💙⛓🤍🫀🍍🔁❤️🔥⛓🪢🔪🍍🔁❤️🔥⛓🪢🔪🍍🔁❤️🔥⛓🪢🔪📸🫐♿🗺️
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:: :: ::
˙˙::::: ::::: ::
::.....:: ::....::
˙˙˙˙˙˙˙ ˙˙˙˙˙˙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⣼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⠃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡇⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣷⠀⠀⢺⣿⣿⠂⠀⢠⡄⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⢠⠏⠀⠀⠀⠉⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀
⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣰⠃⠀
⢿⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢀⠀⠀⠀⡼⠁⠀⠀
⠈⣇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠀⠀⣼⠁⠀⠀⠀
⠀⠘⣆⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠁⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠈⡇⠀⠰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⢀⣤⠞⠁⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠻⡄⠀⠀⠀⠘⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢿⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⠤⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⣤⠀⠀⠀⠀⢳⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠚⠋⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉⠙⠀
🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨
🟨🟨🟨🟨🟨⬛⬛⬛⬛🟨🟨🟨🟨
🟨🟨🟨🟨⬛🟥🟥🟥🟥⬛🟨🟨🟨
🟨🟨⬛⬛⬛⬛🟥🟥🟥⬛🟨🟨🟨
🟨⬛🟦🟦🟦🟦⬛🟥🟥⬛⬛🟨🟨
🟨⬛🟦🟦🟦🟦⬛🟥🟥⬛🟥⬛🟨
🟨🟨⬛⬛⬛⬛🟥🟥🟥⬛🟥⬛🟨
🟨🟨⬛🟥🟥🟥🟥🟥🟥⬛🟥⬛🟨
🟨🟨⬛🟥🟥🟥🟥🟥🟥⬛🟥⬛🟨
ඞ𐐘🔪ඞඞඞඞ(≖_≖ )
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⠤⠔⠒⠢⣄⡀⠀⠀⠀⠀
⠀⣠⣤⠤⠐⠒⠒⠂⠒⠊⠉⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀
⠀⡇⠈⠁⠉⠙⠢⠄⠠⣄⡀⠀⢀⡀⠤⠒⠒⠤⠔⠋⠉⠑⠚⠉⠈⡉⠉⢀⠝⠀⠀
⠀⡼⠀⠀⠀⠀⠀⣀⡀⠘⡀⢦⠀⠀⡀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠼⠇⢀⠇⠀⠀⠀
⠀⡇⠀⠀⠀⠠⣾⠿⠃⡜⠀⠀⡳⠔⠋⠉⠓⢤⡴⠚⠙⠓⢶⠀⠀⡠⠞⠀⠀⠀⠀
⢀⠇⢀⣤⠀⠀⠀⠀⠀⢱⠀⢸⠁⠀⣰⣿⣿⡆⢱⢀⣶⣿⡆⣧⢸⠀⠀⠀⠀⠀⠀
⢸⠀⠘⠁⠀⠀⠀⠀⢰⠉⠇⢸⡀⠀⠻⣿⡿⠃⣸⠘⣿⡿⢃⣇⠜⠀⠀⠀⠀⠀⠀
⢨⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠑⠤⣀⣀⡠⢞⣩⣗⠒⠚⠁⣇⠀⠀⠀⠀⠀⠀⠀
⢎⠀⠀⠀⣠⣾⡿⢠⡋⠀⠀⠈⠀⠀⡀⠀⠀⠀⠙⢦⣀⣀⣸⠟⠀⠀⠀⠀⠀⠀⠀
⣸⠀⠀⠀⠛⠋⠁⠀⡗⠀⠀⠐⠊⢩⡏⠉⠙⣷⣒⣋⣏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀
⢣⠀⠀⠀⠀⠀⠀⢸⠀⠤⠀⠀⠀⠨⣍⣉⠽⠁⠀⠤⢿⡀⣜⠀⠀⠀⠀⠀⠀⠀⠀
⣸⠐⠛⢀⣀⣀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠿⢶⣾⡍⢲⠀⠀⠀⠀⠀⠀
⠱⢤⣀⢸⠀⠀⠈⠙⢲⣄⡤⢴⢠⣤⣴⣾⡟⣻⣏⣀⣤⣼⣿⣽⢏⠀⠀⠀⠀⠀⠀
⠀⢸⠤⣝⣆⠀⠀⡴⣍⣉⣑⣺⢛⡚⠻⠿⠿⠿⢿⣿⣿⣿⣁⣨⠟⠙⣦⣄⣀⡀⠀
⠀⠸⣦⣿⣿⣷⣶⣦⣿⣿⢿⡍⠛⣛⣿⣿⣷⣶⣿⡿⠂⠠⠤⢅⠀⣐⢮⡳⢾⠃⠀
⠀⠀⠈⠙⠛⢷⣼⣇⣠⠤⢾⠛⠋⠉⠈⠛⡟⡟⠋⠀⠀⠀⠀⠀⠑⢌⡢⣝⠢⣵⡆
