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