⡟⠉⢉⣅⠀⢀⣸⣀⣤⠤⢤⠤⣤⢤⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣾⣿⣿⠁⣀⡀⢦⠙⡄⠀⠈⢳⣄⠀⠀⢣⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣟⣾⣧⣶⣿⣇⣸⡆⢰⠀⠀⠀⠉⡆⠀⠀⠱⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠈⠉⠉⠠⠄⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⢸⡆⠀⣇⠀⢹⠐⠢⡀⠱⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠿⡿⣿⣿⣏⠀⠋⣿⣿⢧⡏⡿⣄⠹⡄⣜⡆⠀⠈⢳⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠉⠈⢣⠈⢀⠴⢁⡟⡜⢼⣯⠹⣷⡹⣿⣿⣦⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⢰⠁⣼⣆⠀⢀⢾⠞⠁⢸⣿⣧⣙⢿⣾⣿⢣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⣿⣷⢫⠏⠀⠀⢀⢿⠻⣿⣷⣽⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣬⣏⣿⢯⡿⠀⠀⢀⣼⡸⣧⢈⡙⠻⣿⣸⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⣰⠖⠛⠛⣿⣿⣿⡧⣒⡪⠥⡤⢧⠙⣟⡾⣿⡿⢸⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⢟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠁⠀⣀⣀⣹⣿⣿⡿⠁⠀⠀⡠⣾⣋⡉⠉⠁⠀⠸⡄⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢸⠀⠘⠁⠀⠈⢿⣿⡇⠀⡠⠊⢀⡇⠀⠙⠠⡀⠀⠀⣧⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇ ⠀⡇⣆⠀⠀⠀⠈⢿⣁⡫⠴⠊⢸⣷⣦⣄⡑⠮⣓⠦⠼⡆⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀ ⠀⠀⠈⢆⠀⠀⣠⠞⠁⠀⠀⢀⡇⠈⠉⠉⠉⠉⠭⣝⡟⠛⡄⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀ ⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠘⣄⠀⠀⠙⢷⣄⠀⢀⣀⡴⠞⠛⡟⢿⣿⣷⣦⣄⣀⣀⣀⣀⣰⣿⠃⠀⠀ ⠀⠀⠀⠀⠈⢷⡈⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⣠⣾⡀⠀⠀⠀⢘⣷⣶⣶⣾⣿⣿⣿⣥⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢶⣄⣠⠿⢿⣿⣿⡴⣶⣿⡿⣿⣿⣦⣠⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠘⢻⣿⣌⠛⠋⠁⠀⢁⡟⠹⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣽⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠙⠦⡄⠀⠀⠘⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⠘⠀⠀⡄⠦⠙⠀⠀⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠟⣿⣿⣿⣿⣽⠀⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⠹⡟⢁⠀⠁⠋⠛⣌⣿⢻⠘⣄⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⣠⣦⣿⣿⡿⣿⣶⡴⣿⣿⢿⠿⣠⣄⢶⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⣥⣿⣿⣿⣾⣶⣶⣷⢘⠀⠀⠀⡀⣾⣠⠀⠀⠀⡀⣷⣿⢠⠀⠀⠀⡈⢷⠈⠀⠀⠀⠀ ⠀⠀⠃⣿⣰⣀⣀⣀⣀⣄⣦⣷⣿⢿⡟⠛⠞⡴⣀⢀⠀⣄⢷⠙⠀⠀⣄⠘⠀⠀⡎⢀⠀⠀⠀⠀⠀⡀⣸⠀⠀⠀⠀⢱⡀⢧⠈⠀⠀⠀ ⠀⠀⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣠⠀⠀⠀⠀⠀⠀⠀⣄⢿⠙⠀⡄⠛⡟⣝⠭⠉⠉⠉⠉⠈⡇⢀⠀⠀⠁⠞⣠⠀⠀⢆⠈⠀⠀ ⠀⡞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠹⠀⡆⠼⠦⣓⠮⡑⣄⣦⣷⢸⠊⠴⡫⣁⢿⠈⠀⠀⠀⣆⡇⠀ ⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠻⠀⣧⠀⠀⡀⠠⠙⠀⡇⢀⠊⡠⠀⡇⣿⢿⠈⠀⠁⠘⠀⢸ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢹⡄⠸⠀⠁⠉⡉⣋⣾⡠⠀⠀⠁⡿⣿⣿⣹⣀⣀⠀⠁⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⢟⠀⠀⠁⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⢸⡿⣿⡾⣟⠙⢧⡤⠥⡪⣒⡧⣿⣿⣿⠛⠛⠖⣰⢢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⢸⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢼⣸⣿⠻⡙⢈⣧⡸⣼⢀⠀⠀⡿⢯⣿⣏⣬⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⣽⣷⣿⠻⢿⢀⠀⠀⠏⢫⣷⣿⡟⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⣿⣾⢿⣙⣧⣿⢸⠁⠞⢾⢀⠀⣆⣼⠁⢰⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣴⣦⣿⣿⡹⣷⠹⣯⢼⡜⡟⢁⠴⢀⠈⢣⠈⠉⠁⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⢳⠈⠀⡆⣜⡄⠹⣄⡿⡏⢧⣿⣿⠋⠀⣏⣿⣿⡿⠿⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⣀⠀⠱⡀⠢⠐⢹⠀⣇⠀⡆⢸⡇⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠄⠠⠉⠉⠈⠀⠀⠀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠱⠀⠀⡆⠉⠀⠀⠀⢰⡆⣸⣇⣿⣶⣧⣾⣟⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⡆⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⢣⠀⠀⣄⢳⠈⠀⡄⠙⢦⡀⣀⠁⣿⣿⣾⣿⣠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⣀⢤⣤⠤⢤⠤⣤⣀⣸⢀⠀⣅⢉⠉⡟