Family Guy Jesus Text 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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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢴⡒⠛⠒⠖⠚⠓⢦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠖⠛⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀ ⠀⢠⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢧⠀⠀ ⡎⠻⠀⠀⠀⠀⠀⠀⣉⠔⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠉⡀⠀⠀⠀⠈⠶⢢ ⠘⠒⡅⠀⠀⠀⢀⠚⠒⠂⠤⢷⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠤⠬⢦⠀⠀⢀⠬⠞ ⠀⠀⠈⠢⡀⠀⠸⡤⠤⠤⠤⡼⠀⠀⠀⠀⠀⡵⠀⠀⢤⠤⠄⠀⡞⠀⡠⠃⠀⠀ ⠀⠀⠀⠀⠈⠒⢄⡉⠂⠐⠒⠁⠀⠀⣀⠤⠤⡤⠄⠀⠈⠁⠒⢉⠤⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⢀⣀⣀⣀⣈⣀⡀⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⡶⠛⠉⠁⠀⠉⠙⠳⣄⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⢿⣿⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⠀⠀⠀⢀⣴⣶⣄⠀⠈⢳⡀⠀⢀⡿⠀⣴⠞⠳⢦⣼⣿⣿⣇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣤⣤⠶⠛⠁⣾⠏⢳⡄⠀⢷⡀⢸⡇⣼⠃⠀⠀⠻⠛⢹⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢻⡇⠀⠀⠀⠀⠀⠀⢿⡀⠸⣿⠙⠳⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠸⣧⣤⣤⠶⠶⠶⠶⣿⠇⠀⡿⠀⠀⠈⠻⣟⠛⠉⠙⣻⠏⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡀⠀⠹⣧⡀⠀⠀⢀⣴⠟⠀⣸⠇⠀⠀⠀⠀⢹⣦⣴⠾⠋⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⣄⠀⠈⠙⠛⠛⠋⠁⠀⣰⠟⠀⠀⠀⠀⣠⣾⣧⣀⣀⣀⣤⠾⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠳⣤⣀⣀⣀⣀⣴⠞⠋⠀⠀⠀⠀⣰⠟⠀⠀⠉⠉⠉⠁⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣾⣉⢻ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸⡇⠈⢳⣤⣴⣟⠭⢹⡆⡾ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠷⣦⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣾⠇⠀⢸⡟⠉⢻⡄⢸⡟⠁ ⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠘⠻⠶⣶⣟⣠⣤⣴⣾⣿⠿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⠃⠀⢀⣧⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⠏⠉⣿⣿⣿⡿⠁⢀⣿⠙⣧⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡶⠞⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣷⣽⣷⣄⡀⠀⠀⢀⣀⣠⡿⠀⠀⠹⠿⠋⠀⠀⠾⠃⢀⣿⣷⣶⡶⠶⠛⠉⠀⠀⠀⠘⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠴⠟⠁⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⠿⠿⠛⠛⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⡏⠀⠈⠛⠛⢿⣓⡀⠀⠀⠀⠀⠰⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣇⠀⠀⠀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⣀⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⠴⠒⠲⢄⠀⠀⢠⡎⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⡀⠀⢰⠃⠀⣠⠀⠀⢣⠀⠘⣇⠀⠘⠂⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⣿⣿⣿⣇⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⠈⠢⣤⡤⠚⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⠟⡛⠏⠀⠀⠈⠙⠒⠚⠁⠀⡀⠀⠀⠀⠈⠳⡄⠀⠈⢦⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣦⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡤⣄⡀⠀⢀⡟⠀⠀⠀⢇⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣯⣀⠀⠀⠀⢸⡄⠀⠀ ⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣿⡇⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣋⣁⣀⣈⠆⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢖⣂⣈⣹⡀⠀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⣀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣟⢶⡶⠤⠤⠤⠤⢤⠀⠀⠀⣠⣀⣠⣾⣿⣿⣿⣷ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠉⠲⣄⡀⠀⠈⠓⠒⠚⢁⡜⢿⣿⣿⣿⣿⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠓⠲⢤⣤⣴⡋⠀⢸⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠻⠿⣿⠿⣿⣿⣿⠏⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠀⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⣭⣙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣉⠛⣛⣉⠁⠀⠀⢀⣤⣴⣦⣤⣀⣶⡆⣾⣿⣿⣿⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⠟⠉⠉⠙⢿⣿⣿⣇⢻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣦⡙⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣩⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣴⡾⣿⣿⡛⢋⠉⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣉⣤⣶⣤⣤⡀⠀⠀⣴⣿⠟⠁⣩⣿⣿⣿⣿⣿⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢇⣾⣿⣿⣿⣿⣿⣿⡆⠺⠿⠋⢀⣾⣿⡿⢫⣾⣿⠟⢮⣝⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣳⣾⣷⡄⠀⠈⢿⢸⣿⣿⣿⡿⣫⣶⣿⣿⣿⣷⣄⢻⡿⢋⣴⣿⣿⠟⣠⣴⡿⠷⣟⣯⣤⣶⡶⣶⣄⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠃⠈⠛⢿⣦⣀⣈⡈⢿⣿⡟⣼⣿⣿⣿⣿⣿⠿⣛⣃⣀⣘⠿⠟⢣⣾⣿⡿⠃⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣼⡿⠋⠉⠀⠀⠀⠀⠀⠘⠿⣸⠧⡄⠻⠁⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣷⣄⢻⡟⠋⠀⣼⣿⣿⣿⠋⠉⠵⠿⣿⣿⣿⣿⣿⢋⣷⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠋⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣷⡄⣶⣶⣆⣻⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣀⣠⣴⣮⢻⠇⠀⣷⡄⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣷⣤⡀⠀ ⠀⠀⠀⠀⣿⡇⠀⢰⣯⣽⠉⠉⢩⣍⣉⣉⣩⣭⣥⣭⣍⣻⣥⣭⣭⣜⠿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡸⢿⣿⣿⡿⠀⠀⠀⢹⣷⣀⣀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⢀⣼⠿⠃⠀⢸⣿⡇⠀⢸⣿⠻⠟⠿⠿⠿⠿⢿⣿⣿⠋⠛⣻⣭⣴⣶⣄⠉⠛⠿⠟⢫⣾⣿⣿⣆⣀⡈⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⡴⠟⠛⠁⠀⠀⢸⣿⡧⠀⣾⣿⡀⠀⢠⣼⡻⣿⣿⣿⣿⣿⣿⠎⣿⠿⠟⠃⣀⣴⣿⣿⠈⣙⡻⠿⠃⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡇⠀⣼⣿⡇⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⣾⡛⠻⣿⡇⠀⣿⣧⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠃⠀⢠⣤⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣠⠾⠛⢿⣿⣷⣿⣿⣿⣧⠹⠃⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⢸⣶⡅⢐⡿⠏⠀⠀⠀⢀⣴⣿⣷⡌⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀⣤⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⢻⣧⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠘⢿⣧⠀⢸⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⢰⣿⠆⢸⣿⣿⣿⣿⢿⣿⣧⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢸⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣤⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣉⠉⠻⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠋⢰⣿⣿⣧⣦⡀⣀⣴⣶⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧⬛🟫🟫⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛🟩⬛🟩⬛🟫🟫⬛⬜ ⬜⬜⬜⬛⬛⬛🟫🟫🟫🟫🟧🟫⬛⬛⬛🟫🟫🟫⬛⬜ ⬜⬜⬜⬛🟫🟫🟫🟫🟫🟫🟧🟧🟫🟫⬛🟫🟫🟫⬛⬜ ⬜⬜⬛🟫🟫🟫⬛🟫🟧🟧🟫🟫🟫🟫⬛🟫🟫🟫⬛⬜ ⬜⬜⬛🟫🟫⬛🏻⬛🟧🟫⬛🟫🟫🟫⬛🟫🟫🟫⬛⬜ ⬜⬜⬛🟫🟫⬛🏻⬛🟫🟫⬛🟫🟫🟫⬛🟫🟫🟫⬛⬜ ⬜⬜⬜⬛🟫⬛🟨⬛⬛🟫🟫⬛🟫🟫⬛🟫🟫⬛⬜⬜ ⬜⬜⬜⬜⬛🟫🏻🟩⬜⬛⬛🏻⬛🟫⬛🟫🟫⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🏻⬛⬜🏻🏻🏻⬛⬛🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻🏻🏻⬛⬛🟫🟫⬛⬜⬜⬛ ⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻⬛⬛🟫🟫🟫🟫⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟩⬛🟫🟫🟫🟫🟫🟫⬛ ⬜⬜⬜⬜⬜⬜⬛⬜⬛🟩🟩🟩🟩⬛🟫🟫🟫🟫⬛⬜ ⬜⬜⬜⬜⬛⬛🏻⬛⬜⬛🟩🟩🟩⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛🏻🏻🏻⬛🌫️⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🏻🏻🏻🏻⬛⬛🌫️⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🏻🏻⬛⬛⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬜⬜⬛🟩🟩⬛🟪⬛🟪⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩⬛🟪⬛🟪⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛🟩⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏻⬛⬛🟪⬛🟪⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻⬛🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻⬛🏻⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏻🏻🏻⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🏻🏻🏻⬛⬛🏻🏻🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🏻🏻🏻⬛⬜⬛🏻🏻⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🏻🏻⬛⬜⬜⬜⬛⬛🟩🟩⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟩⬛⬛⬜⬜⬜⬜⬜⬛🟩🟩⬛⬜⬜⬜⬜ ⬜⬜⬛🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜⬛🟩🟩⬛⬜⬜⬜ ⬜⬜⬛🟩🟩⬛⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩⬛⬜⬜⬜ ⬜⬛🟩🟩🟩⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛🟩⬛⬜⬜⬜ ⬛🟩🟩🟩⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜🏿⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏿⬜⬜ ⬜🏿🟫🏿⬜⬜⬜🏿🏿🏿🏿🏿🏿🏿⬜⬜⬜🏿🟫🏿⬜ 🏿🟫🟫🟫🏿⬜🏿🟫🟫🟫🟫🟫🟫🟫🏿⬜🏿🟫🟫🟫🏿 ⬜🏿🟫🟫🟫🟥🏿🟫🏿🟫🏿🟫🏿🟫🏿🟥🟫🟫🟫🏿⬜ 🏿🟫🏿🏿🟥🏿🟫🟫🏿🟫🏿🟫🏿🟫🟫🏿🟥🏿🏿🟫🏿 ⬜🏿⬜⬜🏿🟫🏿🏿🏿🏿🏿🏿🏿🏿🏿🟫🏿⬜⬜🏿⬜ ⬜⬜⬜🏿🟫🏿🏻⬛⬛🏻🏻🏻⬛⬛🏻🏿🟫🏿⬜⬜⬜ ⬜⬜⬜🏿🟫🏻⬛🏿⬜🏻🏻🏻⬜🏿⬛🏻🟫🏿⬜⬜⬜ ⬜⬜⬜🏿🟫🏻🟪🏿🏿🏻🏻🏻🏿🏿🟪🏻🟫🏿⬜⬜⬜ ⬜⬜⬜🏿🟫🏻🟪🟪🏻🏻🏻🏻🏻🟪🟪🏻🟫🏿⬜⬜⬜ ⬜⬜⬜⬜🏿🏿🏻🏻🏻🏻🏻🏻🏻🏻🏻🏿🏿⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏿🏻🏻🏻🏻🏻🏻🏻🏿⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🏿🏿🏻🏻🏻🏿🏿⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🏻🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥⬜🟥🟥🟥🟥🟥⬜🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜⬜🏻🏻🏻⬜🟥🟥🟥🟥🟥⬜🏻🏻🏻⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏻🏻🏻🟥🟥🟥🟥🟥🏻🏻🏻⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏻🟥🟥🟥🟥🟥🟥🟥🏻⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪⬜🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪⬜🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪⬜🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🌫️⬜🌫️⬜⬜⬜⬜⬜⬜⬜⬜⬜

⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣄⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠻⠷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏ ⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀

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⠀⠀⢀⣀⣤⣤⣴⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⣄⣀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣾⣿⣶⣶⣶⡆⢠⣶⣿⣿⣿⣄⠀⢀⣿⣿⣿⣿⣇⠈⠒⠒⠚⠋⢠⣤⣤⣶⣶⡆⠀⢰⣶⣿⣿⣿⣷⡀⢀⣴⣿⣿⣿⣿⠆ ⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⢰⣾⣿⣿⣷⡎⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠋⠀ ⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣹⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⡏⠹⣿⠏⢻⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣶⣶⣶⡆⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⡟⠋⢹⣿⣿⣿⣷⢻⣿⣿⡇⠀⠉⠀⢸⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠸⠿⢿⣿⡇⠀⠀⠿⠟⠋⠀⠉⠉⠙⠃⠀⠀⠀⠘⠛⠛⠋⠁⠉⠉⠉⠉⠉⢾⣿⡿⠿⠿⠿⠿⠟⠃⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⠘⣿⣿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⢠⣶⣶⣾⠀⠀⠀⢰⣶⣶⣶⡎⣿⣿⣿⣄⠀⠀⣼⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣷⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠙⣸⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⣶⣶⣶⣶⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⢿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣀⣉⣹⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠿⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🏻🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🏻🟥🏻🟥🏻🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬛🟥🟥🏻🏻🏻🏻🏻🏻🏻🟥🟥⬛⬛⬜⬜ ⬜⬜⬜⬛🏻🏻🟥🏻🏻🏻🟥🏻🏻⬛🟥⬛⬜⬜ ⬜⬜⬜⬛🏻🏻⬛🏻🏻🏻⬛🏻🏻⬛🟥⬛⬜⬜ ⬜⬜⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻⬛🟥🟥🟥⬛⬜ ⬜⬜⬛🟥🟥⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥⬛⬜ ⬜⬛🟥🟥🟥🟥⬛🟥🏻🟥⬛🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥⬛🏻🟥🟥🟥🏻⬛🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥⬛⬜⬜🟥🟥🟥⬜⬜⬛🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🏻⬜⬛🟥⬛🟥⬛⬜🏻⬛🟥🟥⬛⬜ ⬜⬛🟥🟥⬛⬛🟥🟪🟪🟪🟥⬛⬛🟥🟥🟥⬛⬜ ⬜⬜⬛⬛🟥🟥⬛⬛⬛⬛⬛🟥🟥🟥⬛⬛⬜⬜ ⬜⬜⬜⬜⬛⬛⬛🟥⬛🟥⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⡄⠀⠀⡀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠁⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣾⣿⣿⣿⣿⡿⠋⠹⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⢀⣿⣿⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⢸⣿⣿⡏⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣒⠉⠉⠑⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠤⠴⢯⠔⢀⡠⠔⠓⠊⠉⠉⠉⠉⠒⠊⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢋⠀⠀⠠⠃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀ ⠀⠀⢀⠴⠓⡆⠀⡠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠃⠀⠀⠡⠊⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠐⠁⠀⠈⢀⠀⢸⠀⠀⠀ ⠀⡿⠖⡇⢠⠃⠀⠀⠀⠀⠀⢀⡴⠊⢀⠤⠒⠒⢄⠀⠀⠀⢀⠤⠘⠦⣸⠀⠀⠀ ⡼⠀⠀⠇⢸⠀⠀⠀⠀⠀⢀⠎⠀⠐⡏⠉⣉⠉⠉⢣⠀⠠⠓⠉⡉⠉⠙⡟⠀⠀ ⢇⣠⡆⠀⢸⠀⠀⠀⠀⠀⡌⠀⠀⠀⢃⡀⠀⠀⢀⠎⠀⠀⠱⡀⠀⠀⠠⡇⠀⠀ ⢸⠁⢣⠀⠸⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠘⠖⠈⠁⠈⠆⠀ ⢠⠀⡀⠁⢀⠧⣤⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⡆ ⠈⡆⢇⠀⢎⠀⠌⢄⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢹ ⠀⡇⠈⠢⠈⠢⢤⠀⠈⠐⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢸ ⠀⠱⡀⠀⢄⠀⠀⢆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡜ ⠀⠀⠈⠳⡈⠒⠤⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠁ ⠀⠀⠀⠀⠈⠂⠤⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠲⡶⠥⣈⣩⠭⠃⠀⠀⢀⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢁⣢⣄⠀⠀⠀⠀⠈⠒⠒⠊⠀⠀⡠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢑⡄⠀⠀⠀⠀⢀⠔⠲⢍⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠉⠒⠒⠀⡀⡜⠈⠀⠀⠈⠢⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠊⠐⢄⡀⠘⠅⠂⠤⠤⠁⠡⠜⡄⠀⢀⠞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣌⠔⠒⠢⡀⠉⢢⠈⢆⠀⠀⠀⠀⠀⠘⡠⢻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡄⠀⠑⠌⠆⠀⠀⠀⠀⠀⠇⢸⠸⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣤⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⣠⡾⠿⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢠⡾⠋⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠛⠙⠻⣧⡀⠀⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⢨⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣿⣀⣀⣀⣀⣀⣰⣶⣆⠀⢀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⣿⣿⣷⣶⣿⣿⣇⣹⣏⠉⠉⠉⠉⠙⠛⢻⣶⡾⠏⠀⠀⢸⣧⣤⣤⣤⣤⣤⣼⣿⣿⡀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⡿⠛⠉⢉⣹⡿⠟⠛⠋⠉⠛⠛⠷⣦⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⢻⣅⠀⠀⠀⠀⠈⠉⠉⠛⣷⡿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡏⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣶⠶⠶⠿⠿⠷⠶⠾⢿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⡃⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⡶⠶⠦⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⢿⣿⣇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠈⠙⢿⣿⣷⡀ ⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠁⢀⣤⣶⡟⠛⠛⠃⠀⠀⢹⣿⣧ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠉⣩⡅⠀⠀⠀⠀⢀⣭⡉⠉⠛⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⠟⠉⠉⠻⡆⠀⠀⠀⠀⢈⣿⣿ ⠀⢹⣿⡇⠀⠀⠀⢀⣴⡾⣻⣇⠀⠀⠀⣼⠟⣿⡀⠀⠀⠀⣾⢿⡇⠀⠀⠀⠀⣴⡌⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏ ⠀⢸⣿⣷⡾⠀⢠⡾⠁⣰⡟⣿⠀⠀⣸⡏⠀⠸⣇⠀⢀⣾⠃⠈⣿⠀⠀⠀⣼⢿⣧⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁ ⠀⢀⣿⣿⠃⢠⣿⡇⢀⣿⠀⢹⣇⢀⡿⠀⠀⠀⣿⣠⡾⠁⠀⠀⢻⡆⢀⣾⠋⠀⣿⠀⠀⠀⢀⣼⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⠀⣀⣀⣤⣶⣿⡿⠋⠀⠀ ⠀⢸⣿⣿⠀⢸⡏⢿⣼⡏⠀⠀⠹⣾⡇⠀⠀⠀⠸⠟⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⣿⠀⠀⣰⠿⢻⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀ ⠀⠈⣿⣿⡀⠀⢻⣌⣻⡇⢀⣀⣀⣬⣤⣴⡶⠶⠶⠶⠶⠶⢶⣤⣬⣁⠀⠀⠀⠀⣿⣤⠞⠁⠀⢸⡇⠸⡇⠀⠀⡆⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣿⣷⣄⠀⠉⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢦⣄⡉⠁⠀⠀⠀⢸⡇⣸⡇⠀⢸⡇⠀⣀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢿⣶⣶⣦⣴⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣤⣿⡿⠋⠀⢀⣾⣷⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣶⣦⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠉⢠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⡙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠛⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠻⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠟⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⡉⠓⡆⢰⠦⠤⠤⢤⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠧⠤⣷⣶⣧⣾⡀⠰⠆⠀⡇⠀⠀⠀⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠔⠊⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⢸⠀⣀⡀⠤⠤⡤⢤⣄⣀⣀⠈⠛⢛⠋⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⣘⡀⢸⠀⠀⢈⣉⣉⣉⣣⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠉⠙⢍⡑⠲⢤⣀⣀⡤⠏⢀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢀⣴⣿⣿⣶⣤⣤⡤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⣠⠒⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⢀⠔⠁⠉⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢆⠀⠀ ⠁⣠⠀⠀⢣⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⡠⢊⡭⠙⠛⠓⠤ ⡷⠃⠀⠀⠀⠱⢼⡦⢄⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⢀⡤⡪⠚⠁⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⣀⠤⣀⣁⡀⠉⠒⠚⠋⠉⠉⠉⠉⠽⠓⣊⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠈⠉⠙⠛⠓⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀ ⠀⠀⡰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡄⠀⠀⠀⠀⠉⠳⣄⠀ ⠀⣾⣡⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁⢳⠀⠀⠀⠀⠀⠀⢈⣧ ⢰⡟⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⢳ ⢸⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸ ⡆⠁⠀⠀⠀⠀⠀⡷⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣸ ⢧⠀⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠳⣄⠀⠀⢀⡇ ⠘⣆⠀⠀⠀⣠⠒⠉⠑⠒⠲⠔⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠉⣧ ⠀⠈⢣⡀⠀⠹⡀⠀⠀⠀⠀⠀⠊⢀⠤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇ ⠀⠀⠀⢙⡶⠖⠚⠓⢦⠀⠀⠀⢰⡏⠉⠉⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀ ⠀⠀⠀⠘⣅⣀⣀⣠⣼⠃⠀⠀⠘⢦⠤⠤⠤⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠈⢲⡖⣒⠅⠀⠀⠀⠀⠀⠩⣒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⢰⡎⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⠀⠀⠀⠀⢀⡴⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠈⠙⠤⢤⣶⣖⣁⣀⣀⡸⠟⠿⢦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠂⠉⠉⠉⠉⠑⠒⠠⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠊⢁⣀⣀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⢸⣾⡟⠁⠉⠐⢄⠀⠀⠀⠉⠉⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⣰⣿⣏⣄⣒⡒⠢⡀⢣⠀⠀⢀⠔⠊⠉⠙⠲⢝⠢⣄⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⣴⣿⠏⡏⠀⠀⠈⠱⠇⢸⣀⡠⠁⣠⣒⠒⠢⡀⠈⢂⣿⣷⣦⡀⠀⡇ ⠀⠀⢠⢮⣿⠇⠀⢯⠉⠉⠓⣢⠟⠁⠀⠇⢰⠁⠀⠈⠙⢾⡄⢸⣿⣿⣿⣿⣦⢱ ⠀⢠⣻⣿⠃⠘⢄⠀⠑⠒⢺⠁⠀⠀⠘⡀⠸⡉⠉⠐⠢⡼⠀⢸⣿⣿⣿⣿⣿⡊ ⠀⣿⣿⡟⠀⠀⠈⠑⠂⠀⠒⢣⠀⠀⠀⢡⠀⠙⠂⠀⠊⠀⣠⢻⣹⣿⣿⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠑⠦⢀⡀⠠⠒⠁⡘⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣀⣈⠒⣄⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇ ⠀⠘⢿⣿⣿⣄⠀⠀⠀⠀⢠⠺⠤⠤⡶⠃⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⠙⠻⠿⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⢀⣠⠄⡖⠂⠀⠀⠀⠀⠀⠻⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⡠⠒⠁⠘⡄⠐⠤⣀⡀⠀⣀⠠⠊⢀⣾⣝⡫⡉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⢀⠎⠀⠀⠀⠀⠈⣢⣄⣀⣈⣁⣀⡠⠔⠋⠀⠙⣿⣮⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⣉⡉⠑⠢⡤⠊⠁⠀⠉⠓⢦⡤⠔⠒⠉⠉⠙⠲⣾⣿⣷⢣⠀⠀⠀⠀⠀⠀⠀ ⡙⠀⠈⠑⢲⣁⡀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡄⠑⡌⣆⡈⠙⠄⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠢⣀⢘⣄⠏⠀⠈⢱⠆⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⠀⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⠶⠦⠤⣄⡈⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⣀⡇ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠖⠋⠉⠑⠒⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⣀⡤⠤⢤⣘⢦⡙⠢⠤⢤⡤⠴⠋⡇⠀⠀⠀⠐⠶⠀⠀⠀⢸⠀⠀ ⠀⡼⢁⣴⣶⣶⣌⠑⠉⠑⢠⠞⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀ ⢸⠁⣿⣿⣿⣿⣷⠷⣄⠀⣏⣀⡴⠊⠀⠀⠙⠦⢄⣀⣀⣀⡤⠚⠁⠀⠀ ⠸⡄⣿⣿⣿⣿⣿⣿⡏⢳⣄⣀⠀⠀⠀⠀⠑⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀ ⠀⢳⡸⡿⣿⣿⣿⣿⣿⣿⣤⣿⣩⣿⣩⣷⣶⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣝⢿⢻⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣦⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠙⢦⣿⠛⣿⣿⣿⣷⣦⠀⠙⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣼⡿⠛⡿⣇⠀⢹⣿⣿⡿⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢛⣒⢛⣋⡩⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢻⣿⠀⠀⠀⠀⣸⡿⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣀⣀⣀⣀⣿⡇⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⣠⣾⡿⠟⠛⠛⠻⢿⣷⣄⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀ ⣿⣿⠿⠿⠿⠿⠿⠶⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⠶⠾⠿⠿⠿⠿⢿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⣿⣿⣿⣿⣶⣾⣿ ⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠈⢻⣿⣷⣶⣶⣾⣿⣿⠋⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⣿⡇⠈⠉⠉⠁⢸⣿⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡇⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠄ ⠀⠙⢿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠉⢻⣿⣿⣿⡿⡙⢿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣴⣀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⠛⠻⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢠⢒⠉⠓⢦⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠔⠒⡤⡦⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⣿⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠐⠇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠍⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠠⠁⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⣿⣿⣿⠱⣴⣶⣶⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⠀⠀⠇⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠗⣿⣿⠀⢀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠧⠂⠐⠀⠀⢹⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⡔⠀⠀⠀⠀⢿⣿⣿⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠇⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠁⠀⠀⠀⢌⠈⠙⠿⣥⣒⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠀⡢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠴⡀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠡⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠐⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⠘⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣤⣠⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⡐⠀⠀⢀⠛⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⣤⡀⠀⠀⢀⠀⢉⠢⠄⠀⠤⡔⠏⠉⠙⢃⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⢠⡄⠀⠈⢿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢣⠸⠵⡶⢄⠇⠀⠀⠈⠄⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢺⠃⠀⢀⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣕⠦⣶⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⢂⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⣸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣮⡟⡄⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⠀⠛⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⡀⠀⣰⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠈⠂⠬⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⣰⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠢⡀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠉⢁⠌⠀⠀⠀⠀⠆⢠⠀⢠⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠘⢠⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠄⣤⡀⠁⠠⡀⠀⠀⢹⣆⠀⢀⠀⣳⣰⣟⠤⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠄⠀⠀⠛⠋⢰⡶⡸⠀⠤⠼⢿⡐⠲⠽⠛⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⡐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣦⣌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠙⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠸⣧⠀⠀⠀⠀⠻⠃⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⠟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠙⠿⣦⣀⣀⣠⣴⡾⠋⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⠁⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⢿⠇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠷⢶⣶⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⣿⡛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣛⣉⣀⡀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣉⣉⣉⡙⠛⠛⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣍⣁⡀⢀⣀⣈⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⣸⡇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⠻⠿⠿⠿⠶⠶⠶⠶⠶⢿⣷⡀⠀⠀⠀⠀⠀⣰⣷⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣴⡾⠟⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣠⡾⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⠙⠻⢷⣦⣄⣀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣶⣦⣀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣏⠀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣈⠙⠻⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⠋⣁⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣶⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣤⣶⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁ ⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢿⠃⠀⢀⣼⣿⣿⣿⣿⣧⡀⠀⠸⡏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀ ⠀⠀⠊⠉⠁⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⠿⠿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠈⠉⠑⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠷⣶⣾⣿⣿⣿⠿⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡥⠢⢄⡀⠉⠉⠁⢀⣀⠤⡀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣀⡀⣀⠉⡇⢠⠋⠉⠀⠀⠘⡄⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢛⡻⠿⠚⠢⣤⠭⠛⠁⠘⣖⠒⢚⠛⣤⢃⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⠋⠀⠀⠀⠀⠁⠢⠤⠄⠤⠋⠉⠉⠉⠉⠙⠻⣿⣿⡿⠷⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣀⠤⣴⠖⠲⡦⠤⢄⡀⠀⠀⠀⠀⠀⠈⣏⠴⢖⠂⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣴⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠸⣧⠀⡔⡹⡄⢰⠹⡀⡰⢹⠀⡰⡏⠑⢄⠀⠀⠀⠀⢸⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⢸⢣⡇⠱⠇⣀⣛⣁⠘⠖⠁⡇⡠⢺⢣⠀⠀⠀⣸⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⠋⠉⠻⣿⣿⣿⣿⡄⠀⠀⠹⢦⣙⣋⣉⠉⠁⠀⠀⠉⠑⠢⢭⣀⣸⡜⢠⣧⣴⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⢈⣩⣿⣦⠀⠀⠀⠀⠀⠀⣲⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⡿⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠉⠩⡉⠛⠛⠛⠶⠶⢦⣤⣀⠀ ⠀⠀⠙⠛⠛⠁⠀⠀⢸⣿⣿⣿⣿⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⡏⠉⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣟⠀⠠⡠⠀⠀⣰⠠⢀⣀⠀⠀⠀⠀⠙⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣄⠀⠣⣀⣔⠁⠀⠀⣿⠛⠷⠶⠶⠾⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣼⡅⠈⠉⠂⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣴⣶⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠉⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⢫⠖⢁⠔⠂⢀⡻⠋⠛⠻⠟⠻⠻⣷⣦⣤⣀⣀⣀⣀⣤⡶⠛⠉⠉⠙⠉⠉⢁⡈⠉⢝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⣇⣠⡣⠔⢚⡡⠀⢀⠀⠀⠀⠀⠀⠈⠻⢿⡏⠉⠀⠀⠉⠉⠉⠉⠙⠓⢦⡀⠀⠈⢢⠀⠳⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡠⠒⢉⠔⠊⠁⠀⣠⠶⠒⠶⣄⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣇⣀⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠶⢾⣤⡤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣠⣴⠶⠛⣛⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡿⣉⣤⣶⣿⣿⣿⣿⣿⣿⡿⠖⣒⣶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⠞⠉⠀⠀⠛⠙⠓⢤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢦⣀⠀⠀⠀⠀ ⢀⡿⢻⣿⣿⣭⣥⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⠈⢧⡀⠀⠀ ⠈⠻⣮⣭⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⡀⣠⡾⠿⠶⢾⣠⡄⠀⠉⢹⣆⡀ ⣠⠼⠀⠈⡝⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⢀⣀⣀⣘⡖⠀⠀⠀⠴⣹ ⢯⡂⠀⠀⡏⠉⠙⠉⠉⠹⠀⠀⡠⠀⠀⠀⠀⢾⡉⠉⠉⠁⠀⠀⣯⡁⠀⢀⠖⠁ ⠀⠙⣄⠀⠑⢄⣀⣀⡠⠂⠀⠀⠓⠀⠀⡀⠀⠋⠷⣤⣀⣀⡠⠞⠂⠀⣠⠊⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠋⠘⠀⠁⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢲⠶⡦⠤⠤⠶⡖⢲⠛⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⢸⣤⣇⠀⠀⢀⣷⣾⠐⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⠚⠛⠋⠉⠉⠉⠛⠛⠳⢇⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣁⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠉⠑⠢⢄⣀⡠⠔⠒⠒⠒⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⣇⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬛⬛🟦⬛⬜⬜⬛🟦⬛⬛⬜⬜ ⬜⬛🟦⬛🟦🟦⬛⬛🟦🟦⬛🟦⬛⬜ ⬜⬛🟦🟦⬛🟦🟦🟦🟦⬛🟦🟦⬛⬜ ⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛⬜ ⬛🟦🟦🟦🏻🏻🏻🏻🏻🏻🟦🟦🟦⬛ ⬜⬛🟦🟦🏻🟦🟦🟦🟦🏻🟦🟦⬛⬜ ⬜⬜⬛🟦🏻⬛🏻🏻⬛🏻🟦⬛⬜⬜ ⬜⬜⬛⬛🏻⬛🏻🏻⬛🏻⬛⬛⬜⬜ ⬜⬛⬜⬜⬛🏻🏻🟩🏻⬛⬜⬜⬛⬜ ⬛⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬛ ⬛⬜⬜⬛⬜⬜🟦🟦⬜⬜⬛⬜⬜⬛ ⬛🟦🟦⬛⬜⬜🟦🟦⬜⬜⬛🟦🟦⬛ ⬛🏻🏻⬛⬜⬜🟦🟦⬜⬜⬛🏻🏻⬛ ⬜⬛⬛⬛⬜⬜🟦🟦⬜⬜⬛⬛⬛⬜ ⬜⬜⬜⬛⬜⬜⬛🟫⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜🟫⬛🟫🟫⬜⬛⬜⬜⬜ ⬜⬜⬜⬛🟫🟫⬛🟫🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬛🟫🟫⬛🟫🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬛🟫🟫⬛🟫🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬛🟫🟫⬛🟫⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥⬛⬜ ⬜⬜⬜⬛⬛⬛⬛🟥🟥🟥🟥⬛ ⬜⬜⬛🟫🟫🟫🟫🟫🟫🟥🟥⬛ ⬜⬛🟫🟫🟫🟫🟫🟫🟫🟫🟥⬛ ⬛🟫🟫🟫🟫🏻🏻🏻🏻🟫⬛⬜ ⬛🟫🟫🟫🟫🏻🏻🏻🏻🟫⬛⬜ ⬛🟫🟫🏻⬛🏻🏻⬛🏻🏻⬛⬜ ⬜⬛🏻🏻⬛🏻🏻⬛🏻🏻⬛⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🟩⬛⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🏽⬛⬜ ⬜⬜⬜⬛🏻🏻🏻🏻⬛🏽⬛⬜ ⬜⬜⬛🟧🟧🟥🟥🟧🏻🏽🏻⬛ ⬜⬛🏻🟧🟧⬜⬜🟧🏻🏻🏻⬛ ⬜⬜⬛🟧🟧⬜⬜🟧🏻🏻🏻⬛ ⬜⬜⬛🟧🟧⬜⬜🟧🟧⬛⬛⬜ ⬜⬜⬛🟧🟧⬜⬜🟧🟧⬛⬜⬜ ⬜⬜⬛⬛⬛🟦🟦🟦🟦⬛⬜⬜ ⬜⬛🏿🏿🏿⬛⬛🟦🟦⬛⬜⬜ ⬜⬛🏿🏿🏿⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⡛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠪⣿⣿⣷⣀⢠⠮⠭⠭⠴⣀⣀⡜⠒⢒⠒⠓⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢁⣷⣿⡿⠁⠀⢁⠀⠐⠀⠀⡇⠀⠉⠀⠢⣀⡐⠀⠉⠐⠠⡀⠀⠀ ⠀⠀⠀⢀⠃⣴⣿⣿⡇⠀⠀⠀⠑⠠⠄⠪⠀⠀⠀⢀⡀⠈⠐⠀⢄⠀⠀⠐⡀⠀ ⠀⠀⠀⠘⢰⣿⣿⣿⡇⠀⠀⠀⡠⠄⡀⠈⠀⠈⠉⠀⠀⠉⢐⠒⠊⠀⠀⠀⢱⠀ ⠀⠀⠀⡆⢾⣿⣿⣿⣿⠀⠀⠀⣷⣤⣀⣾⣉⣉⡆⠈⠉⢃⡈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠈⠉⠉⠀⠀⠀⠀⠘⢟⠛⠿⣿⣿⣷⡶⠲⠬⠄⣀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢀⠀⠀⠀⢀⠂ ⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡠⠂⠀ ⠀⠀⡜⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡠⠢⢀⣀⠠⡢⠊⠀⢠⣾ ⢠⠞⣧⡀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⠠⠐⠁⠀⢀⣴⠿⠋ ⠁⠀⣿⡷⠄⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⢀⡀⠠⠒⠈⠀⠀⠀⢀⣴⡟⠁⠀⠀ ⠀⢸⣿⡇⠀⠢⠀⠀⡠⠒⠀⠑⠄⢰⠒⠪⡀⠀⢰⣤⣀⣸⣷⣶⣿⠏⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡂⠍⠲⢶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢾⢄⡄⡅⡄⠠⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⠃⠀⠰⠖⣒⠢⢀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢐⠟⠐⠃⡠⠃⢠⡀⠀⠈⠻⡿⠃⡒⠂⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠘⡘⠒⠠⡄⠘⠀⡅⣰⡀⠀⠀⠳⠁⠁⠀⠇⠀⠀⠀ ⣴⣿⣿⡿⠟⠛⠿⣿⣿⡆⠀⣼⣿⣿⣷⣕⠔⢂⠠⡇⠀⠀⠔⠀⠀⠊⠀⠀⠀⠀ ⢿⡿⠋⠀⠀⠀⠀⢈⣿⣿⢀⣿⣿⣿⣿⣿⣷⣁⣈⣠⡀⠈⠀⠀⡖⠋⢄⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⡀⠊⠀⠀⠀⠀ ⠀⠀⢀⣴⣶⣶⣶⣼⣿⣿⣿⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣶⣀⣠⣷⡆⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⢿⣿⣿⣿⡿⡿⢿⣿⣿⣿⡿⠿⠏⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢊⠀⠀⠉⠋⠉⠥⠬⠭⠛⠛⠓⠚⠛⠛⠇⠓⠀⠠⠀⡘⡄⠀⠀⠈⠠⡀⠀ ⠀⠈⠂⠤⠣⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡒⢂⠀⠒⠄⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠄

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⣿⢩⠖⠈⠐⠒⠒⠒⠴⠫⢍⢢⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⢀⣂⠀⠀⠀⠈⠐⠼⡜⠀⠀⠀⠀ ⠀⠀⣇⠀⡀⡘⠣⠀⠀⠀⣀⣠⠀⠀⢠⠱⡀⠀⠀⠀ ⠀⠀⢈⠦⢦⠮⣀⠀⠀⠀⣀⣁⠢⡕⣸⠀⢱⠀⠀⠀ ⠀⠀⡜⠀⣠⠀⠾⠅⣀⡀⠩⠬⠀⢃⠇⡆⠀⡆⠀⠀ ⠀⢠⠁⢠⠇⠣⢄⠀⢋⠅⠀⣀⠜⠉⠀⢱⠀⢰⠀⠀ ⠀⡜⠀⢸⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠸⡀⠈⡆⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀ ⢠⢀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀ ⢸⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⡆ ⢗⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡺ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⣀⣤⣤⣤⣤⣀⠈⠙⠻⢿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⡿⠋⠀⠀⢀⣾⣿⡿⠿⠿⢿⣿⣷⡀⠀⠀⠙⢿⣿⣷⡄⠀⠀ ⠀⢠⣿⣿⠏⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠹⣿⣿⡄⠀ ⢠⣿⣿⠏⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠹⣿⣿⡄ ⢸⣿⣿⠀⠀⠀⢠⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⢸⡇⠀⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⢸⡇⠀⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇ ⠘⣿⣿⣆⠀⠀⢸⡇⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⠃ ⠀⠘⣿⣿⣆⠀⢸⣧⣠⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⠃⠀ ⠀⠀⠘⢿⣿⣷⣄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣠⣾⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠒⠦⣤⠤⠒⠇⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⢀⣰⣄⡀⠑⠢⣀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀ ⢀⡴⠛⠛⠛⢻⣿⣿⡇⠀⢰⣏⠀⠀⠉⠢⢀⠀⠙⠲⠤⢤⣀⣀⠱⠤⣀⠀⠀⠀ ⢸⠀⢋⢽⠀⠈⣿⣿⡇⠀⢹⠉⠒⠦⣄⡀⢀⡏⠀⠀⢲⠤⠤⠴⠒⢷⠀⡷⠀⠀ ⢻⠀⠈⢈⣦⠴⠛⠉⠀⠈⠉⠉⠉⠑⠢⢾⣋⣀⢀⣀⡿⣆⡀⠀⠀⠈⣗⡁⠀⠀ ⠸⢄⡔⠋⠀⠀⠀⣀⢠⡤⠤⠀⣀⠀⠀⠘⠀⠲⡄⠀⣳⠤⣌⣉⠒⣶⠋⠉⠳⡄ ⠀⢸⠔⠀⣠⠔⠉⠀⢠⠛⡄⠀⠀⠈⠓⢄⠀⠀⢸⠉⠁⠙⠋⠈⠉⠓⢎⠉⠀⢹ ⢰⠃⡠⢾⠉⡇⠀⠀⡸⠀⠹⡀⠀⠀⠀⡞⡇⠒⠒⢲⡒⠒⠒⢤⡀⠀⠀⢣⢀⡜ ⡏⠀⡇⡞⠀⢣⠀⢀⠇⠀⠀⢇⠀⢀⠜⠀⢱⠀⢠⠏⡇⠀⠀⡼⡏⢆⠀⣸⠏⠀ ⢣⠀⠑⢧⣀⡈⣧⣎⠀⠀⢀⣸⣴⣋⠀⠀⢸⡠⠋⠀⢀⢀⠜⠀⡇⠈⡆⢹⠀⠀ ⠈⠓⠦⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠤⢼⡊⠀⠀⡇⣠⠇⠈⡇⠀ ⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠐⠤⣟⣁⠇⢰⠃⠀ ⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠶⠤⠤⠴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠲⠶⠤⣤⣤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