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