⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠒⠉⠉⠉⠁⠐⠦⡀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣀⣀⠀⠀⠀⠀⠀⠀⠙⡀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠒⣤⣿⡴⡞⠉⠉⠉⠒⢤⠀⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠊⣡⠏⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠌⠈⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢧⠞⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠳⣵⡀⠀⠀⠐⡄⠀⠈⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⠃⠀⠀⠀⠀⠀⢸⡀⢀⣤⠾⣷⠀⠀⠀⠈⠓⠄⠀⠀⡑⠀⠀⠀⠀⢤⡀⡘⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⢰⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢿⡵⡟⠁⠀⠀⠀⠀⠀⠀⠀⣰⠧⡀⠀⠀⠀⠀⠈⠓⢶⠯⠷⠀⠀⠀⠀⠀ ⠀⠀⠀⢯⠃⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⡇⠉⠓⢦⡀⡠⡤⠴⠀⠀⣰⣃⣀⣙⣦⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⢸⠀⠀⠀⢰⠁⠀⠀⣠⡴⢶⠛⠓⠲⠆⠀⡇⠀⣠⣂⡠⠾⠛⠉⣀⣥⠀⡙⣆⠀⠀⠀⡠⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣾⡄⠀⠀⢺⠀⠀⣼⢿⠝⣡⡿⡆⠀⠀⠀⠷⠚⠁⠉⠀⠀⠀⠈⣿⣿⠀⠀⡇⢣⡀⠀⣷⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⠉⠢⢼⣿⣄⢸⡷⢸⡀⢻⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⠀⢀⠇⠈⣿⢸⠈⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⢨⡇⠀⠀⠈⠉⠈⠳⢇⠀⢷⠀⠉⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⠏⠀⢰⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠐⣧⠀⠀⠀⠀⠀ ⠀⢰⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠺⢷⡀⠀⠀⠀ ⠀⣇⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠆⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀ ⠸⠏⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡀⠀⠀⠀⠈⠳⢤⡀⠱⣄⠀ ⠀⠀⠀⠀⢮⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢣⠀⠀⠀⠀⠀⠈⢿⠙⠋⠁ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⣟⡒⠶⢤⣤⣀⣀⣀⣠⠴⠚⣏⠀⠀⠀⠍⠀⠀⠀⠀⠀⢀⡈⢇⠀⠀ ⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠶⠿⣯⡇⠀⠀⠀⠈⠉⠉⠀⣀⣤⣿⢶⣤⠠⡇⠀⠀⠀⠀⠀⠀⢷⠀⢆⡀ ⠀⠀⠀⢠⠃⠀⠀⡀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠘⠣⢤⣤⣠⣄⣀⠤⠜⠀⠃⢻⣿⣿⠇⡇⠀⠀⢀⣇⠀⢄⡘⢿⢄⣧ ⠀⠀⢸⠃⠀⢀⣼⠁⠀⠀⡱⣄⠀⠀⠙⠷⣆⠠⠀⠀⢀⡾⣗⣽⡀⠀⠀⠀⣼⠇⡜⠀⢥⠀⠀⡎⠈⠧⣄⢹⠾⠀⠀ ⠀⠀⢮⠴⢾⠛⠨⡄⠀⢠⡃⠀⣹⠒⠤⠤⢹⣦⣀⣠⣯⣿⣽⣾⣿⡀⠒⢉⣿⠀⢈⠗⠀⠳⡄⣇⡀⠀⢹⣹⡄⠀⠀ ⠀⠀⡾⠀⡰⠀⢂⢧⢠⠓⠀⢠⠇⠀⠀⡆⠈⣿⡈⠙⢱⣷⣧⣼⡀⠀⠀⢸⡇⢠⠏⠀⠠⠋⢁⡏⠀⢠⠄⢻⡶⠀⠀ ⠀⠀⡇⢠⠁⠀⡂⠈⠎⢰⠁⡘⠀⠀⠀⡅⢸⢸⣇⠀⣾⣻⢾⣻⣇⠀⠀⡿⢠⠋⠀⠠⠁⢀⠎⠠⡄⡺⠀⠈⡗⠀⠀ ⠀⢰⡇⡆⠀⢰⢠⡆⢀⠇⠀⠃⠀⠀⢘⠀⢸⠈⣾⠄⢸⣟⣿⣟⣿⠀⢸⣧⡗⠀⠰⠁⠀⡞⠀⢰⣿⠃⠀⣰⣏⠀⠀ ⠀⡞⠈⠁⢰⠆⣾⢁⡾⠀⠸⠀⠀⠀⠂⠀⢸⠀⠹⡆⣾⣾⣽⢾⣿⡀⢸⠆⠁⢀⠃⠀⢨⠁⠀⠈⣏⠀⢰⠃⢹⠀⠀ ⠀⣃⡀⠀⣋⣠⠿⠨⠃⠀⠆⠀⠰⠘⠀⠀⡼⠀⠀⠿⢟⣓⡫⢿⣻⡇⣿⠃⠀⠇⠸⢀⠃⠀⢰⡸⣿⣠⢃⠀⠼⠀⠀