⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠒⣒⣋⣉⣉⣙⣒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠐⠒⠒⠒⠂⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⢋⠤⠖⠊⣉⣀⡀⠤⢄⣀⣈⡉⠑⠢⢄⡙⠢⣀⠀⠀⣠⠖⢋⡡⠴⠒⠋⣉⣉⣉⣉⣉⡛⠒⠤⣌⡑⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⢏⡥⠊⣡⠴⠺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⠳⣌⡓⢋⡤⢊⣡⠔⠚⠉⠀⠀⠀⣶⠀⠀⠀⠉⠓⠦⣈⠳⣄⡱⣄⠀⠀⠀⠀ ⠀⠀⢠⠞⣰⠋⣠⠞⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠪⣗⡯⠚⠉⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠈⠳⣌⠙⣏⠳⡄⠀⠀ ⠀⢠⠇⡜⠁⡴⠁⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠈⠳⡈⢣⡘⣆⠀ ⢠⠏⡘⠀⡸⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢳⡀⢣⠹⡄ ⡞⢠⠇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⢣⠘⡆⢹ ⡇⢸⠀⡞⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸⡄⢷⠘ ⡇⢸⠀⡇⠁⠀⢠⣧⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⡇⢸⢰ ⢇⠸⡄⢳⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⠇⡏⢸ ⠸⡆⢃⠘⡆⠀⠙⠛⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⡾⢰⠃⡞ ⠀⠹⡜⢦⠹⡄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡸⢡⡏⡼⠁ ⠀⠀⠱⣌⢧⡙⢄⠀⠀⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⡴⣡⣏⡾⠁⠀ ⠀⠀⠀⠈⢢⡙⢮⡳⣄⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣠⣾⡼⣡⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⡙⢮⡳⣀⠀⠀⠀⠀⠀⠀⢀⡆⠈⠛⠋⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⣞⡝⣡⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡳⣄⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠸⢿⡟⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡳⣄⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⣠⢾⡷⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡵⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡢⡀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡵⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡢⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣠⢞⡽⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⢯⡢⡀⠀⠈⠙⠃⠀⠀⠀⠀⣠⢞⡿⣿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢝⡢⡀⠀⠀⠀⠀⣠⢾⡷⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢝⢦⡀⣠⣾⡵⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡛⣯⡽⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