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