Derpyhooves Emojis & Text

Copy & Paste Derpyhooves Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠶⠙⠁⠀⠀⠀⠀⠙⠡⢒⠤⣀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠶⠙⠁⠀⠀⠀⠀⠙⠡⢒⠤⣀⠀⠀⠀⠀⢀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠫⢢⣄⣰⠏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠏⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⢏⣴⡽⡗⠁⠀⠀⡠⣤⡶⠚⠓⠉⠉⢁⣠⠮⠂⠀⠀⢀⣀⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣘⡩⠟⣙⠏⠀⡠⡴⢷⣻⣸⣧⠀⠀⠄⣶⣯⣥⣤⠤⠖⠿⣯⡵⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⣯⡴⠽⣫⣀⢸⣏⣿⡿⡆⠀⠀⠀⡴⠋⠐⠢⠀⠀⠈⢳⠞⠁⠀⠀⢀⣾⡇⠀⣠⡶⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢼⡄⠀⠀⠉⠻⣿⠸⣿⡇⠀⠀⣼⣿⠉⠉⡀⢠⠀⠀⠀⠓⠒⠀⠀⣻⠿⣇⡼⠋⠀⠀⣠⡏⠀⡀⠖⠋⠉⠉⡁ ⠀⠀⠀⠀⠙⣦⡀⠀⠀⣇⠡⡸⠀⠀⠀⣿⣿⣆⠀⡇⢀⠀⠀⡘⠀⠀⠀⣰⠟⣦⡟⠁⠀⠀⣴⣿⠿⠋⠀⠀⠀⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠙⢦⣀⣼⠼⠒⠀⠀⠀⢿⣧⣿⣿⠇⡘⢀⠔⠀⠀⢀⡼⠊⠀⣿⠁⠀⠀⢾⡯⠋⠀⠀⠀⢀⢴⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⢙⣄⠀⠆⠀⣆⠀⠈⠙⠻⠿⠼⠒⠁⠀⠀⢠⠝⠀⠀⠀⡴⠛⢷⠸⠋⠀⠀⠀⢀⢔⠝⠁⠀⠀⠀ ⠀⠀⠀⢰⠺⠓⠀⠀⠘⠛⠷⣤⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⡠⠂⠀⠀⡇⠀⣸⠀⠀⠀⢀⣴⣷⣥⠄⠀⣤⣄⠀ ⠀⠀⠀⠀⠘⠦⣠⣀⠀⠀⠀⠈⣿⠒⠒⠤⣤⠤⢤⡖⠂⠁⠀⣾⡼⣷⠀⠀⠀⠇⢠⣯⠔⠲⣄⠈⠁⠀⠀⠀⠀⣀⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠣⢦⡄⡘⣦⠀⠀⠈⠀⣜⠀⠀⠀⢸⡹⠁⣯⠀⠀⠀⣦⠞⠁⠀⢠⡟⠀⢀⣠⣴⠦⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠭⢯⡳⣄⠀⠀⡿⠀⠀⠀⠘⠁⠀⣩⡤⢤⣄⣩⠀⢀⣴⣏⣴⣾⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠋⠀⠀⠀⠙⢯⠁⠀⣄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠙⣶⣞⠁⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⠈⣧⡀⣟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⠸⣿⠇⡠⡔⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⢰⡗⠛⠛⠛⠓⠒⠒⡏⠀⠀⠀⠀⠀⠀⢸⠓⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⡄⣀⣀⣀⠠⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣗⠤⣀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠈⠑⢦⡀⠀⢱⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⡿⠖⠚⠛⠛⢢⡀⠘⡆⡸⣠⡾⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠳⣦⡤⠤⠤⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⢳⢠⢃⠞⠋⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠉⠐⠒⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠦⠤⠴⠒⠋⠉⠁