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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣷⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⡟⢋⠛⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠋⣹⣦⠉⠃⣀⣶⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣖⢿⡼⠀⣀⠀⢩⠏⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣷⣾⠷⠸⠀⣼⣶⠶⠾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣁⣤⡤⠞⠋⠁⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠙⢦⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢾⡿⠋⠉⠙⠛⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠃⠀⣀⠀⠀⠀⠻⣄⠀⠀⠀⠠⡄⡆⠀⠀⠀⢻⡀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡴⠉⠀⠀⠀⠀⠀⢠⣴⠏⠀⠀⢰⡇⠀⠀⠀⠀⢻⣆⠀⠀⠀⠁⢻⡀⠀⠀⠈⡇⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠉⢦⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣤⠤⠖⠛⠉⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢨⢻⣇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⢡⠀⠀⠈⠙⢦⣤⡀⠀⠸⣯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠇⠀⠙⣷⣄⣠⣾⣍⣁⡀⠀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠻⠶⢬⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣧⣴⣶⡶⢶⣶⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⡾⠟⠉⠀⠀⠀⠈⠻⣦⣽⣀⠀⠀⠀⠙⠶⢄⡀⠀⠀⠀⠀⠀⠿⣷⣄⠀⠀ ⠀⠀⠀⣼⣿⡿⡟⠛⠋⠉⠛⠷⣿⣄⣀⣤⠄⠻⣤⣀⠀⠀⠀⠀⠀⣠⡄⠁⣠⡴⠛⠁⠀⠀⣠⠊⠀⠀⡆⠀⠀⠉⠙⢶⣄⠀⠀⠀⠀⣁⣤⣤⣴⠾⠿⠶⢦⣹⡆⠀ ⠀⠀⢰⡿⣡⠟⢷⡀⠀⠀⠀⠇⠘⠋⠉⣷⠀⠀⠀⠀⠉⠀⠀⠉⢁⣩⡿⠟⣉⣀⣀⣀⣀⣉⡁⠀⢀⣀⣻⡶⠒⠉⠁⠀⠉⣿⡶⣶⠶⠟⠁⢸⣷⡄⠀⣿⠀⠙⣿⡄ ⠀⠀⠀⢠⡏⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠈⠿⠶⠦⠤⠤⠤⢶⣿⡏⠉⠿⠛⠿⠿⠭⠉⠉⠉⠉⠉⠉⠉⢿⡅⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠈⢁⣼⣿⠀⠀⠿⠃ ⠀⠀⠀⣾⠁⠀⠰⠀⠀⠙⠳⣤⣀⣀⡀⠤⠤⠤⠤⠤⣄⣀⣸⣯⠀⠀⠀⢰⣦⠀⠀⠈⠳⣤⣦⢀⠀⠀⠈⠛⠓⠒⠶⢤⣀⢘⣿⠟⢦⣀⡀⠀⢀⣺⣧⡿⠀⠀⠀⠀ ⠀⠀⣸⠏⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠙⠷⢄⡀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⣿⡄⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⣰⠟⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢿⣀⣠⡾⠻⣦⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀ ⣴⠏⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠇⠀⠈⢻⡄⠀⠀⠀⠀⠀ ⣿⣸⡿⠋⢁⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⣄⣿⡄⠀⠀⠀⠀ ⢻⣿⠀⠀⡈⠘⠛⠲⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣿⣿⠇⠈⣿⠀⠀⠀⠀ ⠈⠙⣆⠀⡁⠀⠀⠀⠀⣠⡟⠉⠉⠉⠛⠻⠶⢬⣀⣀⡀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠭⠉⠹⣶⣷⣾⠟⠀⠀⠀⠀ ⠀⠀⠹⣧⣠⡄⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣻⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠳⣆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣴⡖⠶⣶⢶⣺⣿⠿⠋⠙⠿⣔⠶⠀⠠⠄⠀⢠⢄⣶⣿⠟⠁⠀⢀⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢧⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠉⣩⣹⣿⣿⡉⠁⠀⠀⠀⣠⡌⠙⠓⡒⠒⠒⠿⠟⠉⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠈⠛⠻⠄⠀⠀⠀⠀⡠⠟⠙⠂⡇⠀⠀⠀⢸⡇⠀⠀⠀⠙⣧⠀⠀⠀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡞⠀⠀⠀⣰⠁⠀⠀⠀⠘⢧⠀⠀⠀⠀⠘⡄⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢻⡄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠊⠀⢀⡞⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠙⣄⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡠⠊⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠈⠓⠦⣤⣀⡈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢦⣙⢧⠘⢳⠈⠀⠁⢸⠏⢫⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡈⢰⢧⠀⢿⠀⣽⠟⢠⢧⠁⠉⠉⠉⠈⠀⠀ ⠀⠁⠞⣡⠾⣠⣀⣄⢿⠾⣠⣄⢦⠛⠈⠀⠀⡇⣴⠳⠈ ⠀⣽⣤⡶⠀⠀⠀⠃⣸⠀⠀⠀⢧⠀⣀⣤⠤⣤⠒⠁⢿ ⠀⡅⠻⠎⠙⠂⠀⡀⢱⠀⠀⠀⡀⢠⠀⠀⠀⠁⠆⣡⡾ ⠈⣿⣨⣤⣿⢤⠦⠹⡍⢩⠉⠉⡏⣼⠷⠬⣤⢶⠙⡟⢀ ⣷⣾⣴⣠⣄⢦⠛⢈⠁⠋⡴⣠⠀⠀⠀⣄⠦⠒⣟⣾⠀ ⠀⣇⢤⠳⠈⠀⠀⣧⣠⢷⠀⠀⠋⠠⠉⠚⠗⠼⣠⢀⠀ ⠀⡆⠙⠀⣧⠀⠀⡄⠀⡄⢰⠀⢁⡼⣀⠀⡥⢸⠀⠀⠀ ⠀⠀⡀⣄⡄⢳⠉⠀⠀⠀⠀⠉⡾⠂⠀⠒⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⠳⠖⣳⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⣿⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢳⣼⣶⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣠⣽⣿⣿⣿⣶⣧⣬⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⢀⣿⡿⣯⣿⡆⠙⡜⠀⠻⣿⣿⣿⡦⠤⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⡤⠒⠀⢠⣲⣿⣿⠁⢘⣻⣷⠀⢸⣧⠀⠻⢿⣿⣧⡀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣄⣴⣶⣿⣟⢉⡟⠀⣾⣿⣿⣤⣌⣿⣆⠀⢸⣎⠻⣯⡀⠈⣺⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣾⣿⣿⣿⡏⣠⣴⣿⣿⣿⣿⠿⡿⣿⣶⣶⣿⣦⠈⠻⠿⣷⣧⡀⠀ ⠀⠀⣸⣿⡟⠿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡿⣋⣤⡜⠒⡪⢽⣻⣿⣿⣇⣤⣤⣾⣿⣿⡄ ⠀⠀⢹⠉⢳⣄⠈⠉⠻⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠉⠀⠸⣿⡋⠁⠙⣱⡃⠸⠇ ⠀⢀⡆⢰⣿⣿⠿⣒⣚⣉⣩⣷⣾⣿⣿⣿⣀⡈⠻⣿⡿⢿⣟⢿⡷⢿⡿⢶⣾⡿⠃⠀⠀ ⢀⡾⣠⣽⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣿⣼⣿⣿⣦⣾⣷⣤⠙⣆⠀⠀⠀ ⢸⣿⢋⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡆⠀⠀ ⠀⠹⣴⣟⣿⣿⠋⠉⠙⠿⣿⣿⣾⣿⢼⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⡿⠃⠀⠀ ⠀⠀⠙⠻⣿⣇⣀⠀⠀⠀⠈⣙⠿⣿⣿⣿⣿⠿⠟⢻⣿⣿⣿⣿⣿⠟⢁⡠⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠒⠒⠛⠓⠚⢻⠀⠀⡹⠖⢹⠄⠀⡎⠀⠙⡟⠋⡧⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⡸⠁⢠⠊⠀⠀⠸⣄⠀⠸⡄⠘⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠂⢉⣰⠁⠀⡇⠀⠀⠀⠀⠈⢣⠀⠘⠦⣈⣓⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣄⣀⢀⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡉⢹⣿⣿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠋⣭⡟⣟⢿⣿⣇⠸⠋⣿⣿⡁⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣟⠹⣤⣹⣿⣿⣌⡙⡼⢿⣴⣆⢿⣿⣾⣆⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣇⣀⣾⣿⣿⣿⣿⠉⠀⢚⠉⢿⣾⣿⣿⣿⣧⣀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠀⠠⣿⡀⠀⠀⢴⣿⣾⠇⠉⠉⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢸⣧⣼⣿⣿⣀⢀⠀⣿⡇⠀⠀⠘⣿⡿⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣾⣿⣿⣿⣿⣶⣾⣶⠸⣿⡄⠀⣸⣿⣿⣤⣴⣶⣶⣶⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⣿⣿⣿⠟⠋⠈⠀⢹⣷⣰⣿⣿⣿⡿⣿⣻⣟⣯⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠻⣿⣷⢀⠀⢠⣰⣤⣿⣿⣿⣿⣳⡿⣽⡷⣯⣷⢯⣷⣻⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⣹⣥⣾⣿⣿⣿⣿⡿⣿⣟⡷⣯⢿⣷⣻⣟⡾⣟⡷⣯⡿⣽⣻⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⢿⣯⣿⡽⣞⣿⣳⣯⢿⣻⣟⣾⣽⢾⣟⡿⣽⡷⣟⣯⣟⡿⣾⡽⣯⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⢿⣟⣿⣻⡽⣷⣻⣽⢯⣿⢾⣟⡿⣾⣽⣿⡿⣽⣾⣻⢷⣟⣿⣾⣿⣿⢿⣽⣻⢾⣽⣳⣯⢿⣳⣯⡿⣞⣯⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣟⣷⣿⣿⣿⣿⣿⣿⣿⣯⣟⣷⣻⣾⣿⣻⣽⣞⣯⣿⣻⣽⢿⣿⣷⣻⢯⣟⡷⣯⢿⣽⡷⣯⣟⣿⣻⣿⣿⣿⣶⣦⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⣿⡽⣾⢿⣽⢾⣯⢿⣽⢯⣟⣿⣾⣿⣾⣿⢿⣟⡷⣿⣻⢾⡽⣿⣾⣿⣿⢿⣽⣻⢾⣽⣯⡷⣿⣽⣻⢯⣷⢿⣻⣽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⡿⠿⣿⣿⣿⣿⣟⣾⢷⣿⣿⣿⣳⣯⣟⣾⣽⡾⣟⣿⣿⣟⣯⡿⣽⢯⡿⣾⡽⣷⣻⡾⣷⣻⡾⣽⣟⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢿⣯⣟⡷⣯⣿⢾⣻⡷⣟⣯⣿⣿⣿⣻⡽⣟⣾⡽⣿⣞⡷⣿⣳⣯⣟⣯⣟⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⣼⠁⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣟⣾⣽⣳⣯⣟⡿⣾⣽⣻⢷⣟⣯⡿⣽⣳⢿⣽⣳⢿⡽⣯⣟⣿⡾⣷⣯⣟⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣻⡾⣽⣻⣽⡾⣟⣷⣿⣿⣿⢿⣻⡾⣽⣻⢯⡿⣽⣷⣻⣽⡷⣟⣷⢯⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢰⡾⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣾⣽⣳⡿⣽⡷⣯⣟⡿⣾⢯⣿⡽⣯⢿⡾⣽⢯⣟⣷⣻⡾⣽⣿⣿⣿⣟⣷⣻⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣽⡷⣟⣿⣽⣷⣿⣿⣿⣿⣿⣞⣿⣳⣿⣻⡽⣟⣿⡽⣞⣯⣷⣟⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⣤⣴⣦⣤⣀⣀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣷⣟⣯⢿⣳⡿⣽⣯⢿⣞⣿⡽⣿⣽⣻⣯⣟⣾⣷⣿⣿⣾⣿⣿⣿⣞⣿⢾⣟⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⢿⣿⡿⠉⠉⠘⠋⠙⠛⠰⣿⣙⡿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⡷⣟⣯⣷⢿⣻⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣀⣠⣤⠶⣦⣴⡿⢁⣠⣞⠋⠉⡟⠙⡛⠿⢶⣤⣄⣀⠀⠀⠈⣻⣿⣿⣿⣽⡿⣞⣿⣳⣯⢿⣞⣿⡽⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⢿⡿⠿⣿⣾⢿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣠⣿⣿⠿⠉⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⣉⣙⣛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⢀⡄⠛⠉⠁⣀⢾⣿⣿⣄⡜⠁⠈⣄⠀⠸⣷⣄⠀⠀⢀⣉⣿⣿⣷⠞⠃⠀⠙⠻⢿⣿⣿⣷⣻⣽⣯⢿⣞⣿⣿⡿⠉⠀⠈⣿⣧⣿⣿⣿⡿⠁⢘⣧⠀⠈⠻⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⢀⣾⣿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠉⠉⠀⢦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⣀⣄⣠⣀⣤⡞⣁⣠⣤⣄⣏⣈⣿⣿⣘⢻⣶⣠⣿⣆⣴⡛⣿⣷⣾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣿⡿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣿⠟⠁⠀⣼⣿⠀⠀⠀⠈⢻⣿⣿⡄⡀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣾⣿⢯⡟⣾⡽⣿⣷⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⡉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠁⠀⠀⣰⣿⣿⠀⠀⠀⣉⣳⢻⣿⡇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢯⣳⢯⢷⣻⡽⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣟⣿⢿⣻⣟⣿⣻⢿⣿⣿⣾⣿⣿⣿⣻⡾⣟⣾⣽⣿⣿⣿⣯⣟⣾⢷⡿⣿⣯⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡆⠀⠀⠉⠉⠿⠿⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣯⣳⢯⣟⡷⣿⣳⣟⡿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣽⣿⡿⣯⣟⡿⣞⣷⣟⣿⣞⡷⣯⡟⣿⢻⣿⣿⣿⣽⡾⣿⣿⣿⡷⣯⣟⣯⣿⣿⣞⣿⣿⣿⣆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⢗⣯⣟⡾⣿⢷⣻⣽⣻⢷⣻⣟⣿⣿⣷⣦⣤⣀⣀⣀⣀⣤⣤⣴⣾⣷⣶⣷⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⣰⣿⣿⣟⡷⣿⣽⢾⣟⣯⡷⣿⣿⡿⣽⢧⡻⣜⢯⡞⣽⣻⣿⣿⣿⣿⣿⣿⣽⣾⣻⣾⣿⣿⡿⣟⡿⣿⢿⣿⢿⣿⣿⣿⣷⣶⣤⣄⠀⠀⢹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣭⣟⡾⣽⣻⣽⣟⣯⡷⣿⣻⣽⣾⣻⣾⣽⣿⣿⣿⣿⢿⡿⣿⣻⣟⣯⢿⡽⣯⢿⡽⣯⣟⣿⣻⢿⣿⣿⣶⣿⣿⡿⣞⣿⣳⣯⣿⢾⣯⣟⡷⣿⣟⡿⣾⣵⢫⡞⣽⢲⣯⣽⣻⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣟⡿⣽⣻⣟⣾⣿⣳⣟⣾⡽⣟⣿⡿⣿⣶⣾⣿⣿⣿⣾⣽⣿⢿⣿⣷⣦⣤⣤⣤⣾⣿⣶⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⣳⢯⣟⡿⣽⡾⣽⣾⣻⢷⣻⣷⣿⣿⡿⣟⣯⢷⣻⣞⣯⣟⡷⣟⣾⡽⣯⢿⣽⢯⣟⣷⣻⡾⣽⣟⣾⣿⣿⣻⣽⣻⢯⣷⣟⡷⣯⣿⢾⣽⣻⢷⣻⣽⣷⣻⣯⣟⣾⣛⣶⡳⣟⡾⣿⣿⣿⣿⡿⣯⣟⣯⣿⢾⣻⣟⡷⣯⣷⣻⢷⣻⣽⣻⢯⣷⣟⣿⣻⢿⣿⣿⣿⣟⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡷⣯⣟⣯⡿⣽⢿⡽⣟⣾⣽⣿⣿⢿⣯⢷⣻⣽⣾⣿⢿⣞⣯⡿⣽⣟⡷⣿⣻⣟⣾⣟⡿⣾⣽⣻⣽⣾⣿⣿⣳⣯⡷⣿⣻⢷⣯⢿⣽⣾⣻⢷⣻⣟⣯⣷⢯⣷⣟⡾⣷⣟⣾⣽⣳⡟⣷⣿⣿⣿⣟⣷⣻⣽⢾⣻⣽⡾⣿⣽⢾⣻⢿⣽⣳⡿⣿⣷⣛⢶⣫⢿⣽⣻⣿⣿⡾⣽⣻⠾⣽⣻⢿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⢯⣟⣷⣯⢿⣽⣻⣯⣿⣿⣿⡿⣯⣟⡿⣾⣿⣟⣯⢿⣞⣯⣿⣳⢿⣻⣞⣿⣳⡿⣞⣷⣯⢿⣳⣯⢿⣽⣞⡿⣽⡷⣯⢿⣳⣿⣻⢾⣟⡷⣯⣟⡿⣽⣾⣻⢾⣻⢷⣯⢿⣳⣯⣷⢯⣷⣻⢷⣯⢿⣿⣿⣯⣟⣾⣟⣯⡷⣿⣳⣯⡿⣯⣿⣞⣯⣟⣿⣿⡽⣮⣳⣟⣾⢯⣟⣿⣿⣷⣯⣟⡷⣯⣟⡾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⡿⣯⣟⡿⣾⡽⣯⣷⣿⣿⡿⣟⣷⣻⣷⣿⣿⢿⣳⣯⣟⣯⣿⣳⣯⣟⡿⣽⣻⡾⣽⣻⣽⢷⣯⢿⣯⣟⡿⣾⣽⣻⣽⣻⣽⣟⡿⣾⡽⣿⣞⣿⣽⢾⣟⡿⣾⡽⣟⣯⣿⢾⣟⣯⣷⢯⣿⣳⣿⣻⣞⣯⢿⣿⣿⡾⣷⢯⣷⢿⣯⢷⡿⣽⣷⣻⡾⣽⡾⣯⣟⣿⣳⢿⡾⣽⣻⣽⡾⣿⣿⣾⡽⣿⣳⢯⡷⣯⣟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⢿⣽⡾⣟⣷⢿⣿⣿⡿⣯⢿⣽⣾⣻⢿⣽⡾⣟⣯⡷⣿⡽⣾⣳⢿⣞⡿⣯⣷⢿⣻⣽⡾⣟⣾⣟⣾⣽⣻⢷⣯⢿⣽⣿⣷⡿⣽⡷⣿⣳⡿⣾⣽⣻⡾⣟⣷⢿⣻⣽⢾⣟⣾⣻⢾⣻⢷⣻⣿⣿⢾⡽⣯⣿⣿⣿⢯⣿⣽⣻⢾⡿⣽⡷⣯⣷⢿⣯⣟⣷⣯⡷⣿⢯⣟⡿⣽⣞⣿⡽⣿⣿⡿⣽⣻⢿⣟⡷⣾⣽⣻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣽⣻⣾⣽⣿⣽⣿⣿⣿⡽⣟⡿⣞⣷⣟⡿⣾⡽⣟⣷⢿⣳⡿⣯⣟⣯⡿⣽⡷⣯⣿⣻⢾⣽⣟⡷⣯⣟⣾⢯⣿⢾⣻⢷⣻⣿⣿⣯⣟⣷⢿⡽⣷⢯⣷⢿⣯⣟⣯⡿⣾⣻⣽⣾⣻⢿⣽⣻⣟⣾⣿⣯⢿⣽⣿⣿⣿⣿⣳⣯⣟⣯⡿⣷⣻⣟⡾⣟⣾⣽⢾⣳⡿⣯⣟⣯⣿⣻⢾⣽⣻⢿⣿⣿⡽⣯⡿⣯⣟⣷⣯⢷⣻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣸⣿⣿⣿⣿⣿⣿⣿⣿⣻⢷⣯⣟⡿⣽⣟⡷⣯⣿⣳⣿⣻⢾⣟⣯⢿⣳⡿⣽⣻⢷⣟⡿⣾⣽⣻⢷⣯⣟⣯⢿⣾⣻⣽⣻⢯⣿⢯⣟⣿⣿⣿⣾⣻⢿⣽⣻⡽⣟⣾⣽⣳⡿⣽⣷⣻⢾⣽⣟⡾⣟⣾⡽⣿⣞⣯⣷⢯⣿⣿⣷⢯⣷⣻⣽⣻⢷⣻⣽⣻⢯⣟⣾⣟⣯⢿⣳⡿⣽⣞⣯⣿⣳⢿⣻⣿⣿⡽⣷⢿⣽⡾⣯⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⣿⣿⣿⣿⣿⣻⢧⡿⣽⣻⣞⣿⣿⣻⢾⣻⣽⣞⡿⣾⡽⣿⣞⣯⡿⣯⢿⣽⢯⣿⢾⣻⡷⣯⣟⡿⣾⡽⣯⣿⢾⣽⣳⡿⣯⣟⣯⣟⣿⣿⣿⣷⣟⣯⣷⣟⡿⣯⣟⣾⣽⣻⢷⣯⣟⣯⡷⣟⣿⡽⣷⢿⣻⣾⡽⣾⢿⣿⣿⣟⣯⣷⣟⡷⣿⣻⢯⣷⢿⣻⣽⢷⣯⣟⡿⣽⣻⣽⣾⣻⢾⣽⣟⣿⣿⣿⡿⣽⣿⣾⣽⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣳⢏⣯⣟⡷⣿⣽⣻⣿⣿⣿⣯⣷⣿⡽⣷⢿⣳⣯⢿⣽⣻⢯⣟⡿⣾⣻⣽⣻⢷⣻⣽⡷⣟⡿⣞⣯⣟⡷⣿⣽⢾⣻⣾⣻⣿⣿⣿⣞⡿⣾⣽⣻⢷⣻⣽⢾⣯⢿⡾⣽⣳⣿⣻⣞⣿⣽⣻⢷⣯⣟⣯⣿⣿⣿⣯⣟⣾⣽⣻⢷⣻⣯⣟⣯⡿⣾⣻⡾⣽⣻⢯⣟⡷⣯⣟⣯⡷⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣷⢯⣞⡷⣯⢿⣳⣯⢿⡽⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣯⣿⣷⣿⣷⣿⣟⣯⣷⣿⣻⣽⡿⣽⡾⣿⣽⢾⣟⣷⢯⣿⣿⣿⣿⣽⣟⡷⣯⣟⡿⣽⣯⢿⣾⣻⣽⢿⣽⢾⣷⣻⢷⣯⣟⡿⣾⡽⣿⣿⣿⣿⢷⣯⣷⣻⡽⣟⡿⣾⣽⣳⡿⣽⡷⣟⡿⣽⣻⢯⣿⣽⢾⣯⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⣿⣟⡾⣽⣻⢿⡽⣯⣟⣿⣳⣿⣻⣞⡷⣯⢿⣽⣿⣿⠟⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣞⣯⣿⣳⣿⣿⣿⣟⣾⢿⡽⣯⢿⣷⣻⣟⣾⡽⣯⡿⣾⣟⣾⢯⣿⢾⣽⣻⢷⣿⣿⣿⣿⣿⣟⣾⣳⡿⣽⡿⣽⡷⣯⢿⣽⡷⣟⣿⡽⣿⣽⣻⢷⣯⡿⣾⣻⣽⣿⣿⡛⡟⠛⠻⢿⣿⣿⢯⣟⡿⣾⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣟⡷⣯⣟⣿⣽⢾⣯⢷⣯⡷⣟⣿⡽⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣞⡿⣞⡿⣿⣿⣯⣟⣿⡽⣟⣾⢷⣯⢿⣽⢷⣿⣳⢿⣾⣻⣽⣯⣷⣿⣿⣿⣿⣿⣿⣟⣾⡽⣷⣟⣯⢿⣳⣿⣻⣟⣾⡽⣟⣾⣟⡷⣯⣟⡿⣾⣽⢷⣟⣿⣿⢹⠟⠁⠀⠀⠀⢻⣿⣿⣽⣻⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣽⣷⣿⢾⣯⣿⢾⣻⡷⣟⣿⣞⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠾⣙⡻⢿⣿⣿⣿⣿⣿⣿⣾⣟⡿⣽⢿⣿⣻⢾⣽⣻⢯⣟⡿⣾⣻⡽⣟⣾⢯⣿⢾⣽⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⣽⣻⢷⣯⣟⡿⣽⣾⣳⣯⢿⣽⣟⡷⣯⢿⣻⣾⣻⢷⣯⡿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⣿⣿⣯⡿⣷⣻⣟⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣮⣙⠻⢿⣿⣿⣿⣿⣿⣯⡿⣞⣯⣿⣳⢿⣻⡽⣟⣷⢿⣽⢿⣽⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⡾⣽⣻⣟⣾⡽⣯⡿⣾⣽⣻⣽⣟⡿⣾⡽⣿⣾⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣻⣽⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣶⣼⠻⣿⣿⣿⣿⣿⣿⣽⣾⣻⣯⣿⣽⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣷⣯⡷⣿⢯⣟⣷⢯⣟⣾⣽⣿⣷⣿⣿⣿⡿⠙⠁⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⢯⡝⢯⣏⢯⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣏⡻⢏⠻⡿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⢳⣏⢾⣹⢳⣎⢯⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡄⠀⠙⢮⡳⣎⠷⣭⢳⣎⠷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣭⢻⣜⡳⣎⡟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⢭⡳⣎⡗⣧⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⡾⣱⠯⣜⢧⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣦⣤⣤⣀⣀⡀⠀⠀⠀⢀⠀⢀⣠⣴⣿⣿⣿⣶⣤⣀⠀⠀⠀⣷⡹⣞⠽⣮⣽⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⡜⣧⢳⣭⣛⠶⣿⣿⣿⣿⣿⣿⡷ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⡴⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣧⢳⢏⡶⣭⢻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣈⠸⣎⢷⣉⢷⣿⣿⣿⣿⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣷⣿⣿⡼⣹⠮⣝⢾⣿⣿⣿⣿⣿⣿⣟ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡟⣿⣿⢛⡉⠀⠀⠈⠙⠻⢿⣿⢫⣿⣟⠟⠋⠁⠀⢀⣠⣴⣮⣹⣯⣿⣿⡇⣻⠼⣙⢮⣿⣿⣿⣿⣿⣿⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⢻⢸⣿⣳⣿⣿⣿⡿⣻⡖⠠⣤⡀⣀⢰⣿⣿⡏⠆⡤⢠⡖⡈⣹⣷⣝⣻⣿⣿⣞⠇⠝⣞⡹⠞⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣷⣨⡏⣵⣿⣿⣿⣯⣵⣿⣭⣬⣿⣻⣯⣾⣿⣿⡷⣷⣴⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⡤⣏⢷⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣻⡞⣿⢁⠞⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠘⠈⡇⡽⣺⣿⣿⣿⣿⣿⣿⠷ ⣿⣿⣿⣿⣿⣿⣽⡎⠠⠘⢸⣟⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⠟⠿⡿⠛⣿⡿⣿⣿⣿⣿⣿⣿⢏⣾⡿⠘⢠⢇⡟⢸⣿⣿⣿⣿⣿⣿⡹ ⣿⣿⣿⣿⣷⢸⡿⣇⡁⡀⠚⣿⣿⣝⣿⣿⣿⣿⣿⣵⣿⣿⡂⠈⢕⡂⡁⣸⣿⣮⢿⣿⣿⣿⢳⣿⣿⡧⢤⡟⢼⡸⣿⣿⣿⣿⣿⣿⣷⡝ ⣿⣿⣿⣿⣿⣾⣷⠸⣷⢹⣦⢿⣿⣿⢿⣿⣿⣿⣻⠿⠋⠁⠀⠈⠀⠀⠀⠀⠈⠉⠓⣹⣿⣿⣾⣿⣿⡇⠿⣨⢇⡳⣿⣿⣿⣿⣿⣿⣿⡹ ⣿⣿⣿⣿⣿⣿⣾⡀⣿⣷⡍⣾⣿⣿⡞⣿⣿⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⣿⣿⣿⡇⢄⡳⢎⡅⣿⣿⣿⣿⣿⣿⣯⢳ ⣿⣿⣿⣿⡷⣿⡿⣱⣿⡿⡼⢸⣿⣿⣧⢻⣿⣿⠁⣠⣀⣄⣠⣤⣦⣦⣤⣤⣶⣶⣦⣈⣿⣟⣿⣿⣿⢉⠆⢸⡹⣼⣿⣿⣿⣿⣿⣿⡜⣯ ⣿⣿⣿⣿⣿⣿⡇⣽⣿⡟⡵⠎⣿⣿⣿⣎⢿⣿⣾⣿⣿⣿⣿⣿⣛⣛⣋⣽⣿⣿⣿⣿⡿⣽⣿⣿⡿⣈⣆⠱⣣⢿⣿⣿⣿⣏⣿⣿⡝⣾ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⡽⣭⢻⢈⡻⣿⣿⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⣡⢣⣿⣴⢩⢻⣿⣿⣿⣿⣿⣿⡝⣾ ⣿⣿⣿⣿⣿⣿⡃⣿⣿⡳⢮⢹⡇⡚⢬⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠲⣁⣾⣿⡏⣣⣿⣿⣿⣿⣿⣿⡇⣝⣾ ⣿⣿⣿⣿⣿⣿⣷⣿⣿⣓⢯⢸⣇⡙⢦⡙⡀⡛⢿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⡿⢩⣐⠣⡝⣼⣿⣿⠿⢡⣿⣿⣿⣿⢸⣿⣧⢏⣾ ⣿⣿⣿⣿⣿⣿⢹⣿⡷⣭⠞⣾⢻⣰⣶⣝⠰⡈⢥⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⠴⠃⠊⠑⠈⠋⢁⠠⢀⠠⣿⣿⣿⣿⣿⣿⣟⠾⣿ ⣿⣿⣿⣿⣿⣿⣼⣿⣟⠶⡋⣽⣾⡟⠛⠛⢃⠑⠀⠙⠂⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠁⢂⠐⠂⠄⣿⣿⣿⡟⣿⣿⢸⣫⣿ ⣿⣿⣿⣿⣿⡟⣿⣿⣯⡝⢧⣿⣿⡗⠠⠈⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡀⠀⠈⠄⡨⢀⠊⡐⠀⠂⠄⡉⠙⠻⢿⠧⣳⣿ ⣿⣿⣿⣿⣿⣇⣿⣿⡗⣾⡙⣿⡿⠟⠀⠡⢈⠄⠂⠄⠀⠀⠈⠀⠀⠁⠀⡀⠀⠀⠀⡀⠀⢀⠁⠒⡀⢂⠐⠠⠁⠌⡐⠠⢁⠢⢀⠂⠄⡉ ⣿⣿⣿⣿⣿⣏⣿⣿⣹⠶⠉⠁⡀⠰⠀⠁⠆⡈⠰⠈⡀⠀⠀⠆⠁⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈⡰⠰⠈⡀⠱⠈⠰⠀⠁⠆⠰⢀⠈⠰⢀ ⣿⣿⣿⣿⣿⢸⠿⠋⢁⠠⠐⠠⠐⡁⠂⢁⠂⠄⡁⠒⠠⢁⠀⠀⠀⠄⠈⠀⠀⠂⡀⠄⡈⠄⠂⠄⡁⢂⠄⡁⠂⡐⠀⠀⠌⡁⠂⠌⡐⠠ ⣿⣿⣿⡿⠛⠀⠄⡈⠄⢂⠡⠘⠠⠐⠀⠠⢈⠐⠠⢁⠒⡀⢂⠐⠠⢀⡐⠈⠄⡡⠐⡀⠐⡈⠌⡐⠐⡀⠂⠔⠠⠀⠀⠄⠀⠀⠈⠀⠀⠁ ⡿⢋⠡⢀⠂⣁⠢⠐⡈⠄⠂⠁⠂⠀⡀⠀⠂⠌⡁⢂⠐⠠⠂⠄⡁⠂⠄⡁⠒⠠⠁⠄⡡⠐⣀⠂⢡⠀⠃⡀⢂⠀⠀⠠⠀⠁⢀⠈⠀⠀ ⠀⠄⠂⡄⠂⠄⠂⠁⠀⠀⠀⠂⠀⠁⠀⠀⢈⠐⡀⠆⡈⠡⢈⠐⠠⢁⠒⡈⠄⠡⠈⢔⣀⣡⣤⣬⣤⣬⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣄⣁ ⣬⣤⣷⣤⣵⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡁⢀⠂⡐⠄⢂⠁⡂⠌⡁⢂⣤⣴⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡐⠈⠄⢂⣰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠡⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠂⠤⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠄⠨⠀⠿⠛⠛⡛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⠖⠳⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠒⠀⠂⡾⠉⠀⠀⠀⠀⠉⢳⡄⣄⡀⠀⠀ ⠀⠀⠀⢸⡥⠀⣀⡼⢁⠀⢰⡄⠀⡄⠀⠀⣧⠀⠙⡆⠀ ⠀⢀⣠⠼⠗⠚⠉⠠⠋⠀⠀⢷⣠⣧⠀⠀⠈⠳⢤⣇⠀ ⠀⣾⣟⠒⠦⣄⠀⠀⠀⣠⡴⠋⠁⢈⠛⢦⣄⣠⣴⣾⣷ ⢀⡟⠙⢶⣤⠬⠷⣼⡏⠉⠉⢩⡍⠹⠦⢤⣿⣤⣨⣿⠈ ⡾⣡⠆⠁⠀⠀⠀⢠⡀⠀⠀⠀⢱⡀⠀⠂⠙⠎⠻⡅⠀ ⢿⠁⠒⣤⠤⣤⣀⠀⢧⠀⠀⠀⣸⠃⠀⠀⠀⡶⣤⣽⠀ ⠈⠳⣴⡇⠀⠀⠈⠛⢦⣄⣠⠾⢿⣄⣀⣠⠾⣡⠞⠁⠀ ⠀⠀⠈⠉⠉⠉⠁⢧⢠⠟⣽⠀⢿⠀⢧⢰⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢫⠏⢸⠁⠀⠈⢳⠘⢧⣙⢦⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠛⠋⠒⠒⠒⠒⠒⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠒⠒⠒⠒⠛⠐⠀⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⠉⡀⣄⠣⠈⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⡜⢀⠁⠉⠋⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣⠀⠀⢆⠘⠀⠀⣄⠳⠀⠀⠀⠀⠀⠀⠋⢠⠀⠀⡜⠀⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠞⢀⠀⠀⡎⢀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⢺⠀⠀⢣⠈⠀⠀⡇⢸⠀⠀⠇⢸⠁⠋⡜⢀⠀⠀⡅⠙⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⡤⢀⠋⢿⣻⣟⢿⣿⠛⠛⡼⠀⠀⠀⠉⢯⣛⢛⣍⠯⠓⠈⡆⣶⣰⠀⠀⠀⠀⠀⡀⣒⣒⠿⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠋⣿⣾⣶⣴⣤⣦⣶⣷⣿⣿⠻⠟⣿⣿⣾⣶⣶⣶⣷⢿⡻⢬⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣷⠿⠙⠀⠀⠀ ⠀⠀⠀⠀⠋⡾⢹⠀⠁⡟⣼⢀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣴⣠⠀⠀⠀⠀⠀⠁⡈⣤⣿⢿⣻⠻⠙⠀⠀⠀⠀⠀⡟⣠⠀⠀⣧⣀⢳⠀⠀ ⠀⠀⠀⡇⣼⠃⣿⠿⣿⡾⠐⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢠⠀⠀⠀⠀⠀⠀⠀⡄⢿⠘⡀⣤⣦⣶⣶⣶⠿⠻⠛⡿⣛⠉⠉⠈⠀⠸⡄⠻⠀ ⠀⠀⠀⡆⢿⣿⣾⣴⣼⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣧⠈⠀⠋⣿⢸ ⠀⠀⠀⠀⣆⣸⠀⠀⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣼⣠⣯⢸ ⠀⠀⠀⠀⠀⣆⠙⠀⠀⣆⢸⠈⠀⠀⠀⠀⠀⠀⠀⡤⢽⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡶⢠⠀⠁⡼⠀ ⠀⠀⠀⠀⠋⡿⣿⢿⠿⠙⣏⢻⠉⡉⠈⠀⠀⠀⠀⠁⡏⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠰⠀⠀⠀⠀⠀⠀⠉⠋⠖⣶⣀⠀⠀⠁⡼⠀⠀ ⠀⠀⠀⠏⣴⣎⢠⠀⣀⣦⣿⣿⣈⢤⠶⠶⡖⠿⠾⣶⣴⣷⣶⠻⠈⠀⠂⠀⠀⠁⠿⣽⣄⠤⠤⠲⠶⠼⡤⣤⣤⣶⢽⠉⠀⠀⠀⡟⠀⠀⠀ ⠇⢸⠀⡇⡞⢁⠙⠀⠀⠀⡘⣿⢸⠀⠀⠀⠀⡏⠻⠻⠟⡿⠹⡋⣿⣿⢿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠀⠀⠈⡀⣦⠹⠀⠃⣰⠀⠀⠀ ⡄⣿⠻⡏⢫⣿⣿⢹⠟⣼⣤⣤⢿⠙⠚⠵⣉⣀⠲⢀⢋⡿⠱⠋⡴⣉⢟⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡻⣛⣍⢾⠉⠀⡉⢿⣻⡿⢠⠀⠀ ⠀⣆⣿⣻⣯⣀⢀⠀⠀⠀⠉⠀⡀⣦⣷⠻⠛⣈⢄⡡⣜⣀⢁⠋⡿⣿⣿⣾⣴⢀⠀⠀⠀⠀⡉⣾⣴⣠⣀⣇⣿⣿⡿⣿⣿⣿⣿⣴⠀⠀⠀ ⠀⠀⡄⣦⠛⠛⠻⠈⠀⠀⡀⢷⠘⠀⡀⣷⣴⣷⠿⡟⠟⠿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠋⣶⣠⢁⢛⠖⡴⣤⣤⣈⣁⣋⣟⣾⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡘⣄⠦⠷⠹⠈⠀⢧⠈⠀⡀⠀⡀⣷⣿⣠⠀⣇⣿⣿⣸⢀⠀⠀⠀⠁⡾⣠⢀⠀⣀⠁⢉⠋⠾⠶⣾⣤⣠⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢣⠈⠀⠀⣄⢿⠹⠀⢳⠀⠀⠀⠀⡅⣿⠀⠀⠀⣷⣿⠀⠀⠀⠀⠃⣾⠀⠀⠉⠿⠾⡮⣒⠤⠤⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⢀⠀⠀⡄⣦⣷⢾⡜⠀⠀⠀⠀⠀⣧⠀⠀⠀⡄⣿⠘⠀⠀⠀⡇⢀⠀⠛⣴⢍⣠⠀⠀⠁⠊⣰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢣⠈⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⡄⢷⠈⠀⠀⡄⠀⡿⣴⣀⢀⠀⠀⡀⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠖⣽⢻⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⣤⢠⠀⠃⣟⢠⠀⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣝⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣼⠲⠒⠁⠉⠉⠈⠒⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠶⣿⠨⠀⠀⠀⠀⠀⠁⠉⠏⠶⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠹⠉⠹⠟⣾⣸⠋⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣹⢉⣿⠛⣯⣡⣟⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⣦⣾⣷⡽⣶⣥⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⢿⣿⣿⣿⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣾⣶⣶⣤⣄⣄⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⢀⣀⠀⠀⠀⠀ ⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣶⡄⠀ ⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣯⣕⣶⡇⠀ ⢰⣿⡟⠙⠿⠿⠿⣿⣹⣿⠟⠛⠛⠋⠁⠈⠻⣿⣿⣧⠹⣿⣿⠁⠀ ⠘⣟⣤⠠⠀⠤⠀⡘⣿⣿⡷⠄⡀⢐⡒⠻⠻⣿⣿⣿⡇⠿⣫⢤⠀ ⠃⣿⣿⣜⣋⣀⠜⡪⣸⣿⣧⣼⣇⣩⣠⣬⣁⣾⣿⣿⣿⣰⡇⣠⡀ ⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣨⠀ ⣶⡘⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⣿⣵⠏⠀ ⠘⣷⡸⣿⣿⣿⣿⣇⠻⠿⠛⢹⣿⣿⣿⣿⣿⣿⢃⣾⣿⠿⠏⠀⠀ ⠀⠸⡇⣿⣿⡿⠛⠀⠁⠀⠀⠀⠉⠛⢿⣿⣿⣿⢸⣿⣿⢠⡆⠀⠀ ⠀⠀⣇⢿⣿⠁⠀⠀⠀⢀⣀⣀⣀⠀⠀⢿⣿⡟⣸⣿⣿⢸⡇⠀⠀ ⠀⠀⢻⡜⣿⣴⣿⣿⣯⣛⣛⣿⣿⣿⣶⣬⣿⢣⣿⡿⠃⣠⡇⠀⠀ ⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠟⠀⣸⣿⣇⠀⠀ ⠀⠀⠀⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⢂⣼⣿⣿⣿⠀⠀ ⠀⠀⠀⢿⣧⠹⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⣱⢃⣾⣿⣿⣿⣿⣄⡀ ⠀⠀⠀⠸⠿⠷⠔⠭⠭⠭⠭⠭⠥⠶⠶⠾⠇⠾⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣥⣶⡽⣷⣾⣦⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⣡⣯⠛⣿⢉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⣸⣾⠟⠹⠉⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠶⠏⠉⠁⠀⠀⠀⠀⠀⠨⣿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠈⠉⠉⠁⠒⠲⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⣟⠃⠀⢠⣤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⢻⣽⠖⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡀⠀⠀⢀⣀⣴⡿⠀⡄⠀⠀⠈⢷⡄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⠊⠁⠀⠀⣠⢍⣴⠛⠀⢀⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⡜⢾⣷⣦⡄⠀⠀⢀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠤⠤⣒⡮⠾⠿⠉⠀⠀⣾⠃⠀⠀⠀⠀⣿⣷⠀⠀⠀⣿⡅⠀⠀⠀⠀⢳⠀⠹⢿⣄⠀⠀⠈⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠶⠾⠋⢉⠁⣀⠀⢀⣠⡾⠁⠀⠀⠀⢀⣸⣿⣿⣇⠀⣠⣿⣷⡀⠀⡀⠀⠈⢧⠀⠈⠹⠷⠦⣄⡘⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣟⣋⣁⣈⣤⣤⡴⠖⢛⢁⣠⣶⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⡟⠿⣷⣴⣷⡀⠀⠘⢷⡀⠀⠀⠈⠻⠛⠛⣦⡄⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣇⣀⣠⣴⣾⡉⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⢁⣀⣜⡡⢄⣈⠛⠻⣷⣦⡀⠀⠉⠀⠀⠀⢀⣀⣯⣻⣿⣆⠀ ⠀⠀⢠⡿⣻⢿⡉⠀⠉⢾⣍⣛⡻⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⢟⣉⡴⠋⠱⡿⢋⢀⠲⣀⣉⠵⠚⠙⢿⣤⣤⣼⠟⢹⣿⣿⢫⡏⠻⣿⡄ ⠀⠀⠀⣰⠃⠀⠹⣦⡀⠈⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢿⣿⣿⡋⠹⡿⠟⠻⠻⡏⠀⠀⠀⠀⢸⣿⡘⠀⠀⠀⠙⢁⡞⡇⠀⢸⠇ ⠀⠀⠀⡟⠀⠀⠀⠉⢽⣶⣤⣤⡤⠼⠶⠲⠤⠤⣄⣽⠿⠁⠀⠀⠂⠀⠈⠻⣶⣷⣴⣶⠾⠿⡖⠶⠶⢤⣈⣿⣿⣦⣀⠀⢠⣎⣴⠏⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⣀⣶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⠁⠀⠀⠀⠀⠈⡉⠉⢻⣏⠙⠿⢿⣿⡿⠋⠀⠀⠀⠀ ⠀⡼⠁⠀⢠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢽⡤⠀⠀⠀⠀⠀⠀⠀⠈⢸⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⢸⣯⣠⣼⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⠀⠀⣸⣆⠀⠀⠀⠀ ⢸⣿⠋⠀⠈⣧⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣴⣾⣿⢿⡆⠀⠀⠀ ⠀⠻⡄⠸⠀⠈⠉⠉⣛⡿⠛⠻⠿⣶⣶⣶⣦⣤⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⣿⠿⣿⠃⣼⡇⠀⠀⠀ ⠀⠀⢳⣀⣧⠀⠀⣠⡟⠀⠀⠀⠀⠀⠙⠻⣻⢿⣿⣤⡈⠁⠀⠀⠀⠀⠀⣠⣴⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⢹⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⣷⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡻⢿⣷⣶⣶⣶⣾⣿⣿⣟⠻⣿⣿⣷⣶⣦⣤⣴⣶⣾⣿⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣒⣒⡀⠀⠀⠀⠀⠀⣰⣶⡆⠈⠓⠯⣍⢛⣛⢯⢹⠻⡟⠀⡼⠛⠛⣿⢿⣟⣻⢿⠋⢀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⡅⠀⠀⢀⡜⠋⠁⢸⠇⡇⢸⢸⡇⠀⠀⠈⢣⠀⠀⢺⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⡎⠀⠀⢀⠞⠀⠀⡇⠀⢧⠀⠀⠀⠀⣇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡜⠀⠀⢠⠋⠀⠀⡼⠀⠀⠀⠳⣄⠀⠀⠘⢆⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠁⢀⡜⠁⠀⠀⡇⠀⢀⡇⢀⠀⣸⠀⠀⡟⡆⠀⠀⠈⠣⣄⡀⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠐⠛⠒⠒⠒⠒⠇⠀⠃⠈⠟⠉⠙⠏⠳⠀⠙⠒⠒⠒⠒⠒⠋⠛⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠛⢻⡑⣓⡋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣼⣿⡆⡝⢿⣿⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⡤⢿⣠⡿⠤⠞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢟⡤⠴⠋⠀⠀⠀⠈⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀⡀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡜⢦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⠀⠉⠙⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⡠⠔⠂⠀⠀⢤⢖⡾⠃⠀⡆⠀⠀⠀⠹⣆⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡘⣇⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⢀⡠⣖⠵⠊⠀⠀⢠⠇⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⠑⢾⣽⠆⠀⠀⠠⡀⣳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣂⣭⠔⠚⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⡄⠀⠙⠢⣄⠀⠀⢸⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠀⠀⣀⣠⠔⠂⢀⡴⠃⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⣼⣿⣿⣆⠀⡄⠀⠀⠹⡄⠀⠀⠀⠙⠒⠡⢼⡀⠀⠀ ⠀⠀⠀⢀⣼⣿⣭⣴⣶⣶⣾⡟⠉⠁⠀⣀⠴⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⢁⠏⠉⠻⣾⣿⣄⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠈⢢⡀ ⠀⠀⠀⣾⣿⣿⠻⠩⠍⣻⢿⣷⣶⣶⣾⣿⣦⣄⣀⣀⣠⣴⣾⣿⣿⠿⢋⡠⠤⣦⡷⠂⢐⠲⠬⢉⡻⣷⡄⠀⠀⠀⣀⢤⣤⢴⡶⡤⣀⢳ ⠀⠀⠠⢋⠞⠘⢆⠀⠀⢹⠒⠒⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡭⠤⢏⠤⠭⣏⣠⣴⣨⡶⠂⠈⠁⠀⢹⣷⢦⠞⠁⠈⢯⠟⣰⡇⠈⢾ ⠀⠀⠀⡜⠀⠀⠀⠑⢤⡀⠀⠀⠀⢩⠟⠛⠛⠛⠛⢟⡻⠏⠈⠈⠙⠒⠦⣀⠀⣇⠀⠀⢀⣧⣀⣀⠀⠀⢸⣿⣆⠀⠀⠀⠀⡰⠃⣧⠀⠘ ⠀⠀⢀⠃⠀⠀⠀⠀⢀⣨⠝⠒⠚⠉⠉⠉⠉⠙⡲⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡶⠚⠁⠀⠀⠀⠈⠙⠢⣿⢧⣕⣢⣤⣾⣴⡿⠃⠀⠀ ⠀⢀⠎⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠛⢿⠋⠀⠀⠀⠀ ⢠⠏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠳⡀⠀⠀⠀ ⢸⣷⡶⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣼⢳⠀⠀⠀ ⠘⣿⠀⠀⠀⠻⠦⢤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣿⠟⠈⡇⠀⠀ ⠀⠈⣆⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⠻⣿⣿⣿⣷⣄⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠝⠛⣇⠀⡴⠃⠀⠀ ⠀⠀⠙⣦⣿⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⠪⣛⢿⣷⣤⣀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣧⣀⡀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⡸⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣦⣿⣀⡀⠀⠀⠀⠀⠀⠀⢀⢈⡑⠬⣛⠿⣿⣿⣿⣿⠿⠟⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠴⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠀⠀⠀⠀⠸⢾⡇⠀⠀⠉⢢⡠⠤⠙⡀⠀⠀⢠⠋⠀⠉⠻⡭⠽⠓⢸⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡰⠋⠀⠀⢠⠁⠀⠀⠸⡀⠀⠀⠀⠸⡄⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢰⠃⠀⠀⡴⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀⢡⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠜⠁⢠⠇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠣⡀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⡠⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⢢⣄⠀⣈⣣⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠿⠟⢿⣿⣿⣿⠿⠿⠿⠟⠛⡛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠈⠉⠻⢿⣦⣔⡀⠀⠙⢳⠆⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟⠋⠁⠉⠉⠛⠻⠻⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⡿⠿⣿⣿⣿⡿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠉⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠪⠉⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⢠⣦⣀⣀⣀⠀⠆⠀⣠⣤⣤⣴⣾⣷⣄⠀⠀⠘⣆⠀⠀⣾⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠠⠛⣟⣿⣛⣿⢧⠀⠀⢈⣻⢿⡯⢭⣄⣄⠀⠀⠀⢸⣀⠔⡛⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣼⠀⠀⠣⠴⠿⣣⢕⠇⠀⠘⠃⠸⠖⠟⠓⠾⠁⠀⠀⠀⠏⢸⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠗⣿⣿⠛⠛⠛⠛⠛⣻⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠊⣰⠋⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⠈⢇⠀⠀⠀⠀⠸⣄⣀⣤⡆⠀⠀⠀⠀⠀⠀⡼⠁⠀⣀⣰⠏⠀⣿⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⢸⠀⠀⢀⣤⣿⣾⣿⣿⣿⣶⣤⡀⠀⠀⠀⡇⠀⠀⡟⢹⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⡀⠀⣾⣿⣿⣿⡿⠿⠿⠿⣿⣿⡀⠀⢠⠇⠀⠀⡇⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡄⢣⠀⠋⠀⠀⠐⠤⠤⠀⠀⠀⠉⠓⠀⡜⠀⢀⣼⠟⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⣿⠇⠀⠸⡇⠀⡟⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢿⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡽⠃⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡀⠘⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠎⡼⠁⠀⠀⠀⠀⠻⢤⣍⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣤⠞⣇⣀⣈⣫⣒⣒⣒⣒⣒⣚⣉⣉⣁⣸⣁⣀⣀⣀⣀⣀⣀⣀⣈⣙⣟⡒⣄⣀⣠⣿⣟⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠎⠿⠡⡿⡿⠿⠿⠿⠿⠿⠿⠿⠸ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣰⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻ ⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣿⣿⣭⣭⣭⣭⣤⣤⣀⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⢡⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⣿⣿⣿⣿⣿⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢸ ⠀⠀⡆⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⢠ ⠀⠀⠀⣄⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀ ⠀⠀⠀⠀⡀⣦⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⢘⠘ ⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠋⠂⢀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣿⣿⣿⣿⣿⣿⣿⠆⢲⡀⠶⢘

