⠠⢌⠰⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠹⣿⣯⣻⡝⣯⡻⣝⣻⣿⣿⠋⠀⠀⢀⣀⣀⣀⡀⠀⠀⠸⡷⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠐⡌⢢⠉⠤⢉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⡤⠤⠖⠒⠲⠤⣤⡀⠘⡆⠹⣷⣏⡾⣳⡝⣯⣽⣿⡟⣠⣴⠞⠋⠉⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡌⢢⠉⢆⠃⠤⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡤⣴⠶⣛⠟⡻⠶⣤⣌⣉⡉⠀⢻⣿⣵⣷⣽⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠲⠬⣤⣉⣂⡉⠆⢡⢂⡿⠀⠀⠀⠀⠀⠀⠀⣠⡶⢾⣿⣷⣦⠷⢿⣷⡟⠛⠛⠳⠿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠈⠙⠉⢉⣩⣉⣉⠛⠳⣦⡀⠀⠀ ⣒⠶⠤⡄⠈⠉⠙⠒⠋⠀⠀⠀⠀⡀⠀⣠⣾⣿⣿⠟⠉⣿⠀⢾⡁⠀⣸⠂⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠓⠛⠉⠉⠛⠿⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⢠⠏⠀⠀⠀⠉⢲⡈⢻⡄⠀ ⣀⣉⣉⣉⣀⡀⠀⠀⠀⠀⠀⢀⠒⢠⣾⣿⠟⠋⠀⠀⢰⡏⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣷⣄⠐⣇⠀⠀⠀⠀⠀⠀⡇⢸⣇⣀ ⠀⢆⠡⢉⣘⡇⠀⠀⠀⠀⠀⢁⣴⣿⡿⠃⠀⣀⣤⣴⣾⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠈⢦⣀⠀⠀⠀⠀⠳⢌⣉⠀ ⢁⢊⣐⡦⠾⠃⣀⠀⠀⡀⣠⣾⡿⠋⢀⣴⣿⣟⣯⣟⣾⣳⢿⣼⣳⢯⣟⡿⣷⣦⡀⠈⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⣩⣉⠓⠲⢤⣀⠀⠀⠀ ⡼⠟⠃⣀⡠⠜⠛⣠⠇⣠⣿⡿⠃⣠⣿⡿⣧⢿⣼⣻⣼⣻⠼⠿⠿⠿⣼⣻⢧⣟⡿⣿⠟⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠻⠿⣿⣿⣤⣀⠘⢧⡀⠀ ⡴⠒⠋⠁⠀⢀⠞⢁⣼⣿⠟⠀⣴⣿⢯⡿⣽⣻⣞⣿⣭⠀⠀⠀⠀⠀⠀⠙⢻⡾⣵⢿⡄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠉⠉⢏⣷⣤⠙⡄ ⡀⠀⠀⠀⢠⠏⣠⣿⣿⠋⠀⣼⡿⣯⢿⣽⣳⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣟⡇⠀⠀⢻⡆⠀⠀⠀⢀⣀⣤⠾⠛⠋⠁⠹⣇⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⣠⡾⠋⣁⠴⠃ ⣏⠓⠤⣠⠏⢠⣿⡿⠁⠀⣼⣿⣻⣽⣻⢾⣽⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠈⠿⢤⠖⠛⠉⢁⣤⣤⣶⣾⢿⡷⣿⢷⣦⣄⡀⠀⠀⠀⠀⠀⣾⠋⠀⠚⠥⠤⠄ ⣟⢷⣦⡈⢠⣿⡿⠁⠀⣰⣿⢯⡷⣯⣟⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣽⣳⢯⡿⣽⢯⣟⡾⣽⢿⣷⣦⡀⠀⠈⠛⠛⠛⠛⠶⣶⡆ ⣯⣞⠶⣹⠛⢿⣁⠀⢠⣿⣯⢿⣽⣳⣟⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⢯⣟⡾⣽⢯⣟⣾⣿⠾⠽⠯⠿⣾⣽⣻⣦⠀⠀⠀⢀⢶⣄⠸⢤ ⠻⣿⣷⣝⣳⠶⡾⣄⣾⡿⣞⡿⣞⡷⣯⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣾⡿⣽⣻⢾⡽⣯⣿⣾⣟⣿⣦⠀⠀⠀⠀⠙⢷⡿⣷⠀⡠⠞⠀⢸⣶⣧ ⠀⠈⠉⣿⣷⣯⡵⣚⢿⣿⣽⣻⣽⣻⣽⣻⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣾⣿⣽⣳⢯⡿⣽⡿⠙⢷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡶⠉⠀⠀⢸⣿⣿ ⠀⠀⢰⣿⡇⠉⠛⠾⠭⢿⣾⣳⢯⡷⣯⣟⣿⠞⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⢸⣿⣳⢯⣟⣯⢿⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣿⣿ ⠀⠀⢸⣿⣇⠐⠂⠄⡠⠈⠻⣿⣯⣟⡷⣯⢿⣾⣿⣥⣴⣤⣀⣀⣀⣀⣠⣾⣿⠃⠀⠀⠀⠀⠀⢠⣿⡿⣽⣻⢾⡽⣯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⣿⣿ ⠀⠀⢸⣿⣿⡄⠁⣢⠴⠶⢤⣄⡛⠿⣽⣯⣟⡾⣽⢯⡿⣽⣻⢿⡿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢺⣿⡽⣷⢯⡿⣽⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⣿⡏ ⠀⠀⠀⣿⣿⣷⠀⡏⠀⣀⡀⠈⠙⢷⣌⠉⠛⠻⠿⢯⣿⣳⣯⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡽⣯⣟⣷⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⢠⣿⣿⡇ ⠀⠀⠀⢹⣿⣿⣿⠵⢻⡿⠱⡆⣠⡾⣿⣄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣟⣷⣻⢾⣽⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢸⣿⣿⠁ ⠀⠀⠀⣸⠟⠉⠀⢠⣿⣥⠶⠋⠁⢀⣿⣩⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⡾⣽⣻⢾⣽⠛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⣾⣿⡏⠀ ⠀⣠⠞⠁⠀⠀⢠⡿⠋⠀⠀⠀⢠⣾⠟⠁⢸⡇⠀⠀⢺⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣻⣯⢿⡿⣿⣷⣦⣤⣀⡀⢀⣀⣴⣾⣿⡿⠁⠀⠀⠀⣿⡿⠁⠀ ⢾⠁⠀⠀⠀⣠⡞⠀⠀⠀⠀⢠⡿⠁⠀⠀⣾⠇⠀⠀⠹⣧⣴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣽⣷⣯⣿⣽⣻⣿⣿⣿⣻⣷⠏⠀⠀⠀⠀⣼⣿⠁⠀⠀ ⠈⢣⣤⡄⠀⢻⣷⠀⠀⠀⣴⡟⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣭⠙⣭⠉⡍⢻⣷⣤⣶⣶⠛⠛⠉⠓⣶⣦⡄ ⠀⢀⠈⠀⠀⠀⠙⠻⠞⢻⢿⡇⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢷⡆⠀⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⣤⡶⠶⠶⠖⠦⣴⣿⣿⡹⢎⡽⡳⢶⠦⣴⢖⡻⢽ ⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠻⠉⠀⠀⠀⢀⣤⡀⠀⠀⠀⢱⡟⠁⠀⠀⡀⠢⢀⠘⠻⠿⢿⣿⣶⣽⣎⡽⣚⡼⣙⢮ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣧⢻⡿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣿⠇⢀⡤⠠⣿⣷⡀⢻⡿⡖⠶⣀⠂⠀⢀⣼⣿⣿⠟⠛⠛⠷⠷⠿⠾ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡅⣠⣾⡿⠿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢰⡏⣠⠏⠀⠀⣼⠀⢹⡟⠀⢻⡴⠃⣀⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⣞⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣻⡿⠃⠀⠀⠀⠉⠙⠛⠻⣿⣿⣶⣦⣤⣀⣠⡾⠋⠀⠀⢠⣿⠟⠁⠀⠀⢰⣇⡴⠋⠀⠀⢸⣧⣾⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠠⠀⣻⢂⣄⠀⠀⠀⠀⠀⠀⢀⣾⣇⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⢻⡿⣽⣻⢿⣿⣿⠃⠀⠀⠀⣿⡿⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠈⣿⠛⠉⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠌⠀⣼⠁⡼⠈⠀⠀⠀⠀⠀⠀⣀⣿⢧⣿⡀⠀⠀⠀⠀⠀⡸⠉⠀⢸⣿⣳⣟⡿⣾⠇⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢹⣇⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠳⠈⣼⠂⡼⠁⡐⠀⠀⠀⠀⠀⡐⣻⣿⣾⢻⣷⡄⠀⠀⠀⠀⢃⠀⠀⠀⢻⣷⣻⣾⣯⣤⣤⣄⣤⣴⡞⣛⠷⣤⣤⣤⡶⠋⠁⠟⠦⣤⠤⣤⣿⡟⠀⠀⠀⠘⣿⡄⠄⠀⠀⠀⠀⠀