⠀⣀⣠⠤⠒⠒⠊⠉⠀⣀⠜⡇⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⣀⣠⠴⠚⠁⠘⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⣤⠶⠶⠛⠋⠁⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⡆⣸⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢀⡛⠛⠀⠀⠀⠀⠀⠀⠀⠄⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠙⠳⢤⣀⠀⠀⣀⠄⠀⢻⡼⡃⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⡴⠊⠀⣇⠀⠀⠀⣧⠀⠀⠀⡜⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠟⠛⠛⠛⠛⠛⠛⠛⢋⡁⠀⠀⢠⠘⡄⠀⠀⠘⠀⠀⠀⠇⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⢰⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⣀⣤⠴⠒⠋⠉⠁⠀⠀⠀⠀⡴⠀⢸⠀⠀⣧⡀⠀⠀⠀⠀⢀⠘⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠚⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⡏⠀⠀⣼⣿⡀⠀⠀⢀⣾⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀⠤⠄⠐⠒⠒⠀⣠⡶⠋⠀⠀⢰⠇⠀⠀⣻⢿⡿⠀⠀⠸⠿⢷⠀⠀⣧⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⠆⣸⠀⠀⠀⠘⣄⠀⠀⠀⠀⢀⡜⠀⠀⣷⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⢠⡾⠋⠀⠀⠀⣠⠎⠀⡇⠀⠀⠀⠀⠈⠛⠓⠾⠛⠉⠀⠀⠀⡟⢣⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢠⡿⠁⠀⠀⢠⠞⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢼⣇⠀⡔⠀⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⣀⡑⠫⡀⡆⢀⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠠⣀⣀⣀⠠⠿⠚⠉⠀⠈⢂⣀⡵⠋⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⣄⠀⢀⣁⠠⠤⠀⢀⣀⠀⠀⢠⠃⠀⢠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠂⠀⣀⡤⠒⠉⢀⡀⠤⠒⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠈⠓⠎⠩⠁⠀⡀⣴⣍⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠕⢦⡀⠀⠀⠀⠸⡁⠍⠀⠀⠀⠀⡀⠘⡉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠈⠁⣒⣈⡠⠋⡆⠀⢰⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠊⠉⠉⠉⠉⣉⠄⠀⢀⠑⡀⠈⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠁⣠⠄⠒⠈⠁⠀⠀⡐⢸⠀⢡⡀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⢃⠠⠤⠤⠀⡠⠊⠀⡄⠀⠸⡷⠀⠰⢧⠀⡇⠀⣀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⡤⠚⠁⢀⠂⠃⠀⠘⠤⢄⡤⠌⠀⡷⡀⠀⠉⠒⢤⠀⠀ ⠀⠘⠀⠀⣼⠁⠀⡔⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠀⠀⠀⠀⠱⠀ ⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣭⣷⣶⣤⣼⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡡⢀⣽⠟⠋⡹⠇⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣿⡷⠋⠀⠀⢠⠡⠄⠛⢿⠉⠒⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣾⣿⠟⠁⠀⢳⠀⠀⠈⠲⡀⡄⢸⣇⠀⠀⢻⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⠞⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⠋⠀⡀⠀⠀⠘⠀⣴⣶⠈⠀⠀⣠⣿⠀⠀⢸⡏⣿⣿⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⡿⢿⣿⡿⠛⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣤⣤⡊⠀⠀⠀⠀⠀⠀⡠⠀⠀⣠⣦⣥⠀⠀⢸⣷⣧⣦⣿⣿⠿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣴⣧⠈⠱⠀⠈⠛⢦⣰⣦⣹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⠝⠛⢿⣶⡄⠀⠀⡠⠊⢀⣤⣾⠟⠁⢹⡄⠀⠈⣿⣿⣿⣿⣿⣾⠋ ⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⢠⡟⠀⠀⢁⠆⠀⠀⣠⠙⠻⣿⣿⣟⢄⠀⠀⠀⠀⠀⠀⠀⡜⡠⠊⠀⠀⠀⠉⢿⣦⣌⣤⣾⠟⠋⠀⠀⠀⢸⠇⠀⠀⠈⠙⢿⣿⣿⠁⠀ ⠀⠀⢀⣠⣶⣿⣿⡏⠀⠀⣼⠃⠐⠀⡅⢠⡄⠀⡇⠀⠀⠈⠛⢿⡄⠱⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢸⣄⣼⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣛⢻⢸⡇⠀⠀⢹⢓⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠄⠀⠁⠎⠀⠀⠀⡔⠁⠀⠈⢤⣄⠰⠀⠀⠀⠀⠉⣿⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣏⣽⣿⣿⣿⣿⠇⠀⠀⣾⠛⢷⣄⠀⠑⢄⠀⠀⠀⠀⢀⣴⣿⡿⠿⣶⡀⠀⡇⠀⠀⠠⡿⣿⠠⠁⠀⠀⠀⢀⣿⣿⣀⣀⣀⣤⣾⣿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⠟⠀⠀⢰⡇⠀⠈⠙⢿⣦⣌⠑⠄⢀⣴⡿⠋⠀⠈⢆⠘⡇⠀⠱⡄⠀⠀⠀⠁⡠⡢⠒⠊⠉⠉⠉⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠛⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠉⠛⢿⡶⠛⡏⠀⠀⠀⠀⠀⠑⠘⢄⠀⠈⠂⠠⢤⣂⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢨⣿⡶⠃⠀⠀⠀⡀⠀⠀⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡁⣾⣯⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠒⠂⠀⠚⠿⠦⠤⢄⡀⢀⠁⠿⠙⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠑⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
𓇼 ⋆.˚ 𓆝⋆.˚ 𓇼𓇼 ⋆.˚ 𓆝⋆.˚ 𓇼˖°𓇼🌊⋆🐚𓇼 ⋆.˚ 𓆝⋆.˚ 𓇼𓇼 ⋆.˚ 𓆝⋆.˚ 𓇼𓆉🌊🤍🥥
⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡚⡶⢾⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣾⠟⢫⠀⠊⠈⢯⠙⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⣤⠼⡿⠀⠀⠀⠀⠀⢀⣀⡁⠀⠀⠐⡃⠀⣚⠀⣾⣟⣷⣤ ⠀⠀⠀⣠⠖⢰⠃⠁⠈⡲⢾⣦⡀⠀⠀⠀⠘⠈⠙⢦⣀⣪⠴⠋⢸⠄⠘⢿⣿⠋ ⢀⣴⢿⢿⠀⡧⠀⠰⠄⠁⠀⠙⠈⠀⠀⠈⢀⡀⠀⠈⢾⡁⠀⠀⡘⠀⠀⠀⠀⠀ ⠻⣿⣿⠏⠀⡏⠳⣄⡢⠀⣠⠞⠛⢢⠐⠀⠘⠃⠀⠤⠜⠃⠀⢺⡟⠀⠀⠀⠀⠀ ⠀⠉⠁⠀⠀⢃⠀⠀⠙⣯⠃⠀⠀⠀⠂⠀⠐⠐⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⡦⠀⠰⠇⢀⠀⠸⠇⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢻⣀⠀⠀⠀⠀⠀⢠⣾⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠇⢸⣿⣿⣷⣄⠀⡰⢛⡇⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⢋⣩⠴⢿⣿⣠⣾⠇⢹⢦⠻⣾⠁⣼⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠉⣀⡴⠋⠀⣴⣾⠿⠛⣁⣴⡿⣼⢀⠘⢷⣿⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢟⣿⡿⠋⠀⣠⡾⠋⠀⠀⢰⣿⣥⣶⡿⠟⢋⡴⢃⡎⡗⠀⠈⢿⠦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⠟⢡⣿⠟⠀⢠⡾⠋⠀⠀⢀⣴⢿⡟⠋⠁⠒⠚⠋⠀⣼⣻⠁⠀⠀⠈⣧⠙⢧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⢰⡿⠃⠀⣰⡟⠁⠀⠀⢠⠟⠁⢸⡇⠀⠀⢤⡀⠀⠀⣏⠀⠀⠀⠀⠀⠈⠳⣤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢏⡄⢀⣿⠃⠀⢰⡿⠀⠀⠀⠀⡇⠀⠀⢀⡇⠀⣤⣤⡉⢢⡀⠻⠂⠀⠀⠀⠀⠀⢀⣾⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⡞⠀⣼⡇⠀⢠⣿⠁⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠿⣿⠿⡾⠃⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⣾⠀⠀⣿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡆⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡆⣾⣿⢀⡇⠀⠀⣿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⢧⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⢻⡇⠸⡇⠀⠀⠈⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠸⣦⠇⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠀⠀⢸⣷⠀⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢻⡀⠀⠀ ⠀⠀⠀⢀⣠⢿⡟⠀⠀⠸⣿⡆⢣⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⠻⣆⡀⠀⢠⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀ ⠲⠴⠶⠟⢁⣼⡇⠀⠀⠀⢹⣿⡌⢧⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠛⠶⢾⡆⠀⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀ ⠀⢠⣤⡶⠛⢸⡇⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣠⣄⠀⠀⠀⠀⢽⣄ ⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⣿⠻⣧⡀⠀⠀⠀⠀⠀⢳⠀⢰⢱⣦⠀⠀⠀⠀⢠⡿ ⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠹⣿⣿⣷⣄⢠⣿⠀⠈⢿⡀⠀⠀⠀⠀⠈⣇⠈⠺⣿⣷⡆⠀⢰⣿⠅ ⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠘⢿⣿⣿⣿⣿⠀⠀⠀⢳⡀⠀⠀⠀⠀⢿⣇⠀⠈⠉⠀⠀⢨⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠙⠿⣿⣿⣿⣦⡀⠈⣧⠀⠀⠀⠀⠘⢿⡦⣄⣀⣤⠴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⣿⠟⠿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⣼⡟⠀⠀⠈⠙⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡿⠁⠀⠀⠀⠀⠀⣿⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⢰⠇⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠘⣿⡇⠀⠀⠀⠀⠞⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⠀⠀⠀⠀⠀⢠⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢸⣶⣦⡀⠀⡰⡏⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠤⠒⡪⠽⣿⣧⣼⠏⣯⠻⣞⢀⣃⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋⢁⡴⠋⠀⣼⠟⣋⣴⡾⣻⣄⡈⠻⣏⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢫⡿⠋⢀⡴⠋⠀⠀⣸⡿⠿⢛⡡⠜⢁⣿⠃⠀⠘⡙⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⢰⡟⠁⣠⠟⠀⠀⣠⠚⠹⡇⠀⢀⡀⠀⢸⠁⠀⠀⠀⠑⢤⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡡⢠⡟⠀⢠⡏⠀⠀⠀⠃⠀⢀⠇⢠⣤⡍⢦⠘⠀⠀⠀⠀⠀⣸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣱⠁⣸⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⢸⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⡇⠀⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠰⡀⠀⢡⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⡜⠈⣿⢸⠀⠀⠈⠃⢸⣿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢱⠀⠘⣼⠁⠀ ⠀⠀⠀⠀⢀⣼⠁⠀⣿⡈⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢰⠟⣧⠀⠀⠀⠀⠀⠀⠈⡆⠀⢳⠀⠀ ⢀⣀⣀⡴⢊⡏⠀⠀⢹⣧⢱⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⣾⠀⠘⢦⣄⣰⠀⠀⠀⠀⡇⠀⠀⢧⠀ ⠀⠀⣡⡴⠛⣇⠀⠀⠈⢿⣧⠁⠀⠀⠀⢿⣷⡀⠀⠀⢀⣿⠀⠀⠀⠈⠉⢆⠀⠀⣀⠁⠀⠀⠸⣄ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢻⣷⡀⠀⠀⠘⣿⣷⡄⠀⢸⡟⢷⡀⠀⠀⠀⠈⡆⢰⣹⣄⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠹⣿⣆⠀⠀⠘⣿⣿⣦⣼⡇⠀⠳⡀⠀⠀⠀⢱⡈⠹⠿⠇⠀⢾⠇ ⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠻⣿⣿⣷⣄⠀⢳⠀⠀⠀⠘⣷⣄⠀⢀⡠⠊⠀ ⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⡿⠻⣿⣷⣼⡆⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣸⠇⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⢸⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⡄⠀⠀⠀⠇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢲⢢⢠⡶⣭⡿⣳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢾⡇⠦⢥⢞⣿⣐⡿⣁⣿⢳⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢿⢱⠈⠋⠉⠉⠙⠳⢮⢿⣟⣍⠻⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣕⣾⡀⢁⣽⠞⡛⡳⣄⠘⡇⣀⣸⣧⡿ ⠀⠀⠀⠀⣀⡶⣶⣶⣶⡀⠀⠀⠀⣠⠶⢞⣿⣵⡎⠲⠀⢯⡶⣿⠀⣇⠛⣩⠉⠀ ⠀⠀⢀⠘⡯⣝⠋⣭⣽⣿⣢⠄⠀⣿⢣⣞⣯⡟⣥⡀⠀⠠⠁⠁⢠⣹⠀⠀⠀⠀ ⡴⡋⠭⢖⡿⢽⡧⢘⣯⡙⢿⣷⠤⠭⠿⢿⣿⡾⠜⣱⢸⠒⠚⠒⠋⠁⠀⠀⠀⠀ ⢷⡡⢾⠾⢛⣿⣟⣦⢸⡇⢠⡝⡀⠀⠀⢿⣰⣿⣼⠟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⡟⣷⡡⠷⠾⢾⣉⠀⠸⢿⠁⠿⢷⠰⠶⠿⠄⢀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣞⣨⣵⡷⢯⣼⣜⢳⡆⡴⠚⢠⣾⢳⠒⢶⠀⡾⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠻⢿⣮⡟⢻⣏⣔⠾⢃⠇⠀⡎⢘⡇⠀⢸⠀⢳⡼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣆⣸⣼⢾⡛⠛⠊⠀⢸⠀⠀⡇⢨⡇⠀⢸⠀⠸⢇⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠻⠾⠦⠓⠀⠀⢠⡇⠀⠀⡷⠶⠇⠀⠾⡀⠀⠸⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣶⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦⣶⣶⣶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⣼⣿⡿⢠⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣿⣿⡇⢸⠀⠀⠘⠁⢻⣿⣿⣿⣿⠟⠉⠁⠀⠀⡇⢹⢿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢿⣿⣇⠈⢄⠄⢀⣄⠀⠙⠿⣿⠏⠀⣠⠀⠠⡰⢀⡜⢸⣿⣿⡿⠀⠀ ⠀⡀⠤⠤⢈⣻⣿⡍⠃⡔⠁⢹⣧⠀⠀⠀⠀⠎⣿⣷⡄⠘⣱⠅⢸⡿⠿⠥⢄⠀ ⡌⠊⠁⠀⠡⢚⣿⡇⠀⡷⣴⣟⣿⡀⠀⠀⢰⣶⣻⡿⡷⠀⢸⢠⡓⠈⠀⠈⠱⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
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⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢦⣤⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠛⠃⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢳⣄⢀⡾⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⢿⡇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠹⣦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⠛⢧⡀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⣧⡀⠀⠀⠹⣦⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠛⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⡠⠀⡄⠐⠠⠐⠠⠐⠠⠐⠠⠐⣀⠂⡰⢀⠂⡔⠀⢆⠰⡀⢆⠰⡀⢆⡐⢢⠐⡂⢆⠒⡄⢒⡐⢂⠒⡐⢂⡒⡐⢂⡒⠰⣈⠒⡰⠌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠁⠐⠈⠀⠈⠀⠁⠈⠀⠁⠀⠈⢀⠁⠂⠁⠂⢀⠈⢀⠡⠈⠄⠁⠌⠠⢁⠘⢀⠃⠌⠠⢁⠂⠄⠡⢀⣁⣦⠵⣒⣧⡥⠮⠕⠒⠒⠒⠓⠒⠒⠢⠭⠤⣂⡔⡈⠔⠨⡐⠄⣃⠘⡰⢈⠒⡘⠤⡘⢌⠡⡙⢂⠥⢙⠰⣈⠑⢢⠙⡐⢋ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠂⠠⠀⠐⠀⠈⠀⠄⠂⠁⠈⠀⠄⠁⠈⠄⠈⡐⠀⠠⠐⠀⠡⠀⢂⠠⠀⢂⠈⡐⠠⠁⠄⡈⠄⢂⠈⡐⠠⢨⢞⣱⣾⣿⡿⠟⠉⠁⠀⠀⠀⠀⣀⣀⣤⣀⣀⣀⣐⣠⣤⣬⢭⠾⡁⢄⠃⠤⡑⠠⢃⡘⠄⢣⠐⡌⢢⠑⡌⢢⢁⠒⠤⡉⢆⠱⡈⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠠⠐⠀⠁⠠⠀⠈⢀⠐⠀⠠⠐⠀⠠⠈⠀⠌⠀⡀⠂⠄⠐⠀⠄⠁⢂⠐⠀⠂⠄⡐⣴⣿⣿⣿⣿⠏