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

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