉⠙⠺⢍⡛⢷⣮⣓⡬⠳⡥⢳⡙⢦⡙⢦⢓⢮⡹⣷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀ ⠀⣻⢼⣛⡶⣝⢾⡱⣏⡞⣧⢟⣾⠟⢣⢂⠃⣽⣯⡳⣏⠿⣜⢯⡳⣭⢞⡳⣞⣷⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣾⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠙⣦⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⣽⣿⢿⣾⣥⣛⢦⡙⢮⡍⠶⣱⢚⣷⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢾ ⠀⣹⢎⡷⣹⢞⣭⢻⡼⣹⢎⣿⣯⠞⢩⣂⡿⢠⡙⢷⣏⡟⣮⡳⣝⢮⡞⣵⢫⣾⠿⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣶⣶⣶⣾⠿⠿⠟⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠳⣾⡀⠀⠀⡆⠀⠀⣀⣠⣤⣴⣿⣿⣿⣷⡶⢭⣙⡻⠿⢶⣜⣣⢇⡫⣜⠻⣦⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣟ ⠀⢸⣏⠾⣵⢫⣞⣳⢽⣧⣿⠏⢰⡇⣼⢸⡇⠙⢷⡌⠹⣿⡲⣝⢮⣳⢺⡥⣏⣿⢀⣟⢨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠸⣧⠀⠀⣵⣴⡿⣿⡟⠉⠉⣿⣿⣯⣤⣀⣀⣀⠉⠻⢶⣯⣭⣛⡿⠷⢿⣼⣿⡎⢳⣄⠀⠀⠀⠀⠀⠀⢀⡿⣞ ⠀⢸⣎⠿⣜⣳⢎⡷⣫⡾⠁⠀⢨⡇⢸⢸⡇⠀⠀⢻⡄⠘⣿⡝⢮⡳⣓⢮⣓⢿⡀⣿⠀⢷⣬⣦⡀⠀⠀⠀⠀⠀⠀⠿⢿⣯⣤⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡿⡏⢁⢿⡇⠀⢰⣿⡯⠍⠩⠉⠉⠁⠀⠀⠀⠀⠈⠙⠉⠙⠛⠒⠶⠤⣦⣬⣻⣦⣄⠀⠀⠀⠀⣿⢽ ⠀⠐⣯⢻⡜⣧⢻⣼⡟⠁⠀⡐⢸⡇⢹⢨⡇⠀⢀⠀⢷⡀⢸⣿⢣⢷⣩⠶⣹⢾⡇⢽⡀⢘⡇⣧⠈⠃⠀⠀⠀⠀⢤⣤⣀⣤⣭⣿⣿⣿⠛⠛⠛⠛⠋⠙⠉⠉⠉⠉⠉⠉⠉⠙⠛⢻⣿⠛⠛⠛⠛⢿⣷⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡞⢸⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣟⡾ ⠀⠈⣷⢫⡞⣵⢫⣾⠁⠀⠂⢀⢸⡃⢜⠰⡇⠀⠀⠀⠘⡇⠀⣿⡿⣎⠮⣏⡵⣺⡇⢺⡅⠘⣿⡜⡆⠀⠀⠀⠀⠀⠈⠉⠉⡉⠉⣉⣛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢀⣼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠸⣿⣿⡏⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣻ ⠀⠀⡽⣣⢟⡼⣳⡿⠀⠀⠈⠀⢸⡇⠘⢸⡇⠀⠀⠀⠀⡇⠀⣿⣿⣜⡳⡭⢶⣹⣧⢸⡇⠀⠹⣿⡹⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣿⡟⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠛⢿⣷⣿⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣼ ⠀⠀⣱⢏⡾⣱⢯⡟⠀⠀⠁⠈⢸⡧⣯⣴⡇⠀⠀⠀⠀⡇⠀⣿⣛⡶⢭⣓⠯⣾⢹⡆⣟⣤⠀⢈⢳⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⣿⣿⣿⣧⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣾⣿⡿⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢾ ⠀⠀⢜⡯⣜⢧⣻⡇⠀⢀⡤⠛⣩⠤⣈⠛⠧⣀⠀⠀⢀⡇⠀⣿⢺⡝⣎⠧⣟⣿⠈⣇⢹⡼⠀⢀⠲⣿⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⢢ ⠀⠀⢸⡳⣝⢮⣽⡇⢠⡟⢠⠞⠁⠀⠈⠙⢦⡈⠳⡄⠀⡇⠀⣿⣣⢟⡼⣛⣼⡇⠀⣿⠀⢻⡄⢀⠀⢉⢹⣮⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⡆⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⣢ ⠀⠀⠨⡷⢭⡞⣼⠇⡼⢠⡏⠀⠀⠀⠀⠀⠀⠈⠳⣆⠈⢿⡀⣿⡼⡹⣜⡳⣼⡇⠀⢹⡆⠀⢻⣆⠈⢀⠀⠉⠿⢎⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡀⠀⠀⠀⣸⠇⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠰ ⠀⠀⠀⣟⣣⢟⣼⡃⣟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠛⣿⡵⢣⢧⠳⣽⠀⡄⠘⣧⠈⠀⠹⣧⠀⠈⠄⡀⠣⠿⣮⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠉⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠳ ⠀⠀⠀⣝⡲⣋⢾⡅⢸⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⢿⣝⢮⣹⣿⠀⡀⠀⣿⠀⡁⢂⠈⢷⡈⢀⠠⠀⠄⠀⠉⠳⣯⣓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱ ⠀⠀⠀⢳⣷⡙⣾⡃⠀⢧⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⢻⣷⣼⡗⠦⠁⠀⢸⡇⢐⡀⠎⡀⠻⣆⠀⡐⠈⡀⠌⢀⠀⠉⡝⠺⠿⣗⣦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣄⣀⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱ ⠀⠀⠀⠈⠙⠻⣾⡇⠀⠘⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠹⣿⡏⠁⠀⠀⠚⣧⠠⢐⠠⠐⠡⠈⠳⣄⠐⢀⠀⠂⣈⠀⣄⡀⠄⣀⣈⣉⡒⠉⠉⣉⣛⣲⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱ ⠀⠀⠀⠀⠀⢤⡈⠷⣄⠀⠘⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⢻⣅⠀⠀⠀⠈⢻⡄⠂⠄⡉⠄⠃⠄⡉⠷⣄⠠⠁⠉⠻⢯⣉⢭⠛⠽⠓⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡱ ⠀⠀⠀⠀⠀⠀⠉⠲⣌⡙⠦⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠃⣰⠀⠀⠀⣈⣧⠈⠄⠂⠠⢃⠐⠌⡐⠈⠳⣄⠡⠀⡀⢙⠪⣗⢦⡀⠀⠈⠒⠲⢤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢹⣧⡀⠄⢻⣼⡆⢿⡄⡁⠂⠌⡐⠠⠁⠂⡌⠳⣤⠀⠂⠘⡘⠷⣝⢦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⢷⡔⠨⢿⡇⠘⣿⣔⠈⠠⢀⠂⠁⠂⠄⢁⠈⠛⢦⣅⠀⠠⠸⣳⡝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢻⣕⠪⣿⡄⢹⣿⣷⣈⠠⢈⠄⠡⠈⠄⠨⠑⠠⠘⠳⣦⡀⠀⠙⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡱ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⣷⣸⣷⠀⢿⣿⣷⣔⠀⢂⠡⠈⠄⠡⠘⢠⠁⠆⡀⠙⢳⣄⡠⠙⣞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡀⠀⢀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠒ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⣠⢴⣒⣚⣒⣲⣤⢄⡀⠙⠦⡈⠳⣞⣦⠘⣿⣿⣿⣷⡄⢀⠃⢈⠠⠁⠂⠌⡐⠠⠑⠠⢈⠙⠷⡉⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⢀⡴⠚⠉⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡟⠁⠀⠀⠀⠀⠈⠉⠓⠻⢶⣄⣀⠈⠻⣦⠘⣿⣿⣿⣿⣦⡈⠀⠆⢈⠈⠐⡈⠁⠌⡁⠌⠰⠠⠀⠆⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢬⣷⠘⣿⣿⣿⣿⣷⣎⡀⢂⠌⡐⠀⢡⣤⡐⢈⠠⠁⠌⡐⢈⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣿⣿⣿⣻⣿⣷⡆⠐⠀⠌⠠⣇⠙⢦⡀⠃⢂⡐⠂⡐⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠀⠀⠀⠀⡀⢀⣀⣈⣙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⣿⣿⣿⣿⣿⣿⣦⠈⠠⢀⢻⡀⠀⠙⢦⡀⠄⠂⠄⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⣿⣿⣿⣻⣿⣿⣷⡀⠄⠸⡇⠀⠀⠈⠻⣄⠁⢂⠐⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⣿⣿⣿⣟⣿⣿⣷⡀⠁⣧⠀⠀⠀⠀⠘⢧⡀⠌⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠱ ⠈⠀⠀⠀⠀⠀⠘⠒⠦⢤⣄⣀⣀⠀⠀⠉⠺⠽⣲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