⠀⠀⠀⠀⠀⠘⠻⠿⡿⡷⠛⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣤⣇⣇⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣷⣷⣤⡾⣿⣷⣄⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢻⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠘⢧⠀⠀⠉⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⢐⣲⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠦⣤⣤⡀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠈⠙⠏⠙⠲⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⠾⠋⠀⠀⠀⢠⡶⢦⠀⠀⠸⡇⠀⠀⠀⠀⢠⡤⠔⣦⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡟⠁⠀⠀⠀⠀⠀⢸⡀⠈⣧⠀⠀⢻⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣶⣶⣿⣿⣿⣭⣽⣯⣭⡝⠛⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣆⠀⠀⠀⠀⠀⠈⣧⡀⢹⡆⠀⠀⢳⡀⠀⠀⠀⠀⣏⣀⣤⣤⡤⠴⣶⣶⣾⣿⣿⣭⣽⣿⣧⠈⠉⠁⠀⠀⠀⠀⠀⣀⣤⠶⢶⣄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠘⢷⣼⠇⠀⠀⠀⣷⠀⠀⠀⠀⠿⠵⠖⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⣿⡇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡦⣤⠶⠲⢦⣤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⣠⠞⠉⠀⠀⠀⢀⣴⡿⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠈⠛⢷⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠋⠁⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠙⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⣀⣤⣤⠶⠾⠿⣯⣤⣤⡄⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⣰⠞⢻⣇⠀⣿⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠛⠁⠀⠀⠀⠀⢸⡇⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⡀⠈⣧⡀⢿⣆⠀⠙⢿⡃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⣶⣾⡿⠛⠉⠉⢹⣿⣿⡆⠀⠀⠀⠀⠀⠈⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠉⠉⠛⢷⣄⡀⠹⣦⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠉⠀⠀⠀⣾⠀⣇⠀⢀⣀⣈⣟⠿⠁⠀⠀⠰⠦⡀⠀⢸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢉⠻⣦⡈⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠶⠶⠶⠶⠿⠀⠉⠉⢻⠉⢹⣿⡆⠀⠀⠀⠀⠀⡇⠀⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢠⡏⢨⡛⢦⡀⠙⢦⡀⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠘⠃⠀⠀⠀⠀⠀⠈⢁⣴⠏⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⢧⣀⡇⠀⠻⣦⡈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠋⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣄⠀⠈⠉⠀⠀⢸⡌⠻⣦⡀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣠⡴⠦⣄⣀⡀⠀⠀⢀⣀⡠⠶⠟⠋⠉⠀⣀⣠⠴⠟⢩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠟⠀⠀⠀⠀⠀⠀⢿⠀⠈⠻⣦⡀⠙⢷⣄⢶⡛⠚⢛⡁⠀⠀⠀⠈⠉⠛⠛⠉⢁⣀⣤⠤⢖⣚⣋⣁⣀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠻⣆⡀⠙⢧⡙⣿⠟⠀⠀⠀⠀⠀⣠⣶⣟⠛⠭⠀⣠⡾⠋⠁⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⠈⠙⠛⠶⠶⠒⠛⣿⠲⠒⠛⠋⠉⠳⣄⡼⠟⣁⣤⣀⣀⡴⢶⣾⣿⠇⠙⠳⣤⠞⠁⠀⠀⠀⠀⠀⣀⣀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠦⣤⣤⣀⣀⣀⡀⠀⢹⠀⠀⠀⠀⠀⢰⣯⣼⣟⠉⠻⣿⣥⣤⣴⡏⠙⣷⡴⢶⣒⠚⠛⢛⣿⣿⣯⣭⠉