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