⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣒⢫⡼⢞⣛⡞⢧⡛⡴⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠒⣬⠏⡞⡟⣸⠽⣎⣽⠰⢸⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡨⢠⣷⣸⢹⡅⣿⡀⢿⣸⣷⠀⣇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⣯⢼⣿⣯⣿⣽⢻⡇⢸⣿⣿⡔⣼⠠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣷⣻⣟⣧⣧⠻⠇⠇⣼⣟⣿⡇⣿⠱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⣻⢹⡿⠿⠇⠀⠀⠀⠸⠿⢿⡇⣿⢜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣸⡏⡇⠀⠀⠀⠀⠀⠀⠀⢸⢳⣿⢪⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⣹⣧⢳⣤⣀⡀⠀⢀⣀⣤⣾⢼⡿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣏⣿⣿⡜⣿⣿⠀⠀⠀⣿⣿⣿⣾⡇⣷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠉⠛⠷⡋⠉⠀⠀⠀⠈⢉⣷⠛⠉⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⢤⢀⠀⠀⠁⡏⠁⠨⣀⠄⠂⠁⣿⠀⠀⡀⡤⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠹⡎⠀⢱⣦⣄⡇⣠⣾⡿⣷⣄⠀⣸⣴⡎⠀⢱⡏⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⢹⠁⠀⢸⣿⣿⣿⣟⣯⣿⣽⣻⢿⣿⣿⡇⠀⠈⣿⡨⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣶⠇⠀⠀⢺⣿⣻⢷⣯⣟⣾⢷⣻⣟⣾⣷⡏⠀⠀⠸⡇⣿⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⢀⣾⣿⡽⣟⣾⣽⣻⣿⣻⢾⣻⣾⣷⡀⠀⠀⢱⣻⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⣿⣿⣿⢿⣹⣿⡿⣿⣏⣿⢿⣿⣿⣇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣰⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠽⣇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢰⡏⢰⣿⣿⠛⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣆⠹⡆⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⡟⢠⣿⣿⣟⣿⣿⢯⣿⢿⡾⣿⣿⣿⣿⣿⣿⣆⢙⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣾⢡⣿⣤⣿⣻⣟⣾⣉⣿⡿⣟⣿⣿⣿⣿⣿⣿⣭⣆⠳⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣠⠟⣳⣿⡿⣯⣟⠿⣽⣻⣟⣿⣿⣻⣽⣻⣿⣿⣿⡿⢽⣿⣆⠩⣄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⣰⠟⣰⡿⢿⣽⡿⣽⣶⣿⣻⢾⣻⣷⣧⣼⡿⣿⣿⣿⣷⣾⣿⣿⣆⠙⡢⠀⠀⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⣴⠇⣰⣿⣿⣾⣿⢿⣽⣻⡷⣟⡿⣯⣿⢷⣯⢿⣿⡿⣿⣿⣿⣾⣿⠛⣆⠈⣧⠀⠈⠣⡀⠀⠀⠀⠀ ⠀⠀⡠⠞⠁⠈⠒⢺⣿⡶⢻⣿⣟⣾⣿⣻⢾⡿⣟⡿⣧⣾⣟⡿⣾⣟⣿⣽⣾⣿⡷⣿⣟⣿⣿⣧⣸⡇⠀⠀⠈⠓⢄⠀⠀ ⠀⢼⠅⡠⠀⡀⢀⣿⣿⣿⣿⣻⢾⣟⣾⡛⣻⣿⣻⣽⣟⣷⣻⣽⣷⠿⣿⢯⣷⢯⣿⢷⣻⣽⢿⣿⣷⣻⡀⢀⡀⢴⠨⡷⠀ ⠀⡼⠈⣴⣿⢡⣿⣿⣿⣿⣋⣻⣿⣽⣟⣿⣻⣽⡷⣟⣾⣯⣟⣷⣻⣶⡿⣿⣽⣻⣿⣉⣿⣯⢿⡿⠿⣷⣺⡌⣿⠤⠐⢧⡀ ⠘⠷⠞⠉⠈⢹⣯⣩⣿⣾⣟⣿⣳⣿⡾⣯⣟⣾⣽⣿⣤⣿⣻⣞⡿⣿⣽⡷⣯⣷⣟⣿⣻⢾⣟⣿⣾⣿⣿⡍⠉⠀⠑⠺⠇ ⠀⠀⠀⠀⠀⢠⡟⠛⢿⣿⣾⣽⣻⣷⣛⣿⣽⣳⣯⣷⣟⡷⣟⣯⣿⣽⡷⣟⣿⢾⣽⡾⣿⣻⣾⣯⣿⡿⢻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⡙⠻⢿⣿⣾⣿⣿⣾⣯⣷⡿⣞⣿⣉⣿⣷⣻⣟⣿⣳⣾⣿⣽⡿⢟⠋⢁⣤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠂⠤⢆⣠⣌⡙⠻⣿⣿⣽⣿⣿⡾⠿⡟⠛⠛⢛⡋⣡⡴⠮⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢯⣟⡷⣦⣦⣤⠤⣴⣶⣻⣟⢿⡻⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠘⡜⣡⠓⣿⠀⡿⣌⠳⡘⢢⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠨⢔⠢⢍⢿⠀⡿⢠⠃⢥⢃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠎⠴⣉⢾⠀⣯⠑⣊⠦⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡜⣡⢜⣾⠁⣿⡜⣤⢪⡕⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡞⣵⣫⡟⠀⢸⣟⡖⡣⢎⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠪⡔⢢⢻⡇⠀⢸⡗⡬⡑⠎⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⠱⡈⠧⣹⡇⠀⢸⡇⣒⢉⠖⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