⠀⠀⠀⣠⣴⡶⣿⣶⣶⣶⢾⣿⡽⠯⠿⠽⠿⠽⠿⠶⠬⣐⡌⠰⣀⠃⢆⠰⠉⡄⠣⡐⢡⠘⡠⢃⠌⡘⠤⡑⢌⠢⡑⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠂⠀⠄⠀⠄⠂⠀⠄⠁⠠⠀⠠⠐⠀⠌⢀⠈⠐⡀⠂⠁⡐⣴⣾⣿⣿⣿⠟⠁⠀⠀⢴⣾⣿⣳⣿⣟⣯⠷⠋⠉⢀⣠⣤⣤⣤⣀⣀⠀⡐⠀⠄⠽⣆⠄⢊⡐⠌⡡⢐⠡⡘⠄⢣⠐⡡⢊⠔⡡⠘⡄⢣⠘⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠈⠀⠂⠀⠄⠂⠁⠀⡀⠂⠀⠄⠀⠂⠠⠀⠁⠄⠂⠀⠂⡀⠂⢈⠀⠄⠐⢀⣸⣿⣿⢷⣿⡃⠀⠀⣠⣾⣿⢿⣞⣿⣷⢻⡁⣠⣴⣾⣿⣽⣟⣿⣛⣿⢻⣿⣿⣿⣦⣌⢫⡉⠔⡠⠊⢄⠡⢂⠅⡊⢄⠣⡐⢡⠊⠔⡡⠘⠤⡉⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠄⠂⠀⠀⠀⠀⠂⠀⠄⠁⠀⠂⠀⠁⠠⠁⡀⠂⠁⡀⠐⠀⠂⢀⠐⣬⠆⣿⣿⣯⢿⡏⠠⠀⣰⣿⢷⣿⣟⣯⡿⠁⡀⢹⣯⣷⣷⣿⣾⣿⣿⣽⣾⣿⢿⣿⣿⣿⣿⣿⠙⢠⠐⠡⠊⢄⠃⡂⢅⠂⢆⠑⣂⠉⢆⠡⡉⢆⠱⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⡀⠈⠀⡀⠁⠐⠀⡀⢀⠐⠀⠀⠄⠁⠈⠀⣾⣿⢸⣿⣿⣯⣿⠁⠀⠀⣿⣿⣿⣾⣯⡿⠁⣼⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⢁⠢⠌⡁⠎⢠⢂⠡⠌⢌⠢⢘⠠⢉⠢⡑⠌⡄⢣⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠁⠀⠀⡀⠀⠠⠀⠐⠀⡀⠀⠈⠀⡐⠈⠀⠀⣿⣿⣿⣿⣽⡷⣿⠃⠀⢰⣿⣷⣿⣟⣾⡇⠀⣿⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇⡐⢂⠘⡠⢁⠢⠌⠒⡠⠊⠤⠑⡨⠐⢌⠒⡨⠄⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⠀⠄⠀⠂⠁⠀⠐⠀⠁⠀⡀⠂⠐⢸⣿⣻⣿⣾⣟⣿⠰⠀⠸⣾⣿⣿⣯⣿⡇⢀⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠐⢄⠊⢄⡁⠆⠒⣈⠡⡐⠡⢊⠡⡐⢩⠀⢎⠐⡡⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠁⠀⠐⠀⠀⠄⠀⠂⠀⢁⠈⢀⠈⠀⠄⠀⣐⡀⠖⢻⣿⣿⣿⣿⣿⣆⣀⡀⢹⣿⣿⣿⣿⡷⠤⢿⡇⠀⠀⠀⢱⠈⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠠⢋⠠⠌⢠⠐⡈⠡⠄⡒⢈⠡⢂⡁⠆⡁⢎⠠⠃⡔⠡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠐⠀⠀⠀⡀⠠⠀⠀⠸⡉⢉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠻⠟⠁⠀⠀⠀⠈⠃⠀⠀⠄⠊⠀⠀⠀⣿⣿⡻⣿⣿⣿⣿⡿⢀⢁⠢⠐⡈⠄⢂⠡⡁⠒⡈⠤⢁⠢⠐⡌⠰⢀⠃⡜⠠⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠄⠀⠀⠂⢡⠀⠱⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⣂⣀⠀⠀⠀⠈⠙⠻⠸⠭⠿⢛⠳⡀⠂⠄⡡⠈⢌⠠⢁⠰⢁⢂⠡⢂⠡⠒⢠⠑⡈⠔⠠⢃⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⡀⠀⠂⢀⠈⠀⢀⠀⠂⠀⠈⠢⡀⠻⣭⠩⢍⢫⡙⡍⢓⡆⠀⠀⠀⠀⠀⡠⢐⡩⢐⣒⣭⣽⠶⠄⡀⠀⠀⠀⠀⠀⢀⠌⠀⡇⢂⠐⡁⠂⠌⡐⠌⡠⠌⡈⠆⣈⠂⠔⡈⠄⢃⠔⠂⡌⠡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⢄⣶⣽⣄⡈⠓⠦⣄⣐⠈⣄⡇⢦⣲⣴⣴⣦⣴⣴⣾⣟⣻⣿⣆⠀⠀⠀⠑⢠⠀⠀⠒⠃⠀⠀⡇⢂⠐⠠⢉⠐⠠⢂⠡⠐⡐⠰⠀⡜⠠⢁⠊⠤⠘⡐⢨⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣞⣫⣿⣿⣿⣿⡆⠤⣀⠉⣉⡩⣥⣀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⡆⠀⡠⠐⠁⠀⠀⠀⠀⠀⣰⣥⡀⠌⡐⢀⠊⡁⠂⠄⠃⠤⠑⡈⠄⡑⢂⠡⠘⡠⢁⠆⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⢸⣆⠙⢦⣿⣼⣇⡀⠀⠀⠈⠙⠿⣿⣿⣯⣴⡖⠋⠀⠀⠀⠀⠁⠒⠒⣚⠿⣽⡇⠐⡀⠂⠔⠠⠉⠄⡡⢂⠡⢐⢈⡐⠤⢁⠢⢁⠢⠄⠡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