⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⡀⠀⠀⠃⠤⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡴⠃⠈⠀⠠⠤⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣦⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣼⢠⢄⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⢤⠄⠀ ⠀⠀⠶⢪⣤⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⢠⡟⠃⢀⠀⡠⠤⠖⠒⠒⠒⠒⠒⠒⠲⢤⣤⣀⢀⠀⠛⣫⠚⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⢰⢨⣿⡤⠂ ⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣖⡀ ⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢸⣿⣿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠁ ⠀⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠓⢀⣙⣲⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣾⣏⣒⠿⣭⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣺⣭⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⢿⣷⣻⣬⣲⠾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣀⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⣠⠖⠋⠁⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢛⡏⣓⢿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢽ ⠀⠀⠀⠀⠀⠀⠀⢀⢎⡤⠀⣀⠚⠁⠈⠀⠀⠈⠁⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣢⣂⠢⠤⢀⣀⠀⠈⠋⠁⠈⠛⠿⢿⣿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⢀⡾⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡇⠛⠁⠘⣿⣿⡏⠿⠛⠳⢶⣤⣉⡳⣦⡀⠀⠀⠀⠘⢿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣿⡜⠃⠀⠚⢟⠁⠀⠀⠀⠘⡇⠀⠀⠀⠀⠘⣏⠙⢻⣯⢳⡄⠀⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⣸⠋⠛⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⡎⢷⠀⢰⡀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡾⢁⣿⣤⠤⠤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⢶⣦⣷⠸⣇⠈⣷⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⡀⢻⡆⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⢸⡇⢸⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⢸⣧⠸⣇⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢸⣿⠀⢻⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠈⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⢀⣷⠀⠀⠘⣧⠀⠀⠀⠀⢸⡈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡟⠀⠀⠀⢰⠏⠀⠀⢀⣦⠀⠀⠀⠀ ⠴⠇⠀⢸⡿⡄⠀⠱⡘⢷⡀⠀⠀⠘⣇⢿⣿⣿⣦⣄⣠⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠇⠀⠀⣠⠏⢀⠆⠀⣸⠿⠀⠀⠀⠀ ⠀⠀⡀⠜⠳⣌⢦⣀⡃⠈⠻⣦⠀⠀⢻⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⢻⡇⡟⠀⢀⡴⠁⠀⣿⣀⡴⣡⠞⠀⠀⠀⠀ ⠀⠐⠿⢀⡀⠈⠱⣿⠃⠀⠀⠈⠳⣄⠘⢿⣄⠀⠀⠀⠀⡌⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠠⡀⠀⠀⢸⣤⡿⣹⢁⡴⠋⠀⠀⠀⠻⣏⠈⠁⠀⠀⠐⠀⠀ ⠀⠈⠉⢙⣈⡉⠟⠁⠀⠀⠀⠀⠀⠈⠳⢦⣻⢷⣄⣰⢸⣅⡀⠀⠀⣸⡀⠀⠀⢠⣇⣀⣀⢰⣷⣄⣠⣯⢿⣸⠿⠋⠀⠀⠀⠀⠀⠀⠘⠿⣉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢷⣄⠈⠉⠉⠉⠙⢓⣛⣛⣛⣓⣛⣛⣽⠟⢉⣉⢀⣠⣼⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣶⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