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡿⣿⣿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⠹⠀⠋⠛⠛⠛⠛⠿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠛⠈⠀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠿⣿⣿⣿⣿⣾⣶⢠⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⢀⠀⠀⠀⠀⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣴⣤⢀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣠⢁⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣧⣿⣿⣿⠘⠀⠀⠁⠟⠿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠃⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⣿⣿⠿⡿⣿⣿⣾⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠙⠈⠀⠀⠀⡀⣦⣿⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣿⣿⣿⣤⣤⣀⠀⠀⠁⠟⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠂⡿⣿⣿⣰⠀⠀⠀⠀⠀⠁⠟⡿⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⣄⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠁⡟⣿⣿⣴⣄⣤⣶⣿⣿⣿⢿⠛⠙⠀⠀⠀⠁⣿⣿⣼⠀⠀⠀⠀⠋⡿⣿⣿⣾⣴⠀⣄⣷⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠁⠟⣿⣿⣴⢀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣾⠀⠀⠀⡇⣿⣿⢠⠀⠀⠇⣿⣿⣿⣴⣀⠀⠀⠀⠀⠀⣀⣦⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⢿⠈⠀⠀⡇⣿⣿⠀⠀⠀⡇⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⣿⣿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠙⡟⣿⣿⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣶⣶⢹⠛⠿⣿⣿⣿⣿⣿⣾⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣌⣷⣿⣿⣿⢻⠈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⡿⣿⣿⣿⣾⣴⣤⣀⡀⣦⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⣿⣿⣿⣰⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⣿⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⡼⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⢰⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢸⠀⠀⠀⠀⠀⠀⠁⠛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢸⠀⠀⠀⠉⠛⡿⣿⣿⣿⣿⣿⣶⣴⣤⣦⣷⣿⣿⣿⣿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣆⣿⣿⣿⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⡛⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢹⠋⠟⡿⣿⣿⣿⣿⣶⣤⢀⠀⠀⠀⠀⠀⠀⡀⣤⣷⣿⣿⣿⣿⠻⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⠈⠀⠀⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡋⣿⣿⣿⣿⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⣿⠈⠀⠀⠀⣄⣤⣤⣀⣀⣀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⡿⣿⣿⣿⣿⣿⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣦⣷⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣶⣴⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠿⠿⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⢿⠛⠉⠀⠀⠀⠀⠀⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⣿⣿⣿⣿⣿⠿⠛⠈⠀⡄⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣷⣿⣿⣿⣿⢿⠻⣟⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡿⣿⣿⣿⣿⣴⣤⣀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣶⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣾⣴⣀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣿⣿⣿⣿⣿⢿⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠋⡿⣿⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣿⣇⣿⣿⣿⢸⠀⡀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⠈⡀⣷⣿⣿⢹⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠋⠛⡿⣿⣿⣿⠿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⣿⢠⡿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⢸⠀⡄⣿⣿⣿⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⠻⠉⠉⠋⠛⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣸⡇⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠀⣧⣿⣿⢸⠀⠀⠁⠋⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⢀⡄⣿⣿⣿⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠿⡿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠸⠋⣿⣿⣿⢸⠀⠇⣿⣿⣿⣿⣾⢰⣀⣤⣦⣶⣶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣷⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⢀⠀⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣶⣤⣠⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⢿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⡄⣶⣶⣷⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⠿⣿⣿⣿⣿⣾⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⠻⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣾⣴⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣿⣿⣿⣿⠀⠀⡇⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣿⣿⢿⠀⠀⠀⣿⣿⢻⠟⡿⣿⣿⣿⣿⣾⣀⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⣿⣿⣶⣤⣀⣀⢀⠀⠀⡇⣿⣿⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⠀⠀⠇⣿⣿⣿⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⠀⠀⠀⡇⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠟⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⡏⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⠙⠉⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡷⢷⣼⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣠⣽⣿⣿⣿⣿⣿⣾⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣿⣿⣿⣿⣇⠻⣿⣏⢻⣿⣿⣿⡤⠠⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣎⡠⠖⠀⢠⣲⣾⣿⡇⣿⣿⣿⡀⣿⣿⡄⣿⣿⣿⣇⡀⠀⠈⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣡⣴⣾⣿⣿⣿⡿⣱⣿⣿⣿⣷⣿⣿⣧⠹⣿⣯⢻⣯⡀⠈⣾⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣟⣴⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⣷⡙⠿⣿⣿⣧⡀⠀ ⠀⠀⣼⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⢥⡼⠑⡠⣝⡻⣿⣿⣿⡷⣶⣿⡿⣿⡀ ⠀⠀⢹⠋⣳⣄⠉⠁⠙⡿⠿⠿⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠉⠀⠀⣿⡋⠀⠙⣡⡇⠻⠇ ⠀⢀⡟⣼⣿⣿⣿⣓⣻⣯⣭⣿⣾⣿⣿⣿⣤⣈⠻⣿⣿⣿⣿⣿⡷⣿⡿⢶⣾⡿⠃⠀⠀ ⢀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣿⣷⣦⡹⣆⠀⠀⠀ ⢸⡿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠹⣼⣿⣿⣿⠏⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢻⡿⠃⠀⠀ ⠀⠀⠙⠻⣿⣇⠀⠀⠀⠀⠈⣙⠿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⠟⢁⡤⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠒⢻⠀⠀⣹⠞⢻⠀⠀⡞⠀⠙⣏⠉⡧⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡸⠁⣠⠎⠀⠀⠙⣄⠀⠸⡄⠘⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⣰⠃⠀⡇⠀⠀⠀⠀⠈⢣⠀⠘⠦⣈⣓⡄⠀⠀⠀⠀⠀

⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿ ⡄⠀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⢴⣦⣀⠀⣼⣿⣿⣿⣿⣿ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣟⢭⣇⣿⣿⣿⣿⣿⣿ ⣿⡿⣿⠟⠻⠿⠿⡏⣿⡿⠛⠛⠉⢉⢿⣿⣾⣻⣿⢿⣿⣿⣿⣿⣿⣿ ⣿⢣⣯⡾⣠⠀⠀⡝⣿⡟⣠⡨⠍⣩⢻⣿⣿⡷⣳⣒⢿⣿⣿⣿⣿⣿ ⡿⠈⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠑⢾⣿⣿⣿⣿⣿ ⣿⣦⠹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣯⢮⣿⣿⣿⣿⣿⣿ ⣿⣷⣳⣻⣿⣿⣿⠌⠭⠉⠻⣿⣿⣿⣿⣷⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⡟⡏⣿⠏⠀⠀⠀⠀⠀⠀⠉⣿⣿⢻⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⢷⣻⣤⣾⣶⣲⣟⣿⣷⣦⣼⣿⣾⡿⣷⣵⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡏⣇⣻⣿⣿⣏⣿⣿⣿⣿⡿⣵⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣛⣿⣶⡫⢿⣿⣿⣯⣭⣽⡿⢻⣿⣿⣿⣿⣿⣾⣭⣿⣟⡿⢿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠌⣩⣌⠻⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢛⣭⣿⣽⢁⣶⣿⣿⣿⣿⣶⡌⢻⠻⢿⣿⣿ ⣿⣿⣿⡇⢚⣿⠿⢃⡾⣿⡏⢻⣿⢻⣿⣿⠘⣿⣦⢹⣿ ⣿⡿⠟⣃⣨⣥⣶⣟⣴⣿⣿⡈⠟⠘⣿⣿⣷⣌⡛⠸⣿ ⣿⠁⠠⣭⣙⠻⣿⣿⣿⠟⢋⣴⣾⡷⣤⡙⠻⠟⠋⠁⠈ ⡿⢠⣦⡉⠛⣓⣈⠃⢰⣶⣶⡖⢲⣆⣙⡛⠀⢛⠗⠀⣷ ⢁⠞⣹⣾⣿⣿⣿⡟⢿⣿⣿⣿⡎⢿⣿⣽⣦⣱⣄⢺⣿ ⡀⣾⣭⠛⣛⠛⠿⣿⡘⣿⣿⣿⠇⣼⣿⣿⣿⢉⠛⠂⣿ ⣷⣌⠋⢸⣿⣿⣷⣤⡙⠻⠟⣁⡀⠻⠿⠟⣁⠞⣡⣾⣿ ⣿⣿⣷⣶⣶⣶⣾⡘⡟⣠⠂⣿⡀⣿⡘⡏⢷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣯⡔⣰⡇⣾⣿⣷⡌⣧⡘⠦⡙⣿⣿⣿ Omning it rn

