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