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