⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⣿⠛⡜⠳⣌⢫⠟⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⡔⢋⠘⠡⢈⠃⡙⠠⠬⡝⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⢯⡝⡘⠀⢎⣰⣧⣶⣤⣅⡣⡜⡜⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡳⣌⠀⡘⣿⣿⣿⡿⣿⣿⣿⣾⣌⢣⣻⣿⣿⣆⠀⠀⣠⣴⣾⣿⣿⣿⡿⢿⣿⡿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠛⠙⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣗⢧⢢⢹⣿⣿⣿⣿⣟⣿⣿⣿⣿⡤⣓⣿⣿⣿⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠉⢻⣦⣽⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡓⠀⠀⣰⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣤⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣿⣿⣿⣿⣿⣮⠳⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⢿⠿⠿⠿⡛⠟⡛⠟⠛⠟⡛⠟⠻⢛⠿⡿⣿⣿⣿⣿⣿⣿⣯⣟⡼⣣⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠚⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣤⡀⢀⣀⣀⢀⣰⣾⣿⣿⣿⣦⡀⠀⠀⣠⣤⣶⣿⠿⠛⠛⠉⠉⠡⢀⠂⠂⠀⠢⠁⠣⢢⡙⠂⠐⠢⠈⠠⡑⣀⠂⠑⠒⢼⣭⣿⣿⣿⣿⣿⣷⣭⠷⣭⣻⣿⣿⣿⣿⣿⣿⡿⣟⡻⡟⣟⠿⣻⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⡲⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣶⡿⠿⠛⠉⠈⠤⠉⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣝⣮⢳⡙⣎⠳⢡⢻⣿⣿⣇⡀⠀⠀⠀⠀⣈⠶⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠌⠖⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠛⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡝⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣜⢮⣋⠗⠀⡂⡁⢎⣿⣿⣿⣿⣿⣿⣶⣽⣶⣎⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠋⠋⠙⣿⣿⣿⣿⣿⣿⠟⠁⠀⡀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣦⣿⣿⣿⣷⣋⠖⣀⠊⠄⢣⣘⣾⣿⣿⡛⣝⠫⡟⠿⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢿⣿⣿⣿⣷⣤⣼⣴⣾⣿⣿⣿⣿⣿⣮⣕⡸⡹⡔⡹⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢱⡉⢳⣈⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⢻⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⣿⣷⡍⢂⠰⣋⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠧⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⡀⡑⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣭⢻⣿⣿⣿⣿⣿⣿⠃⢌⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣫⢖⣻⢛⠛⢉⠀⣀⢎⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣮⡁⠆⣌⢲⣽⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⢠⣤⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠈⢷⣦⣍⡛⠿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⠀⣼⣿⡟⠛⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠿⠳⠦⠉⢹⡛⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⣛⣷⣿⣿⣿⣿⣿⣷⣦⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣻⣿⣾⣿⣿⡌⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠻⢿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣼⣿⣿⠿⣻⠉⠈⠻⣿⣿⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⡟⣿⣿⣿⣿⣿⡯⣷⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⣀⠈⠣⠀⣠⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣾⣿⣿⢏⠑⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⣷⠘⣿⣿⣿⣿⣇⢿⡄⠀⠀⠀⢸⣿⣿⣦⠀⠀⠀⠀⠈⠛⠿⣶⡀⣈⣩⢿⣿⣿⠀⠀⣀⣤⣴⣶⣿⣿⠿⠛⠁ ⠀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣿⣿⣿⣁⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⢀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⣿⣿⢿⣿⣿⣺⣆⠀⠀⠀⢨⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠹⡇⠈⢿⣿⣿⣿⣶⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀ ⠻⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⢉⡄⠀⠀⢠⣾⣿⣿⣿⣿⣟⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣷⡘⣿⣿⣿⣮⢿⣿⣯⡽⣄⣴⣤⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠐⢻⢄⡸⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠹⣿⣿⣿⣏⣴⣠⣶⣿⣿⣟⣽⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠾⢿⣿⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠒⢷⣾⣎⣽⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡶⢿⣿⣿⣿⣿⠿⢛⣽⣿⣿⣿⣿⢟⠏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⣼⣿⣿⠆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢿⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⡿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⡿⣿⣶⣿⣿⣿⣿⡿⠟⠀⠈⠀⠀⠀⠀⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣷⣶⣄⣠⣿⣿⣿⠋⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⣠⣴⣭⣿⠟⠛⠋⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢤⣤⣿⣿⣿⡿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣾⣿⡿⠿⠟⠛⠉⠉⢻⣿⣿⣎⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠰⠿⠋⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡄⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⠉⠉⠉⠉⠉⠹⢿⣿⣿⣹⣿⠀⠀⣰⣿⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣈⣱⣿⣿⡿⠁⠀⠈⠙⠻⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣮⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡀⠀⠀⠀⢺⣿⣟⣂⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣷⣄⣤⣾⣿⣿⣿⣿⡿⠃⣀⣠⣤⣾⣿⣿⠆⠀⢠⣤⡀⠘⣳⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣝⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣴⣿⣿⣿⡿⠿⠿⠋⠀⠀⠀⠛⠏⣶⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⡿⠟⠛⣿⣿⣷⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢀⣀⣀⣹⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⡿⣟⣯⣟⡾⣯⣽⣳⣯⣷⣿⣿⣿⣿⡿⣟⣿⣿⣷⣶⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⣤⢦⣽⣾⣿⣿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣽⣿⡿⣯⢿⡽⣛⡾⣝⡾⣭⣿⣾⣻⣼⢻⡽⣾⣽⣻⣽⡿⣽⣾⣷⣯⣿⣻⡷⣟⣯⣿⣿⣿⣿⠛⠉⠁⠀⢀⣴⣶⣦⣠⡴⣄⣾⣿⣿⣿⠃⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⣠⣶⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⢯⣿⣿⣿⢿⣽⢾⣽⢯⣿⣽⣿⢿⣻⣟⡿⣽⣻⣽⣻⣽⣟⣯⣿⣿⣯⣟⣽⣳⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣻⣷⣶⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣤⣤⣿⣿⣿⡿⠛⢿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣟⣯⣟⣾⡿⣿⣟⣯⢿⡾⣿⣿⢿⣯⡿⣯⢿⣽⣯⢿⡽⣯⣷⣟⣿⣳⣟⣷⣞⣷⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣼⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡅⠀⠀⢰⣉⣀⡀⠀⠀⢀⣠⣿⣿⣿⣽⡾⣽⢾⣿⣿⢿⢯⡟⣽⡳⣯⣟⡾⣽⡿⣿⢿⣾⡿⣿⣯⣿⣾⣿⣳⣿⣾⣿⣾⣿⣿⡏⠀⠈⠉⠛⠛⠛⠋⠀⣀⣶⣾⣿⣿⣿⣟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣯⣹⣿⣿⣿⣿⣦⣄⣸⣿⣿⠿⣄⣤⣿⣿⣿⣿⣿⣞⣿⣽⣿⣿⣽⣻⠾⣽⣳⣻⣵⣯⣽⣳⣻⣽⣻⣞⣽⣳⣿⣾⣿⣽⣿⣿⣟⣿⣿⣿⣿⣷⠄⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣯⣟⣿⣷⣿⣿⡿⣿⣿⣷⣿⣷⣿⣾⣯⣿⣿⣿⡟⠛⡿⢿⣿⣿⣿⣿⠿⠋⢀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⣼⣭⣹⠟⠿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⣿⣿⡍⠉⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠁⢀⣀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⡏⣐⣿⣿⣶⣶⣷⣿⣿⣿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠿⣿⡿⠆⠀⠀⢉⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣼⣿⣿⣿⣿⣟⡁⣀⣾⣿⣦⠀⣻⣿⠿⣿⣿⣿⣿⣏⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⢉⣼⣿⣿⠟⠁⠀⣤⣦⡀⠀⠀⠀⣀⣩⣵⣦⣄⣀⠘⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿⣿⣤⣿⣿⡟⠁⠀⠀⠀⠛⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣻⣽⣿⣿⣡⣤⣄⠀⣠⣾⣿⣿⣿⣆⢠⣶⣶⡄⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣻⣿⣿⣿⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⡿⣝⡞⣧⢻⡞⣽⢳⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡳⣟⣿⣿⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⠏⠙⠿⠟⠃⠀⠀⠀⢹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣯⠀⠀⠀⢀⣀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⡿⣼⡹⣞⡷⣽⢎⡟⣮⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣳⢿⡹⡶⣏⡿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⣿⡟⣿⡿⣟⠋⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢥⠻⡭⣙⢺⣿⣿⣿⣦⣼⣽⣿⣿⣿⣿⣿⣗⠀⠒⣾⣿⣿⡿⠃⠉⠙⠛⠻⠛⠛⠛⠻⣿⣿⣷⡽⣎⡷⣽⣫⢞⡵⣫⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢷⣏⢿⣿⣱⢯⢿⣽⣻⣟⣿⣿⣿⣧⣤⣶⣶⣦⣴⣶⣤⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣳⣾⣿⣿⣮⣷⣿⣿⡿⣹⣿⣿⣿⣿⣿⣯⣘⣿⣿⣿⣮⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠠⠀⠉⠉⠀⠀⠀⠀⣠⣤⣴⣤⣤⣴⣿⣿⣿⣱⢯⣞⡷⣽⣎⢷⣹⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣾⢯⣷⣏⣿⣳⢞⣷⣻⢾⣿⣿⣿⣿⣿⠿⠉⠙⠛⢋⡁⡸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡿⣽⡞⣽⡞⣼⣹⢳⣮⢯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣿⡞⣶⡹⣞⣧⣟⡿⣞⣿⣿⣿⣷⣶⣦⣤⡐⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⢩⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣦⣄⣠⣶⣿⣿⣿⣿⣿⣯⣟⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⢯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣟⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣛⣿⣿⣿⣿⣟⡰⣺⣿⣿⣿⣿⣿⣿⣿⢏⡽⣻⣯⣿⣷⣌⠃⡆⣤⢭⣝⣻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠛⠛⠛⠛⠉⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡻⠽⣾⣿⣣⡞⣏⢧⡓⢌⠥⣋⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡞⣿⣿⣿⣿⣿⣿⠜⣦⢋⡶⣹⢞⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢳⡝⣼⣿⣿⣿⣿⣏⠶⣩⢎⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⢔⡹⢿⣿⡿⠿⣩⠞⣰⣋⠶⣙⠾⣭⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣓⠾⣼⠿⢿⣛⠻⣌⡞⡱⢎⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡏⠴⡘⢆⡏⢳⡱⢥⡚⡥⢎⡽⡹⣞⡵⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣯⣟⣽⣟⣿⢣⣛⡴⣍⠳⣹⣿⣿⣿⡏⡝⢫⠿⡹⢯⣝⡫⣅⠛⣿⣿⣿⣿⣿⢡⠒⡍⢦⡙⣆⠳⢎⠶⡹⣜⠲⣝⠶⣹⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⣬⣳⡰⢻⣿⣿⡁⠜⢃⠯⠱⣋⠜⡱⢂⡍⢾⣿⣿⣿⣏⠶⡹⢌⡣⣝⡰⢋⡎⠵⣣⠼⡹⣌⡟⣱⢏⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢟⣻⢿⣧⠔⡤⠼⣍⠙⠻⢿⣿⣿⣿⣷⣣⢝⣬⣿⣿⣷⣈⠢⢌⡱⠌⡎⢱⢂⠼⣿⣿⣿⣿⣏⠲⣡⢋⢶⡡⢎⠱⣌⠓⣤⢋⡕⢮⡜⢧⡏⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⣧⢞⣼⣿⣿⣿⣿⣿⣿⣾⣥⠂⣼⠛⣿⣿⣿⣿⣮⠿⣿⣿⣏⡒⢌⡒⢩⢐⢣⡘⣾⣿⣿⣿⡿⢌⠳⣤⠋⠦⡑⢌⡓⠌⡙⢄⠣⢜⢣⡚⡵⡺⣭⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣓⣾⣿⣿⡿⣍⢯⢛⡹⢿⣿⣿⣿⣦⡝⢡⡙⢿⣿⣿⣷⣏⣿⣿⣷⣚⠿⢣⠾⡿⣟⣿⣿⣿⠿⢓⢊⠱⢂⡙⠰⡉⢆⡰⠑⡌⢆⢃⠎⡖⣹⢲⡙⣦⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢧⢯⣿⣿⣯⡝⣯⢎⡵⢃⠦⣌⠻⣿⣿⣿⣦⡙⢍⠻⣿⣿⣿⣿⢿⣿⣿⣷⣿⣾⣿⣿⢿⡛⡌⢣⡁⢎⡜⠡⢂⡱⢐⠢⢥⠓⡜⡌⢎⡜⢬⡱⢮⡱⢣⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣬⢻⣿⣿⣴⡻⡝⣮⡸⣍⢞⡐⠦⡌⠿⣿⣿⣿⡈⢖⡙⢿⣿⣿⣿⣯⡝⣻⠿⣛⢭⡒⣣⠱⡈⢦⠙⠢⢌⠑⣂⠱⢊⡑⢪⢱⣘⣜⣢⡞⢦⡙⢦⡝⢧⡺⡽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⢧⣿⣿⣿⣷⣳⠻⣟⡱⣎⠾⣙⠲⣌⠰⡙⢿⣿⣷⣸⣾⣾⣿⣿⣿⣿⣿⡆⡟⡜⢆⠳⣤⢣⡙⠤⡙⠰⣈⠒⡄⢣⢥⣹⣾⣿⣿⣿⣏⡜⡡⠞⣱⢊⢧⢳⡽⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⢿⣿⣿⣿⣜⡿⣜⡳⣭⡞⢶⡹⢌⢣⡰⢩⣿⣿⣿⡄⠹⡘⣿⣿⣿⣿⣿⡴⣻⣌⢳⢂⠣⢌⠱⡈⠥⢐⢠⣼⣷⣿⣿⣿⣿⠟⢏⠱⢌⡱⢚⡴⣛⢎⡳⣽⣻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⢻⣿⣿⣿⣞⣳⡭⢷⣣⣝⣮⡝⢮⣡⠳⣖⡼⣿⣿⣷⡰⡡⢿⣿⣿⣷⣻⣜⡳⡜⢂⢇⡞⡜⢆⡱⣸⣶⣿⣿⣿⠟⡟⡙⢌⠸⣠⢋⠶⣣⠙⡴⣉⢮⣳⢳⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⢯⣻⣿⣿⣿⣳⣏⡷⣽⣛⢦⡝⣦⢧⢻⡼⡱⢿⣿⣿⡔⠐⢢⣿⣿⣿⣿⣾⣧⡵⣊⡞⣜⣜⣦⣷⡿⠟⣋⠙⡌⢒⡰⠌⢆⠓⠤⣉⢒⣡⣚⣴⣱⣎⣵⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣳⢎⣿⣿⣿⣷⡿⣽⢶⣯⢟⡽⢮⡼⣳⢯⣽⡙⣿⣿⣧⣉⣆⣿⣿⣿⣿⣟⣿⣿⣧⣿⣿⡿⣟⡡⢆⠳⣀⠳⢌⢣⠰⣉⣦⣭⣶⣷⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣻⣮⡿⣞⣣⠷⣭⡷⣯⣟⣿⣿⣏⠰⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡟⡴⡑⢎⡱⣌⣲⣾⣾⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡜⣧⢻⣿⣿⣿⣿⣷⣻⣽⡷⣿⣿⣳⡿⣾⣿⣿⡏⠷⣬⣿⣿⡿⢿⣿⣿⣿⡿⣭⡗⣾⣱⣼⣾⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣹⣿⣏⣿⣧⣹⣿⣿⣿⠈⢡⣼⣿⣿⡇⠀⣿⣿⣿⣹⣤⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡻⣴⢻⢿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⢿⡜⣦⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣏⡶⣍⣛⣿⢿⡿⣿⢿⣟⢫⡜⢆⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⡟⢫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣾⣽⣎⣲⣭⣚⣼⣷⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢻⣿⣷⡦⠣⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢿⢿⣿⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣼⣿⣿⣿⢟⣻⣭⣶⣾⡿⠟⠛⠛⠛⠉⠉⠛⣿⣿⠈⢺⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⢦⣋⣾⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢈⠰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⡾⣘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢂⠐⣺⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣭⡞⣿⣷⣤⠂⠀⠀⠀⠀⢀⣼⣿⠃⠀⣬⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡽⣞⣻⣿⣷⣦⣄⣤⣶⣿⠛⡁⢀⣸⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣿⡶⣭⡛⡟⣟⡋⢉⠀⠰⣠⣷⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣧⣿⡼⣧⣽⣦⣌⣱⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣛⢻⠿⠿⡿⠿⠟⣉⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