⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⣟⣽⣿⡿⠛⢡⣴⣿⣦⡤⠉⣉⡻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⢟⣿⣿⠛⠀⠀⠀⠀⠀⠀⡶⠸⠿⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⠋⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠉⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣸⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣙⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣧⡘⣷⡀⠀⠀⠀⠀⠀⠀⣨⠹⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠇⠘⣷⡀⠀⠀⠀⠀⠀⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠹⣆⠐⣦⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠛⠁⠀⠀⠀⠈⢧⡈⠻⣦⠳⣄⠀⠀⠀⠀⠀⠀⣼⡇⠸⣵⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠁⠈⠻⣦⡀⠀⠀⠀⣿⠀⠀⠙⠧⣤⣹⣛⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠈⢻⣷⣄⢸⣿⠀⠀⠀⠀⠈⠑⢋⡁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠁⣤⠙⠛⢿⣽⣇⠀⠀⠀⠀⠀⠈⢳⡄⢦⡀⠀⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇⠀⠀⠀⠘⡇⠀⠀⠈⠳⣄⠀⢿⠿⢠⡄⠀⠀⠀⠀⠀⠻⡌⢷⡄⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣷⠀⠀⠀⠀⠙⢦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣷⢀⣷⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢾⣧⣄⣀⠀⠀⠀⠀⠀⣟⠀⢹⣀⡇⠀⠀⠀⠀⠀ ⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⢠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠚⠛⠁⠀⠈⢹⠃⠀⠀⠀⠀⠀ ⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠋⠀⠆⠀⠀⠀⠀⠀⠀⢀⣴⠞⢀⣰⠆⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⢠⡟⠀⠀⠀⠐⣦⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⢛⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⠟⠀⠀⠀⠀⠀⠘⢧⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢸⡀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢸⠈⡇⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⢻⠀⠀⠀⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠰⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⢆⠘⣆⠀⠀⠀ ⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣷⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣾⣿⠟⢛⠃⠀⠀⠴⠂⠀⠀⠀⠀⣿⡞⠃⠹⣆⠀⠀ ⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⣹⣿⣿⠾⠋⠀⠀⠲⠀⠀⠀⠀⠀⢸⣉⣀⠀⠀⠙⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⢸⡿⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣝⣉⠿⠦⠀⠀⠀⠀⠀⡶⠀⠀⠀⢸⣯⠹⠳⣄⠂⢹⡀ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡝⠻⠿⢷⣦⠀⠀⠀⢶⡀⠀⠀⡼⣿⠟⢀⠀⠀⠀⢠⣀⣷