⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣠⣤⡤⣤⣤⣤⣤⣤⣤⢤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⢻⣟⣯⣟⢾⣳⢟⣳⢧⣟⣞⣧⣟⣯⣞⣧⣟⡾⣽⡻⣟⡶⣤⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣻⣳⢯⣟⣞⡿⢮⡷⣞⣯⢯⣿⣹⡟⣾⡽⣞⡾⣵⣞⡷⡾⣽⣳⢿⣹⣽⣳⢯⣽⣻⢦⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⣠⢶⢯⣟⣯⠷⣯⣟⢾⡽⣞⣯⠿⣽⣞⣻⢶⣏⣿⣳⡽⢯⣽⣳⢾⣽⢻⡵⣯⣻⢧⡷⢯⣟⣞⡷⣻⢾⡽⣦⣄⠀⠀⠁⡀⠀⠀ ⠀⡀⠀⠀⢀⡾⣽⢯⣟⡾⣞⢿⣳⣞⣯⣟⡽⣞⡿⣳⢾⡽⢯⣞⡷⣭⣟⢿⣺⣭⣟⡾⣏⡿⣵⢯⣟⣽⣻⢾⣹⢾⣽⣛⣾⣳⢯⣗⡀⠀⠈⢀⠀ ⠀⠀⠀⢀⣿⢻⣧⢿⣼⡻⣟⡿⣇⡿⣼⡼⣻⣟⣧⣟⣿⢻⡿⣼⣻⢧⣟⡿⣇⡿⣼⣻⣻⢟⣟⡿⣼⢇⡿⣟⣟⡿⣜⡿⣤⣟⡿⣼⣻⡀⠀⠀⡀ ⡆⠀⠀⡾⣞⣟⡾⢯⣶⣻⡽⣳⢯⣟⣧⣟⡷⢯⣞⡾⣭⢿⡽⣳⢯⣟⡾⣽⡽⣽⣳⢯⢷⣻⢾⣝⣯⠿⣝⣯⢾⣽⣫⣽⣳⢯⣽⣳⢟⣶⠀⠀⢰ ⠁⠀⠀⣿⡽⡾⣽⣻⣞⣵⣻⣽⣛⣮⢷⡾⣽⣻⢾⣝⣯⣟⡾⣽⣛⡾⣽⣳⢯⡷⢯⣻⢯⡽⣾⡽⣞⡿⣽⡞⣟⣶⣻⣞⣭⣟⡾⣭⣟⡾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣟⣿⣻⢷⣦⡀⢠⣾⢿⡆⠀⣰⣿⢷⡄⣰⣿⣻⣟⣿⣳⣄⠀⠀⣤⣾⢿⣻⣟⡷⣦⠀⣴⣿⣟⣿⣻⢷⠀⣾⣟⣿⣻⣟⣶⡄⠀⠀⠀ ⠀⠀⠀⣿⣽⡇⢈⣿⣳⡇⢸⣿⢯⡇⠀⣽⡾⣟⡇⣼⡷⣿⠉⢺⣯⢿⠀⣾⡿⣽⠛⠛⠚⠛⠋⠀⣿⣳⣿⡚⡛⠉⢈⣿⣾⣳⠉⣾⢷⣻⠀⠀⠀ ⠀⠀⠀⣿⣽⣻⣿⣽⣻⡄⢸⡿⣯⡇⠀⢾⣽⣟⡇⣼⢿⣽⡶⣿⣽⠟⠀⣿⡽⣿⢰⣿⣻⢿⣦⡀⣿⢷⣯⣟⡿⡇⠰⣟⣾⣟⣾⡽⣿⠃⠀⠀⠀ ⠀⠀⠀⣿⣷⣇⣀⣯⣷⢿⠸⣿⡽⣧⣀⣿⡽⣾⠇⢾⣻⣷⠉⣿⣾⢦⡀⢿⡽⣿⣤⣉⡽⣟⣾⠅⣿⣻⣾⣉⣁⣀⠰⣿⣳⣯⢹⢿⣽⣄⠀⠀⠀ ⠀⠀⠀⢿⣾⣽⣻⣾⠽⠃⠀⠹⠿⣽⣯⢷⡟⠋⠀⢻⣷⡻⠀⠹⣾⣟⠇⠈⠻⠷⣯⡿⣽⠟⠋⠀⢿⣳⣯⣟⣿⡻⠐⢿⣽⠞⠀⠻⣽⡾⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⢀⣤⣤⣄⡀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣻⢾⣽⣧⠀⢀⣾⢿⡽⣯⢿⠄⢠⣿⣟⣾⡽⣧⠀⠀⣿⣯⢿⣽⣧⠀⠀⢰⡿⣽⢯⣿⠆⠀⠀⣠⣾⣟⡷⣟⣾⡽⣯⡿⣿⣆⠀⠀⠀ ⠀⠀⠀⣿⣯⢿⣳⣿⣠⡿⣽⣯⢿⣻⠏⠀⢸⣷⣻⢾⣻⣽⠀⠀⣿⡽⣟⣾⣽⣧⠀⢸⣟⣯⣿⡽⡆⠀⣼⣿⣳⣯⢿⡻⠝⠻⠷⢿⡳⠋⠀⠀⠀ ⠀⠀⠀⣿⣽⣻⣟⡾⣷⣻⣟⣾⡟⠁⠀⠀⢸⣷⣻⣟⣯⣿⠀⠀⣿⣟⣯⢿⡾⣽⣧⡼⣯⣷⢯⣿⠅⢸⣟⣾⡽⣯⠃⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⣿⡽⣷⣻⢿⡽⣷⣻⢷⣦⡀⠀⠀⢸⣞⣷⢿⣽⣾⠀⠀⣿⣾⣻⢯⡿⣻⢾⣽⣷⣻⣯⢿⡆⢸⣻⣞⣿⣽⠀⢾⣽⣳⡿⣽⢯⣷⠀⠀⠀ ⠀⠀⠀⣿⢿⡽⣯⣿⠻⣽⣯⢿⣳⡿⣆⠀⢸⣟⣾⢯⣷⢿⠀⠀⣿⣳⣿⣻⡇⠘⢿⣳⣯⡷⣟⣿⡄⠘⣯⣟⣾⣽⣧⣀⠉⢓⣿⣟⣯⣿⠀⠀⠀ ⠀⠀⠀⣿⣟⡿⣽⣻⠀⠹⣾⣟⣯⢿⣻⡇⢸⣽⡾⣿⡽⡿⠀⠀⣿⣟⡾⣷⡇⠀⠘⢿⣳⡿⣯⣷⠆⠀⠘⢯⣷⣟⡾⣟⣿⣻⣽⣾⣻⠞⠀⠀⠀ ⠀⠀⠀⢻⣯⡟⣿⠃⠀⠀⠘⢻⣾⡟⡏⠁⠀⢳⣿⢳⣿⠃⠀⠀⢻⣯⣿⡗⠁⠀⠀⠈⢻⣽⣷⡟⠀⠀⠀⠀⠙⠚⣿⣯⣷⡟⣷⠛⠁⢠⡄⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠋⠀⠀ ⡀⠀⠀⣿⢻⣟⢿⡻⣟⡿⣻⡟⣿⡻⣟⣿⢻⣟⢿⣻⢟⣿⢻⣟⢿⣻⢟⣿⢻⣟⢿⣻⡟⣿⡻⣟⡿⣻⡟⣿⣻⢟⣿⢻⣟⢿⣻⢟⣿⣻⠀⠀⠀ ⠃⠀⠀⠙⣿⣺⢯⣟⣽⣳⢯⣟⣳⠿⣽⡞⣟⡾⢯⡽⣾⢽⣛⡾⣯⡽⣾⢽⣛⡾⢯⣷⢻⣳⠿⣭⢷⡯⣟⣳⢯⣟⡾⣛⡾⣯⡽⣞⡷⠏⠀⠀⡐ ⠀⠂⡀⠀⠈⠑⢿⣺⢧⣟⣯⢾⣽⣻⣳⢿⣹⡟⣯⢿⣹⢾⡽⣻⣼⣻⡵⣯⢿⣹⣟⢾⣏⣿⢻⡽⣏⡷⣯⠿⣽⠾⣽⣏⡿⣵⡻⠉⠁⠀⢀⠐⠀ ⠀⠀⠀⠂⢀⠀⠀⠀⠉⠚⠉⠳⠷⢏⣷⢯⣷⣻⡽⣏⣯⢿⣹⢷⣻⣼⢻⣭⡟⣷⣞⢿⣺⣭⢿⣝⣯⣽⣳⡿⠽⠛⠓⠚⠉⠀⠀⠀⣀⠔⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠁⠈⠉⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