⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⣀⣀⣀⣈⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⡇⠀⠀⣾⣟⠛⠋⠉⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀
⢀⣤⣴⣶⣿⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⢀⣀⢹⡆⠀⠀⠀⠀⠀⠀
⢸⡏⠀⢸⣿⠀⠀⠀⢿⣿⣿⣷⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⣼⡇⠀⢸⣿⠀⠀⠀⠈⠻⠿⣿⣿⠿⠿⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀
⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣷⣶⣶⣶⣤⡀⠀⠀
⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⢻⡇⠀⢸⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡇
⠈⠻⠷⠾⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣧⣀⣠⣴⡿⠙⠛⠿⠿⠿⠿⠉⠀⠀⢠⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢈⣩⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⠏⠀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀
⠀⠀⠀⢸⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠉⠉⠁⢤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠉⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠿⠿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡛⠻⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀
⠀⠀⠀⢀⣤⣤⣤⣿⡟⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⠿⠿⠿⠿⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠳⡀⠙⠦⣀⠹⡝⠿⣿⡛⠛⠳⠶⣤⣀⠀⠀⠀⠀
⠀⢀⣾⡿⠋⠉⣹⡿⠀⠀⠀⠀⢀⣾⡿⠟⠉⠀⠀⡔⠊⠉⠉⠉⠒⢌⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠛⢹⣇⠀⠱⣄⠀⠈⠉⠀⠀⠈⠻⣦⡀⠀⠈⠙⢷⣦⡀⠀
⠀⣾⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠳⠤⠄⢀⠤⠤⠊⠀⢹⣿⡷⠶⠶⠶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⢻⣦⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠻⣧⠀
⠀⣿⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢻⡇
⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠉⠲⢤⣀⡀⢀⡰⢻⡇⠀⠀⢸⣷
⢰⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⠿⠟⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠉⠉⢀⣾⠁⠀⠀⠘⣿
⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣿⣄⣤⣴⣶⡶⢾⣯⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠞⠛⠋⠉⠁⢻⣆⣼⣿⢿⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠈⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣀⣤⣴⠶⠟⠛⢹⡇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⢿⡿⣿⡏⢹⡇⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀
