⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢏⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣧⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠁⠀⠀⢀⢀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠙⢛⣓⣽⣨⣽⡵⣷⢥⢧⣿⣡⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⢋⠉⢀⡥⠞⠋⠁⠀⠀⠀⠀⠐⠫⣺⡽⡝⣿⠲⣥⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣛⣗⡨⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠈⠻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⣧⣎⣾⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡘⡷⣃⣚⣕⡆⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡐⣠⣿⣝⣿⢛⣽⢾⣒⠶⣥⡶⠁⠀⣀⡄⣀⡀⣀⠀⠀⠠⢀⣀⣀⡀⠀⠀⠸⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠰⠭⢣⣿⡼⣃⣟⣣⣧⡟⠾⣪⢭⡀⠀⠘⢊⢸⣴⡧⣮⣷⣤⣀⠀⡒⠒⢬⠝⠂⠁⢿⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⠳⠮⣉⠉⠩⣛⣯⣽⣮⡳⣧⣟⡄⡫⢮⠏⠅⠀⠀⠀⡿⠏⠈⠀⣠⣤⢭⣛⡿⣦⡺⢪⣴⠴⣒⣉⣻⠉⠀ ⠀⠀⠀⠀⠀⠀⣴⠏⢀⠀⠀⠀⠈⡇⠀⠀⠙⣿⢋⡬⣥⣛⠟⣮⣿⠁⠀⠈⢈⠂⠣⢤⢀⡞⠁⠀⡀⠙⣿⡄⡃⠀⠱⣟⠀⢈⡙⢶⠀ ⠀⠀⠀⠀⠀⡜⠁⠀⠇⠀⠀⠀⠀⠸⡄⠀⢸⡇⣇⡴⢤⡽⡆⣿⡅⢤⠓⠂⠤⠌⠉⠒⠸⣆⠀⠀⠉⠀⣸⠇⠁⠀⠀⠙⢧⡄⢀⡾⠀ ⠀⠀⠀⠀⣼⠀⠀⡼⠀⠀⠀⠀⠀⠀⢱⠀⢸⣯⠸⠄⢼⣄⠳⣿⡄⠠⢠⠁⠀⠀⠀⠀⠀⠈⠳⠦⠴⠊⠁⠀⠀⠀⠀⠀⠀⠙⢧⡁⠀ ⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣆⢸⠻⣆⠀⣀⠉⠰⣳⣒⣠⣡⣀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⡸⣇⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠸⡈⡆⢹⠊⠉⠁⢾⢟⣱⣧⢘⢥⢴⠓⡚⠋⣀⣁⡄⠄⣀⣴⠎⠉⠀⠙⢦⡀⠀⡀⠀⠀⡇ ⠀⠀⢠⡇⠈⠁⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢷⠈⣣⣄⣺⣽⡾⡮⣿⡝⠵⠷⡵⢙⡞⣡⡴⢶⣺⣵⡙⡐⠶⡦⢄⡀⠀⠈⠀⠀⠀⢠ ⠀⠀⣿⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣮⠀⠸⣰⡾⣝⡷⠣⣟⡷⣻⣿⣲⡽⢿⣽⢽⣷⣺⣝⣣⣺⣿⠒⣦⡭⠧⣀⡀⠀⠀⠘ ⠀⠀⣏⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣱⠏⣼⣻⣏⣛⣭⠧⣿⢿⡂⠳⠀⠁⠈⠈⠉⠉⠀⠘⠈⢹⣷⢯⡀⠙⠣⠤⠜ ⠀⠀⣇⡅⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣞⣏⣃⣿⣰⣟⣽⣿⣻⠁⢄⠀⠠⠔⠉⠉⠛⠒⠒⠒⠚⣏⠁⠀⠀⠀⠀⠀ ⠀⢸⠋⠣⠀⠀⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣆⡹⣗⣟⢺⡵⣡⣓⣿⠶⣘⢆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⠀⠈⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠏⢸⢳⢚⣧⣮⣹⢿⣧⢯⡾⢧⣷⢥⢦⣀⠀⠀⠀⣠⣾⢳⡆⢀⣀⠀⠀⠀⠀ ⡼⢡⠀⠀⠀⠀⠀⢣⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⢻⢒⡾⣈⡟⢹⢾⡾⣲⣿⣺⣻⡽⣽⣟⣿⣹⣽⡟⢵⠒⠓⢡⠂⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡈⢻⠈⣽⣚⡯⢭⢵⠟⢽⣏⣻⣗⢿⢳⢻⡿⠋⠀⢀⡠⠔⠧⣀⢀⡀⠀