⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣟⢶⣳⢮⣇⠿⣽⣿⣿⣿⣿⣟⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⣽⣿⣿⡞⢧⣏⡷⣎⠿⣽⣿⢿⣿⣿⢿⣷⣿⣞⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡯⣼⣿⣿⡿⡘⢧⢚⣿⣾⡽⣹⢿⣿⣻⣿⣿⡟⣿⡟⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⣽⣿⢿⣇⣽⣾⣈⣻⣿⣿⣿⣿⢿⣟⣻⣿⣿⣿⣞⣽⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⡏⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡟⡶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⠍⠀⠈⠙⠻⣿⣷⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⠹⢿⣿⣿⣿⡷⣏⣾⢻⢧⡻⣽⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢁⢦⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣜⣷⣯⡳⣽⣿⣿⣻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⠟⡛⣿⣿⣿⣿⣿⣶⠶⠖⠒⠀⠀⠀⠠⡐⡩⢿⣿⣿⣿⢷⣻⣷⣿⣳⣟⡾⣽⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣰⣮⣷⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠣⢥⣙⡿⣿⡿⣯⣿⣿⣿⣯⢷⢯⣟⣳⠿⣜⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⢿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠴⣘⢇⠺⣼⣳⣿⣿⣿⣿⣿⡿⣿⣛⡾⣭⢟⣽⡹⢶⣹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⠰⣈⣞⣿⣿⣿⣿⢿⣿⣿⡿⣽⡳⢯⣷⣝⣾⢯⡟⣭⣷⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠴⢾⢿⣿⣿⣿⣿⣿⣿⣿⡿⣏⢿⡱⣏⢯⡻⣟⠿⣧⣻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠉⢷⣌⠢⡍⢾⢻⡽⣻⣿⡿⡿⢧⡛⣜⢣⢛⡜⣲⢽⣸⣛⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢂⠉⢎⣳⡿⠟⡏⠱⡉⠆⠱⡈⢆⢣⡘⢬⣛⣶⣿⣿⣿⣿⣟⣷⣿⣿⣿⣻⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠀⠃⠀⠁⠀⠈⠄⡑⣈⢦⣽⣾⣿⣿⣿⢿⣻⣽⣿⣿⣿⡿⣞⣳⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⣶⣜⣶⣿⣿⣿⠻⣝⡷⣿⣟⣿⣿⣿⣿⡿⣽⣏⡷⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡴⠶⠟⠊⠔⣰⠿⠏⠱⣈⠻⣼⣿⣿⢾⣿⣿⣿⣿⣽⣳⢾⣽⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⣀⣻⣿⣿⣯⣿⣿⣿⣿⡷⣯⣟⡿⣾⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣟⣷⣿⣿⣿⣿⣽⣳⣯⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⢿⡼⣿⣿⣿⣿⢧⣏⣿⣹⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢤⣦⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢢⣿⣿⡿⣯⣟⣿⣿⣿⣿⣟⡿⣾⣟⣿⣿⣿⣿⣿⢿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠌⠻⣿⣿⣆⠀⠀⠀⠤⡀⠀⢀⠠⠀⡀⢀⠠⢄⣧⣿⣿⣿⣟⡷⣿⣻⣿⣿⣿⣽⣻⡷⣿⣿⣿⣿⣿⡿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⢃⠐⡀⠻⣿⣧⣄⠀⠀⠙⠦⣄⢂⠡⠐⡠⣚⣾⣿⣿⣿⣻⢾⣟⣿⣿⣿⣿⡷⣯⣿⣽⣿⣽⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠤⡀⠀⠐⢻⡽⠿⣷⣤⠀⠀⠀⠀⢂⠱⣰⢻⣿⣿⣟⣳⢯⣿⣾⣿⣿⣿⣿⣟⣿⣞⣷⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢼⠃⠀⠀⢨⣿⣷⣌⠏⡄⠡⢌⣲⣌⠙⠤⢋⣾⡿⡽⣯⣟⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⣰⣿⣿⣿⣯⡙⣿⢆⣻⣿⡆⠌⡱⢾⣱⢟⣳⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⢡⢋⡴⣿⣿⠀⠱⣯⢇⣻⡼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣷⣽⣿⠀⠣⡜⢭⣖⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⣠⣶⡿⢟⣿⣿⣿⣿⣿⣿⢿⣿⡄⠀⠀⢠⣿⣿⣿⣿⡿⢿⡏⢩⠉⡉⢻⣿⡅⠣⡜⣣⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⠿⠛⠉⠉⠀⢸⣿⡇⣾⣄⣿⣿⣿⣿⡯⢁⠃⠌⠂⠡⠀⠈⣿⣯⠐⡥⢳⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣾⡿⠁⡜⣿⣿⣿⣿⡿⠃⠁⠀⠀⠀⠀⠀⠐⣿⠃⡜⡸⢧⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡿⢋⠀⣹⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣼⣿⢐⡸⣓⢯⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣿⢿⣿⣿⡿⠋⢁⢂⢐⣾⡿⠁⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⢿⣦⣱⡹⣾⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⢏⣠⣾⠿⠋⠀⠀⠀⣦⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⡟⣯⣀⠀⢀⣤⣰⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣯⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣷⣸⣿⣶⣾⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢢⢷⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢳⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢈⠱⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⢀⣲⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣅⣺⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⣿⡶⣤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