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"D-don't my muscles make me look cute?" ⠀ (\ __ /) (UwU) _ノ ヽ ノ\_ / `/ ⌒Y⌒ Y  \ (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ  ノ ヽ___>、__/ |( 王 ノ〈 /ミ`ー―彡\ / ╰ ╯ \
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⣄⣀⠀⠀⠊⠁⣼⡶⠿⣦⠀⠙⠁⢐⢶⢀⣴⠿⠋⠁⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠑⠌⠉⠓⠤⠀⠀⠀⣠⠊⢰⠀⣠⡞⢡⡾⠛⠁⠀⠀⠀⠀⣾⣇⣴⣶⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡁⢴⠤⣄⡀⠈⠓⠀⢀⡾⠃⠀⢻⠛⠋⠉⠉⠓⠀⠀⠀⠀⠀⢀⡿⠿⠞⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⡀⠀⠀⠀⠠⢲⣷⠾⣤⣤⣈⣆⠀⠉⠓⡄⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠉⠛⠒⠦⠴⠧⠬⠦⡀⠀⠋⠈⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣠⠀⠀⠁⠀⠀⢾⣻⠡⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⡀⠀⠈⠀⢀⣴⣖⠿⡿⠷⠶⠖⠛⠛⠿⠿⣿⣉⡀⠀⠀⠀⠉⠓⠦⢷⠤⢴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡦⠭⢶⣄⣰⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠥⣀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣮⠗⠤⠀⠀⠀⢀⣽⡿⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠤⡠⣇⠀⣰⡞⢟⡉⠹⣍⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⣟⣯⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠙⣿⣷⣶⣤⣄⢰⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠀⠀⠹⣷⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⣠⣶⡿⠁⢀⣴⠋⠀⠀⠀⠀⣱⡇⢰⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠜⠁⠀⠀⠀⢽⠋⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣇⡞⢨⣿⣎⡻⢍⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢻⡄⠀⠀⢠⣶⡶⠟⣷⣶⠿⠷⢮⡴⠖⠋⣁⡀⠤⠤⠒⠒⢿⣿⠁⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣟⣰⡿⢁⠝⢭⡒⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣤⣌⣷⠀⢤⡾⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⢠⡟⢀⣿⣿⠏⡠⢃⡴⠂⠈⣾⣋⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⡞⣉⣯⢻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⢸⣿⣏⠜⡡⠊⠀⠀⣼⣿⠿⠁⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠁⢀⣴⣿⢾⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠸⠇⣾⣯⢋⠔⠁⡐⢀⣾⡿⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣎⣴⣿⢿⣿⢾⢋⣿⡿⠁⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠖⠛⠛⢷⣄⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠄⠀⠀⠀⠀⢠⡿⣡⠋⢠⣎⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢋⡝⣡⣾⣿⣣⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠉⠉⠉⠉⠉⠙⣻⣦⡄⠀⠹⣿⢶ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠴⢶⡀⠀⠈⣯⠀⢻⠀⠀⢀⣿⣷⠏⢠⢏⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣠⡿⢻⢟⣏⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣷⣄⠀⢻⣄ ⠀⠀⠀⠀⠀⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⢈⡇⠀⠀⢹⡂⢸⠃⢠⣾⣿⡏⡰⢣⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⣟⣠⠃⢮⣿⣿⣿⠇⠀⠐⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣼⣿ ⠀⠀⠀⠀⠀⣰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⠿⠁⠀⠀⢸⡇⠀⢠⣿⢿⣿⠏⢠⣿⣿⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠄⠀⠉⠈⠁⠘⣿⣾⣿⣟⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠈⠉⠚⠻⣿⡙⢿ ⠀⠀⠀⠀⢠⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡄⠟⡏⣰⠋⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣿⡟⢹⣿⠁⠀⠀⢠⡞⠣⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠑⠺ ⠀⠀⠀⢠⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⡼⢠⠇⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣷⣿⠇⠀⠀⠀⠈⣇⠂⠱⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠟⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠈⢆⢹⣧⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⢸⢹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠂⠀⣀⣠⡴⢶⠛⠋⠉⠀⠀⠲⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⡇⡆⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⡏⢸⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣴⣠⣴⠞⠋⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢀⠀⢰⠃⡜⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠉⠀⠀⠀⣀⠀⠀⠀⠱⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣭⣶⣿⣯⣬⣤⣬⣥⣯⣥⣽⣧⣭⣦⣥⣦⣤⣥⣤⣤⣤⣤⣤⣴⣤⣴⣤⣴⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣧⣥⣦⣤⣮⣥⣤⣤⣴⣤⣴⣤⣴⣤⣤⣤⣤⣤⣤⣦⣬⣤⣥⣬⣬⣥⣬⣿⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣤⠈⣿⣿ ⣿⣿⣿⣿⣿⠋⠉⠉⠈⠁⠉⠈⠉⡈⠅⣉⠈⠁⠉⠈⠁⠉⠈⠉⠉⠉⠁⠉⠈⠁⠉⠈⠁⠉⠉⠉⠉⠈⠁⠉⠈⠁⠉⠉⠉⠁⡍⠉⠈⠁⠉⠁⠉⠉⠈⠉⠁⠉⠉⠈⠉⠁⠉⠉⠈⠉⠁⠉⠁⠉⠈⠉⠱⠉⠉⠋⠉⣏⠡⠉⠈⠁⠉⠈⠉⠉⠈⠁⠉⠈⠁⠉⠈⠉⠉⠉⠈⠁⠉⠈⠁⠉⠈⠉⠁⠉⠈⠁⠉⠈⠁⠉⠈⠁⠉⠙⣿⣿⣽⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠒⠰⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⠀⠂⠡⠁⠀⠀⠀⠄⠀⠀⠂⠀⠂⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢏⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⡂⠐⠗⡁⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢹⣿ ⣿⣿⣟⣿⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣈⠬⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠁⢁⡜⠛⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠀⠄⢆⠀⣡⠀⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢠⣿ ⣿⣿⣯⣿⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠋⠖⣍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡶⡀⠃⠀⠉⠘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢸⣿ ⣿⣿⣏⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⢧⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠄⠁⠁⡠⠐⠁⡀⠀⢈⠦⣤⠠⠄⠙⠀⠀⠀⠀⠀⠉⠈⠒⠓⠾⠳⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠑⡇⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢀⣿ ⣿⣿⣟⣿⡅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⡆⣤⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠄⠀⠁⠘⡁⠀⡋⢋⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡭⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢈⣿ ⣿⣿⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠤⡆⠏⡊⣻⣿⢿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠂⢤⠈⠀⠀⠀⠀⢠⣤⣤⣴⣦⣴⣾⣷⣾⣾⣆⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⡹⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢈⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡦⣎⣾⠇⠑⠊⠁⠀⠀⠉⠁⠭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣀⣠⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠠⠃⡌⢃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣿ ⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⡍⠌⠷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⡾⠟⠟⠛⠻⠻⣿⣿⣹⢻⣟⡿⣿⣿⣷⣦⣤⡊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢚⣿ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣤⣶⣤⣶⣿⡿⠿⢿⠻⠈⣿⣿⡿⢿⠛⠂⠿⠟⠉⠁⠀⠀⠀⢀⠀⠀⣿⣷⢭⣻⣏⡞⣷⣹⣛⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢺⣿ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠈⢀⣴⡿⠋⣡⣼⣦⣄⠀⠀⠀⢠⠀⡐⠀⡈⠀⠀⣿⡿⣜⢯⣝⡳⣯⢿⡟⢶⣯⣿⣿⣿⣿⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡟⠁⠀⣇⣀⣄⣤⣤⣀⠀⠀⠀⠀⠀⣴⣵⡇⠠⣿⢸⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⡆⠀⠀⣀⣴⣶⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⢿⣿⣷⣦⡀⣀⣤⣿⣿⣷⣾⣿⢿⢿⣿⣷⡄⠀⢠⡀⠌⠐⠀⢀⣾⣿⡟⣼⣫⡞⣽⡱⣏⣞⣷⣿⡿⠛⠛⠛⠛⠛⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠅⠀⡀⠀⠈⠉⠀⠀⡀⠾⠁⠀⠀⠀⠀⢠⣏⠋⠀⠀⠀⠐⣿⣸⣿ ⣿⣿⣿⣿⡅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣴⣾⣿⡿⠛⠋⠈⠋⠀⠁⢰⣤⣿⣿⣿⢧⣏⡿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣾⣯⣾⣿⡀⠀⠀⠀⠀⠀⣀⣾⣿⢏⣾⡱⣏⠿⣥⣳⣿⡛⠋⠀⠀⠀⠠⠄⠠⡄⠀⠤⠛⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⢧⡇⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⡗⣆⠀⠀⠀⢈⣿⣰⣿ 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⣿⣿⣿⣿⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣧⣐⠋⣿⡷⣹⢯⣶⣟⡳⢮⡽⣻⣿⣿⣦⡄⠄⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⢯⠷⡿⣼⣙⢧⡻⣟⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣀⣀⢐⠃⠀⢀⣰⣾⣿⢯⣳⣯⣿⣿⣿⢻⠭⣟⠿⣿⣿⣤⡄⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣿⣯⢷⡹⣞⣧⣛⣧⣳⣽⣿⣿⣿⣦⡀⢀⠄⠈⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⢸⣷⣻⣿⠋⠀⣤⣂⣶⣤⣿⢿⣿⣿⣿⣷⢮⢽⣮⢻⡵⣣⢟⣎⢷⣽⣿⣿⠛⠛⠛⣿⣿⣦⡀⠉⠀⠁⠀⠀⣠⣾⣿⢏⡷⣫⣾⣿⣿⣿⣿⣧⣟⣼⣻⣾⣿⣿⣷⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⢄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣷⡺⣵⢫⢶⣽⣾⣿⣿⣿⣿⡿⣿⣿⣷⣧⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣽⣿⣦⣿⣟⣿⣿⣿⣿⣿⣿⡹⣎⢷⣮⢳⡳⣝⢮⣿⣿⡿⠁⠁⠈⠀⠀⠉⠛⣿⣿⣯⣤⣤⣼⣾⣿⣿⣻⣾⣿⠿⠃⠀⠟⠻⣿⣿⣿⣷⣿⣿⣿⡿⢷⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡆⠀⠀⣀⠀⠀⠀⠈⠀⠃⠂⠀⠀⠄⣁⠄⠉⡿⣿⣿⣿⣿⣿⣛⠿⠟⠯⠝⢿⣿⣿⣿⣿⣿⣿⣯⣭⠁⠀⠉⠂⠉⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣹⢶⣹⣟⢾⣧⢏⡷⢭⣿⣿⠿⡀⠀⣤⣀⣰⡋⡀⡀⠈⡛