Smurf Dot Art

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

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