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣩⡙⢿⣉⣮⡅⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⡿⢠⡙⢻⣿⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣳⣷⣦⠌⣧⣸⡷⠤⠶⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⢿⣃⡤⠼⠏⠀⠀⠀⠀⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠉⠉⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣝⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣠⠄⠀⠀⢀⣀⣤⣺⠃⠀⡆⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡞⠉⠀⠀⠀⣀⢼⣢⠞⠁⠀⢀⡿⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣀⠳⣜⣷⣢⡄⠀⠀⢠⡀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⠤⠤⣒⣯⠖⠋⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠸⡆⠈⠛⢿⣄⠀⠀⠀⠙⢦⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣷⠶⠞⠋⠉⠀⢀⡀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠓⢦⣄⡠⠋⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⡿⠛⢉⣁⣀⣀⣀⡤⠴⠚⠋⠀⣠⠞⠋⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⢿⠿⢿⣧⣀⣿⡀⠀⠀⠙⣆⠀⠀⠀⠀⠐⠈⠙⠺⢤⡀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢀⣀⣴⡛⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠋⠀⢠⠎⣀⡀⠙⠿⣿⣷⣤⡀⠀⠈⠓⠀⠀⠀⠀⠀⠐⠀⠀⠹⣆⠀ ⠀⠀⠀⣸⡿⣻⢿⠁⠀⠐⢮⡝⠿⠿⢿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣾⣿⣿⣿⠿⠋⡠⠖⢊⢽⡳⠋⡀⣌⠉⠒⣢⡸⠻⢷⣄⠀⠀⢀⡴⠒⣶⢚⣿⢹⡓⢦⣹⡄ ⠀⠀⠀⠋⡼⠁⠈⢧⡀⠀⠀⠋⠉⠙⠮⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⣥⡒⠺⠶⠒⠲⡾⠴⠶⠧⢬⡟⠉⠀⠀⠀⠀⣾⡟⠾⠋⠀⠀⠹⠞⢁⡞⡇⠀⢹⡇ ⠀⠀⠀⢰⠃⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⢠⣋⣉⡉⠉⠉⠙⣯⡽⠓⠀⠀⠈⠉⠙⠲⣤⣀⣿⡀⠀⢀⣨⣧⣤⣤⣀⡀⠀⢻⣿⣦⡀⠀⠀⠀⣠⠞⣰⡇⠀⠈⠁ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⣠⠼⠛⠋⠉⠉⠁⠀⠀⠉⢙⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠞⠉⠀⠀⠀⠀⠀⠉⠑⠾⣿⠧⢽⣓⣶⣴⣷⣾⠟⠁⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠙⢿⡟⠁⠀⠀⠀⠀⠀ ⢀⡞⠑⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⢸⣧⣶⡴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣠⡾⣆⠀⠀⠀⠀ ⠘⣿⡏⠀⠀⠈⣷⣤⣄⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣶⣿⣿⠇⢸⠀⠀⠀⠀ ⠀⠉⣇⠀⠀⠀⠀⠀⠀⢈⡽⠋⠛⠛⠻⠿⣿⣿⣿⣶⣄⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣻⠟⣿⠁⢀⣼⠃⠀⠀⠀ ⠀⠀⠘⣧⣠⡆⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢝⡻⢿⣿⣤⡀⠉⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠈⣧⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣦⡀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡻⢿⣷⣶⣶⣶⣶⣿⣿⣿⠟⠛⢿⣿⣿⣷⣶⣦⣤⣴⣶⣾⣿⠟⠉⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠿⣐⣒⠢⠀⠀⠀⠀⠀⠀⠀⣆⣶⠀⠉⠓⠮⣍⠛⠛⡻⣏⠉⠀⠀⠀⣠⠏⠛⠻⡿⠿⢿⣟⡿⡟⠁⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠒⠚⠉⢻⠀⠀⠀⠀⡠⠟⠉⠁⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⢯⠁⠀⠰⡧⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡜⠁⠀⠀⢠⠎⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⣇⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡸⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠘⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠚⠁⠀⡰⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⢦⡀⠀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⠄⠀⠤⠠⠾⠥⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠭⠷⠦⠤⠤⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢿⣿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣱⣾⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣿⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⠁⠠⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠒⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡗⢉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠠⣰⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣶⣾⡀⠀⠀⠀ ⠀⠀⢀⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢏⣀⣱⣈⡿⣿⣿⣿⣿⡿⢿⡆⠀⠀ ⠀⠀⠈⣿⣷⣄⡉⠙⡿⠿⠿⣿⣿⣶⣿⣷⣿⣏⣁⠀⣿⡉⠈⣱⡎⠃⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠋⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⡿⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⡿⠁⠀⠀⠀ ⠀⠀⠀⠹⣿⣇⠰⠀⢆⠈⡹⣿⣿⣿⠿⠹⣿⣿⣿⣿⠏⣀⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣆⢂⣽⢿⠀⠰⣟⡾⡍⢰⠊⠀⠀⠀⠀⠀⡀⠂ ⡄⠂⠈⠄⠐⠀⠂⠀⡌⠤⣣⣾⣻⠁⠀⠀⠙⢽⣻⣄⠣⣄⠠⠈⠐⠠⠀⠄