⠉⢹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⣿⣿⣯⡙⠛⢿⡟⠛⠛⣯⣭⣿⣿⣿⠉⠳⣆⠀⠀⠙⢿⣇⠀⢸⣿⠿⠿⠃⠀⠈⠛⠛⠛⠋⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠉⠙⠃⠀⢸⡇⠀⠀⠿⠟⠛⠛⠛⠀⠀⢹⡄⠀⠀⠀⠙⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣦⣤⣤⣄⣒⣸⣷⠀⠀⢀⣀⣀⣀⣀⣠⣤⣼⣷⡀⢀⣧⡜⢦⡙⢿⡾⠿⠿⠿⢿⡟⠛⠛⠋⠀⣙⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣰⣾⣿⣿⣶⣄⠀⠀⠀⠀⣴⡾⠛⠀⠀⠉⠉⢹⡿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⣧⠘⣷⣙⢦⣙⠲⣿⠀⠀⠀⠘⢿⣆⠀⣴⠿⣯⣴⡿⠁⠀⠀⠀⣠⣤⣤⣤⣤⣤⡀
⠀⠘⣿⣿⣿⣿⢿⡏⠀⠀⠀⠀⠹⣷⣄⡀⢀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠇⠙⠓⠾⠗⠛⠀⠀⠀⠀⠀⠻⣦⣻⣦⡈⠻⣤⡀⠀⠀⢰⣿⣽⣿⣿⣻⡿⡿
⢀⣼⣿⣿⡟⣁⣀⠹⣦⡀⠀⢀⣴⠏⠙⣿⡷⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣄⣨⡿⣦⡀⠠⣿⣽⣷⣷⠟⣻⡇
⣿⣿⣿⣿⡇⠈⠻⣄⡼⠷⠴⠞⢁⣠⡾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣨⠛⠲⢿⣯⣭⣨⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠿⠿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡛⠻⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀
⠀⠀⠀⢀⣤⣤⣤⣿⡟⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⠿⠿⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠳⡀⠙⠦⣀⠹⡝⠿⣿⡛⠛⠳⠶⣤⣀⠀⠀⠀⠀
⠀⢀⣾⡿⠋⠉⣹⡿⠀⠀⠀⠀⢀⣾⡿⠟⠉⠀⠀⡔⠊⠉⠉⠉⠒⢌⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⢹⣇⠀⠱⣄⠀⠈⠉⠀⠀⠈⠻⣦⡀⠀⠈⠙⢷⣦⡀⠀
⠀⣾⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠳⠤⠄⢀⠤⠤⠊⠀⢹⣿⡷⠶⠶⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⢻⣦⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠻⣧⠀
⠀⣿⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢻⡇
⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠉⠲⢤⣀⡀⢀⡰⢻⡇⠀⠀⢸⣷
⢰⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⠿⠟⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠉⠉⢀⣾⠁⠀⠀⠘⣿
⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣄⣤⣴⣶⡶⢾⣯⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠞⠛⠋⠉⠁⢻⣆⣼⣿⢿⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠈⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⣤⣴⠶⠟⠛⢹⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢿⡿⣿⡏⢹⡇⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀
⠀⢸⣿⡀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⣇⣿⠃⢸⡇⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀
⠀⠀⠻⢿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠻⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢈⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣼⡿⠈⢿⣆⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⣀⣤⣿⠁⠀⠀⠀⠈⠻⣷⣤⣴⣶⡾⠟⠁⠀⠀⠙⠷⢶⣤⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