⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣉⣉⡉⠙⠲⠤⣀⣀⣀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡒⠚⠳⣤⢿⡿⣍⣀⣀⣀⣀⣀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠥⢵⣖⠒⠖⢷⠀⠀⠀⠀⠈⠁⠁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠒⠲⠦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠴⠒⠒⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⣀⣀⣀⡀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⣸⢻⠒⡶⡶⢶⢶⢶⢲⡛⡇⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢀⣀⣀⣀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⠀⢀⡤⣶⠋⡽⢩⠏⡽⢋⡷⢤⡀⠀⠹⡄⠀⠀⠀⠀⠀⡇⡾⢸⠃⠇⣻⢸⢸⡈⡇⢳⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠶⡛⢯⠙⣌⢫⠙⢶⢤⡀⠀⠙⢄⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⣠⡟⣰⠃⣸⢡⠏⣰⠃⡞⢀⡏⢳⡀⠀⢹⠀⠀⠀⠀⢰⣧⡁⣼⣇⣠⣿⣄⣼⢧⣈⣼⡄⠀⠀⠀⠀⡞⠀⠀⣼⠹⡄⢳⡈⣇⠸⡌⢧⠘⣆⢻⣆⠀⠈⢳⠀⠀⠀ ⠀⠀⡸⠧⣤⡼⠟⢡⠇⠰⢃⡎⢠⠃⡼⠁⡞⢠⠟⡇⠀⠘⠧⣀⣀⠀⣸⢸⢻⠀⣟⡁⣿⢸⢸⠈⡏⡇⣧⡀⢀⣀⠴⠃⠀⢸⠛⡆⢳⡀⢳⠘⣆⠹⡌⠇⠘⣆⠻⣷⣤⠼⢷⠀⠀ ⠀⢠⠇⠀⣸⡿⣤⢟⣇⣀⣼⠀⠟⣸⠃⣸⠃⡜⢀⡿⣀⠀⠀⠀⠘⠛⣿⣸⢿⠀⣧⠄⣿⢸⢸⡄⡇⡿⢻⠘⠃⠀⠀⠀⣠⢼⡄⢻⡀⢧⠘⣇⠸⠀⣿⣀⣠⡟⢧⢜⢧⠀⠘⡄⠀ ⠀⡞⠀⢰⢧⢇⡇⡼⡸⠁⡟⣳⠖⣷⡀⢃⡼⠁⡼⠀⡟⢹⠟⢲⠶⡶⣇⠙⣾⡐⢯⣆⠻⣼⡜⢧⣧⠻⣼⠶⡖⣖⠻⡏⢹⡀⢳⠀⢳⣘⢂⡾⡗⢾⢹⡈⢣⢳⠸⡜⡎⣇⠀⢻⠀ ⣴⠃⠀⡟⡞⣸⢰⢣⠇⣸⢡⠇⡼⢠⠏⣹⠛⣾⣥⢼⡁⡼⢀⡞⢸⢡⣿⢛⡟⢹⢋⠏⡿⢹⢹⠇⡏⡟⢿⡆⡇⢹⡀⢳⣀⡷⣬⣷⠋⣏⠙⡄⢳⠘⡄⢣⠘⡎⡇⢣⢱⣹⡀⠈⣧ ⣿⠀⢸⢷⠃⡇⡞⣸⢠⠇⡼⢠⠃⡞⢀⡇⢰⠃⡞⢀⡟⢳⠋⡟⢻⢺⢸⢰⢹⢸⠈⠆⡗⢨⠸⠄⡇⡎⡽⡗⣟⠻⡏⣟⠹⡄⢱⡈⡇⠘⡄⢹⡈⡇⢳⠘⡇⢣⢹⢸⡈⡇⡇⠀⢻ ⣧⣀⣼⣌⣸⣏⢁⣇⠈⢀⣇⠋⣰⣇⠘⢀⣞⠐⠁⣼⡀⠋⣰⣇⢋⣼⣌⡼⣌⣸⣎⣁⣿⣜⣸⣧⣁⢷⣁⣷⡈⣀⣧⡘⢀⣷⡈⠃⣹⡄⠛⢀⣇⠙⣸⣄⠉⣸⡌⣸⣧⣁⣷⡀⢸ ⡇⠀⡍⢸⢹⢹⢏⡏⡿⠙⡏⣟⠹⡏⢹⠋⣏⠹⠏⢹⠉⡏⢹⡉⡏⢸⢸⠀⡏⡏⢸⠃⡟⢸⠁⢇⢯⠀⣯⡏⢹⠁⡇⢹⢋⡏⠹⡏⢹⠈⡟⢹⡏⢻⠹⡏⢻⠙⡋⡇⡇⣧⢸⠀⢰ ⡇⠀⡇⢺⢸⢼⢸⠀⡇⠈⡇⡖⢀⡷⢤⠴⢿⠢⡴⢺⠳⡤⢾⠷⡤⢾⣾⠀⣇⡧⢸⠁⡏⢸⠀⣼⡺⠀⡟⡗⢦⠖⡷⢤⠞⡟⢦⡴⢿⠦⡤⢾⡄⠸⢀⡇⢸⠀⡇⢇⡧⢹⠘⠀⢨ ⡇⠀⡇⡇⢺⢼⢸⠀⡇⢠⡇⢘⡼⡇⠸⡆⢸⡀⡇⢸⡄⠁⢸⡆⠀⣼⣏⠇⣧⠹⢰⡇⡗⣸⡄⢇⣧⠰⣿⢧⠈⢀⣇⠀⢠⡇⢸⠀⡏⢠⡇⢸⢳⡈⢰⡇⠸⠀⡇⡬⡇⢸⢈⠀⠠ ⡇⠀⡇⢣⢹⢸⢸⡆⠃⣼⡏⢻⠀⢻⠀⡇⠈⡇⣇⠈⡟⠒⠛⠛⠛⠛⢻⡺⡉⢳⠋⡙⣟⢻⢙⡏⢨⢟⡟⠀⠛⠛⠛⠒⢻⠇⢸⢸⠃⢰⠁⣾⠀⡿⢹⣇⠸⢀⡇⡇⡇⢸⠠⠀⢰ ⡇⠀⣇⢸⢸⠈⢿⡗⢶⠃⢷⠘⡄⠸⡆⢹⠀⢷⠘⢠⡏⠀⢀⡤⡴⢢⠶⢷⣅⣈⣇⣃⣿⣋⣸⣄⣣⡾⢔⡦⢤⢤⡀⠀⠸⡆⠘⣼⠀⡾⢀⡇⢠⠇⣼⠈⢷⢾⣇⠁⡧⠀⢘⠀⢨ ⣟⠀⢹⣈⣾⡶⡏⢧⠸⡄⠸⡄⢳⠀⣧⠘⡇⢸⠦⠞⠀⡴⡏⢧⠹⡄⢳⡈⡏⠳⣼⡁⡏⢨⣧⠞⣹⢁⡞⢀⡞⡸⢹⣆⠀⠳⠴⡇⢠⠇⣸⠀⡼⢠⡇⢀⡏⣸⠙⣶⣧⡀⡎⠀⢘ ⣿⡤⢾⡟⡇⡇⢧⠘⡆⢳⠀⣷⠈⣇⢸⣆⣀⡾⠀⠀⠀⡇⠸⡌⣇⠱⢀⡷⣬⣾⠙⣷⠵⣾⠋⡷⣥⢾⡀⠚⣰⢡⠏⢸⠀⠀⠀⢣⣀⣰⡏⢰⠃⣼⠀⡼⢠⠇⡼⢸⢡⡏⡟⠤⣾ ⠻⡇⠈⣇⢳⢹⡈⣇⢳⠈⢧⠘⣆⠘⠆⣏⠁⠀⠀⠀⠀⠹⣤⠤⡾⠹⡉⣇⢱⢸⡀⢸⣚⡇⢠⠇⡇⡼⢩⠏⡷⢤⣤⠏⠀⠀⠀⠀⠈⢹⠠⠃⢠⡇⢰⠃⡼⢰⠃⡞⡼⢸⠃⢠⠿ ⠀⣇⠀⢹⡸⡆⢧⠸⡌⣇⠘⡆⢻⡦⠤⠏⠀⠀⠀⠀⠀⠀⠘⢦⡘⡄⢳⣘⣸⣄⣣⡟⣿⢻⣜⣠⣧⢃⡞⢠⢃⡴⠃⠀⠀⠀⠀⠀⠀⠸⠤⠴⡿⢠⠇⣸⢁⡏⣸⢡⡇⡟⠀⣸⠀ ⠀⢸⡀⠘⣇⢣⠘⡆⢳⡘⣆⠹⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡋⠉⡏⢹⡆⠡⡇⢿⢸⠈⢰⠏⢹⠉⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡞⢠⠇⡼⢠⠇⣸⢸⠁⢀⡏⠀ ⠀⠀⣧⠀⢸⡜⡆⢹⡄⢧⢹⣆⢁⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣸⣃⣀⣇⡀⢧⣿⡜⢀⣸⣀⣘⡆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣰⡟⡸⢁⡞⢠⢇⡏⠀⣸⠀⠀ ⠀⠀⢸⡄⠀⢳⢸⡄⢳⠈⡇⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣭⣧⣬⠉⠉⡟⠉⠉⢡⣽⣭⣯⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⢰⠁⣼⠀⡏⣼⠀⢠⡇⠀⠀ ⠀⠀⠀⢻⡀⠘⣆⢣⠘⣦⠘⢸⡆⠀⠀⠀⠀⣤⡤⣤⣤⣤⢴⣮⣭⠭⢼⢸⡦⣭⡽⣦⣿⣴⣯⣭⣴⣋⡯⣭⣭⣽⡦⣤⢤⡤⢤⣤⠀⠀⠀⠀⠀⡇⠂⣰⠇⡼⢱⠃⠀⡞⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠘⣎⢇⠸⡟⠊⠀⠀⠀⣀⣼⣉⣁⣩⠗⡏⡾⢸⣉⣙⣺⣼⣉⠓⠯⣉⣁⣉⣈⣁⣙⣦⣋⣁⣙⡆⣧⢸⢸⣍⣈⣉⣇⣀⠀⠀⠀⠙⢛⠏⣰⢣⠏⠀⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠘⣎⠃⢻⠀⠀⠀⠸⣁⣸⣀⣀⣸⢈⡇⡇⢸⣁⣀⣀⣀⣈⣙⣒⣦⣍⡙⠲⢤⣀⣀⣀⣀⣨⡇⡽⢨⠰⣇⣀⣈⣇⣨⠇⠀⠀⠀⡼⠀⢡⠏⠀⡼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⡀⠘⣦⡼⠀⠀⠀⠀⠀⠹⣤⠤⠼⡇⡆⢹⠘⣦⠤⠤⠤⠤⠤⠤⠤⠤⠭⢳⠦⣌⣙⠲⢤⣼⠃⡇⣼⢸⠥⡤⣴⠏⠁⠀⠀⠀⠀⠧⣴⠋⢀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⢣⠀⠀⠀⠀⠀⠀⠙⢿⣻⠽⠿⠽⠯⠯⠽⠭⠯⠽⠭⣿⠿⠿⠿⢿⣿⣋⡟⠋⠉⠙⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢿⣋⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣶⣦⣤⣤⣴⡶⠾⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