⠀⢸⣿⡀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣼⣇⣿⠃⢸⡇⠀⢠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀
⠀⠀⠻⢿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠻⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢈⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⣼⡿⠈⢿⣆⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⣀⣤⣿⠁⠀⠀⠀⠈⠻⣷⣤⣴⣶⡾⠟⠁⠀⠀⠙⠷⢶⣤⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜🟥🟥🟥⬜⬜⬜🟥🟥🟥⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛
⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜🟥🟥🟥🟥🟥⬜🟥🟥🟥🟥🟥⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬛⬛⬛⬜⬛⬛⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜🟥🟥🟥⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜🟥⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬜⬛⬜⬛⬛⬛⬛⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬜⬛⬜⬛⬛⬛⬛⬜
⬛⬛⬜⬛⬜⬛⬛⬛⬜⬛⬜⬛⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛⬜⬛⬜⬛⬛⬜⬜⬛
⬛⬛⬛⬜⬜⬛⬜⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜⬜⬛⬜⬜⬛⬛⬛⬜⬛⬜⬛⬜⬛⬜⬛⬛⬜⬜⬛
⬛⬛⬜⬛⬜⬛⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬛⬜⬜⬛
⬛⬛⬜⬛⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬛⬜⬛⬛⬛⬜⬛⬛⬜⬜⬛
⬛⬛⬛⬛⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬜⬜⬛⬛⬜⬛⬛⬛⬛⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠷⠶⠶⢶⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠾⠷⠿⠾⡟⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⢀⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⠂⢄⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⢀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡂⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⢾⣄⠀⠑⠄⠀⠀⠀⠀⣿⡃⠀⠀⠀⠠⡇⠀⢈⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⠁⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠹⣧⣀⠈⢄⠀⠀⠀⣿⡅⠀⠀⠀⠐⡇⠀⢈⠀⠀⠀⢀⣺⠟⢱⡦⡄⣻⡇⠀⡁⡠⠓⡦⠖⢲
⠀⠀⠀⠀⠀⠀⠸⣿⡄⢘⠐⡐⠛⣿⡀⠈⢤⠀⠀⣿⠆⠀⠀⠀⢈⣇⠀⠘⡄⠀⢠⣿⢿⠉⠙⠏⣁⣿⠀⢀⠇⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠉⠦⡀⣿⣧⣠⣼⣷⠤⣽⣇⣀⣀⣀⣠⣿⠶⣤⣷⣆⣳⡏⡇⠀⠐⠉⣼⡿⠀⡸⠀⢅⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠉⡁⠉⠉⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁⠀⠀⠀⠈⠉⠀⠑⠄⣠⣼⠏⠁⡰⠃⠀⠀⠓⡄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢿⣤⡀⠙⢄⠀⠀⠀⠘⠁⢀