⣿⣿⣿⣿⣿⣿⣧⠂⣿⠀⠀⠀⠀⠀⠈⢳⡄⠂⣽⠀⠀⠀⠀⠀⠀⠀⠈⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡱ ⠀⠀⠀⠀⢀⣛⣻⡷⠖⠂⠀⠤⡌⠉⣉⠶⠂⠀⠀⠉⠑⠲⠭⠭⠁⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⣿⣿⣿⣷⣿⣿⠠⡗⠀⠀⠀⠀⠀⠀⠀⢻⡄⢺⠀⠀⠀⠀⠀⠀⠀⠀⡿⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠒ ⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⢹⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⢞⣯⠹⣿⣿⡿⣿⡿⢨⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢧⠹⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⢍⡳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⢩ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⢀⠉⠒⠤⣄⣀⡀⠀⠀⠀⣏⢧⣀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠴⠒⢋⣩⠵⠚⢹⣏⣿⡄⢻⣿⣿⣿⠃⣼⠁⠀⠀⠀⠀⠀⠀⣰⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⢣ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠈⢿⡄⠀⢀⣀⢉⣉⠙⠒⠚⠀⠀⠉⠉⠁⠀⢀⣠⠤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⣷⢺⣧⠈⣿⣿⡟⢠⡏⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢥ ⠀⠀⠀⠀⠀⠀⠠⠃⢀⡴⠒⠀⠀⠀⡀⠀⣾⠀⠀⡬⠉⠉⠉⠉⢻⣟⠾⡶⢶⠶⣿⢻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⡆⢹⡟⣠⠟⠀⠀⠀⠀⠀⠀⠀⡟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡤ ⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠠⠀⠁⢀⣿⠀⠄⠀⠂⠐⠀⢨⠀⠽⣷⣭⢚⡵⣊⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣰⠇⡇⣉⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡔ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢨⡿⣿⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠀⢀⡬⠟⢛⣉⠃⢄⡱⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡀⠀⡴⠋⠰⠈⢌⢁⣂⡠⠴⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⢀⣾⢇⠄⣰⢲⡄⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠤⠤⠀⡀⠀⡀⠈⣺⠃⠨⠀⠘⢿⡷⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠊⡀⠈⠡⠄⠵⡈⣌⢢⢈⡆⠀⠀⢒⡊⠁⢠⠓⢁⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠀⠀⡈⠀⣆⡈⢯⠪⢽⡄⠛⠒⣄⣀⣏⠑⠠⠟⡭⠿⣿⠻⠑⠠⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⣿⠟⣸⣿⡃⠀⢀⢻⣗⠨⠔⠂⠄⡆⠀⠀⠀⠀⠀⠸ ⠀⠀⠐⣠⠀⠀⠀⠀⠀⢀⡧⢀⡿⠿⡏⠀⠞⠋⠛⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠍⠈⠁⠀⠐⠀⠆⠀⡌⠀⠘⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠢⣠⣐⣀⠀⠀⠀⠰⡁⠀⢰⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⣴⣶⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀ ⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣸⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⠷⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⢿⣿⣿⣿⣿⢿⠀⢠⣿⣿⣿⠟⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⠟⠘⠀⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠻⠿⠿⠟⠋⠀⠀⢸⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣀⡀⠙⠟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢔⠅⣊⣵⡿⣞⠛⢲⣼⣈⡷⠚⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢃⣾⣿⡿⠋⠜⢀⣟⡷⡁⠀⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠏⠘⡿⢄⢁⡁⠀⠉⠡⢀⡟⠁⠀⢀⣠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⢠⠁⣸⢮⣍⡀⠠⢴⢊⡧⠖⡊⣑⡻⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠞⠀⡇⠀⢳⡔⠂⠆⡮⡇⡬⠥⡶⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡀⠘⢆⡇⠀⠈⠁⡜⣰⠘⢟⣱⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠰⢱⡀⠐⣠⠃⠹⣤⣤⠏⢻⣳⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡆⢠⡞⠈⣩⠋⠳⢀⢰⠀⠀⠈⣄⠙⢍⡉⠁⠒⢄⠀ ⠀⣀⡀⠀⠀⠀⢀⢼⠜⠀⠁⡇⠀⠀⡔⡙⡄⠀⠀⠱⡁⢀⢣⠑⠀⠀⠃ ⢜⡄⠈⠀⣠⠎⣰⣋⣉⣀⣠⡟⠀⢀⠗⠈⠘⠩⢰⠀⠘⡄⠁⠂⠀⠀⡀ ⠈⠚⠛⠈⠑⠊⠀⠀⣠⠞⠁⠀⢠⠏⠀⠀⠀⠀⢸⠀⠀⠰⠀⡠⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣃⠀⠤⠴⠃⠀⠀⠀⠀⠀⠈⣆⠀⠀⡗⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠃⠀⠀⠀⠀
⡠⠖⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⡇⢀⠇⠙⢦⠀⠀⠀⠀⠀⠀ ⢠⠐⠊⠉⠉⠀⠀⠉⠑⢦⠀⠀⠀⣹⠀⠀⠀⠀⣠⢃⡜⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡇⠀⢀⣠⠴⠧⠮⠤⠤⠤⣀⡀⢣⠀⠀⠀⠀ ⠀⠰⡖⢉⠝⠉⠒⠢⢄⡀⠀⡇⣘⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀ ⠀⠀⢇⠎⠀⠀⠀⠀⠀⠙⢦⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀ ⠀⢸⡘⠀⠀⠀⡀⠀⠀⠀⠀⠁⢦⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⢀⠆⡇⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠀ ⠂⠀⡇⢢⡶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠀⠀⠈⣷⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⣇⡟⠀⢹⣷⠀⠀⠀⠀⠀⣠⣾⠟⠋⠻⣿⡶⡀⠀⠀⢸⡆⠈⡉⠒⠲⡆⠀ ⢧⢀⣇⣁⣀⠀⢋⣀⣀⡀⠀⠀⠟⠁⠀⠀⠀⠘⡿⢓⡀⠀⢸⠃⠀⡇⠀⠀⠱⠀ ⢸⡇⠀⠀⠀⠀⢸⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠨⠶⠀⠁⠀⢸⠀⠀⡇⠀⠀⠀⠀ ⠀⢣⡀⠀⠀⠀⠀⠰⠂⠒⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡸⠀⠀⠀⠀⠀ ⠀⠠⠾⠒⠤⣄⠀⠀⡷⠉⠀⠹⠀⠀⣀⠤⠤⠤⢄⣤⠚⠁⠀⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠒⡦⠬⢀⣀⣀⣀⠎⠀⠀⠀⠀⠀⠀⠉⠺⣏⠀⠀⠀⠀⣰⢤⠂ ⠀⠀⠀⠀⣀⣸⣀⣷⣀⣀⣼⣿⣟⣀⣀⣀⠀⠀⢀⣀⡀⣀⣈⣳⡤⣤⢭⣓⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⢀⣀⣤⡤⢤⣤⣀⣀⡀⠀⢸⠁⠈⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⡛⣾⢯⣷⡋⡴⢺⠟⡕⠁⠉⠉⣻⠀⠀⢳⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡞⣷⣽⡀⢳⡽⢀⠏⢸⠀⠀⠀⢸⡁⠀⠀⢸⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⢠⠇⡞⠙⢾⡇⢸⣄⣴⣤⣤⣤⣤⣝⣦⣀⠘⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⡏⠀⣇⣤⠶⠛⠉⠁⣸⢻⢹⣧⣼⣷⣇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢠⣧⠾⣯⣿⢦⡀⠀⠀⢿⢸⣈⣿⣿⣿⣾⠄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡾⠋⠀⠙⢻⣧⣹⣆⠀⠘⣇⠳⣿⣋⠑⠫⠍⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠒⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀ ⠘⠁⠀⠀⠀⠀⠻⣟⣿⠂⠀⠘⠖⠛⢁⡦⡤⣞⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠈⠉⠀⠂⣌⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣞⠁⠀⡴⠀⠀⠀⣼⣿⠿⢟⡅⢸⡆⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄⠳⡄⠙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠓⠒⢺⡏⣿⠤⢖⡿⠁⢛⢿⣦⡤⠤⠤⣤⣾⣠⣴⣶⣶⣒⡲⢤⣉⠑⢦⡀⠈⢆⠹⡀⠸⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⡴⠋⠀⠀⡜⡎⡏⠰⠆⣀⢨⣿⣿⠁⠀⠀⠈⠙⢷⣌⢣⡀⠑⡀⠸⠀⠇⠀⡟⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢹⣤⠄⢀⡜⡹⢁⡇⠐⡤⠿⠄⠉⢻⡄⠀⠀⠀⠀⠀⠻⣆⠹⡀⢡⠀⡄⢸⠀⣿⢹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⣦⣊⡴⠁⡼⠐⠃⠾⣦⠠⣄⣸⠇⠀⠀⠀⠀⠀⠀⢹⡆⢳⢸⠀⡆⠈⠀⣸⠘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠈⠛⠦⠾⠁⠀⠀⠾⠚⠀⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⢸⠀⠇⠀⠀⣿⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠲⡦⠀⢀⣀⣀⣀⣘⣦⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⠈⠀⠀⠀⡏⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⠁⠀⢸⠉⠉⠉⠹⣌⠳⣄⠀⠚⠉⠻⡄⠀⠀⠀⠀⠀⠀⢸⣿⢻⡀⠀⠁⢸⢁⣼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣸⢧⠀⠀⠀⠈⢳⡈⢳⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢸⣿⣇⠇⠘⠀⣯⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡏⠘⣇⠀⠀⠀⠀⢳⠀⢳⠀⠀⠀⠹⣆⠀⠀⠀⠀⣼⣻⢹⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡇⠀⢹⡀⠀⠀⠀⠘⡆⠘⡆⠀⠀⠀⠹⡄⠀⠀⢀⣟⡏⣷⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣸⠁⠀⠀⡇⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⢳⠀⠀⢼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢀⡏⠀⠀⠀⣧⠀⠀⠀⣾⠀⢀⡇⠀⠀⠀⠀⠘⡆⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣄⣀⣀⣠⡤⠞⠓⠒⠒⠛⠁⠀⠀⠀⠈⠉⠹⣅⣀⣠⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠈⡆⠀⠀⠘⡄⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢰⠀⠀⠀⢧⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⢀⣠⡤⠗⠒⠒⠒⠂⠤⢼⡄⠀⠀⣀⡈⡇⠀⠀⠸⠀⠀⢸⠀⠀ ⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢑⡾⠋⢳⣼⡀⠀⠀⡆⠀⢸⠄⠀ ⠀⠀⠈⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⣠⣿⠭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡄⢧⠇⠀⠀⢧⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠈⠲⢄⠀⠀⣴⡟⠁⠀⠈⢧⢀⣤⣤⣶⠘⠁⢀⣠⡴⠞⠀⠀⢠⡇⢸⢸⡀⠀⢸⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⢙⡶⠋⠀⠀⢠⠀⢸⡏⠀⠙⠓⠒⠚⠉⠁⠀⠀⠀⠀⡼⠀⣞⡇⢃⠀⠀⡆⠀⢃⠀ ⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣠⠟⠀⠀⠀⠀⠈⠀⡼⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠁⠸⡄⠀⣧⠀⢸⠀ ⠀⠀⠈⠉⠒⠂⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣀⡤⠞⣿⣾⠋⠿⣶⣶⡶⡶⠲⠒⣿⡷⢀⡾⠃⢾⠀⠀⢣⠀⠸⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠲⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢀⡀⢨⠀⠀⢀⡠⢔⠚⠯⣄⣰⡹⠃⠀⠀⡟⠻⠅⠀⠀⡰⣡⡷⠛⠀⢸⡟⣆⠀⠈⡖⠀⡆⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⡄⠀⠀⠈⢦⠀⠘⢇⠐⢂⠀⠀⠑⠤⢤⠤⢺⡿⠋⠀⠀⢀⣿⡀⠘⡄⠀⢳⠀⢣⠸⡄ ⠀⠠⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⠄⣀⡀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠳⡄⠀⠑⠭⢁⣀⣀⣀⣀⣠⣿⡵⠀⠀⠀⡸⡇⠱⡄⠘⡄⠈⣆⠸⡀⡃ ⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠠⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠤⣀⡀⠙⢦⡀⠀⠘⢷⡦⢄⡀⢀⡟⠉⠁⣆⣼⠂⠀⠀⠀⢧⣇⠀⠘⢆⠙⡀⢹⠀⡇⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠦⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠦⡀⠀⠙⢦⣸⠋⠀⠀⠀⠋⢸⡇⠀⡀⠀⢸⡀⠱⢄⠀⠳⡱⡀⡆⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠀⠤⠤⣀⣀⡀⠀⠈⠢⣄⡼⠃⠀⠀⠀⠀⠀⠘⣤⠀⢳⠀⣹⣌⡓⣬⣷⠶⠛⠋⠙⠚⢲ ⠀⠈⠉⠉⠉⠐⠒⠒⠒⠒⠤⠤⠤⠤⠄⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢺⠃⠀⠀⠀⠀⠀⣠⠴⢿⣦⢴⣦⢧⣧⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠒⠐⠒⠒⠒⠠⠤⠤⠤⢤⣀⣸⠀⠀⠀⠀⠀⡞⠁⠀⠈⣷⡼⠭⠿⣿⣧⣴⣖⣶⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⠖⠒⢒⣾⠤⠬⠭⢻⠆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⠀⠀⠀⠀⠀⣴⣶⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠙⠻⣿⣗⣶⣤⠀⠀ ⠀⠀⠀⢀⣤⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣀⣄⡀⠀⠉⣽⣽⣵⡄ ⠀⠀⠀⠛⣿⡯⣻⢟⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⣄⠀⠛⠙⠙⠁ ⠀⠀⠀⠀⠈⠳⡌⢩⣶⣭⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣆⠈⠓⠎⢯⣻⣿⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡾⢹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⢻⣻⡇⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠇⠚⡧⠀⠀⠀ ⠀⣤⡴⠶⠶⠶⢖⠒⢚⣆⠀⠀⠀⢯⢳⡀⠀⠉⢿⣄⠀⠀⠀⠀⠀⣀⠔⠒⠁⠀⠀⠉⠉⠉⠙⠲⢤⣄⡀⠀⠞⠀⠀⣇⠀⠀⠀ ⢰⣿⡷⡄⠀⠀⠀⠱⡄⢹⡀⠀⠀⠸⣽⣷⡀⠀⡼⠙⣦⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⡈⡟⠀⠀⠀ ⢸⣇⠀⣟⢦⡀⠀⠀⠘⢆⣇⠀⠀⣳⣿⠏⠹⣌⠀⠀⡏⢧⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀ ⠈⣿⠀⢿⣦⠵⡀⠀⠀⠘⣿⠀⠀⢻⡟⠀⠀⠘⢦⡘⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠙⠀ ⠀⠸⡄⠸⡾⣄⠹⡄⠀⠀⢸⠀⠀⢾⣇⣀⠀⠀⣾⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡒⠆⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠹⡜⣦⡹⠀⢀⣼⡧⣄⣠⣷⡏⠙⠛⣿⣀⠀⣼⡝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⣤⠤⣤⠄⠀⠀ ⠀⠀⠀⠙⢄⠙⢌⠻⠖⠁⢸⡇⠘⣿⣿⣷⣀⣀⠘⡇⠀⠈⠉⣼⠉⠉⠛⠓⢒⠲⣛⣛⡛⣟⠀⠀⠀⠀⢠⣿⣏⡼⠀⢘⡇⠀⠀ ⠀⠀⠀⠀⠈⠳⡈⠳⣄⠀⢸⠇⢀⣾⡇⠑⠿⢷⣾⣷⠀⠀⠀⣿⢀⡀⠀⠀⣀⣀⣭⣴⣶⣿⣶⣶⣶⣤⣿⢉⠞⠁⠀⢼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⢬⣓⣾⠤⠚⠀⢧⠀⠀⠐⣮⠇⠀⠀⠀⠋⠙⠿⠿⠟⠛⠁⠒⠚⠋⠉⠉⠀⣠⡿⠟⠁⠀⠄⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣀⣠⣤⢤⡀⢀⣀⣀⣤⠖⠋⠁⠀⡠⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠙⠓⢚⣿⣿⣟⣿⠟⠁⠀⢀⠴⠊⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⢉⠟⠁⠀⠀⠐⠁⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠏⠈⣠⠋⠀⠀⡤⠤⠒⠒⣤⠀⢀⡜⣱⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⡴⠁⠀⣰⠃⠀⣠⠋⠀⢠⠀⢰⣿⢀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⡠⠊⠀⠀⢰⡇⠀⢀⡇⠀⠠⢻⡀⣼⠟⡏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⣿⡆⠀⢸⣇⡟⠀⢹⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠇⢻⣧⣠⣾⠟⠀⢀⣾⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⢲⣔⠋⠉⠁⣀⠴⠋⡼⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠏⠈⢷⡛⠛⠓⠒⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⡀⢀⣀⡠⣺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠫⠭⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡀⡤⠑⠲⠦⠤⠤⣤⣀⡠⠒⠠⡀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠈⠁⠢⡀⠀⠀⢊⠇⠀⣤⠘⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⡚⠅⠒⠈⠉⠉⠉⠉⠐⠢⢀⠀⠈⠄⠀⢸⡀⠀⠀⣶⠞⡄⠀⠀⠀⠀ ⠀⠀⡴⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠔⠊⠁⠁⠀⠀⠀⣔⠋⠆⠀⠀⠀ ⠀⡼⢡⡞⠀⠀⠀⠀⡠⠒⣩⠕⠋⠑⠒⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀ ⠀⡠⡛⠁⠀⠀⠠⠊⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⡂⢸⡄⠀⠀⠀ ⠀⠁⠃⠀⠀⠀⠀⠀⢠⣃⣀⣀⣀⣤⠖⠀⠀⠓⢲⣯⠽⠛⢿⣄⡁⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢸⡿⠛⠛⠻⢻⠀⠀⠀⠀⢸⠀⠀⠀⢧⣿⣲⣤⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢰⣿⠀⠀⠀⠀⠀⢂⠀⠀⣨⠿⠓⠘⡜⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⡦⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⢉⡤⡆⠀⠇⡗⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⢀⠀⠀⢹⣿⣦⣀⢀⣀⠰⠊⠉⢑⣠⠴⠋⢀⠁⢰⢀⡷⠤⠤⠄ ⠀⠀⠘⣇⠀⠀⢸⠀⠀⠀⡿⣿⣿⣿⠑⢌⠡⠤⢼⠀⠀⠀⡘⠀⡄⢸⡷⢄⠀⢀ ⠉⠐⠒⢿⡄⠀⠈⠀⠀⠀⢉⢋⡝⣰⡷⢤⣑⠠⡇⠀⠀⠀⠇⢀⠁⡇⠑⣼⠑⠒ ⠀⠀⠀⠀⢳⡀⠀⡆⠀⠀⠘⠸⡄⡇⢹⡀⠀⡱⡇⠀⠀⢰⠀⠸⢠⡇⠀⣼⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⣤⢶⣛⣟⡳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠾⣭⢳⣛⢦⡼⣽⢞⡯⣝⣻⣛⢮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣏⢿⣸⣧⠿⣎⣿⢏⡾⣱⢏⣶⣭⣛⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢣⣟⡾⣵⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣜⡿⣱⢎⡿⣩⠿⣏⢾⡱⣏⣷⠘⣗⢾⡟⠀⠀⠀⢀⣠⡤⣤⢤⣄⡀⣼⢧⣟⡳⣞⣷⡹⣎⣧⡴⣞⢶⡄⢀⣀⠀⠀⠀ ⠀⠀⠀⣀⣤⡼⢾⡝⣧⢿⡹⢷⣻⡜⣧⢻⣜⠏⠀⡸⠟⠓⠒⢢⣴⢯⡳⣽⠳⣯⡞⡽⣏⢶⡟⣷⣹⢾⡳⣝⢮⣳⣾⣿⢫⡝⣮⣛⠷⣄ ⠀⠀⢸⡳⢧⡻⣭⢿⡜⣯⢻⣧⢿⠾⠵⠛⠉⢠⠎⠀⠀⠀⠀⣼⢿⣮⣽⠇⠀⠈⢻⣷⣹⠾⠿⠶⣯⣳⡝⣮⢳⣭⠷⣎⡷⣹⠶⣭⢻⣹ ⠀⠀⣸⣿⣳⢿⣖⣯⢟⣮⢳⣎⣿⠀⠀⠀⢠⠃⢠⠃⠀⠀⠘⣿⢎⣷⣿⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠉⢻⡼⠛⢄⢠⠀⠙⣧⢻⡜⣧⢻ ⣶⡄⢿⡼⣭⣛⡾⣎⠿⣬⢳⡾⠃⠀⠀⠀⡎⠀⡔⠀⠀⠀⠀⢻⣏⡞⣿⡄⠸⡀⠀⢰⣀⡴⠆⢦⣄⡀⠀⠀⢠⣿⡯⠄⠀⢹⣣⢟⡼⡋ ⠙⢾⣏⣷⠏⠉⠙⠚⠛⠊⠉⠀⠀⠀⠀⠀⡇⢰⠃⠀⠀⠀⢀⣀⣻⣝⠾⣷⡀⠀⢸⣶⡝⠃⢀⣼⣿⣿⣆⠀⢼⣿⣿⠀⠀⢸⣣⢟⡼⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡇⠀⠀⣰⣿⣏⣹⣉⢿⣸⢹⣇⠀⠈⠁⠀⠈⢷⣿⣿⣿⠀⠸⣿⠿⠀⠀⠀⠱⣏⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⡽⡀⢸⢿⡳⢮⡵⣎⠷⣭⢳⣽⡆⠀⣸⣄⠀⣦⠿⠷⠿⠀⠀⠑⠶⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢀⠞⠀⠈⣿⢫⡟⣷⡷⣭⣟⣾⡷⣋⠀⠀⠘⠉⠉⠀⠀⠀⠀⢀⣾⣄⡤⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡼⠀⠀⠀⣸⣧⢻⡜⣷⣹⢎⡷⣹⠽⣦⠀⠀⢀⣄⡀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⠃⡠⠒⠉⠀⠈⢉⣿⢻⡽⣯⢳⣭⢻⣼⣆⠔⠊⠑⠤⡉⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⠠⡁⠀⠀⢢⡠⢻⣎⢯⣷⣭⢳⣎⡷⠯⠓⣄⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢘⡆⢣⠀⠀⠀⠙⢌⠺⣗⣮⣝⡻⢯⡄⠀⣣⠀⠣⡄⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠔⠊⠀⠈⡇⠀⠀⠀⠈⢆⠒⠶⠯⠿⠟⠉⠉⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠁⠙⡄⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀pinky pie💗
⠀⠀⠀⢀⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⠄⠀⠀⣰⠟⠉⠁⠀⠈⣿⡆⠀⠀ ⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⣰⡿⣁⣤⣤⡴⠶⡶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⢀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣯⠀⠀⠀ ⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⡿⢻⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣡⣴⣿⠋⠀⢸⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣄⣀⣀⢀⣀⣀⣀⣠⣤⣶⠿⢿⣅⣸⠀⢀⣸⣆⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠉⠙⠛⠛⠛⠉⣽⢿⡷⠦⣄⠈⠻⣄⢈⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠉⠙⠒⢦⣄⡀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢸⠃⠀⢻⣷⣦⡑⡄⠈⠻⡀⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⢸⡇⠀⠀⠀⠀⡏⠀⠀⢸⣿⣿⣷⡈⢆⠀⢱⡎⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣠⡴⢶⣶⣶⣶⣤⣄⡀⠙⢿⣿⠁⠀⠀⠀⠀⣧⠀⠀⣸⣿⢿⣿⣷⠸⠀⠀⣿⡸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠟⠉⢠⡿⠉⠀⠙⣿⣿⣿⣦⡈⠃⠀⠀⠀⠀⠀⠺⣄⣴⢿⣷⣤⣿⣿⠆⡇⠀⢸⣇⣇⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣄⣠⡏⠀⢠⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⡿⢠⣀⣀⣸⣿⣿⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠈⢹⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⡟⠃⠈⠀⠀⠀⢹⣾⠀ ⠀⠀⠀⠀⢳⠀⠀⢤⡤⠿⠀⠀⠘⡎⢧⡀⠀⣠⡿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣈⠟⠁⠀⠀⠀⠀⠀⠀⡏⡇⠀ ⠀⠀⠀⠘⡄⢧⠀⠀⠀⠘⡄⠀⠀⠱⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀⠀⡤⠖⠋⠉⠀⡀⠀⠀⠀⠀⠀⣼⣳⡇⠀ ⠀⠈⠳⢄⠸⡌⢧⠀⠀⠀⠱⡀⠀⠀⠱⣄⠙⢿⣿⣿⣿⡟⠛⠛⠛⠉⠀⠀⠈⢀⠀⠀⠀⠀⠁⡄⠀⠀⠀⢰⣿⠿⡇⠀ ⠀⣠⣔⣺⣷⣦⡈⠳⡀⠀⠀⠑⣄⠀⠀⠈⠓⣤⡾⠃⠀⠀⢠⠖⠁⠀⠀⢸⡀⠀⠀⠀⠀⢠⣼⠁⠀⠀⢰⣿⣟⣧⠀⠀ ⠀⠈⠻⣿⣿⣍⡉⠃⡙⢦⡀⠀⠈⠳⢄⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣤⣶⣿⠋⠀⠀⣰⡿⠁⠈⠙⠀⡀ ⠀⠀⠀⠈⢻⣿⣿⣛⠿⢦⣙⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣥⣼⠏⠀⢀⣾⣿⡅⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠘⠎⠙⠿⣷⣦⣌⡳⢍⡓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡠⠚⣠⣾⠟⠃⠈⠇⢸⡆⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠿⠿⣷⣶⢈⠙⠿⠶⠤⡤⠄⠀⠀⠀⠀⢀⣀⣀⡤⡴⠞⠋⠛⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢹⣿⠁⠀⢀⣀⠀⠀⢠⠄⠀⠀⠀⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⡶⠦⠤⣤⡏⢑⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⡇⠀⠳⡹⡄⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⠛⠀⢀⡇⢹⠀ ⠀⠀⠀⠐⢹⣿⣿⣿⣿⣿⣿⡟⣀⢶⣟⡴⠃⣠⠶⢿⡵⢾⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢟⡵⠟⠋⠀⣸⠛⣿⣆⠹⣏⠀ ⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⡟⠙⣦⡀⠀⠀⢇⣰⡿⣿⡄⢹⠀ ⠀⠀⠀⠀⡏⠸⣿⣿⡿⢹⣆⣴⡿⣷⠀⠀⠸⣿⣷⣿⠇⣼⠀ ⠀⠀⠀⠀⠁⠀⣿⣿⢻⣆⠻⣿⣿⣿⡇⠔⠒⣙⠛⠍⢪⡟⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⠀⠻⣧⡪⠉⠝⠁⢗⣀⠝⢀⣴⠏⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣽⣶⣿⣿⣿⣷⠦⠤⠤⠶⣾⣿⣿⡀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀ ⠀⠀⢀⣿⢿⣿⣿⣿⣻⡏⣹⠃⠉⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⠁⣿⣿⣿⡏⣿⣿⣿⠀⠀⠀⠀⢸⡏⢻⣿⡟⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⡇⢹⣿⣿⡄⣠⠀⠀⠈⠀⠀⡿⣧⠇⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡇⣼⣿⣿⣿⡟⠀⠀⣶⠀⠀⢳⠋⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢠⠟⢁⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀ ⠀⢀⣠⣾⢟⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷⠀⠀ ⠚⠛⠉⠐⠋⢀⣻⣿⣿⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣆⡀ ⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣦⣤⣤⣤⣤⣿⣤⣤⣤⣤⠼⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣆⣴⡛⢡⢑⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢻⡅⠁⠀⢻⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢇⡠⠟⢧⡆⠀⡐⡁⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⠤⡀⠀⠀⠀⣰⡙⠲⠄⠑⠚⠉⠁⠋⠤⠶⠦⡄⠀⠀⠀⠀⠀ ⠀⢊⡾⡢⣄⢠⠋⠿⣷⠀⠀⣤⣄⡀⢠⠀⠠⠊⠀⠀⠀⠀⢀⠀ ⠀⠈⡖⠻⡽⣾⡄⠰⣈⡐⠘⠻⠏⢫⠃⠀⠀⠀⠀⠀⢀⠐⡙⠀ ⠀⠀⠐⢜⠐⠱⢿⣢⢑⣛⣉⣀⠠⠂⠀⠀⣀⠠⠄⠦⠁⠬⡇⠀ ⠀⠀⠀⠀⠁⡂⠏⣹⠀⠀⠀⢆⠀⣠⠲⠍⣄⡈⢒⠊⠒⡼⠀⠀ ⠀⠀⠀⠀⠆⠈⣄⢼⠀⠀⠀⠀⢉⡁⡥⢂⠰⠈⡜⡄⠊⠀⠀⢀ ⠀⠀⠀⢀⠀⠀⢡⣈⢄⢀⠃⡘⠀⡈⠉⢻⢺⣏⢅⢌⠂⠤⠴⣺ ⠀⠀⠀⠸⡆⠐⠆⡅⢀⠃⢀⠓⠰⡚⠢⡀⠀⢞⢦⠢⡁⠀⢈⡟ ⠀⠀⠀⠀⠙⠃⠋⠀⢀⠀⠈⠓⢄⢠⠁⢨⢱⠀⢋⠑⠂⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠠⢈⣆⠀⡨⢳⠀⠈⣢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⠳⠏⠹⢄⡥⠉⠄⢀⢂⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡴⠟⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⠤⣀⠀⠀⠈⡕⢤⡒⠂⠉⠀⠀⠀⠀⠈⠉⠥⠒⠒⠒⠒⠂⠄⡀⠀⠀ ⢀⠁⠀⠀⠑⡤⠊⢹⠁⡹⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠣⡀ ⢸⠀⠀⠀⡐⠁⠀⠀⢇⠀⢀⠗⡄⠀⠀⠀⠀⡀⡄⣀⡀⠀⠀⠀⠀⢀⣀⠅ ⢸⠀⢠⢠⢁⠀⠀⠀⠈⠆⠁⡠⠁⠀⠀⠰⢠⠟⠀⣀⠀⠸⠈⠉⠁⠀⠈⠂ ⢸⡀⠈⣸⡌⠀⠀⠀⠀⠘⠈⠀⠀⠀⢀⡷⠉⡲⠚⠒⠲⣶⢷⠀⠀⠀⠀⠀ ⠀⢧⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣠⠀⠀⠀⡇⡆⢺⠀⠀⠀⠀ ⠀⠈⠳⣀⢠⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠁⠒⠎⠊⠀⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⢂⠀⠀⠀⢐⣉⡾⠊⠉⠀⡀⠔⠂⠩⠀⠀⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠢⠀⠀⠈⠹⠀⠀⠀⠀⠀⠁⠀⠀⡠⡇⠀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢑⠤⣀⣀⠀⠀⠀⣈⠇⠠⠐⡾⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠸⡀⠀⠀⠀⠏⠀⠀⠈⠒⠊⠀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠑⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠈⠦⣀⠃⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⠚⠓⠂⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡠⠴⣖⠒⠒⠲⣶⠒⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠊⠁⠀⠀⠀⠉⠒⢄⡘⢷⡀⢰⡆⠙⠢⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠟⠒⠒⣾⠓⡦⣤⣄⣀⠀⠙⠪⣷⡈⡇⠀⢀⠞⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠟⣉⡬⡶⠒⠻⣁⡜⠑⣤⣉⠶⠒⠛⠋⠙⠒⠎⠀⠀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡔⠉⢇⠹⡄⠀⠙⣦⣰⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡓⠦⡈⢦⠈⠢⣼⡉⠃⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⡼⠀⢸⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⡀⠈⠢⡑⢴⡇⠈⡄⠀⢀⠎⠀⢀⡀⡀⢈⣶⡞⢀⣀⣏⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⣲⣄⠱⡼⣿⣶⡆⠀⠈⠀⣀⣼⣷⡓⢺⣿⡿⠋⣸⠘⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⢻⣦⣤⣷⣧⢿⣿⠇⠀⠘⡟⣿⣿⣟⣷⣺⠿⠀⢀⡟⡂⠰⡼⡇⠀⠀⠀⠀⠀⣀⡤⠔⠒⠛⠛⢶