⣭⡉⠁⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⡄⠀⠀⠀⠘⢿⣿⡟⣿⢻⣿⡟⣾⣿⣿⡿⠛⠉⠀⠈⠻⣿⣿ ⡟⣴⡾⠷⠄⠀⠀⠈⣿⣸⣿⢸⣿⣹⣣⠟⠁⠀⠀⠀⣀⣤⣄⣈⠻ ⣿⠇⢠⢠⡲⠀⠀⠀⠀⣿⣿⣞⣧⠇⠀⠀⠀⢀⠴⠮⠭⣿⣿⣿⣿ ⣯⣤⠀⡎⠑⢰⠃⢰⠀⢻⣿⣿⡟⠀⠀⠀⡜⠁⢠⢠⡄⠀⢹⣿⣿ ⢋⡳⡠⢃⢠⣵⠑⣸⡬⠘⠯⢭⡑⢆⠎⡕⢠⠸⠠⠷⢉⡢⠀⣻⣿ ⣧⣳⣝⠑⠙⢆⣥⣞⣡⣾⣿⣿⣮⣆⠐⣿⡐⢦⡡⠴⠧⡬⡰⣽⣿ ⣿⣧⣝⣛⣯⣾⣿⡇⣿⣿⣿⣿⣿⣿⣮⣷⣕⢮⣅⣚⣭⣾⢝⣾⣿ ⣿⣿⣿⣿⢟⣶⡻⢷⣿⣿⣿⣿⡿⢫⣽⣻⢿⣿⣾⣭⣯⣧⣿⣿⣿ ⣿⣿⢟⢵⣿⡿⣵⢸⣿⣿⣿⣿⣷⣇⣿⣿⣧⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⠱⠊⠀⠀⠉⠉⠻⣿⣿⡿⠋⡅⠜⠛⠛⠛⠓⠽⣿⣿⣿⣿⣿⣿ ⣏⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣗ ⣏⠀⢀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣿⣿⣿⣿ ⠆⡔⣵⠀⠀⠙⢿⣿⣶⣶⣦⣦⣤⣤⠐⠀⢀⠀⠀⠀⣿⣿⡿⣾⣿ ⠸⡀⣿⠀⠀⠀⠀⠘⡘⠛⠛⠛⠃⠀⠀⠀⢸⣄⠀⠀⢿⣿⢧⣿⣿ ⠷⡁⣿⢰⣿⡆⠌⡐⠠⢁⠌⢠⠁⢂⠀⣀⠸⣿⢰⡀⢸⡟⣾⣿⠏ ⣴⠳⢹⣼⣿⠄⠒⠠⢁⠂⠌⠠⠌⡀⢚⣿⣧⣿⢸⣿⣼⣹⣿⠏⠀ ⢸⣏⠜⡧⢿⣷⣮⣴⣀⣊⣄⢃⣰⣈⣼⣿⣿⡼⣾⣿⣳⣿⠋⢀⠂ ⠀⢿⣆⣿⣷⣿⣭⣽⣿⣛⣛⣛⣛⣻⣛⣛⣯⣶⡿⣵⡿⠃⢀⠂⠄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣿⢏⣯⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣨⣷⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠄⠒⡀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠐⠂⠀⠀⠀ ⠀⠀⠀⠀⢸⢊⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⢸⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣶⣾⡀⠀ ⠀⠰⣿⠛⢻⣿⣿⣿⣿⣿⣿⡿⢟⡥⡴⣴⣬⡝⠿⣿⡿⢻⡿⡻⡆ ⠀⢰⣿⣷⣄⣂⣹⣛⣛⣻⣿⣿⡿⣿⣿⣿⣧⣄⣀⣷⣀⢄⣴⠇⠁ ⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀ ⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠈⢿⣿⣿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠟⠁⠀ ⠀⠀⠙⠻⠤⣴⣀⣄⣤⠙⠻⣟⣟⠉⢈⢿⣻⠟⠟⡉⠔⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣰⣟⠌⠀⠘⣳⡽⡆⢘⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠐⠨⣼⢳⡎⠀⠀⠀⠈⢳⡻⣦⣀⣢⠀⠀⠀⠀

