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