⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣁⠡⡀⣄⠢⡐⢄⠢⠄⡄⢂⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⢳⡌⢧⡱⣌⢧⡹⣌⢧⢫⡜⣥⢫⣜⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⢏⡳⢽⣳⡽⣮⢷⡽⣎⣯⢷⣹⢮⣷⣮⣷⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠮⣜⢎⡞⡼⣡⢏⡻⣽⣻⢾⣽⣞⣯⣿⣟⡾⣳⣭⢷⣻⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⣞⣥⢻⣜⡳⣝⢮⡳⣝⢯⣿⢾⣽⣿⣳⢾⣽⣳⢯⣟⣳⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⢷⣝⣮⠷⣞⡽⣞⣧⢟⡾⣭⢿⣿⣻⢷⣯⣟⣾⣽⣻⢾⣽⣞⣷⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡾⣼⣻⡽⣶⣻⠷⣽⣻⣼⣳⡟⠊⢻⡿⣾⣽⣻⣽⢯⣿⢾⣽⣻⣽⣯⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⢾⣽⣳⢯⣟⡷⣯⣟⣷⣻⣞⡷⠂⠀⠀⠹⣷⣯⣟⣾⢿⣽⣻⡾⣯⣷⣻⢾⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣳⣟⡿⣾⣽⣻⡾⣽⣷⣻⣞⡷⡯⠃⠀⠀⠀⠀⠹⣾⢯⣟⡿⣞⣯⡿⣷⢯⣟⣯⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢯⣷⢿⣽⡷⣯⣷⢿⣻⣞⣷⢿⡽⠃⠀⠀⠀⠀⠀⠀⠻⣯⡿⣽⡿⣽⣻⣽⣟⣯⡿⣽⡷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣽⢿⡾⣯⣷⣟⡿⣞⣿⣽⣻⢾⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣯⢿⣽⣻⡾⣽⣾⣻⣽⣻⢷⣻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡽⣟⣯⡿⣷⣻⢾⣟⣯⣷⢿⣽⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⢿⣽⣳⣿⣻⢾⣽⣳⣿⣻⢯⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣳⣿⣻⣽⣻⢷⣟⡿⣾⣻⢾⣯⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣾⣟⠾⡽⣿⣽⣳⣯⣟⡿⣽⣾⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣟⡷⣟⣾⣽⣳⣿⣻⢾⣟⣷⢿⣯⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠻⠾⡽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣻⢾⣻⢿⣽⢾⣻⣾⡽⣿⣞⣯⣿⢾⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣳⣿⣻⢯⣿⢾⣟⡿⣾⣽⢷⣻⣽⣾⡛⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣾⣻⣟⡿⣽⢯⡿⣽⢯⡿⣽⢯⣿⣻⢾⡶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣻⣽⡾⣯⣿⣽⣻⡾⣟⣷⣯⢿⣯⣷⡟⠀⠀⠀⢀⣠⣤⣾⣻⣽⣻⢾⣽⣳⣟⡾⣽⢯⡿⣽⢯⡿⣽⢯⣟⡾⣽⢯⣟⡷⣯⢿⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣳⢿⣻⣿⣷⣿⣾⣷⣿⣯⣷⣿⣿⣿⣿⣤⣤⣶⢿⣻⣽⣳⣯⣟⡷⣿⣻⢷⡿⣾⡽⣯⢿⡽⣯⢿⡽⣯⣟⣾⣻⣽⣿⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣟⡾⣽⢯⣟⣾⣽⣻⢷⣟⣿⣻⣽⣻⣞⣷⣯⢷⣟⡾⣿⣽⣳⣯⣷⣻⣽⢷⣻⣯⢿⡽⣟⣿⣯⣿⣟⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣽⣻⣽⣻⣞⡷⣯⣟⡿⣞⣷⣻⣞⣷⣻⢾⣽⣻⢾⣻⢷⣯⢷⣟⣾⡽⣾⣻⣽⢾⣻⢿⣽⣳⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⣴⡿⣽⢯⣟⣯⣟⡷⣯⣟⣷⣻⡽⣯⢿⡽⣟⣾⣽⣻⢾⣻⢾⡽⣾⡽⣯⣷⣻⢯⣟⡾⣟⣾⣽⣻⡽⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⣿⣿⡽⣿⢾⣳⣯⣿⢷⣻⣾⢷⣟⣯⣿⣻⣯⢷⣯⣟⣯⣟⣯⣟⣷⣻⢷⣯⣟⣯⢿⣽⣻⠾⠓⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⣿⣯⣿⣿⣿⣟⣿⣾⣿⣿⣯⣿⣿⣻⣽⡿⣽⣻⢾⡽⣾⡽⣾⡽⣾⣽⣻⢾⡽⣞⣿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣟⡷⣯⢿⣽⣳⣟⣷⣻⢷⣯⣟⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣻⣽⡿⣷⣿⣻⣾⢿⣾⣟⣷⣿⣯⣿⣟⣿⣷⠀⠀ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣻⣞⣷⣻⢾⣽⣻⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣽⣟⣯⡿⣟⣾⢿⣽⣻⢷⣻⣟⣾⣽⡷⣿⢯⣿⣧⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⡾⠝⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢾⣽⣻⣽⢾⣻⠾⠛⠉⠀⠀⠀⠀⠀⠉⠛⢷⣟⡆ ⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