⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠙⢋⢉⣯⣑⢶⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⣠⣼⡿⠿⢿⡯⠁⠀⠀⢿⠟⢹⣽⣣⡀⠀⠀⢀⣇⠔⠀⠀⠨⣑⡜⢭⠣⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⣎⣁⣳⣀⣂⣴⣿⣿⣷⣤⣠⣤⣴⣤⣤⣀⠀⢀⢘⣿⣿⢳⠀⠀⠈⠀⠀⠀⠀⢠⠢⣑⠆⠱⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠞⣉⣵⡿⠿⣻⣿⡿⠿⠛⠉⠉⠁⠔⠀⠀⠉⢿⠁⡀⡀⢉⢺⡞⣿⣾⣿⣶⣄⠀⠤⡐⠀⣈⣀⣀⡞⠁ ⠀⠀⠠⠤⠀⠐⣿⣿⠖⣋⡃⣨⣤⠿⠟⣰⡿⠋⠁⠀⠀⠀⠀⠀⢘⣉⣚⣀⣘⡜⠃⢏⣥⣻⣌⡷⢈⠿⠙⣿⣿⣿⡉⠀⠀⠀⠀⠻⣿⡀ ⠀⠀⢀⣀⣀⣀⣨⣿⢹⣿⣿⡟⠛⣩⡟⠛⠒⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣼⠅⠐⢩⣿⣾⣿⣷⣿⣾⣾⣹⣿⢻⣿⡄⠠⡀⣰⣰⣇⡙ ⠀⠀⠈⢠⠀⠀⣼⣞⡅⠙⠛⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡵⠠⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣷⣾⣿⣿⡏⠀ ⠀⠀⠀⠀⠃⣼⡿⣎⠀⢠⠂⢾⠃⠀⠀⠀⢀⣤⣬⣦⣄⠀⠀⣄⣠⣖⡉⠉⡀⠠⣼⣿⣿⠿⡂⠹⣿⢿⣷⢀⣹⣿⣿⣿⢹⣿⣳⡿⠀⠀ ⠀⠀⠀⠀⢠⣿⣦⣀⢄⣀⣔⣿⣤⣤⣶⣟⣈⣻⣿⡛⠿⣶⡵⣿⣿⡀⠙⢳⡂⠘⠟⠘⣧⣾⢿⣤⡻⢿⡌⣽⢷⣿⣗⣾⣿⣿⣁⣤⠖⠆ ⠀⣀⣰⡹⡽⣿⣿⣿⠏⢢⣽⡿⡨⠽⣿⠛⠻⠋⠁⠹⣦⠈⢩⣿⡿⡧⡓⠒⠂⠀⠤⠠⣁⠀⠀⠀⠀⢎⣽⣿⣿⣿⣗⡿⣿⣿⣯⣽⠁⠀ ⢀⣠⠟⢰⣷⣿⢿⢿⣪⢈⢿⣣⡈⡀⠀⠀⠀⠈⠀⢀⣿⣷⣾⢿⢃⠸⠛⡄⠀⠀⠀⠀⢠⠷⠶⢶⣿⣿⣷⣟⣿⣿⣷⢇⣿⣻⣿⠋⠀⠀ ⠀⠰⠀⢸⣿⣿⣾⣾⣮⣿⡮⡛⠣⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠧⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠨⡟⠉⡹⣫⣿⢟⠝⣼⡿⣁⠋⠀⠀⠀ ⠀⠒⠳⣼⣿⣿⣿⡏⣭⣏⢺⡀⠀⠀⠀⠀⣀⣴⣿⣾⡓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠏⠂⠴⠃⠉⠓⢉⣼⠿⠫⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠛⠓⣖⠒⢴⠞⠉⠉⠀⠉⠓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠲⢟⣦⣠⡽⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⠀⠀⣀⣀⣀⠠⠤⠤⠐⠒⠉⠀⠀⠙⣄⢰⣿⡏⠙⠲⠌⣑⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⠁⠉⡤⡑⡦⢄⠀⠀⠀⠀⠀⠀⣿⣿⠗⠈⠻⣆⠀⠉⠓⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠈⠘⠜⠀⠀⠀⠀⠀⠀⢠⣻⠋⠐⠣⠀⠈⢳⠆⡀⠀