🟥🟥🟥🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟫🟥🟥🟥🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧 🟫🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟫🟥🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧 ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟫🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧🟧 ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥 ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🟫🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥 ⬛⬛⬛🌇🌇⬛⬛⬛⬛⬛🌇⬜⬜🌇🌇⬛⬛⬛⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫 ⬛⬛🌇⬜⬜⬜💟🌇⬜⬜⬜⬜⬜⬜⬜🌇🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌇⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🌇🌇⬜⬜⬜⬜⬜🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌇⬜🌇🌇🌇🌇⬜⬜🌇⬛⬛⬛🌇⬜⬜⬜⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌇⬜🌇🌇⬛🌇⬜⬜⬜🟫🌇🌇⬜⬜⬜⬜⬜⬜💟⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬜🌇⬜⬜⬜⬜⬜⬜🌇⬜⬜⬜⬜⬜⬜🟧⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛💟⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜💟🟧⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜💟🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛💟⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜💟⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌇⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🌇⬜⬜⬜⬜⬜💟💟💟⬜⬜⬜⬜⬜⬜⬜⬜💟🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛💟⬜⬜⬜⬜🟫🟫🌇🌇⬜⬜⬜⬜⬜⬜💟🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛🌇⬜⬜🌇⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜💟🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛🌇⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜💟🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛🌇⬜⬜🌇🌇⬜⬜⬜⬜🌇🌇⬜⬜⬜⬜🟧🟥🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛🟫 ⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜💟🟧💟🟫⬛⬛⬛⬛⬛⬛⬛⬛🟫🟫 ⬛⬛⬛💟⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜💟🟧⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛🟫🟫 ⬛⬛⬛🟫⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥💟⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛🟫🟫 ⬛⬛⬛💟🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧🟥⬜⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛🌇💟💟⬜⬜⬜⬜⬜⬜⬜💟🟥💟⬜⬜⬜🟫⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛⬛🟫⬜🟧💟💟💟💟💟💟💟🟥🟧⬜⬜⬜⬜⬜🌇⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬛🌇💟⬜⬜🟥🟥🟥🟥🟥🟥🟥🟧⬜⬜⬜⬜⬜⬜⬜⬜💟🌇⬛⬛⬛⬛⬛⬛

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠻⠛⠟⠻⠛⠟⠻⠛⠟⠻⠛⠿⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⢶⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠈⠁⠉⠙⣿⣦⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠈⠁⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⢷⣹⢞⣻⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣅⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡹⢧⣛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣏⣯⣿⣿⣿⣿⣿⢯⣳⢏⡾⣝⡾⣹⢶⣫⡽⣫⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣄⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⣟⡽⣣⣟⢮⡽⢶⣛⣯⢽⣚⢿⣿⣿⣿⣿⣾⣝⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣏⣷⢻⣾⣿⣿⣿⠿⠯⠷⢯⣾⣝⣾⣱⣯⣳⣳⡽⣳⢮⢷⡝⣮⢟⣽⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡹⢧⣛⡾⣝⡾⣱⣟⣼⣏⣾⣏⣷⣺⠽⠾⠯⠟⢿⣿⣿⣿⣿⢮⣝⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⣳⡽⣺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠛⠓⠿⠽⠯⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠽⢧⠟⠚⠛⠓⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣮⢳⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⢮⣳⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢟⣿⢻⡟⣿⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣳⢮⣻⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⡮⣟⣼⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣦⢤⡤⣤⣤⢤⣬⢷⣫⣽⢻⡤⣤⢤⡤⣤⡤⣤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⣿⣿⣿⣯⣷⢫⣟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡝⣾⣹⣿⣿⣿⣿⣿⣹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡺⣟⡽⣺⡵⣏⢿⡼⣳⣭⢻⡼⣳⣝⣮⢏⣷⢫⣯⠽⣖⣻⡵⣏⡷⣹⢯⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣮⢟⣿⣿⣿⣿⣯⣷⢫⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡽⢾⣿⣿⣿⣿⣿⢲⠋⠀⠀⢀⣼⣳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣱⠿⣜⣳⢷⣹⡞⣧⢟⡵⣞⢯⣳⡏⠉⠉⣟⡮⣟⡼⢯⡽⣖⣻⡼⣝⡧⢿⡼⣹⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡗⣦⡀⠀⠀⢻⢾⣹⢿⣿⣿⣿⣿⣳⡽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣹⣿⣿⣿⣿⡿⣎⡿⣆⡀⣰⢿⣇⣷⢾⣉⡷⣀⠀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⣸⣹⢏⡷⢿⣉⡷⣏⣶⢿⡹⣾⢹⡾⣇⣏⡇⠀⠀⣏⣷⢏⣹⢿⣸⡹⣶⢿⣸⡹⣇⡿⣉⣷⢏⡆⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠀⣰⣾⢿⣸⡹⢷⣷⣀⣀⣸⣏⢷⣏⣿⣿⣿⣿⣷⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣻⣿⣿⣿⣿⣏⠷⣽⢳⡻⣭⢷⡺⣵⣫⢷⣹⢏⡷⣦⣀⣴⣿⣿⣿⠆⠀⠀⠀⠀⣟⡧⣿⡹⣏⡷⣽⢺⡵⣫⢷⡹⣏⡾⣝⣮⡇⠀⠀⣟⣮⢯⡳⣏⡷⣝⣧⢯⣳⡝⣧⡟⡽⣎⡿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡶⢿⣹⢮⡗⣯⢽⡻⣜⣳⢯⡳⢯⣞⡽⣞⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣻⣿⣿⣿⣷⣾⣿⣷⣫⢗⣻⢮⣽⢣⣟⢮⡗⣯⣳⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣟⣳⢧⡟⣵⡻⣼⢻⣼⣛⢮⡟⣵⣛⣞⡶⡇⠀⠀⡿⣼⢳⣏⡷⣽⢺⣼⢳⢧⣻⢵⣫⢟⣵⣛⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣯⡳⣏⡾⣝⡾⣹⣝⡮⢷⡻⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⡽⣾⣹⡾⣜⣻⡼⣫⣞⣷⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⡽⣺⡝⣧⡟⣵⡻⣖⢯⣻⢼⡳⣝⣮⡽⡇⠀⠀⣟⣧⠿⣜⣳⣭⢷⣫⢟⡮⣗⡯⢾⣹⢮⣽⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣵⢻⡼⣳⢏⡾⣽⣳⣏⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡱⣏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡹⣧⣿⣿⣿⣿⣿⡥⣤⢤⡤⣄⠀⠀⠀⠀⠀⢿⣳⡽⣣⡟⣧⢟⡾⣹⢮⣗⢻⡝⡶⣽⣣⢤⡤⡿⣜⡯⣏⡷⢮⡗⣯⠾⣝⡾⣹⢏⡷⣫⠎⠀⠀⠀⠀⢀⣠⣤⢤⡤⣤⣹⣿⣿⣿⣿⣿⡼⣳⢯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢻⡵⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⣫⠷⣝⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⡿⢯⣝⡧⣟⡽⣹⣇⠀⠀⠀⠀⠀⠙⠳⢯⡽⣞⣽⣺⣭⢷⣚⣯⠾⣝⣧⢯⣏⢷⣏⣷⣹⢧⣻⡽⣚⡷⣻⡝⡾⣭⠿⠚⠁⠀⠀⠀⠀⢀⣾⢻⡼⣏⡾⣳⣝⣻⢿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⡳⢯⡽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢳⣝⡯⣽⢺⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣝⡷⣺⣝⣮⢽⡳⣞⡧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠈⠉⠉⠉⠉⠉⠉⣱⣻⢮⡏⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⣭⢷⡻⣼⢳⣝⡮⢷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢺⡵⣻⢭⣛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣏⠿⣜⣳⡽⣳⢻⣿⣿⣿⣿⢯⢿⡿⣿⣿⢿⡿⢯⣝⢯⡞⣵⣏⡾⣼⢳⣏⢷⣹⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢯⡾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡹⢧⣯⢳⣏⠿⣼⡹⣏⡾⣵⢫⣟⡿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣯⡳⣽⢣⡿⣹⣎⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣹⢞⣯⢻⣜⣳⡽⣻⣿⣿⣿⣿⣫⢾⣹⢳⡮⣟⣼⣛⣮⢟⣼⡳⣞⡵⢯⣳⢞⡯⣞⡽⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢾⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣮⡽⣻⣜⢯⡞⣯⣳⣽⣣⠿⣜⡿⣼⣹⢳⡞⣼⡳⡽⣾⣿⣿⣿⣷⣏⢷⣫⢷⡳⣝⡮⣟⣿⣿⣿⣿⣦⡀⠀ ⣦⡀⢀⣾⣿⣿⣿⣿⢯⣳⢏⡿⣜⡯⢾⣱⣻⣽⣿⣿⣿⠓⠙⠊⠙⠃⠛⠘⣶⡻⣼⢫⣶⢻⡵⣻⡭⣗⣯⢳⣏⢷⣳⢻⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⣏⡷⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣞⣳⡽⣣⠿⣵⢞⡯⣞⣳⡽⣞⣧⢿⣹⢞⡵⠋⠓⠙⠃⠛⠑⠛⣿⣿⣿⣿⢾⣹⢮⡗⣯⣳⠽⣞⡽⣿⣿⣿⣿⣷⡀ ⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣾⣽⣾⣽⣯⣷⣷⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣷⣿⣷⣧⣬⣽⣷⣷⣿⣾⣾⣿⣾⣿⣾⣷⣿⣾⣯⣿⣽⣯⣷⣯⣿⣾⣯⣿⣽⣯⣿⣽⣷⣿⣾⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣷⣾⣷⣿⣽⣿⣾⣿⣾⣽⣶⣿⣭⣤⣽⣷⣯⣷⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣾⣷⣿⣷⣯⣿⣽⣾⣽⣿⣿⣿⣿⣷