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⠻⠋⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣵⢫⢗⣮⢻⠼⣹⣝⣳⣾⣿⣾⢶⣿⣿⣿⣿⠇⠀⠐⠀⠸⢣⣽⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡅⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⠀⣿⣟⠻⠀⠈⠐⢠⡀⠂⢠⡢⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⠀⠌⠀⠼⣿⣿⡿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⠀⠸⢿⣦⠀⢀⣼⣿⣿⣿⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣟⠉⠉⠉⠉⠉⠘⣿⡿⠁⠀⠀⠀⣤⣾⣿⣟⣛⢶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣖⢻⣧⣠⣼⣿⣷⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⣿⣀⣠⣰⣾⡿⢩⣽⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢤⣿ ⣿⣿⣿⣿⡃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⠋⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣿ ⣿⣿⡿⣿⣷⡀⢀⣄⣀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣠⣀⣤⣠⣤⣤⣤⣤⣤⣾⣟⣛⣿⡇⣠⣤⣤⣤⣠⣤⣤⣠⣀⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣄⣠⣄⣤⣠⣄⣤⣄⣤⣄⣤⣄⣤⣠⣠⣄⣠⣄⣤⣠⣄⣤⣤⣴⣦⣤⣿⣛⣻⣿⣿⣿⣿⣿⠛⣛⠃⢀⣄⣠⣀⢀⡀⢀⣀⢀⣀⢀⣀⠀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣄⣠⣄⣠⣤⣬⣿⣿⣿ ⣿⣿⣇⠛⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣷⣶⣶⣾⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿ ⢽⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣶⣴⣶⣤⣶⣤⣶⣶⣶⣶⣴⣶⣤⣤⣶⣦⣴⣶⣤⣴⣤⣴⣤⣴⣤⣴⣤⣴⣦⣴⣦⣴⣦⣶⣦⣶⣦⣴⣦⣴⣶⣤⣶⣤⣶⣤⣴⣦⣴⣦⣴⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣴⣦⣤⣦⣤⣴⣤⣶⣤⣶⣤⣶⣤⣴⣤⣴⣤⣴⣦⣴⣧⣤⣦⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣾⣿⣿⣿⣦⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⠀⠘⠛⠛⢻⣿⣿⠟⠿⠶⠶⠶⡦⠀⣾⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠈⠻⠿⠿⠟⠃⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠙⢋⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⡉⢉⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠚⠀⠻⠟⠀⠁⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⠒⠛⠃⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠐⣶⡖⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠙⢁⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⣤⣤⣤⣤⡤⣄⣀⣀⣀⣀⣤⢤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣤⣤⣤⣤⢤⡤⠤⠤⢤⣤⣤⢤⡤⠤⠤⣤⣤⣤⢤ ⠉⠉⠙⢇⡿⠋⠉⠉⠉⠛⣼⠋⠉⠁⠉⠉⢣⡟⠉⠁⠉⠉⠹⣸⠉⠉⠁⠈⠉⠇⡏⠀⠀⠀⠈⠙⠀⡇⠀⠀⠀⠀⠸⠘⡇⠀⠀⠀⠀⢹⠘⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⠤⠤⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⠉⠉⠉⣉⠉⡉⠉⣉⠉⠉⠉⠉⢉⠁⢈⡉⣉⡁⠉⣉⡉⡉⢉⢉⢉⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⣿⣿⠟⠁⢸⡿⣿⣿⣿⠻⣿⣿⣿⣯⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠉⠠⠁⠈⠋⠉⠈⠉⠉⠀⠈⠁⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⢩⡀⢱⢰⣱⡄⢠⣿⡿⠀⠀⠘⠁⠻⠟⠃⣀⡉⢹⣿⣿⡀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⢀⣤⣤⣶⣿⣿⣾⣧⣿⡿⠈⣿⡇⣩⣭⣿⣷⠤⣾⣿⣿⣽⡏⢻⣿⠇⠈⡿⠄⡦⢠⣀⠄⢀⣬⡙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⣠⣴⣿⡿⠛⣩⣿⣿⠙⠛⠟⠉⠉⢻⡀⠙⠛⠛⡋⠀⢉⡙⠛⠁⠀⢸⠟⠉⢻⣷⣿⣿⣾⠿⠛⠿⣿⣯⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠒⢋⣼⣋⠀⠀⣼⠛⣿⠀⠀⠀⣀⡀⠈⠁⠀⣀⣼⢯⣤⡤⢷⣄⡀⢀⡜⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠘⢯⣸⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣾⠀⠀⣐⣀⣁⣤⡿⠃⠀⠉⠉⠙⠻⠓⣒⣶⣾⠟⠑⠢⣘⣄⠛⠷⣶⣿⣷⠾⠟⢁⣼⣀⣴⣖⣄⣀⠀⢀⣀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⣀⡀⠀ ⣿⣿⣿⣿⣿⣿⣷⣌⠉⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠁⠀⢀⡉⢻⡍⢷⣄⠘⠛⠓⢠⣴⠋⢃⣾⣻⠹⣟⡝⢆⠒⠛⠘⠛⠻⠿⠿⢿⣻⣤⠀⠀⠀⠀⠀⠻⡉⠙⠚⣟⣷⠒ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠊⠈⢱⣿⣯⣟⠋⡟⢟⣿⢟⣓⡶⡾⡯⠭⣭⣉⣀⡀⠀⢣⠹⢧⠳⠀⠀⠀⠀⠀⡴⠋⠀⢹⠳⢦⣀⠀⠀⠀⠘⡄⠀⢸⢻⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣦⣄⡀⢠⠀⠀⠀⠀⠀⢻⣿⣾⣿⣱⣰⣸⢾⠨⣿⢉⢡⣿⣿⡇⠃⡏⣯⣿⡦⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡼⠀⠀⠈⠉⢀⣤⡶⠃⠀⠈⡏⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣀⣀⠀⠉⠛⢷⠀⠀⠀⠀⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⡮⢽⣾⣴⣧⣫⣷⠇⠀⠀⠀⡄⠀⢀⡼⡁⢠⣀⣠⣧⣶⣷⡾⠞⠛⠋⠁⠀⣤⠀⢱⣹ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠟⠀⠀⠀⠀⠀⠀⠀⢸⡷⠉⠛⣷⣿⣿⣿⣿⣿⣿⡟⠛⣻⣦⣴⣿⣙⣿⡀⠀⠀⠀⠀⢸⣾⣾⡾⣿⣿⣿⣯⣿⣿⡋⠁⠀⠀⠀⠀⠀⢸⣦⣘⡟ ⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣦⣤⣀⣉⣨⣿⣿⣿⣿⣄⡀⠉⢻⣿⣻⣹⢁⣻⠀⠀⠀⠀⢸⡄⢹⣷⣤⣰⣜⠉⣡⣿⣭⣶⠀⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣇⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣹⢫⢻⡟⣿⢟⡿⠿⣿⣷⣦⣤⣶⡿⠿⡛⠁⠀⠀⠀⠀⣟⣧⣘⣙⣛⣛⣛⣛⣛⡛⣻⠯⠤⠄⠀⣠⣶⣾⣿⣿⣿ ⣿⣿⣟⣻⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣨⡿⣨⣸⢁⠁⢸⢱⣋⡼⢸⢣⡎⡟⢹⢷⣖⢢⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠒⡄⠀⠀⠀⠀⣜⣶⠬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢍⡺⣄⡀⠤⠴⣻⢣⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠤⠄⣀⣀⣀⡠⢤⡇⢣⠃⣀⣠⡆⠈⣇⢎⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣎⠔⠈⢀⡊⠐⠂⢸⡄⣧⡆⣞⠁⢿⣿⠸⡾⡅⡰⠉⠀⠯⠉⠁⢐⣄⠀⠀ ⢠⠮⠄⡤⠔⠋⠁⠀⢀⡼⡿⢨⣭⣇⡀⠀⡸⢠⠗⣞⣷⠀⣀⠀⠈⠢⣀⠈⢆⠀ ⠀⠑⢦⣄⠀⣀⡠⠴⠋⠀⣻⠤⡿⡁⠿⠿⠳⠃⢠⠁⠩⡢⣀⠀⠀⠀⠈⠑⠺⡄ ⠀⠀⠀⠉⠛⠻⢦⠬⠄⢚⠿⠀⠈⠱⢀⡀⣀⡀⠁⠀⣠⠣⠈⠑⠲⡤⢄⠀⢠⠆ ⠀⠀⠀⠀⠀⠀⠸⡀⠈⣼⠶⠂⠀⠀⢙⡿⠓⠊⠀⢈⢻⠒⠥⣠⡥⠧⠤⠒⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠡⣸⠃⠀⠀⠀⠀⠀⡏⠁⠀⠀⠈⡙⡄⠀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⣼⡴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⠀⠀⠀⢸⠄⠀⠀⣰⣄⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣄⠀⠀⠘⠀⣠⣾⣿⣿⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⣷⣶⣷⣿⣿⣿⣿⠿⢻⣢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠿⠃⢀⠹⣿⣿⣿⣿⣿⣿⠻⠀⠈⠙⠾⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⣃⡴⠃⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡅⠀⠀⡰⠃⠀⠀⠀⠀⣼⣠⠆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠄⢀⡼⠁⠀⠀⠀⠀⣲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⣸⡇⠀⠀⠀⠀⢀⡏⣀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⣠⣾⣿⣿⣶⡀⠀⠀⠀⢰⣇⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣿⣿⣿⣿⣿⣿⣷⣦⣷⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
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