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⠭⠿⠟⠁⡴⠋⠀⠀⠀⠧⠜⠛⠻⠗⠁⠀⠀⡸⠃⢣⡴⠃⡇⠀⠀⢀⡴⠊⢁⡠⠐⠒⠤⣄⠀⠈⢢⡈⠙⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢤⣠⠂⠀⠀⠀⠀⠀⣀⠤⠀⢀⡇⣸⣟⣁⢰⠃⠀⡴⠋⡠⠊⣁⠠⠤⠲⠤⣀⠑⢄⠀⢳⡀⠀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢛⠖⠉⠉⠁⠀⠀⢀⣾⣿⣛⠉⠀⡞⢀⡞⢀⣾⠕⠋⣀⠤⠤⠤⠤⣌⠳⡀⠱⡀⡇⠀⠀⢸⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠉⠲⢄⡀⡞⠀⠀⠀⠀⢀⡴⡿⣿⣯⡍⣹⡾⠁⡼⢠⡟⠁⡴⠊⠀⠀⠀⠀⠀⠀⠑⡝⡄⢹⡇⠀⠀⡟⡿⣧⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣾⡘⠀⢳⣋⡿⢫⡗⠰⣧⡎⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⠟⠀⠀⡜⢀⠇⣿⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢷⢤⣀⡇⠀⠀⠀⠀⠘⣏⣉⣉⡡⠔⢁⣷⢡⠀⠙⣅⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠜⠁⠀⣠⠞⠀⡜⠀⣟⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠈⠣⠈⢻⠀⠀⢄⠀⠀⣯⠀⠀⢀⠔⠋⣽⠿⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡤⠚⠁⢀⡜⠀⣸⣿⡆⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠘⡄⠀⠈⢣⡀⢸⡖⣉⣠⣶⠿⠛⠀⢰⣼⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⡠⠊⢀⣴⣿⠏⣷⡀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⡸⠁⠀⡇⠀⠀⠈⡏⠲⢍⡉⠁⠀⢢⡀⠄⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠁⢀⣴⣿⠟⢁⡾⢹⠁ ⠀⠀⠀⠀⠀⠀⠙⠤⠴⠁⠀⠀⠃⠀⠀⠀⢹⠀⠀⠈⠙⠒⡶⠿⢦⡀⠀⠀⠉⠉⠑⢄⠀⠀⠀⠀⠀⣼⣿⣿⣶⠿⠋⠁⡰⣻⢁⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⠈⠑⡦⢄⠀⠀⠈⠳⡄⠀⠀⠀⠘⠿⣉⣀⣠⠔⠋⡴⣡⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠈⢣⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⢣⣀⠴⢋⣴⠃⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⢳⡀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢳⡞⡟⢹⡸⢻⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀⢣⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⠳⡱⣈⣹⠟⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠃⠀⠀⠀⠀⠀⣷⣤⣤⣴⠁⠀⠀⠀⠀⣸⣤⣄⣀⣈⡇⠀⠀⠀⠀⠹⡄⠀⠀⠘⠢⠬⠽⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣷⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠟⠻⣿⣿⡟⠉⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⣠⠴⠖⠛⣙⣒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⣦⠀⢈⣽⠁⠀⣠⠟⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣼⣿⣶⣋⠤⠒⠈⢉⣽⠀⠉⢢⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣥⡵⠞⠉⠁⣰⠁⠀⢀⠀⠈⠙⠲⢄⡀⣤⠀⢀⣤⣄⠙⢦⣀⣾⡿⠟⠉⠀⣀⡜⣀⠞⠙⠀⠀⠀⡇⡿⠶⢦⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿ ⠟⠀⠀⠀⠀⣿⠀⢀⠀⠱⡄⠀⢦⠀⠻⣿⣤⣿⣿⣿⡞⡉⠙⠋⠀⠠⡶⠋⠉⠙⠳⣄⣀⣀⠔⠀⡦⠖⡚⢹⠃⠀⠀⠀⠀⣀⣴⣿⣿⣿ ⠀⠀⠀⠀⢰⣿⠀⢸⠃⠀⢱⠀⠘⣆⠀⣹⡿⠛⠉⠉⠛⢷⡄⠀⠀⠀⡇⠀⣀⣀⡀⠈⢧⠐⡀⠀⠀⢰⠁⣾⡀⠀⠀⣴⠟⠉⢻⣿⣿⣿ ⠀⠀⠀⠀⠸⣿⠣⡄⢧⠀⠘⣧⡀⢈⣿⠋⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢣⣾⣿⣶⣿⠤⠬⢿⢽⡀⠀⢰⠀⢇⢳⡀⠀⠣⣄⡀⣸⡿⣿⠿ ⠀⠀⠀⠀⠀⢹⣦⡈⠪⡁⠀⠀⠈⢹⠃⠀⣴⠛⣿⣉⣷⠀⢀⣸⢄⠴⠊⠁⠀⠈⠇⠀⠀⡞⠀⠈⢳⠀⠳⢼⣄⠙⠦⣤⣤⠽⢋⡴⠋⠐ ⠀⠀⢀⣀⡀⠀⠙⢤⣁⣬⠷⠤⢤⣿⠀⠀⣿⣀⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⡇⠀⠀⠀⢣⣀⣀⣀⣙⠒⠒⠒⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⢹⡆⢀⡞⠉⠀⠀⠀⠈⢻⣦⡤⠛⠉⠀⢶⠀⠀⠀⠀⠀⢀⡤⠚⣁⣤⣶⣼⣄⡇⠀⠀⠀⢸⡿⢷⡶⠤⣽⣶⠀⠀⠀⠀⠀⠀ ⠶⠤⠤⠶⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠈⠳⢤⠤⠔⠊⣁⢠⣾⣿⣿⣿⣟⡛⢻⠀⠀⠀⣼⡇⠀⠉⠓⢦⡙⢦⠀⠀⠀⠀⠀ ⠊⠀⠀⠀⢀⡟⠀⠀⠀⣰⠟⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠹⣦⡀⢹⣿⠟⠛⠧⡄⠰⣿⢸⠀⠀⢰⣿⠃⠀⠀⠀⠀⠹⣦⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠃⠀⠀⠀⣏⠐⠋⠀⢀⡿⠛⣩⠟⠀⠀⠀⠀⠀⠙⢿⣿⡏⢧⣠⣤⣤⠾⢡⠏⠀⣠⡿⠃⠀⢀⣤⢤⡀⠀⣿⢿⡀⠀⠀⠢ ⠀⠀⠀⠒⢦⠀⠀⠀⠀⠙⠦⣤⣤⡾⠁⡼⠛⠋⠉⠉⠓⢦⡀⠀⠀⠙⠳⠤⣍⣈⠤⠔⠁⢀⡴⠃⠀⠀⠀⣸⡁⠠⠷⢀⡟⣸⡇⠀⠀⠀ ⠦⣄⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣀⠀⢀⣀⠠⢾⠁⠀⠀⠀⢠⣿⣷⣄⣤⡼⠿⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢖⣶⡶⠚⠁⠐⠒⢦⡈⣧⠈⠛⣿⢶⣶⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁⠘⠉⠀⠀⠀⢀⣠⣴⡷⣿⠤⠚⢹⠉⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠏⠁⠈⠿⠁⡠⢿⢀⡠⠴⠛⣲⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⢣⠀⠀⠀⠞⠁⠋⠀⠀⠀⠚⠒⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⠤⣤⣤⢾⣯⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡄⠀⢀⣼⠟⠁⠀⠀⠀⠈⣆⡠⠖⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣿⡗⠿⢷⣀⠀⠀⢶⣤⣄⣠⣤⣟⠉⠉⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠈⠳⠶⣾⡿⠛⠛⠿⢻⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣶⣿⣍⣤⢀⠀⠀⢨⣧⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣷⣦⣮⣤⣀⣸⣿⣿⣽⣿⣿⡀⠀⠘⠿⣇⠀⠀⠀⢠⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠉⠈⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡖⣀⠀⣿⣄⠀⢠⠏⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠆
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⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠫⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢏⢢⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣨⠒⡊⠁⠀⠀⠀⠀⠀⠉⠂⡴⠁⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠛⢤⠁⠱⢄⣀⠠⠄⠀⠀⡜⠀⠀⡀⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠃⠀⠄⠀⠳⡡⠊⡀⠠⢤⡶⢊⡃⠀⠐⢁⠷⠐⣄⠀⠀⢀⠤⠂⠀⠀ ⠀⠀⡎⠀⡜⠀⠀⠈⡰⠉⢁⠉⣡⣴⣿⡿⠀⠀⢹⠁⠃⢸⣤⠊⠀⢀⠤⠂⠀ ⠀⠀⢇⠀⡇⠀⠀⠀⡇⠀⢨⡾⣋⣿⡿⠀⠀⡠⠃⠀⡄⠸⠇⠀⡰⠁⠀⠀⠀ ⠀⠀⠈⢆⠘⠀⠀⠢⡰⡀⠈⢃⢀⠽⠋⡀⡨⠂⠀⡐⠀⢰⠇⢠⠁⠔⠁⠀⠀ ⠀⠀⠀⠀⠁⢢⠀⡠⠋⠘⠂⠀⠉⠀⣼⠊⠀⠀⠔⠀⠀⡞⠀⠆⡌⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⡇⠢⡀⠀⠀⡀⠴⣾⠇⠀⢀⠊⠀⠀⠜⠀⠔⠸⠀⠀⡔⠁⠀ ⠀⠀⠀⣀⢀⡜⠀⠀⠈⠉⠉⠀⢰⢸⠀⠠⠁⠀⢠⠊⠠⠊⢀⠃⣀⠔⠁⠀⠀ ⠀⠀⠀⢣⠉⠀⠀⣰⠀⠀⠀⣰⣧⡺⡀⡆⠀⢠⢟⠜⠀⡠⠁⡄⠂⠀⢠⢄⡀ ⠀⠀⠀⠀⠈⠒⠾⠥⠀⠒⠁⡞⢾⡧⡷⡇⠐⡈⡄⠰⣂⣠⣤⣀⡸⠒⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢿⣄⠀⡷⠋⠀⠀⠙⢄⠀⠙⠒⣀⠾⠀⡑⠄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⡄⠂⠁⠀⣸⠄⠀⠀⠀⠀⠉⣉⡉⠰⣄⠎⠀⠀⠀⠱⠀⠀ ⠀⢀⠤⠐⠒⠒⠂⠬⢀⡀⠀⠇⡄⠀⠀⣇⡠⠊⢹⠂⢊⣼⠀⠀⠀⠀⠐⡆⠀ ⠄⠁⠀⢀⠠⠤⠠⠄⣀⠈⠙⠠⡀⠀⠀⢹⠁⠀⠀⠀⣰⠇⠀⠀⠀⢀⠌⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡈⠑⠂⠸⠤⠄⠐⠋⠂⠀⠀⠀⠄⠂⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⣀⡀⠀⠤⠒⠁⢀⢴⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠄⠀⠀⣀⠀⠀⠀⢀⣀⡠⢔⡡⠂⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠛⣿⢿⡿⡒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢸⡿⣽⣿⣷⣄⡆⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⠋⠀⠀⠀⠀⣀⣴⠿⠛⠋⠉⣉⣙⣦⣀⠈⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡀⠈⠣⡀⠀⣠⡾⠋⣁⠤⢶⠚⠻⠤⣀⡀⠀⠉⢁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⢃⣼⢋⡠⠊⠙⠒⢬⣳⡂⠤⣤⣠⡭⠝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣄⠉⢠⡞⡡⠫⣄⠤⣤⣤⣄⠈⠁⢠⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⢲⣿⠞⠀⡶⠃⠀⣿⣁⣿⣦⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄⣀⡀⠀⠀⠀⠀⠀⢀⡉⣿⠛⠁⠀⢇⠀⠀⠸⡿⣿⣿⠀⠀⠙⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡤⠊⠁⢀⠤⠐⠂⠈⢷⠒⠠⡖⢦⣸⠈⢻⡁⠀⠀⠈⠢⣀⣀⣈⡵⠃⠀⠀⢤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⠀⢀⡔⠁⢀⠔⠒⠒⠂⢧⡀⣱⣄⠙⡦⢤⣻⡄⠀⠀⠀⠀⢤⣤⢤⣤⣤⣒⣉⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⡘⠀⢀⠏⠀⢴⠒⠒⢋⣟⣠⡚⣺⣧⣠⢿⠿⣶⢄⡀⠀⠀⢿⠙⠣⠤⣀⠸⣍⣉⣽⣿⣿⣶⠻⡗⠢⢄⣀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠸⠀⠀⢠⡷⠔⠋⣽⣥⡉⢹⣩⣦⣼⠀⠈⠑⠻⢶⣶⣿⡷⠤⣀⠀⠉⠓⠢⡭⠿⠿⠿⠯⠥⠤⠤⠬⠵⠶⣄ ⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⡇⠀⢀⡈⢇⠀⢠⣿⣿⠇⢸⢻⣿⣿⠀⠀⠀⠀⡼⣿⡷⡙⠢⠤⠋⠐⠢⠄⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼ ⠀⠀⠀⠀⡸⠀⠀⠀⡇⠀⡇⠀⢸⠙⠚⠂⠸⡌⠁⠀⣿⣜⣿⣿⡇⠀⠀⣴⣥⡿⢧⣇⠀⠀⠀⣀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠃⣰⡇⠀⡇⠀⡇⠀⢸⠀⠀⠀⡠⠷⠀⢰⡿⠛⠛⡷⢷⠀⠀⢇⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣌⠓⠀⠚⡽⠀⢀⠇⢠⠃⠀⡜⠀⠀⢠⠁⠀⢀⣿⠃⠀⠀⡇⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡈⠓⠒⠊⠀⠀⡜⠀⡜⠀⣰⠃⠀⠀⡎⠀⠀⠈⡛⠀⠀⠀⢱⣼⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢄⡀⣀⠤⠊⣠⠜⣠⠔⠁⠀⠀⢸⡇⠀⠀⠀⡇⢧⡀⠀⢀⣿⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠑⠒⠛⠋⠉⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠛⠀⠀⠀⠀⠸⢄⣀⣀⣀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⡒⠒⠒⠒⠤⢀⢀⡠⠪⠄⠃⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢢⠀⢀⠔⡊⠅⠒⠀⠉⠉⠁⠐⠠⣈⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠓⠠⢀⣀⢼⣔⡕⢌⣒⣀⠐⠢⢄⠀⠀⠀⠀⠀⠑⡈⠢⡀⠀⠀⠀⢄⠀ ⠀⠀⡎⠀⠀⠀⠰⠉⠉⢳⠁⢀⠀⠁⠢⡀⠁⢂⠀⠀⠀⠀⠈⢂⠘⢆⠀⠀⠸⠡ ⠀⠀⢡⠀⠀⠀⡇⠠⠑⢌⢷⠀⢡⠀⠀⠈⢆⠀⠑⢄⠀⠀⠀⠀⠑⠠⠭⠞⠁⢠ ⠀⢰⠉⢆⠀⠀⡇⡇⠀⢈⠘⢇⢸⠣⡀⠀⠈⣆⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⢀⠄ ⠀⠈⡄⠈⠢⡀⣇⠈⢀⠢⣄⣔⣉⠉⢪⡑⠂⠼⢕⣤⣀⡀⠉⠒⠒⢒⡲⠞⠁⠀ ⠀⠀⠈⠢⣀⠝⢹⠄⠲⢽⢛⣔⠊⣷⠀⢱⠀⢀⣾⠔⢳⡀⠉⣿⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠀⠈⢆⠀⢸⢸⣭⣿⠁⡇⠀⡆⡈⣇⣷⠉⡇⠀⢨⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠈⠢⡑⢄⠙⠹⠧⠤⠥⢐⠓⠅⠓⠣⠼⠤⠐⠉⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠐⡄⢣⠀⠀⠀⠀⠈⠐⠒⠀⠀⢀⠬⢂⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⢄⣀⣠⣇⡸⠐⢲⠂⠠⠤⠤⠤⡄⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⠗⠝⠛⠣⡀⡸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠼⠊⠀⢀⠀⣏⠀⠀⠀⢰⠀⠰⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⡲⠝⠛⠛⢂⣤⠔⡯⠜⠀⠉⠑⡄⢸⠀⠀⢷⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⠊⠀⠀⡲⠽⣉⢙⠔⣒⣒⣢⠀⡴⢥⠼⡄⠀⡨⣄⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⢟⡀⠀⠀⠀⠁⠒⢻⢹⠀⠀⣉⣪⠀⡼⠂⢟⠱⠇⠘⡤⠤⠃⠀⠀⠀⠀⠀⠀⠀ ⠈⠪⢂⡤⢤⣤⠤⠚⠫⣑⠩⠒⡾⠓⠓⠒⠉⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠉⠁⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⣼⢿⣇⣄⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠘⠸⢿⣿⡗⢲⠄⣀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⠀⠀⠙⠛⠛⡳⠧⢤⠀ ⠀⠀⠀⢠⣼⣿⣲⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⡿⢦⡀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠈⠻⣯⠷⢌⡳⡌⣟⣲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠙⡆⠀⠀⠀⠈⠈⠀ ⠀⠀⠀⠀⠀⠈⢳⡄⠉⣽⢢⣉⣳⣬⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⠘⢧⣀⣻⡟⢯⢿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠈⠈⠿⣞⣷⣷⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⢠⡇⣀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢹⡌⣿⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠉⣿⠀⠀⠀⠀ ⢀⣤⣤⠤⠤⠤⠤⢴⠒⠒⣛⡇⠀⠀⠀⠀⢻⡙⣧⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠉⠛⠢⣤⣀⠀⠀⠀⡸⠃⠀⠀⣿⠀⠀⠀⠀ ⢸⣯⣧⡀⠀⠀⠀⠈⠳⣄⠈⢻⡄⠀⠀⠀⠀⡇⣿⣦⠀⠀⠀⣱⠹⣇⠀⠀⠀⠀⣰⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠐⣿⠀⠀⠀⠀ ⢸⠃⠏⣿⣄⠀⠀⠀⠀⠈⢧⠈⢧⠀⠀⠀⢠⢹⢸⣾⢦⠀⠴⠃⠀⢸⢣⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⡋⠀⠀⠀⠀ ⣾⡄⠀⣿⠉⢦⡀⠀⠀⠀⠈⢳⣼⡄⠀⠀⢨⣦⣾⠃⠈⢳⡄⠀⠀⡸⠀⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀ ⢹⡇⠀⢹⢰⡤⢽⡀⠀⠀⠀⠀⢻⡇⠀⠀⠸⣿⠏⠀⠀⠀⠹⣆⠰⠃⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂ ⠈⢷⠀⠀⣧⢧⡀⠹⡄⠀⠀⠀⠈⡇⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⣷⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠀⠹⡌⢷⡀⠹⡆⠀⠀⠀⢳⠀⠀⠈⢸⢘⡶⢦⣀⣰⡗⠛⠁⠀⣄⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣳⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠹⡀⢿⣦⡁⠀⣠⠴⣿⠳⣦⣀⣿⣼⠁⠀⠀⠙⣷⣦⠀⠰⣜⣆⠙⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣶⠒⢲⣖⠀⠀⠀ ⠀⠀⠀⠈⠷⡀⠙⢦⠙⠿⠞⠁⠀⢸⠀⠈⣿⢿⣿⣶⡀⠀⠀⠈⡇⠀⠀⠈⠉⢠⡏⠁⠉⠉⠉⠓⢒⡲⠚⢛⢋⡉⣿⠉⠀⠀⠀⠀⠀⢰⣿⣯⢀⡟⠀⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⠈⠳⣄⠀⠀⠀⢹⠀⠀⣬⣾⠀⠫⣽⣿⣭⣸⣱⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢙⣋⣤⣀⣿⣀⠠⠤⢠⡀⢰⣿⠏⢩⠟⠀⠀⢀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠱⢄⡈⠲⣄⡈⡏⠀⣠⠏⢻⠀⠀⠀⠉⢙⡿⡿⠀⠀⠀⠀⣿⠦⢶⣦⣤⣤⣴⡶⠶⢛⣋⣹⣿⠿⠿⠯⠉⠋⢹⣿⣷⡴⠋⠀⠀⠀⢈⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠼⠿⠚⠉⠀⠈⢷⠀⠀⢀⣨⠿⠃⠀⠀⠀⠀⠈⠀⠉⠍⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⣠⠾⠟⠉⠀⠀⠐⠀⢀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠀⠀⡀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⡤⣖⣛⣉⣩⣭⣷⣤⣶⣿⣿⡿⠋⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣯⢤⡿⠋⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠀⡼⠋⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⡴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⡿⠁⠛⢀⡞⠀⠀⠀⢠⢀⣠⠤⠤⣀⠀⠀⠀⣠⠏⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⣠⠞⠁⠀⢠⠏⠀⠀⢀⡔⠋⠀⠀⠀⠀⣿⠀⠀⣰⠋⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡴⠃⠀⠀⢀⡏⠀⠀⢠⡇⠀⠀⢀⡆⠀⢸⣿⣧⢰⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⣾⠀⠀⠀⣼⠀⠀⠀⠂⣇⠀⣤⠇⢹⠁⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣿⠀⠀⢸⢻⣷⠂⠀⠀⢸⠀⣿⠀⠀⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⢸⣿⡇⠀⢀⣾⡾⠁⠀⠀⣿⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣦⡈⠈⢷⣷⣶⣭⠞⠁⠀⢀⡼⢹⠘⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠹⣦⡘⠁⠀⠀⢀⣠⠴⠋⢀⡟⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢧⠋⠹⣶⠶⠯⠿⠷⠶⠊⠉⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡠⠤⠄⠀⠤⠴⢊⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠲⠤⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠂⠠⢄⡀⠀⠀⠀⠀⠀⡇⠀ ⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⠤⢤⠐⡇⠠⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⡇⠀ ⠈⠉⣩⠏⢯⠉⠉⠉⡠⠔⠮⡑⡀⠀⠀⢡⢰⠀⠱⡀⠀⠀⠀⠀⠀⠑⡄⢀⡇⠀ ⠀⡴⠃⠀⠈⢃⠔⠉⠀⠀⠀⠈⢺⡀⠀⢸⠠⢧⡀⠈⠗⠢⣀⠀⠀⠀⠘⡦⡁⠀ ⡰⠁⠀⢀⢔⣑⣂⣤⣀⠀⠀⠀⠈⣇⠔⢁⣀⠀⠑⢄⠈⠢⢀⡱⢄⠊⡇⢳⠘⢄ ⠓⠒⢢⠋⠁⠀⠀⠀⠈⠑⢄⠀⢀⠋⠀⠁⠀⠀⠀⠀⠁⠀⠀⠑⡆⡔⠵⢸⠐⡈ ⠀⢠⠁⠀⢀⣠⠔⣒⢟⠃⠒⢥⡌⠀⠀⢀⣤⣴⣾⣤⣀⡠⠀⠀⠉⠀⠀⢸⡀⢱ ⠀⡇⠀⣴⠋⢀⡞⠁⡌⠀⠀⠀⠁⠀⣀⣿⠋⢻⣿⡂⠙⢶⡄⠀⠀⠀⠀⠘⡈⢨ ⠀⢠⢪⠃⢠⡟⠀⣸⡇⠀⠀⠀⠀⠀⠈⠹⣀⣾⡿⣿⡀⢸⠇⠀⠀⠀⠀⠀⠃⠘ ⢸⠆⠇⢀⢷⠁⠀⣿⢣⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠸⡀⠀⢸⡌⠀⠀⢿⡆⢆⡀⢀⣠⡄⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁ ⠀⠣⡆⠘⣡⠀⠀⠘⣇⢸⠙⢫⠁⠀⠔⠀⣰⡀⠀⠀⠀⠐⠠⢄⡀⠀⠀⡰⢡⠀ ⠀⠀⠙⢄⠹⢆⠀⠀⢈⡆⠀⠀⠑⠤⣤⣴⡿⠟⡀⠀⠀⡇⠘⠒⠂⠭⡒⣱⡯⠁ ⠀⢤⠐⠒⢓⣒⣉⠭⠔⠣⡀⠀⠀⠀⠈⠿⠀⢀⠇⠀⠀⡇⡄⠀⢀⢎⢌⠞⠁⠀ ⠀⠀⣑⣦⣈⣢⣍⣈⠀⢠⠈⢒⡤⢀⣀⠀⠀⠁⠀⡀⢤⠁⣇⠔⠁⡡⠃⠀⠀⢀ ⠂⠁⠀⠀⠀⠀⠀⠀⢡⢠⠀⢀⠁⠀⠀⣼⡿⠛⠉⠀⡸⠚⠁⠀⠀⠀⠀⠀⡠⠊ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⣀⢀⢀⣈⠞⠉⠀⢀⠤⣊⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠒⠲⣶⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⣀⠀⠀⠈⠻⡺⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡠⠔⣒⣿⣿⣿⣿⣷⣄⡀⢱⡈⢻⡆⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⠖⠉⣠⣾⣿⡿⢿⣧⠉⠉⠉⣿⡶⣧⣀⡿⠋⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡵⠁⣴⣿⣿⣿⣿⡗⢻⣹⠀⠀⡽⢿⣷⡈⠈⠀⢨⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣴⢿⣿⣻⡿⠃⡤⠬⠁⠀⠸⣇⣾⡏⠑⠀⢀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⣿⡾⠁⠀⠱⣿⣧⡄⠁⠀⠀⠀⠀⠀⣀⣱⠄⠀⣿⠋⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⠃⠀⠀⢠⠏⠀⢻⡀⠻⠷⡄⠀⠀⠀⠀⣠⡾⡿⠀⣀⣠⠴⠖⣫⣵⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⢀⡏⠀⢀⡼⢿⣶⣤⣄⡀⠀⠒⢻⠏⢰⣷⠟⠋⢉⣇⣉⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠇⠀⢸⠁⠀⠙⣿⡀⣠⠖⢀⡏⢠⡏⡟⠀⠐⣟⢠⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠸⡄⠀⢸⠀⠀⠀⠸⣿⠁⠀⣸⠀⡾⣯⣱⣤⠉⢁⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠻⣆⢸⠀⠀⠀⠀⡇⠀⡸⢹⢰⡇⠈⢿⣊⣽⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⠻⣆⠀⠀⠀⡇⢀⡇⠘⣾⡇⠀⠀⢙⡷⣿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⡇⢹⣄⡀⠀⢀⣾⠁⠀⠘⠿⣶⣶⠿⠁⠈⢿⢾⣟⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣧⡾⠈⠛⠛⣽⠋⢿⡆⠀⠀⣠⠀⠀⠀⠀⢸⡆⠈⠻⣍⠉⠉⠛⠒⠦⢤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡟⢁⡠⠤⡾⠃⠀⠀⠉⠓⢒⣿⠀⠀⠀⠀⠀⢿⠤⡀⠈⠳⡦⢄⡀⠀⠀⠙⢧⡀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⡼⠋⠉⠀⢸⡇⠀⠀⠀⢀⡶⠋⠸⣆⠀⠀⠀⠀⠘⣆⠈⠢⠀⠹⡄⠉⠢⡀⠀⠈⠃ ⠀⣠⢛⠋⠑⡆⠀⠀⠀⣠⠖⢉⣾⠯⠄⠀⠂⠐⠚⢻⡄⠀⠀⠘⣧⠈⠃⠝⠦⠤⢤⣀⠀⠈⢷⡄⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⠰⡇⢸⠀⠀⠀⠀⣠⡞⠁⣠⣚⣁⣀⣀⣀⣀⣴⣿⠟⠁⠀⠀⣴⠟⠀⠀⠀⠈⠐⠂⣿⠀⠀⠈⢳⠀⠀⠀⢣⠀⠀⠀⣀⠌ ⠀⠘⠢⠽⣿⠖⣛⣡⠴⠚⠉⠀⠀⠀⠀⣠⠿⠋⠁⠀⠀⢐⡿⠃⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢧⠀⠀⢸⣠⡴⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠘⡄⢠⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣀⣠⠤⠶⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣷⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
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