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⠀⠀⠀⢦⣙⢧⠘⢳⠈⠀⠁⢸⠏⢫⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡈⢰⢧⠀⢿⠀⣽⠟⢠⢧⠁⠉⠉⠉⠈⠀⠀ ⠀⠁⠞⣡⠾⣠⣀⣄⢿⠾⣠⣄⢦⠛⠈⠀⠀⡇⣴⠳⠈ ⠀⣽⣤⡶⠀⠀⠀⠃⣸⠀⠀⠀⢧⠀⣀⣤⠤⣤⠒⠁⢿ ⠀⡅⠻⠎⠙⠂⠀⡀⢱⠀⠀⠀⡀⢠⠀⠀⠀⠁⠆⣡⡾ ⠈⣿⣨⣤⣿⢤⠦⠹⡍⢩⠉⠉⡏⣼⠷⠬⣤⢶⠙⡟⢀ ⣷⣾⣴⣠⣄⢦⠛⢈⠁⠋⡴⣠⠀⠀⠀⣄⠦⠒⣟⣾⠀ ⠀⣇⢤⠳⠈⠀⠀⣧⣠⢷⠀⠀⠋⠠⠉⠚⠗⠼⣠⢀⠀ ⠀⡆⠙⠀⣧⠀⠀⡄⠀⡄⢰⠀⢁⡼⣀⠀⡥⢸⠀⠀⠀ ⠀⠀⡀⣄⡄⢳⠉⠀⠀⠀⠀⠉⡾⠂⠀⠒⡤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣄⠳⠖⣳⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠟⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠋⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠇⠀⠀⠀⠀⠀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠤⢄⡀⣀⡴⠖⠚⢙⣿⢿⡟⢿⡄⠈⠙⠻⡿⠟⢩⡌⣿⡷⠦⣄⣠⠴⠒⠋⠁⠐⠺⢦⡩⠄⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠉⠈⣹⠆⣿⣦⠙⢧⡀⠀⠀⣸⣿⣄⣇⡈⠙⠦⣄⢀⠀⣀⡾⣣⣼⣧⣤⣬⣿⣤⡀⠀⠀⠀⠀⣦⡱⣴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠂⢠⣞⣡⣯⣴⣶⣶⣧⣀⣤⣤⣏⢀⣼⣿⣿⣿⣿⣿⡿⠟⢱⣾⣷⣤⣈⣷⣿⣾⣿⢿⡟⠛⢛⣿⣿⣿⣷⣄⡀⠀⠳⡌⠈⠉⣍⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢚⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣧⡀⠉⣻⣿⢿⡟⢿⣛⢣⣾⠧⣤⣾⣿⣿⣿⣿⣿⣷⣶⣿⣯⡀⠀⢹⡇⠀⠀⠈⢧⡀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡜⢡⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⢐⣿⣾⣥⣼⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣛⠻⣿⣷⣾⣯⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢵⠼⣿⣾⡻⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣦⣧⠼⣿⣿⣿⣿⣿⡌⡟⢀⣹⡦⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⣸⠷⠚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠙⠻⠿⣿⣿⣿⣄⣸⣿⢿⣿⠟⣵⠟⠉⠀⠀⠀⠈⢦⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⡰⠃⠀⣾⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣽⣶⣦⣤⠤⠤⠤⣌⣙⣿⣿⣿⣿⣆⣷⡤⠟⠲⠶⣄⠀⢀⣴⣿⣿⡿⣦⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⡆⠀ ⠀⢰⠃⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣇⠀⠰⢿⣿⣿⣿⣷⣦⢴⡄⠉⢻⣿⣿⣿⠿⡁⠀⠀⠀⠀⢿⣴⣿⣿⣿⣿⣧⢻⠙⠮⣿⣿⣄⣈⣉⣿⣿⣿⣿⣿⣿⡆⢸⡇⠀ ⠀⡾⠀⠀⢀⣴⣿⣿⠿⠟⢋⣴⣿⣿⣿⡟⠁⠀⠙⣆⠀⢸⣌⠉⠉⣹⣏⡀⠉⠀⢿⠁⢸⣶⡾⠃⠀⠀⣠⢀⣿⣿⣿⣿⣿⣿⣿⡜⣇⠀⠀⠈⠉⠓⠦⠤⠬⠿⠿⠿⠿⠶⠞⠀⠀ ⠀⣇⠀⢠⣾⣿⣿⡟⢷⣄⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢧⡘⣿⣧⡀⠉⠉⠁⠀⠀⣿⠐⣻⠏⠁⠀⠀⢰⣿⣿⣿⡿⠟⣹⣿⣿⣿⣷⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⢾⣿⠿⠿⠥⠞⣿⣿⣿⣿⣿⣿⣿⣧⠀⠖⠒⠀⠙⠻⠿⣿⣄⡀⠀⠀⢰⡇⠀⣿⠀⠀⠀⣠⣿⣿⠟⠫⢀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣶⡶⠀⠈⣩⠛⠒⢲⠟⢻⠧⠶⠒⢋⡟⢻⠃⠀⣠⣿⣿⣿⡿⠿⠛⠛⠋⠻⠿⠶⢦⣅⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣤⡖⠋⠁⠀⠀⣾⣀⣿⠀⠀⣹⠶⠿⢯⣤⣾⡿⣿⠟⠋⢀⣄⢀⣀⣀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣿⣿⣿⣿⣿⣿⣿⡇⠙⠻⣿⣿⣆⢠⣽⠓⠒⠒⠲⣿⣿⡟⠚⠉⠀⠀⣰⣿⡟⠛⠃⠻⠿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⢀⡤⠐ ⠀⠀⢄⡀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⣻⣼⣯⣿⣿⣿⡈⠁⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⣴⣿⣏⣩⣤⣤⣴⣶⣾⣿⣿⣿⣿⣯⣿⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⣞⣥⣾⣿ ⠀⠀⢦⡙⢦⣀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣿⣿⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣴⣾⠃⢀⣠⣾⣿⣿⣿⣿⣿ ⠀⠀⠈⠓⢦⣌⠛⢦⡀⢷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⣹⣿⣿⣿⣿⡿⣿⣿⣿⣿ ⠀⠀⠀⠀⠟⠽⢧⡀⣩⡿⣯⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣠⣴⣾⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⠰⡦⣠⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠟⣥⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⠀⠀⠀⠉⣛⡽⠛⠲⣤⡀⠈⠉⠉⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠻⣿⡿⠋⢀⣨⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⢀⡾⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿ ⠀⠀⢀⣾⣁⡀⢀⣠⣶⣤⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠸⡛⢤⣤⣿⣿⣿ ⣠⣶⣾⣿⣿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⠉⣽⡟⢉⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢛⣹⣿⣶⣿⣿⣿⣿⣿ ⣿⣿⠿⠋⠁⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⡋⠉⣀⡴⢚⡥⠆⡉⣀⣠⢆⡠⢐⣂⠀⣠⡿⠟⠉⢉⢉⡩⣛⣿⣿⣿⣿⠿⠡⣠⣤⣭⣿⣿⣿⣿⡿⠛⠉⠀

🟦🟨🟫🟫🟫🟫🟫🟦🟦🟦🟦🟦🟦🟦🟦🟦 🟦🟨👁️🟨🟨👁️⬜️🟨🟦🟦🟦🟦🟦🟦🟦🟦 🟦🟨🟨⬛️⬛️🟨🟨🟨🟨🟦🟦🟦🟦🟦🟦🟦 🟦🟨🟨🟨🟥🟥🟥⬜️🟥🟥🟥🟦🟦🟦🟦🟦 🟦🟦🟦🟥🟥🟥🟥⬜️🟥🟥🟥🟥🟦🟦🟦🟦 🟦🟦🟥🟥🟥🟥⬜️⬜️⬜️🟥🟥🟥🟥🟦🟦🟦 🟦⬜️⬜️🟦⬜️⬜️⬜️⬜️⬜️⬜️⬜️🟦⬜️⬜️🟦🟦 🟦⬜️🟦🟦🟥🟥🟥🟥🟥🟥🟥🟦🟦⬜️🟦🟦 ⬜️🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟦🟦⬜️🟦 ⬜️🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟦🟦⬜️🟦 ⬜️🟦🟦🟥🟥🟥🟥🟥🟥🟥🟥🟥🟦🟦⬜️🟦 🟦⬜️🟦🟦🟥🟥🟦🟦🟦🟥🟥🟦🟦⬜️🟦🟦 🟦🟦🟥🟥🟥🟥🟦🟦🟦🟥🟥🟥🟥🟦🟦🟦 🟦🟦🟦🟦🟥🟥🟥🟦🟥🟥🟥🟦🟦🟦🟦🟦 🟦🟦🟦🟦⬜️⬜️⬜️🟦⬜️⬜️⬜️🟦🟦🟦🟦🟦 🟦🟦⬜️⬜️⬜️⬜️⬜️🟦⬜️⬜️⬜️⬜️⬜️🟦🟦🟦

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⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⠖⠳⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠒⠀⠂⡾⠉⠀⠀⠀⠀⠉⢳⡄⣄⡀⠀⠀ ⠀⠀⠀⢸⡥⠀⣀⡼⢁⠀⢰⡄⠀⡄⠀⠀⣧⠀⠙⡆⠀ ⠀⢀⣠⠼⠗⠚⠉⠠⠋⠀⠀⢷⣠⣧⠀⠀⠈⠳⢤⣇⠀ ⠀⣾⣟⠒⠦⣄⠀⠀⠀⣠⡴⠋⠁⢈⠛⢦⣄⣠⣴⣾⣷ ⢀⡟⠙⢶⣤⠬⠷⣼⡏⠉⠉⢩⡍⠹⠦⢤⣿⣤⣨⣿⠈ ⡾⣡⠆⠁⠀⠀⠀⢠⡀⠀⠀⠀⢱⡀⠀⠂⠙⠎⠻⡅⠀ ⢿⠁⠒⣤⠤⣤⣀⠀⢧⠀⠀⠀⣸⠃⠀⠀⠀⡶⣤⣽⠀ ⠈⠳⣴⡇⠀⠀⠈⠛⢦⣄⣠⠾⢿⣄⣀⣠⠾⣡⠞⠁⠀ ⠀⠀⠈⠉⠉⠉⠁⢧⢠⠟⣽⠀⢿⠀⢧⢰⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢫⠏⢸⠁⠀⠈⢳⠘⢧⣙⢦⠀

⣿⣿⡿⣹⢿⣧⣿⡿⠛⠛⠿⣿⣿⣿⣿⡿⠁⠀⠀⣀⣤⣶⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⢄⠈⡇⢸⠀⢠⠀⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⠛⠀⠀⠀⠙⢻⣿⣿⣿⡿⠟⠓⢚ ⣿⢟⡵⢁⣾⣿⣿⠟⡝⢆⠀⠈⣿⣿⣿⡇⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢨⢆⢱⣸⢀⠏⡜⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⡝⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⡠⣛ ⣿⣿⡇⠀⢹⣿⡇⡸⢳⡈⢦⠀⢹⣿⣿⡇⠀⠀⠀⠀⢀⣹⠽⢿⣿⣿⣿⣿⣿⣶⣦⣤⣈⣧⣣⣻⠈⣾⣰⣥⣤⣶⣾⣿⣿⣿⣿⠿⠿⠿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡜⢁⠹ ⣿⣿⡇⠀⢸⣿⣧⠃⠀⣣⠈⢇⢸⣿⣿⣧⠀⠀⠀⣀⣸⡟⠉⢙⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠈⠛⢿⣿⣿⣿⣿⡿⠟⣣⣴⣤⠀⠈⠻⣧⣀⠀⠀⠀⢸⣿⣿⠀⡼⠀⣎⠀ ⣿⣿⡇⠀⢸⣿⣟⠀⢞⠓⠒⡺⢸⣿⣿⣿⠀⠀⠀⠠⡘⣷⣤⣴⣾⣷⡧⣀⣀⣻⠍⡏⢻⣖⠳⡄⢀⠔⣲⡼⢉⣽⢱⣻⠁⠀⠺⣿⡿⠀⠀⣠⠏⠀⠀⠀⠀⢸⣿⣿⠰⣗⠒⣺⢃ ⣿⡿⠛⠋⠁⢸⣿⡄⠀⠑⢾⠁⠘⣿⣿⡟⡀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⢉⡷⠊⢱⠋⠙⣧⠈⠉⡰⠋⠙⡎⠙⠿⣿⠷⢦⣤⣄⣀⣠⡾⢫⠆⠀⠀⠀⠀⣸⣿⡟⠀⢸⠞⠁⢈ ⠁⠀⠀⠀⠀⠀⡏⠙⠦⡀⠀⠳⣀⣿⣿⣇⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡄⠈⠉⠒⠀⠈⠻⠥⠴⠋⠀⠀⠀⠀⠀⣿⣿⡇⢠⠎⢀⡀⠈ ⠀⠀⠀⠀⠀⠀⢱⡀⠀⠘⢄⠀⠀⣿⣿⣿⣆⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣽⣿⡏⠁⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⣿⣿⣿⣿⣦⠀⠱⡄⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣾⣿⣿⡇⠀⠀⠀⣀⠈ ⠀⠀⠀⠀⠀⠀⠀⠸⠈⢳⣤⣄⣰⣿⣿⣿⣿⣿⣧⡀⠈⢦⡠⠔⢊⡽⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⣦⣄⠀⠀⢀⡴⠋⣰⣿⣿⣿⣿⣿⣖⣲⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⣌⡇⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢧⣴⣷⡄⠀⠀⢀⣾⣷⡇⠀⠀⠀⠀⠀⠀⠙⣧⠙⠢⠎⠀⣾⣿⣿⣿⣿⣿⣿⠀⢸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠳⡈⢻⣒⣴⠟⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⡇⠀⠀⢀⣧⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣾⡀⠀⠀ ⠀⠀⣠⠔⠋⠙⢆⡇⠀⢠⠎⠀⣳⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣠⣤⣶⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣀⢤⡙⢿⣿⣶⣶⣧⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠱⡀⠀ ⠀⠈⠀⠀⠀⠀⠈⢇⢠⠎⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⣿⣿⣿⢏⡔⠁⠈⠉⠉⠒⠒⠒⠒⠒⠒⠊⠉⠁⠀⠀⣀⣨⣷⡽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⢚⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠼⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠁⢰ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠛⠧⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⠔⠋⠉⠉⢉⣉⣉⣑⣦⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠁⠀⢀⡈⠠

⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣶⣶⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⢻⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⢹⣿⣿⡀⠀⠀⠀⣾⣿⣠⣶⣿⡆⠀⢀⣴⣶⣿⣷⣶⣄⠀⠀⠀⠀⠀⠘⣶⣿⣆⠀⠀⠀⣾⣿⡇⠀⣠⣴⣾⣿⣶⣶⣤⡀⠀⠀⣷⣿⡆⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⡄⠀⢰⣾⣷⠀⠀⠀⣶⣿⡇⠀⠀⣿⣾⣠⣾⣿⡆⠀⣀⣴⣾⣶⣿⣶⣄⠀⠀⠀⠀⣀⣀⣼⣿⡿⠁⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⢿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠻⠛⠟⠻⠛⠟⠻⠛⠟⠻⠛⠿⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⢶⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠈⠁⠉⠙⣿⣦⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠈⠁⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⢷⣹⢞⣻⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣅⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣈⣡⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡹⢧⣛⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣏⣯⣿⣿⣿⣿⣿⢯⣳⢏⡾⣝⡾⣹⢶⣫⡽⣫⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣄⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⣟⡽⣣⣟⢮⡽⢶⣛⣯⢽⣚⢿⣿⣿⣿⣿⣾⣝⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣏⣷⢻⣾⣿⣿⣿⠿⠯⠷⢯⣾⣝⣾⣱⣯⣳⣳⡽⣳⢮⢷⡝⣮⢟⣽⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⡹⢧⣛⡾⣝⡾⣱⣟⣼⣏⣾⣏⣷⣺⠽⠾⠯⠟⢿⣿⣿⣿⣿⢮⣝⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣟⣳⡽⣺⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠛⠓⠿⠽⠯⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠽⢧⠟⠚⠛⠓⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣮⢳⣟⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣟⢮⣳⣽⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢟⣿⢻⡟⣿⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣳⢮⣻⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⡮⣟⣼⣿⣿⣿⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⣦⢤⡤⣤⣤⢤⣬⢷⣫⣽⢻⡤⣤⢤⡤⣤⡤⣤⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⣿⣿⣿⣯⣷⢫⣟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡝⣾⣹⣿⣿⣿⣿⣿⣹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡺⣟⡽⣺⡵⣏⢿⡼⣳⣭⢻⡼⣳⣝⣮⢏⣷⢫⣯⠽⣖⣻⡵⣏⡷⣹⢯⣗⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⣮⢟⣿⣿⣿⣿⣯⣷⢫⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡽⢾⣿⣿⣿⣿⣿⢲⠋⠀⠀⢀⣼⣳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣱⠿⣜⣳⢷⣹⡞⣧⢟⡵⣞⢯⣳⡏⠉⠉⣟⡮⣟⡼⢯⡽⣖⣻⡼⣝⡧⢿⡼⣹⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡗⣦⡀⠀⠀⢻⢾⣹⢿⣿⣿⣿⣿⣳⡽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣹⣿⣿⣿⣿⡿⣎⡿⣆⡀⣰⢿⣇⣷⢾⣉⡷⣀⠀⠀⠀⠀⢀⣆⡀⠀⠀⠀⠀⠀⣸⣹⢏⡷⢿⣉⡷⣏⣶⢿⡹⣾⢹⡾⣇⣏⡇⠀⠀⣏⣷⢏⣹⢿⣸⡹⣶⢿⣸⡹⣇⡿⣉⣷⢏⡆⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠀⣰⣾⢿⣸⡹⢷⣷⣀⣀⣸⣏⢷⣏⣿⣿⣿⣿⣷⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣻⣿⣿⣿⣿⣏⠷⣽⢳⡻⣭⢷⡺⣵⣫⢷⣹⢏⡷⣦⣀⣴⣿⣿⣿⠆⠀⠀⠀⠀⣟⡧⣿⡹⣏⡷⣽⢺⡵⣫⢷⡹⣏⡾⣝⣮⡇⠀⠀⣟⣮⢯⡳⣏⡷⣝⣧⢯⣳⡝⣧⡟⡽⣎⡿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⡶⢿⣹⢮⡗⣯⢽⡻⣜⣳⢯⡳⢯⣞⡽⣞⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣻⣿⣿⣿⣷⣾⣿⣷⣫⢗⣻⢮⣽⢣⣟⢮⡗⣯⣳⣯⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣟⣳⢧⡟⣵⡻⣼⢻⣼⣛⢮⡟⣵⣛⣞⡶⡇⠀⠀⡿⣼⢳⣏⡷⣽⢺⣼⢳⢧⣻⢵⣫⢟⣵⣛⡇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣯⡳⣏⡾⣝⡾⣹⣝⡮⢷⡻⣽⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⡽⣾⣹⡾⣜⣻⡼⣫⣞⣷⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⡽⣺⡝⣧⡟⣵⡻⣖⢯⣻⢼⡳⣝⣮⡽⡇⠀⠀⣟⣧⠿⣜⣳⣭⢷⣫⢟⡮⣗⡯⢾⣹⢮⣽⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣵⢻⡼⣳⢏⡾⣽⣳⣏⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡱⣏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡹⣧⣿⣿⣿⣿⣿⡥⣤⢤⡤⣄⠀⠀⠀⠀⠀⢿⣳⡽⣣⡟⣧⢟⡾⣹⢮⣗⢻⡝⡶⣽⣣⢤⡤⡿⣜⡯⣏⡷⢮⡗⣯⠾⣝⡾⣹⢏⡷⣫⠎⠀⠀⠀⠀⢀⣠⣤⢤⡤⣤⣹⣿⣿⣿⣿⣿⡼⣳⢯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢻⡵⣻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⣫⠷⣝⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣿⣿⣿⣿⡿⢯⣝⡧⣟⡽⣹⣇⠀⠀⠀⠀⠀⠙⠳⢯⡽⣞⣽⣺⣭⢷⣚⣯⠾⣝⣧⢯⣏⢷⣏⣷⣹⢧⣻⡽⣚⡷⣻⡝⡾⣭⠿⠚⠁⠀⠀⠀⠀⢀⣾⢻⡼⣏⡾⣳⣝⣻⢿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⢟⣼⡳⢯⡽⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢳⣝⡯⣽⢺⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣝⡷⣺⣝⣮⢽⡳⣞⡧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠈⠉⠉⠉⠉⠉⠉⣱⣻⢮⡏⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⣭⢷⡻⣼⢳⣝⡮⢷⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢺⡵⣻⢭⣛⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣏⠿⣜⣳⡽⣳⢻⣿⣿⣿⣿⢯⢿⡿⣿⣿⢿⡿⢯⣝⢯⡞⣵⣏⡾⣼⢳⣏⢷⣹⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢯⡾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡹⢧⣯⢳⣏⠿⣼⡹⣏⡾⣵⢫⣟⡿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣯⡳⣽⢣⡿⣹⣎⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⣹⢞⣯⢻⣜⣳⡽⣻⣿⣿⣿⣿⣫⢾⣹⢳⡮⣟⣼⣛⣮⢟⣼⡳⣞⡵⢯⣳⢞⡯⣞⡽⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢾⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣮⡽⣻⣜⢯⡞⣯⣳⣽⣣⠿⣜⡿⣼⣹⢳⡞⣼⡳⡽⣾⣿⣿⣿⣷⣏⢷⣫⢷⡳⣝⡮⣟⣿⣿⣿⣿⣦⡀⠀ ⣦⡀⢀⣾⣿⣿⣿⣿⢯⣳⢏⡿⣜⡯⢾⣱⣻⣽⣿⣿⣿⠓⠙⠊⠙⠃⠛⠘⣶⡻⣼⢫⣶⢻⡵⣻⡭⣗⣯⢳⣏⢷⣳⢻⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⣏⡷⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣞⣳⡽⣣⠿⣵⢞⡯⣞⣳⡽⣞⣧⢿⣹⢞⡵⠋⠓⠙⠃⠛⠑⠛⣿⣿⣿⣿⢾⣹⢮⡗⣯⣳⠽⣞⡽⣿⣿⣿⣿⣷⡀ ⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣾⣽⣾⣽⣯⣷⣷⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣷⣿⣷⣧⣬⣽⣷⣷⣿⣾⣾⣿⣾⣿⣾⣷⣿⣾⣯⣿⣽⣯⣷⣯⣿⣾⣯⣿⣽⣯⣿⣽⣷⣿⣾⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣷⣾⣷⣿⣽⣿⣾⣿⣾⣽⣶⣿⣭⣤⣽⣷⣯⣷⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣾⣷⣿⣷⣯⣿⣽⣾⣽⣿⣿⣿⣿⣷;༂

╾━╤デ╦︻

𝓯𝓻𝓮𝓪𝓴𝔂

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💥 🥀 ⚤They/Them⚤ ²⁰⁰⁸ ⭑

💥 🥀 ⚤They/Them⚤ ²⁰⁰⁸ ⭑༘˚⋆𐙚｡⋆𖦹.✧˚༘˚⋆𐙚｡⋆𖦹.✧˚જ⁀➴༘˚⋆𐙚｡⋆𖦹.✧˚─── ⋆⋅☆⋅⋆ ──

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👨🏻‍🦳🦽💪🪐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠉⠉⠙⠐⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⢸⠤⠭⠅⠀⠀⢣⠀⠀⠀⠀⠀⠀⠘⣿⣿⣥⣶⡽⣷⣾⣦⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣟⣡⣯⠛⣿⢉⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣳⠒⠒⠉⠁⢇⡠⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠋⣸⣾⠟⠹⠉⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠀⠀⠀⠀⠀⠗⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠶⠏⠉⠁⠀⠀⠀⠀⠀⠨⣿⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⡜⠀⠀⠀⣠⠴⠒⠈⠉⠉⠁⠒⠲⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⡰⠁⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⣟⠃⠀⢠⣤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⢻⣽⠖⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⣀⡀⠀⠀⢀⣀⣴⡿⠀⡄⠀⠀⠈⢷⡄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀ ⠀⠘⡄⠀⡠⠎⠀⠀⠀⢿⣰⠊⠁⠀⠀⣠⢍⣴⠛⠀⢀⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⣧⠀⠀⠀⠀⠀⡜⢾⣷⣦⡄⠀⠀⢀⠀⢧⠀⠀⠀⠀ ⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⠇⠤⠤⣒⡮⠾⠿⠉⠀⠀⣾⠃⠀⠀⠀⠀⣿⣷⠀⠀⠀⣿⡅⠀⠀⠀⠀⢳⠀⠹⢿⣄⠀⠀⠈⢣⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠶⠾⠋⢉⠁⣀⠀⢀⣠⡾⠁⠀⠀⠀⢀⣸⣿⣿⣇⠀⣠⣿⣷⡀⠀⡀⠀⠈⢧⠀⠈⠹⠷⠦⣄⡘⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣟⣋⣁⣈⣤⣤⡴⠖⢛⢁⣠⣶⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⡟⠿⣷⣴⣷⡀⠀⠘⢷⡀⠀⠀⠈⠻⠛⠛⣦⡄⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣇⣀⣠⣴⣾⡉⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⢁⣀⣜⡡⢄⣈⠛⠻⣷⣦⡀⠀⠉⠀⠀⠀⢀⣀⣯⣻⣿⣆⠀ ⠀⠀⢠⡿⣻⢿⡉⠀⠉⢾⣍⣛⡻⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⢟⣉⡴⠋⠱⡿⢋⢀⠲⣀⣉⠵⠚⠙⢿⣤⣤⣼⠟⢹⣿⣿⢫⡏⠻⣿⡄ ⠀⠀⠀⣰⠃⠀⠹⣦⡀⠈⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢿⣿⣿⡋⠹⡿⠟⠻⠻⡏⠀⠀⠀⠀⢸⣿⡘⠀⠀⠀⠙⢁⡞⡇⠀⢸⠇ ⠀⠀⠀⡟⠀⠀⠀⠉⢽⣶⣤⣤⡤⠼⠶⠲⠤⠤⣄⣽⠿⠁⠀⠀⠂⠀⠈⠻⣶⣷⣴⣶⠾⠿⡖⠶⠶⢤⣈⣿⣿⣦⣀⠀⢠⣎⣴⠏⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⣀⣶⠖⠋⠉⠀⠀⠀⠀⠀⠀⠰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⠁⠀⠀⠀⠀⠈⡉⠉⢻⣏⠙⠿⢿⣿⡿⠋⠀⠀⠀⠀ ⠀⡼⠁⠀⢠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢽⡤⠀⠀⠀⠀⠀⠀⠀⠈⢸⣆⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⢸⣯⣠⣼⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⠀⠀⣸⣆⠀⠀⠀⠀ ⢸⣿⠋⠀⠈⣧⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⣴⣾⣿⢿⡆⠀⠀⠀ ⠀⠻⡄⠸⠀⠈⠉⠉⣛⡿⠛⠻⠿⣶⣶⣶⣦⣤⡀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⣿⠿⣿⠃⣼⡇⠀⠀⠀ ⠀⠀⢳⣀⣧⠀⠀⣠⡟⠀⠀⠀⠀⠀⠙⠻⣻⢿⣿⣤⡈⠁⠀⠀⠀⠀⠀⣠⣴⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⢹⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠙⠿⣷⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡻⢿⣷⣶⣶⣶⣾⣿⣿⠟⠻⣿⣿⣷⣶⣦⣤⣴⣶⣾⣿⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠿⣒⣒⡀⠀⠀⠀⠀⠀⣰⣶⡆⠈⠓⠯⣍⢛⣛⢯⠉⠀⠀⠀⡼⠛⠛⣿⢿⣟⣻⢿⠋⢀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⡅⠀⠀⢀⡜⠋⠁⢸⠇⠀⠀⢸⡇⠀⠀⠈⢣⠀⠀⢺⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⡎⠀⠀⢀⠞⠀⠀⠀⠀⢧⠀⠀⠀⠀⣇⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡜⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⢆⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠁⢀⡜⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠣⣄⡀⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠐⠛⠒⠒⠒⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠋⠛⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀

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are you sure?

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Hii my name is Coda!!! I am a polytherian but I am mainly a snake, a calico cat, an opposum. It/he!! I an single but I am 12! I like my friend Saba🥰 Anyway, I'm here to tell you that I saw someone with the alterhuman symbol on there car!!! 👏

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ꪻꪊ )˂⌓˃ (§łłäb ým ķçų$��‍️�� ?eag )°͡ ʖ͟ °͠ ( ͞ںل ̶͞ ̶͞ ̶͞ ͞Ɑ ͞ںل ̶͞ ̶͞ ̶͞ ͞Ɑ kcoc

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🌸🌺🌑🦋☂️

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ℒ𝒢𝒷𝓉𝓆 💙💙💙💙💙💙💙💙💙💙 💙💙💙💙💙💙💙💙💙💙 🦋🦋🦋🦋🦋🦋🦋🦋🦋🦋 🦋🦋🦋🦋🦋🦋🦋🦋🦋🦋 💟💟💟💟💟💟💟💟💟💟 💟💟💟💟💟💟💟💟💟💟 🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸 🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸 💗💗💗💗💗💗💗💗💗💗 💗💗💗💗💗💗💗💗💗💗

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🔶️🔸️◽💓💗 💗💜💙 💗💛💙 💗💓🖤💙🔵 💜◽💙💗 💚◽💙🔵 💜🌚◽🌚💜 🖤🌚◽💜 🖤◽🖤◽🖤◽ 🔶️💛◽💙🔵 🖤◽💜◽ 💙❤🖤 💗💚💙 💗💗◽💗💗 🌚💜◽💗 💚◽💓💗 💙🌊💛🍞 🔵💙💜🎵 👞💛◽💜 ❤🧡💛💚💙💜

𝓷𝓲𝓰𝓰𝓪

😮,🖕,☢

𝓷𝓲𝓰𝓰𝓪εつ▄█▀█●ඞyou are gඞy

spicy, boobs, ( ͜ₒ ㅅ ͜ ₒ), *𝘮𝘰𝘢𝘯𝘴*