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣄⠀⠀⠀⠘⢷⣄⠀⠡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⢼⡟⡀⠀⠀⠀⠠⣿⣿⣿⣿⠀⠀⠀⠄⠁⠀⣀⠀⠀⠀⡁⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠻⣦⠀⠑⡀⠀⠀⠀
⠀⠀⠀⠀⢾⡏⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⡀⠀⠁⢠⣤⣽⣤⣄⠀⠀⡀⠀⠜⠻⠿⠛⠀⠀⠀⠀⡀⠀⠹⣧⠀⠱⠀⠀⠀
⠀⠀⠀⣘⡿⠰⠀⠀⣠⣀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠉⠀⠉⡀⠀⠀⠰⠶⣆⠀⠀⠀⠀⠀⣤⣤⡀⠀⠠⢻⡆⠀⢃⠀⠀
⠀⠀⠰⢿⠇⠀⠀⠀⣤⣭⠀⠀⠀⠀⠀⠠⠀⠀⣤⣄⣁⠀⡀⣀⡄⠖⢲⠲⡄⠀⢀⠀⠀⡀⠀⣭⣭⡅⠀⠀⡘⣿⠀⠸⡀⠀
⠀⠀⣼⣿⠀⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢯⡝⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⢿⣆⠀⠑⡀
⠀⣮⡟⠀⠈⠛⠲⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢹⡦⡀⢀⠀⠀⠀⡀⢔⡎⠀⠀⠀⠀⣀⣀⣀⣠⣬⡴⠶⠞⠀⠀⢹⡇⠀⢳
⣀⡿⣷⣤⣀⡀⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⢗⣄⡀⣦⠇⠋⠀⠀⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⣀⣤⣾⠏⠀⢸
⠃⢌⢩⢸⡟⠛⠻⠷⢶⣦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⡶⠾⠿⠛⢛⡿⠀⢀⠔⠁
⠀⠀⠀⢿⣇⠀⡤⢤⣄⣀⣀⠈⠉⠉⠉⠉⠉⠉⠛⠙⠛⠛⠙⠛⠛⠙⠋⠉⠉⠉⠉⠉⠉⠁⠀⣀⡀⡤⢤⠀⢸⡇⠀⡀⠀⠀
⠀⠀⠀⢸⣿⠀⢩⣷⡞⣶⠽⠚⢭⣯⡽⢯⣖⡖⣦⡒⠐⠂⠒⠐⠂⢲⣔⣲⢲⡼⣭⢯⣵⢫⡷⣣⢟⡾⣹⠀⣸⡇⠀⡆⠀⠀
⠀⠀⠀⢸⣿⠀⢰⣹⢉⠀⠀⠀⠀⠘⠽⣳⢎⡇⠀⡇⠀⠀⠀⡀⠀⢸⣎⢷⣋⠈⠙⠁⠈⣟⠈⢁⡿⣜⠣⠀⣿⠀⠀⠇⠀⠀
⠀⠀⠀⠈⣿⡇⠀⣾⢭⠀⠀⠀⠀⠀⠀⢸⡹⠒⡞⡅⠀⠀⠀⠀⡀⢘⠎⡷⡉⠀⠀⠀⠀⠉⠒⡾⣱⢎⡇⠀⣿⠀⢠⠀⠀⠀
⠀⠀⠀⠀⣿⡇⠀⡽⡞⠀⠀⠀⠀⠀⠀⠹⣜⢣⠁⠀⠀⠀⠀⠀⠀⢘⡎⢷⡱⣤⠀⠀⠀⠀⠀⠈⢳⢸⠇⢰⡏⠀⢸⠀⠀⠀
⠀⠀⠀⠀⢿⣇⠀⣞⠹⡄⠀⠀⠀⠀⢠⠚⡬⡳⠃⠀⠀⠀⠀⠀⠀⢘⡜⢣⡓⠌⠫⠬⣀⢀⠀⢰⢊⡽⠀⢸⡇⠀⡜⠀⠀⠀
⠀⠀⠀⠀⢸⣿⠀⢨⢣⢹⠀⠀⠀⠀⠠⠙⡔⠳⡄⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠐⠁⠎⡜⠠⢃⣾⠀⣸⠃⠀⡃⠀⠀⠀
⠀⠀⠀⠀⢈⣿⠀⢘⢆⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢠⠣⠀⠀⠀⠀⠀⠀⠘⡰⢄⠳⡎⠀⣿⠀⠠⡆⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡇⠘⣎⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⠣⠄⠤⡀⢀⡀⠳⢄⠱⡈⠼⡇⠀⣿⠀⢰⠁⠀⠀⠀
⠀⠀⠀⠀⢀⢿⡇⠀⣯⣿⡇⠀⠀⠀⠀⠀⢀⣀⣰⣮⠀⠀⠀⠈⠀⠀⡁⢊⣶⣿⣿⣿⣷⡈⠆⡡⢫⠁⢸⡏⠀⢈⠀⠀⠀⠀
⠀⠀⠀⠀⡸⠘⣷⠀⢧⣿⣇⠀⠀⠀⠀⠠⣾⣿⡿⣏⠀⠀⠀⢀⣂⣀⡓⢂⢿⣿⣿⣿⣿⢁⣦⣥⢿⠀⢸⡇⠀⢤⠀⠀⠀⠀
⠀⠀⠀⠀⡇⠀⣿⠀⢸⡄⢦⠀⠀⠀⠀⢸⠀⢆⣤⣥⡀⠀⢠⣿⣿⣿⣿⡆⠈⢉⡙⠩⢠⣿⣿⣿⡹⠀⣾⠃⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢣⠀⠹⣇⠈⢞⡌⠦⣀⢀⣠⠾⠡⣿⣿⣟⣿⣆⠈⢿⣿⣿⠿⢡⣷⣿⣿⣿⡄⠿⡿⡧⠃⢠⡟⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢂⠀⠹⣦⡀⠙⠶⣌⡩⢡⣤⣶⣿⣿⣿⠿⢃⠒⣂⣄⡀⢆⠸⣿⣿⡿⡿⣏⡾⢋⠀⣴⠟⠀⢀⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡀⠈⠻⣦⣀⠈⠑⠫⠟⣻⠟⡿⢆⣂⠡⣾⣿⠿⡿⢦⡱⣬⠻⠕⠋⠅⣀⣴⠟⠁⠀⡰⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠉⠻⠶⣤⣄⣀⡀⠉⠉⠈⠁⠁⠈⠁⠉⠉⠀⣀⣁⣥⠷⠟⠋⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⢀⠀⠈⠉⠛⠛⠛⠻⠶⠶⠶⠞⠛⠛⠛⠉⠉⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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