⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⡀⠐⡄⠀⠀⢳⡀⠘⢦⡀⠀⠀⢰⠀⠀⠀⠈⠛⢦⣄⣸⡇⠀⠀⠘⡄⠀⠘⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡇⠙⢆⠘⠆⠀⠀⢳⣄⠀⠙⢦⠀⠀⡇⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣸⠀⠀⡆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⣇⠠⢼⢲⢯⠻⡉⢯⠉⠙⣏⠻⣖⠒⠧⣄⣸⠀⠀⠀⠀⠀⣾⠃⠹⣧⡀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⡏⡇⠀⢳⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⡀⠸⡼⡆⠳⡹⡌⢣⠀⢱⠑⢌⠢⡀⠐⡌⡇⠀⠀⠀⣼⠇⠀⠀⠈⢻⡄⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣥⣧⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⡇⠀⠙⣜⣎⢆⠈⡆⠀⠱⣝⢆⠘⢣⠀⠀⣰⠏⠀⠀⠐⠀⠀⠙⣆⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⡴⠊⢹⢠⣸⡄⡆⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⡇⡇⠀⠀⠈⢾⣞⠀⢇⠀⠀⠈⢮⢣⣸⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡼⡏⢠⠀⢸⢸⠈⣷⡀⢻⢇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⢸⠀⡇⠃⣀⣤⢖⣒⣾⣦⣺⣒⠀⠀⠀⠳⡹⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠸⡀⣠⠋⢸⢧⠈⠀⢸⠘⠀⠘⣧⡘⡌⢆⠀⠀⣀⠀⠀⠘⡆⠀⠀⡏⢸⢸⢰⢊⣵⣾⡿⠿⣷⣲⣾⣿⣿⣦⣄⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⡄⠀⡷⢹⠀⢸⠈⣆⠄⠸⡇⠀⠀⠹⡷⡱⡈⣧⡀⠘⡄⠀⠀⢱⠀⢠⢃⢾⣸⢸⣿⢟⡉⡰⠺⣯⣿⣿⣿⣿⣿⢿⣧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢡⠀⢹⠈⡆⢸⢸⠘⣆⠀⣇⡠⠤⣒⣛⣛⣷⡙⢷⣄⠸⡄⠀⠀⡇⡜⣸⢸⡇⡜⠃⠎⠀⣷⣶⣻⣿⣿⣿⣿⣿⣏⢿⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⢸⢸⠘⡄⠀⢇⢇⠈⡏⡆⢘⣖⣿⣿⡿⣿⣛⣻⠿⠿⣄⠙⢷⣷⠀⠀⢰⢁⠇⣾⢁⠇⠀⠀⠀⣿⠿⠿⣿⣿⣿⠉⠁⢻⢸⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠘⡈⡇⢱⠀⠈⣞⠀⣇⢇⢪⣾⢟⣷⣟⣩⣽⣿⣷⡄⠈⠁⠀⠹⡄⢠⠇⡞⠠⠇⡿⠀⠀⠀⠀⢻⡄⠀⠙⠻⠛⠀⡠⢾⠘⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⢹⡆⡇⠸⡌⢇⠀⠘⣆⠸⡈⣿⡏⣼⠁⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣇⢎⡞⠀⠀⠰⠃⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⡸⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⣇⠀⢸⢳⢸⠀⢱⡈⢆⠀⣏⠣⣷⣿⡇⣿⣿⣿⣿⣿⣿⡏⠉⢻⠀⠀⠀⢫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠘⡄⠈⡏⣇⢇⠀⢳⡈⢆⢻⡄⠈⣿⣧⠸⣏⠁⠈⠻⠿⠃⠀⠼⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⢀⠀⠆⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠘⡄⠸⣾⣞⡆⠸⡵⡌⠛⡝⣄⠈⠙⠳⠙⢦⣀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠊⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⣶⣿⣿⣿⣦⢻⣿⣞⠀⢣⠘⢆⠱⡈⢦⠀⠀⠀⠀⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⡛⠉⠀⠛⠛⠳⣿⡏⠣⡈⢆⠈⠳⣵⡌⢣⠀⠀⠀⠀⠀⡀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠬⡟⢄⡸⠪⣦⠀⠈⠻⢎⣧⠀⠀⣎⠞⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆⡄⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⡆⢸⠓⠀⠀⢸⠈⣧⠘⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡔⠀⠀⠀⢸⢀⠃⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢱⠈⠀⠀⠀⢸⠀⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡟⠀⢰⠁⠀⠀⠀⡎⢸⢀⣧⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⢸⢸⠁⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⠁⢠⠇⢀⠇⠀⠀⠀⣸⡇⡘⣸⢹⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣾⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⢸⠀⡜⠀⡜⠀⠀⠀⡰⢻⠁⣷⠃⢸⡘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠑⠒⠢⠤⠤⣄⣀⣀⡀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠈⣶⠁⢰⠁⠀⠀⡴⠁⡞⢠⠏⠀⠀⣇⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡀⡆⠀⠀⠀⣠⢺⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⢳⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⠇⠀⢀⡜⡇⢰⢁⠎⠀⠀⣀⣸⡜⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⡇⢹⠀⠀⡰⢁⡟⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢻⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡎⠀⣠⠟⢲⣾⣏⣾⣿⣿⣿⠟⡽⠛⠛⠢⠤ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⣵⢹⠸⣇⡰⢁⡿⠀⢱⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠎⢀⠜⠁⣠⣿⣿⣾⣿⣿⣿⢃⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⣰⠁⢯⡆⡿⢡⡿⠁⠀⠀⢧⠀⠀⠀⠀⢸⢧⠀⠀⠀⠀⣀⠔⠉⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢡⣎⠔⠁⠀⣰⣿⣿⣿⣿⣿⣿⢃⡎⠀⠀⠀⡠⠀⠀ ⠀⠀⠀⠀⠀⢀⠏⣰⡏⠀⠈⡿⢡⡟⠣⡀⠀⠀⠈⢆⠀⢀⣤⣾⣾⣶⣾⠟⠋⠉⠑⢒⠾⠤⠤⠤⠤⠤⠤⠤⠤⠒⠊⣹⣵⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⡜⠀⠀⠀⡴⠁⠀⠀ ⠀⠀⠀⠀⢀⠎⣰⢻⠁⠀⡼⢡⡟⠙⡆⠙⠢⣀⠀⠈⢷⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⠾⠒⠊⠉⠉⠉⠉⠒⠤⣀⠀⠈⡽⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⡸⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⠀⠀⢀⠎⡔⠉⠙⠢⣜⢠⡟⢱⢠⢿⣄⡴⢫⣷⡦⣄⡻⣿⣿⡿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠞⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢀⠇⠀⠀⠀⠁⠀⠀⠀⠀ ⣀⣀⣀⠎⠀⣇⣀⡀⠀⠈⢻⠀⢸⡼⡰⠋⠂⣾⣿⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠇⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠀⡜⠀⡼⠈⠉⠛⢷⣄⠘⡄⠸⣿⠃⠀⢠⢻⣇⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