⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢰⢋⢹⡀⢀⡼⠰⡀⠀⡞⡀⣷⠀⠀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⢱⡄⢸⣿⢿⠀⡋⢀⠀⡇⠀⣿⣿⡇⠀⣞⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣯⠀⠘⣿⣻⣀⣙⣼⣴⡁⠀⣿⣿⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠶⢾⣿⣿⢋⣽⣿⣹⣛⠟⣿⣿⠻⠶⣿⣿⣮⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡻⢧⣿⣿⣾⠺⠛⠿⠛⠁⢸⣿⣿⠁⠸⠿⠟⣴⠀⣿⣷⡿⠉⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢧⣀⣹⠿⣿⠆⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠰⣿⡿⢿⠠⢀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⠈⡅⠘⠂⢎⢢⠜⣐⠀⡘⠹⠛⠟⢃⡀⡀⠀⠀⠄⠌⡀⠤⠒⠁⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣿⣯⣶⣬⠀⠀⠉⢁⠉⢈⠃⠀⠂⠊⠈⠐⠂⠉⢀⣠⣤⣴⣦⣶⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣶⣟⡟⠻⣿⣯⣿⣿⣷⣶⣴⣾⢿⣶⣷⡀⠀⠀⣠⣶⣶⣦⢰⣿⢿⣷⡟⣾⣯⠉⡷⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣷⡿⣿⡂⡀⠈⠉⠳⢯⣿⣽⣫⢿⣯⡞⣽⣿⣇⣊⡿⢶⣛⣿⣾⣻⡮⠗⠋⠉⠉⢠⣿⣟⣾⣻⣿⡄⠀⠀⠀ ⠀⠀⢠⣾⣿⢧⡿⣿⣟⡏⣲⡄⠄⠀⣴⣲⠀⠉⠉⠛⠛⠓⠚⠛⡛⠛⠛⠉⠉⠙⠄⠀⠀⠀⠄⡴⢙⢙⣿⣭⢿⣽⣿⡆⠀⠀ ⠀⢠⣏⠻⢿⣿⣽⣿⣏⣷⣙⡉⡣⡀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠙⠛⠁⠀⣀⠠⠤⠄⠖⢀⣾⠆⢀⣘⣨⣿⣯⣿⡾⠃⢹⡄⠀ ⠀⢸⣟⠄⠀⣠⣿⣷⣹⣿⡻⢷⣤⣁⠭⠒⠉⠁⢿⡿⠂⢄⡀⠀⢀⡰⠆⢣⣿⡧⠀⠀⠂⣁⣴⢿⣿⣭⢿⣽⡄⠀⠀⣼⡇⠀ ⠀⢀⣿⣦⠀⡛⢿⡷⠿⣝⡃⣠⣿⣻⣿⣷⣦⣄⡀⣄⠀⣀⡉⢒⡁⠀⠀⢈⠉⣤⣶⣞⣻⣯⡀⠙⡿⢾⠯⡿⠙⠀⣡⣿⠀⠀ ⠀⠈⣿⣾⣷⣦⡄⢈⠁⠘⠃⣿⣿⣯⢷⣿⠧⠉⠉⠓⢲⣶⡟⣿⣶⡓⠒⠚⠉⣿⣿⣽⣳⣿⡇⠻⠃⠀⠀⠀⠔⣱⡟⣽⠆⠀ ⠀⣠⣾⣽⡿⣿⣿⣆⠀⢂⠀⠉⠙⠿⠟⠃⠀⢌⣤⣄⢻⣿⣻⢿⣽⡇⢾⡿⠂⠈⠙⠓⠛⠋⠀⠀⠀⠀⠀⣴⣿⣿⠾⣿⡄⠀ ⢠⠇⣿⣞⣿⣝⣻⣿⣷⡤⣅⢤⣀⡤⣀⠄⣄⠈⠈⠁⠀⠉⠛⠛⠋⠀⠀⠀⢈⡠⢀⣀⣀⡠⢀⠀⠀⣠⣾⠿⠛⢾⣫⣿⠹⠀ ⠐⡎⣿⣿⣾⣳⣯⣞⠿⣿⡻⢿⣿⣟⡿⣿⣶⣌⡐⠢⢄⠀⠀⠀⠀⢀⡤⣶⡿⢟⡻⢛⡟⣿⣷⣾⣵⢾⡻⠿⣐⣟⣿⡟⢰⠁ ⠀⢻⡌⢻⣿⣷⣟⡾⣿⣢⣿⣷⣬⠙⡙⠳⠟⡿⢿⣿⣿⣾⣖⢢⢴⣺⣿⠿⠾⠶⠛⠯⣛⡉⠈⠻⠍⢞⣣⢞⣵⣿⡿⢡⡟⠀ ⠀⠀⠹⣕⣎⠻⣿⣿⣷⣳⣎⡟⣥⢛⣼⡷⠌⣴⣦⠀⠘⠿⣿⣿⣿⠋⠤⡀⢤⠀⢴⠊⣛⢁⡤⣖⢾⣭⣾⣿⡿⢋⣔⠏⠀⠀ ⠀⠀⠀⠀⠙⠶⣄⡙⠻⢿⣿⣾⣽⣳⣞⡽⣶⣡⣍⡊⡔⣄⢮⡙⡥⡠⢔⡰⣂⢬⡤⣞⣮⣭⣷⣾⡿⠿⢋⢁⡰⠝⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠱⢦⣈⣙⠛⠿⠿⣿⣷⣷⣾⣽⣧⣿⣶⣽⣷⣽⣽⣶⣿⣾⣿⠿⠿⠟⠋⡁⣔⠬⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠙⠳⠶⣠⣀⣉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⢉⣀⣠⡤⠶⠙⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠓⠉⠈⠁⠋⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