Apoligetic Emojis & Text

Copy & Paste Apoligetic Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠻⢵⣦⣄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡾⠟⣷⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠲⢿⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣟⡄⠀⠀⠀ ⠀⠀⢀⣿⠏⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣧⡀⠀⠀ ⠀⢠⣿⠏⠀⣾⠃⠀⠀⡠⠤⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠤⠠⣄⠀⠀⢸⡇⠀⠹⣗⡄⠀ ⠀⣾⡟⠀⠀⢹⡆⠀⠀⠉⠑⠿⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠱⠾⠋⠁⠀⠀⣸⡇⠀⠀⢹⣞⠀ ⠘⣿⠁⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠙⠆⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏⠀⠀⠀⠈⣿⠆ ⠀⣿⡄⠀⠀⠀⠀⠈⠉⢻⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡟⠉⠀⠀⠀⠀⠀⢠⣿⠃ ⠀⠹⣷⣄⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⠉⠈⠁⠉⠈⠉⠁⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⢀⣾⠏⠀ ⠀⠀⠉⠿⣷⣤⣀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣤⣶⡿⠋⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀

Related Text & Emojis

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

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