⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠓⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣖⣿⡛⣻⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣟⡿⢶⣤⣤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⣩⡷⡟⠉⢀⡿⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⡀⠀⠀⠈⠲⣝⢷⣺⡿⣿⣶⣌⡉⠲⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠊⢁⣴⣿⡟⠋⠙⣻⠏⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⢷⡽⣷⣼⣹⣿⣿⣶⣄⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢀⡴⠛⠛⢟⣥⣴⡾⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠈⢻⣎⢿⣽⢫⣿⣿⡿⠓⠀⠱⣄⠀⠀⠀ ⠀⠀⡔⠁⡴⢋⣀⣀⣴⠋⠉⡽⠁⠀⠀⢀⡞⠃⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢆⠀⠈⣿⣇⠀⠀⠀⢻⣿⣿⣯⣿⠋⠀⠀⠀⠀⡜⣆⠀⠀ ⠀⠀⠀⠈⣾⣿⣿⣿⡿⣶⣾⠃⠀⠀⠀⡞⡤⠀⠀⠀⢀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠘⣧⠀⢸⣿⣆⠀⠀⠘⣿⣿⣯⣿⣦⣶⣾⣿⣿⣿⡜⡀⠀ ⠀⡇⠀⣸⣿⣿⣿⡿⢆⣿⠇⠀⠀⠀⣸⢱⡇⠀⠀⠀⣼⢀⣿⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⢹⣷⡀⣿⣿⠀⠀⠀⢻⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣷⠀ ⢠⠁⢸⣿⣿⣿⣿⠃⠈⡏⢠⠄⠀⠀⣿⣼⠀⢠⠀⢰⡟⣼⢻⠀⡇⠀⢀⡇⠀⠀⢸⠀⢰⡆⢿⣧⢹⡄⠈⣿⣷⣿⣿⡆⠀⠀⢸⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⢷⡇ ⠀⠀⢸⣿⣿⣿⣿⠀⠀⡇⢸⠀⠀⠀⣷⣿⠀⣏⠀⣿⣷⠏⢸⡄⣿⠀⢸⣷⠀⠀⢸⡀⢸⣧⢸⢿⣞⣿⡄⢹⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⠀⢇ ⠀⠀⡝⣿⣿⠈⣿⠀⠀⣷⣿⡆⠀⠀⣿⣿⣶⣿⢠⣿⣿⠀⠀⢷⢿⣇⠈⣿⣇⠀⢸⣷⣸⣿⣞⡌⠻⣽⣿⣾⣿⣿⣿⣏⠀⠀⢸⣿⣿⡇⠀⢸⡟⣿⣿⣿⣿⠀⠀ ⠀⠀⢿⢿⣿⠀⠹⡀⠀⣿⣿⣿⠀⠀⢻⣿⣿⣿⣾⣿⣿⣤⣄⣸⣿⣿⣧⣿⣿⣧⣸⣿⣿⣏⣻⣧⣀⣙⣿⣽⣿⣿⣿⣿⠀⠀⣼⣿⣿⡇⠀⣾⠁⣿⣿⣿⡟⠀⠀ ⠀⠀⠾⣞⣿⡄⠀⢳⡀⢻⡟⣿⡆⠀⠈⢿⠛⠿⣿⣿⣿⣔⠒⠒⠌⠃⠙⠛⠛⠻⠿⠷⠘⠃⠠⠘⣲⣤⣀⣈⠉⠻⣿⣿⠀⢰⣿⣿⣿⡇⢠⠏⢰⣿⣏⡿⠁⠀⠁ ⠀⠀⠘⠈⠊⣧⠀⠀⠙⢿⠇⣳⣷⠀⠀⢸⣦⡾⠋⠉⠙⢿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠹⢿⣿⣿⡛⠖⠊⣿⢀⣾⣿⣿⣿⡇⠈⢠⡿⠋⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠹⣿⣧⠀⠘⡇⠀⠀⠠⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⡗⠀⢠⣟⣾⣿⣿⣿⣿⡇⠐⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡟⣿⣷⡀⢳⡀⠀⠀⢿⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣧⠻⣿⣿⠳⠵⠤⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠀⣿⣷⠬⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡿⢰⣿⣿⠀⣿⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⡏⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⡀⠀⢸⡇⣸⣿⣿⣠⣿⣤⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣥⣤⣧⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⣿⡇⠀⣾⣇⣿⣿⣿⠋⠉⠀⣿⡏⠙⠦⣄⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣤⣾⠿⠋⢸⡏⠀⠈⢹⣻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣞⣿⣿⠀⠀⣿⣼⢻⣿⣟⡆⠀⢰⣿⠁⠀⠀⠀⠉⠑⠶⣤⣀⡀⠀⠀⠀⢀⣀⣴⠞⠋⠉⠀⠀⠀⠀⣧⠀⠀⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⢠⠞⣼⣿⢿⠀⢸⣿⠉⢦⢻⣿⢳⡀⢸⡇⠀⠀⠀⠀⢘⣿⣶⣿⣯⣟⣿⣿⣟⣿⣿⣿⣶⣿⠀⠀⠀⠀⠀⣻⠀⣾⣿⣿⠏⠀⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀ ⠀⢀⠏⢸⣿⠋⢸⠀⢸⡇⠀⠈⠳⣙⣮⢷⣾⣀⣀⣀⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⠀⡀⣸⣾⣻⡿⠃⠀⠀⣿⣿⣿⡇⠘⣿⣿⣿⣆⠀⠀ ⠀⡞⢠⣿⠇⠀⢸⠀⢸⡇⠀⠀⠀⢈⠾⢿⡇⠀⠀⠀⠀⢄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⡿⠿⠻⠿⠛⢄⡀⠀⠀⣾⣿⣿⠁⠀⠸⣿⣿⣿⡀⠀ ⢰⣃⢸⡏⠀⠀⠘⡆⢸⡇⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢯⣿⡟⠀⢹⣿⣿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⠇⠀⠀⠀⢻⣿⣿⡇⠀ ⠸⣿⣼⠁⠀⠀⠀⠹⡄⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠉⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⣿⣿⡇⠀ ⠀⢿⣿⠀⠀⠀⠀⠀⠙⢦⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀ ⠀⠈⠹⣆⠀⠀⠀⠀⢠⣴⣼⠓⠂⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⢀⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠙⠓⠦⢬⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⣠⣿⣿⣯⠿⠟⠋⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠲⠤⣾⣿⣷⣀⣀⣀⡀⠀⣀⣀⣸⣿⣿⠷⠤⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠈⣿⡍⠉⠁⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣽⡿⠙⣿⣯⣿⣶⡦⣤⣤⣀⡀⠀⠀⠀⣼⣿⡏⠀⠀⠀⣸⡇⢿⡀⠀⠀⢻⣿⣧⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⣹⠃⠀⣿⣷⡏⠹⣿⣿⡏⠉⠉⢹⣿⡻⣿⣿⣷⠤⢤⣤⣿⣴⣽⣷⡴⠶⠾⣿⣿⣶⣿⡿⢉⡉⡽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣷⣰⠏⠀⢠⣿⡿⠀⢸⣿⡸⠀⠀⠀⣾⠃⡜⣻⠈⠉⠀⢀⡷⢨⢰⡐⠦⣧⠀⠀⠀⣿⢫⠽⣿⡄⢳⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣄⠀⢸⣿⡇⠀⢸⣿⣏⠀⠀⠀⣇⠸⢀⡿⠀⠀⠀⢸⣏⢆⠣⡜⡌⣿⠀⠀⠀⣿⢂⡟⣿⡇⡝⡞⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣤⣄⣼⣿⡏⠀⠀⠠⡇⡘⠄⡟⠀⠀⠀⠐⣷⣿⢢⡹⡐⣿⠀⠀⠀⣽⢊⣼⣿⡧⢹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡉⠉⠉⢹⣷⣼⣽⣷⠀⠀⠀⡇⡘⠄⣿⠀⠀⠀⠈⣿⣿⣦⢳⣩⡿⠀⠀⠀⣾⣹⣾⣿⡜⣡⣾⡏⢹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣶⡀⠀⠀⠠⠒⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠓⠲⠶⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⡀⢂⠁⠀⠀⠀⣀⣿⠢⡀⠀⠀⠐⢶⡶ ⠀⠀⠀⠀⠀⠀⣠⡴⢿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠳⡶⡆⠀⠀⠀⢿⡄⠀⠀⠑⢄⠀⠀⠙ ⠀⠀⠀⠀⢀⡾⠋⢀⡼⠂⢁⣾⠃⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠹⢦⣥⣐⡀⣷⠀⠀⠀⠀⠑⢀⠀ ⠀⠀⠀⣴⠟⢀⡴⠋⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠙⣆⠀⠈⢿⡉⠻⢶⣄⠀⠀⠀⠈⢢ ⠀⢀⡾⠃⠀⠸⣄⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢧⠀⠀⠀⠀⡀⠀⠈⢧⡀⠈⢷⠀⠀⠙⢷⡄⠀⠀⠀ ⢀⡾⠁⠀⠀⢀⣾⡟⢻⠃⠀⡄⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⣠⠃⠀⠀⣤⡀⠀⠈⠛⣧⠀⠀⠀⠸⡄⠀⠀⢳⡀⠘⣇⠀⠀⠀⠻⣆⠀⠀ ⡿⠀⠀⠀⢀⣾⡟⢀⡏⠀⢰⡇⠀⠀⠀⠀⠀⢀⡟⡆⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠛⠢⢄⣀⣿⠙⠲⠤⣄⣸⡆⠀⠀⠀⢱⠀⠀⠀⢧⡀⢻⡄⠀⠀⠀⠹⡆⠀ ⠀⠀⠀⠀⡿⠛⠛⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠃⣧⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠃⢀⣠⣼⠿⠿⠿⠿⠿⣤⣘⣧⠀⠀⠀⠘⡇⠀⠀⠘⡇⠸⣇⠀⠀⠀⠀⢿⣠ ⠀⠀⠀⣸⠃⠀⢀⡟⠀⠀⠀⣧⠀⠀⠀⠀⠀⣼⠀⠘⣧⣟⢦⡀⠸⡄⠀⠀⠀⠀⠀⠀⣿⠶⠊⣠⠾⠋⠁⢀⣀⣀⣀⠀⠀⠈⠻⣼⡄⠀⠀⠀⢻⠀⣿⡶⢿⠀⣿⠀⠀⠀⠀⠉⠀ ⣠⠀⢀⡇⠀⠀⢸⠇⠀⠀⠀⠘⣆⠀⠀⠀⠀⣟⠀⠀⠘⠂⠙⠛⢦⣷⣤⠀⠀⠀⣠⣶⠃⢀⡾⠁⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠈⡇⠀⠀⠀⢸⡀⡿⢹⡄⠀⢹⡆⠀⠀⠀⠀⠀ ⠃⠀⡸⠀⠀⡀⣿⠀⠀⠀⠀⠀⠘⢦⡀⢠⣤⣿⣤⠶⠶⠒⠒⠒⠲⠮⠿⣖⠦⣌⣯⠃⠀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⠀⣧⠀⠀⠀⠨⣷⠇⢀⡇⠀⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⣼⡏⠀⢰⡆⠀⠀⠀⠀⣿⢻⣾⠋⠀⠀⢀⣤⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣗⠀⠀⠀⣸⠋⠀⢸⠃⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⢛⡇⣰⣿⠀⠀⠀⠀⠀⣿⡞⠏⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠀⠀⠸⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⡇⠀⣠⠞⠁⠀⣠⠏⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⠀⠰⢀⡾⠁⠈⣷⠏⢸⡆⠀⠀⠀⢰⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡆⠀⠀⠀⠀⠀⠀⠙⢿⣧⣎⣹⣩⣍⣽⣿⡿⠁⣸⠵⢚⣡⣤⡴⠞⣁⡴⢺⡆⠀⠀⠉⣷⡀⠀⠀ ⠀⠘⣿⠃⠀⠀⠛⠀⠸⣧⢀⠀⠀⢸⣿⠘⣧⠀⢻⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⢠⡾⠁⣸⡷⠚⠁⠀⣸⠀⠀⠀⠀⠘⣧⡀⠀ ⣆⢀⡏⠀⠀⠀⠀⠀⠀⢹⣧⠄⠀⢸⣿⠀⠹⡇⠘⣿⣧⡜⠻⠿⠿⡛⣿⣿⡿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⢿⡅⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠘⣧⠀ ⠘⢾⡇⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠸⡟⢧⣰⠇⠀⠈⠛⠿⣿⣷⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⢷⡄⠀⠀⣼⠁⢻⡄⠀⠀⠀⠀⢸⡆ ⠀⠀⠁⠀⠀⠀⠀⠀⢀⣾⠃⠈⠳⢦⣿⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠈⢿⡀⢠⡏⠀⠈⢿⡀⠀⠀⠀⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠉⠱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢤⣄⡀⠀⠀⠀⠀⢀⡴⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠁⠀⠀⢸⡇⠀⢀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⠀⣼⠓⠃⠀⢠⣤⣀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡟⠁⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣧⠀⣾⡆⠀⢸ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠸⣇⠈⠙⠓⠾⢯⣙⡓⠶⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⡇⠀⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⣇⠀⢸ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⣤⠀⠀⢹⡄⠀⠀⠀⠀⠈⣽⠃⠀⠀⠀⠀⣨⡿⠉⣽⣿⣿⣿⣿⣿⣿⢹⣿⣿⣄⠈⠉⠁⠀⣸⡤⠖⠋⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠀⣿⠀⣸ ⠀⠀⠀⠀⠀⠀⡏⠀⢠⣿⠀⠀⣾⢿⡀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣴⡋⠀⢀⠇⠘⠛⢡⣟⢯⣿⢈⣷⡎⣟⣶⡒⠊⠉⠁⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⡟⢠⠇ ⠀⠀⠀⠀⠀⢰⡇⠀⣾⢻⡄⠀⣿⠈⣷⠀⠀⣾⠃⠀⠀⠀⣴⡟⠁⠉⠉⠉⠉⠙⢻⣿⡏⡞⣿⣿⣿⡝⣶⢹⣷⡄⠀⠀⠀⠀⠀⣤⡖⠋⠉⠙⠛⣶⣦⠀⠀⠀⠀⠀⠀⢠⣷⠋⠀ ⠀⠀⠀⠀⠀⢸⡇⢰⡏⠈⢷⣄⢸⡆⢹⣆⣴⠃⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠀⠀⣼⣷⢹⣞⣿⠃⠹⣿⡜⣳⢎⡿⣄⣠⡤⣶⠋⠁⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣼⠁⠀⠀⠙⠻⠧⠄⠛⠃⠀⢀⣤⠞⠛⠲⠤⣤⣀⣀⠀⠀⣰⡿⣬⢳⣎⣿⠀⠀⢿⣺⡱⣏⢾⣹⣦⡀⢹⣀⣤⣄⣀⣠⢞⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣁⠀⠀⠀⠀⠀⠀⢸⡏⢉⣿⠞⣵⢫⣖⣻⡀⠀⢸⣷⣹⢎⣷⠟⠋⠁⠀⢧⡀⢀⣩⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣌⠧⠤⠶⠦⣤⣴⣿⠂⠘⠷⠿⠮⢷⣮⣽⡇⠀⠀⠷⠋⠉⠀⠀⣀⡀⣄⣼⣿⣿⣿⣿⣷⣻⢾⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣷⣄⡀⣀⣴⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠨⢀⣀⣀⣀⣤⡴⢶⡟⠈⠻⣯⢿⣟⣿⣿⣿⣯⣿⢯⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⡟⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣽⣿⣿⣿⣿⣿⣟⡷⣿⣿⣽⢫⣟⡻⢟⣟⣻⣛⡟⣻⣿⣯⣳⣹⢻⣃⡀⠀⢹⣯⣿⣷⣻⢿⣿⣿⡿⣽⣯⣿⣿⣄⠀⠀⠀⣀⣤ ⠀⠀⠸⣧⠙⢮⡳⣄⣀⣀⠀⠀⣤⣾⣿⢿⣳⣿⣿⣿⡿⠋⠈⣿⣯⢿⣿⣻⣟⣷⣾⣭⣏⢮⡵⣎⣽⠋⠀⠀⠉⢿⣿⣏⣿⠷⠞⠋⠉⠙⢿⣿⠉⠻⣿⣿⣽⣷⣟⣿⣿⣿⣿⡿⣿ ⠀⠀⠀⠹⣦⣄⣙⣺⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⠟⠁⠀⠀⣼⣿⡿⠿⢟⠷⠿⢾⣽⣷⣟⣻⣷⣿⣿⣦⣀⣀⣀⡬⠟⠉⠀⠀⡀⠀⠀⠀⠀⢉⢷⣄⡈⠻⣿⣾⣽⣾⣳⣿⣾⠋⠉