⠁⠐⡄⠈⣿⣦⡀⠙⠻⣿⣿⣿⣿⣵⣮⣴⣴⣿⠿⠏⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⡈⢁⠐⠠⠁⠌⠠⢁⠂⡐⡀⠆⡈⠄⠰⢀⢂⠡⠂⠆⠌⠡ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣐⣢⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⣿⣧⢃⠠⠀⠈⠻⣿⣤⡀⠈⠙⠛⠿⣿⣿⣿⣿⣧⣄⣀⠀⠀⢀⣀⣴⣿⠛⣽⣿⡇⠐⡀⠂⠌⠠⠁⠌⡐⠠⢁⠐⡀⠢⠐⡈⠔⠂⢄⠂⠅⢊⠌⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⢿⣟⣿⣻⣿⡽⣿⣿⢿⣦⡄⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⠀⠀⠀⠘⠽⣻⣶⣄⠀⠉⠙⠻⢟⣿⣻⣿⣿⣿⣿⣫⣹⣿⡿⢠⣿⣿⡇⠐⢀⠡⢀⠡⢈⠐⠠⢁⠂⡐⠠⢁⠂⠡⡈⠐⠂⢌⡈⠄⠒⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣯⣷⡿⣿⢿⡾⣿⢯⣿⣿⣞⡿⣽⢿⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡑⢄⠀⠀⢀⠉⠛⢷⣦⣀⠀⠠⢙⠻⣿⣻⣟⣿⣿⣿⣿⠇⢸⣿⣿⡇⢀⠂⢀⠂⡐⠠⢈⠐⡀⠂⠄⡁⠂⠌⡐⠠⢉⠐⡠⠐⡈⡁⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⡿⣯⡷⣟⡿⣾⣽⣳⣟⣷⣯⣿⣿⡽⣿⣿⣷⣿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣤⡀⠀⠀⠀⠀⠀⠀⠑⠝⠻⢿⣦⣑⠠⡀⠈⢐⠀⠈⠻⣿⣦⡄⠈⢋⠿⣿⣷⣟⣿⡿⠀⣹⡿⣷⣧⠀⠐⡀⢂⠠⠁⠄⠂⠄⡁⠂⠄⡁⠂⠄⡁⢂⠰⢀⠡⠐⡐⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⣳⣿⣿⢿⣽⣟⣯⣿⡷⣯⢿⣽⣯⡿⣷⣿⣿⣯⣟⣿⡿⣿⣷⡁⡄⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢧⡀⠀⠀⠁⡀⠀⢻⣿⣿⣦⠀⠑⢽⣾⣿⣿⡇⡀⣿⣿⢿⡽⣆⠀⠄⠠⠐⢈⠠⠁⠂⠄⡁⠂⠄⡁⢂⠐⡀⠂⠄⢂⠡⠄⡁ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣽⣿⣾⡿⣯⣷⣿⠿⢯⠷⣯⣽⣳⢯⢿⣽⣻⣾⣽⣯⣿⣿⣧⣄⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠸⢙⣼⣿⡆⠀⠀⠈⠢⠀⣿⣿⣿⢹⠀⢸⣿⣿⣿⠃⢣⣿⣿⡿⣗⠼⠆⢀⠂⠁⠄⢂⠈⡐⠠⢀⠁⢂⠐⡀⠂⠄⠡⠈⠄⢂⡐⠠ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣯⣿⡟⠩⢁⠉⡄⣾⣿⣾⣿⢿⣿⣞⣷⣯⣿⢿⣿⣷⣿⣿⣿⣶⣿⡿⠿⠛⠛⢉⠛⡽⣻⣿⣿⣿⣿⣿⣿⣶⣤⣦⣄⣾⣿⣿⣾⣆⠀⠀⠁⣿⣿⣿⠆⢀⣼⣿⣿⡇⠄⢸⣿⣿⣽⣿⣆⠀⡀⠠⠁⡐⠀⠂⠄⠡⠀⠌⡀⠂⠄⠡⠈⠄⠡⠈⠄⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣯⣟⣷⡿⠀⠀⠂⢊⣼⣿⣿⣽⣾⣿⣿⣿⣿⣿⢿⣟⣿⣾⣽⣾⣿⠟⠁⠀⠀⠀⠀⠀⠬⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⠋⢠⣿⣿⣿⣿⡇⠀⣺⣿⣿⣞⣿⣮⡀⠀⠄⡐⠀⠌⠐⠈⡀⢁⠂⠄⠡⠈⠄⠡⠈⠄⠡⠈⠄⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣟⣷⣻⣿⠁⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣟⣾⢻⣾⣿⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠤⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠃⠀⢀⣾⣿⡇⢀⣾⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣾⣻⣯⣄⠠⠀⠠⠐⠀⠂⡄⠂⠠⢈⠠⠁⠌⠠⠁⠌⠠⢁⠂⠄ 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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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