⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠰⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⠀⢃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠂⡖⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠠⢸⡄⠢⡄⠀⢇⠀⠀⠀⠀⠀⠀⠰⠁⢠⡞⠀⣼⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢠⠇⢣⡖⠹⡄⠈⣆⠀⠀⠀⠀⢀⠇⠀⡾⢹⡸⠁⣅⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⣼⠀⠘⠃⠀⢫⠀⠸⡄⠀⠀⠀⡼⠀⢰⢧⠆⠇⠀⢻⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠀⡇⠀⠀⠀⠈⡼⡄⠀⢧⠀⠀⢠⠇⠀⣸⣼⠀⠀⠀⠠⢇⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠁⢸⠁⠀⠀⠀⠀⢣⡿⠀⠸⡀⠀⣸⠀⠀⣯⠃⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⡟⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⡟⠀⠀⣿⠀⠀⠀⠀⠀⠈⡇⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⢀⡇⠀⠀⠀⠀⠀⠈⠇⠀⠀⣇⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢱⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⡂⠀⠀⣽⠀⡇⡄⠀⢹⠄⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠺⠀⢸⠀⠀⠀⠀⠀⠀⢈⠇⢀⡀⠿⠀⡇⢀⠀⠸⡇⠀⠀⠀⠀⠀⠈⡇⠀⡷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠗⠀⢸⡀⠀⠀⠀⠀⠀⡼⠀⢸⠀⡇⠀⣗⠈⠀⠀⢷⠀⠀⠀⠀⠀⠀⡆⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠘⡆⠀⠀⠀⠀⢠⠇⠀⢀⢂⡇⠀⢻⠨⢀⠀⠘⣆⠀⠀⠀⠀⢰⠀⠀⡯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⡄⢳⠀⠀⠀⢠⠇⠀⠀⡆⢸⠇⠀⠸⡄⠋⠄⠀⠘⣆⠀⠀⠀⠃⠀⢘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠀⠀⠳⠀⢀⠏⠀⢀⠂⠤⣹⠀⠀⠀⢧⡈⢀⠂⡀⠘⣆⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠋⠀⠀⠠⠈⣀⡏⠀⠀⠀⢸⡄⠀⠀⠀⠐⠀⠣⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⣀⠀⠀⠄⠂⠀⠁⠀⠀⠉⠈⠉⠉⠁⠀⠂⠀⠄⠓⠲⠥⣁⣀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⠂⣠⠔⠒⠉⠑⡂⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠁⠢⣄⠙⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⢁⠎⣁⣐⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⡱⠀⠀⠛⠓⢿⣲⠿⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⡏⠙⠢⡄⠱⡄⠀⠀⠀ ⠀⠀⡔⡝⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠐⠘⣆⢳⡀⠀⠀ ⠀⡸⣸⡁⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡦⢸⠌⣳⠀⠀ ⠀⣸⡿⠃⠀⠈⡆⠀⠠⠀⣀⠀⠤⠐⠀⠀⠌⠀⠀⠀⠄⠒⠂⠀⠢⢀⡤⢂⠐⣀⠑⠸⢥⣸⠃⣾⠓⡄ ⢰⡱⣇⠀⠀⢰⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠌⠀⢀⠈⠒⢬⡢⡀⠌⡄⢨⠒⣯⢮⣳ ⢸⡇⠙⡦⠄⢀⢵⠋⢁⡀⣰⣄⠀⢂⠀⠀⠐⠂⠠⠈⠀⠀⠀⡀⠈⠄⠀⢸⣶⡍⠋⡲⡐⠅⠺⣸⢤⡏ ⠀⢣⡀⠷⢀⢂⡏⢀⠂⠈⠟⠈⠀⢀⠀⠄⠠⠀⠀⠄⠈⡀⢁⠀⠡⠈⡐⢀⠛⠂⡅⡉⢟⡌⠱⣼⢩⡗ ⠀⢸⡽⡄⡞⡜⡐⠀⠤⠂⢀⠂⢁⠠⠀⠂⠄⠡⠐⠠⠁⠄⠂⡈⠄⠡⣐⣀⠂⣔⠠⢁⠚⡾⢡⣇⡞⡇ ⠀⠀⡇⡐⠇⡷⠀⣣⣶⣫⣼⣤⣧⣔⣁⢂⠈⠄⡁⠂⠌⡐⠠⣐⣬⡶⣶⣶⣿⣿⢷⠂⣉⡇⣹⢯⣾⠇ ⠀⠀⢻⢀⠊⡇⠰⠀⣸⡟⢭⣿⣿⠿⣷⣶⠁⠐⠠⠔⠀⠀⢱⡿⠏⣸⣿⣿⣹⣿⣾⠀⠰⡇⡜⢺⠟⠀ ⠀⠀⠘⡎⡃⡇⠁⠆⠹⡀⢻⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠚⠣⠀⠹⣿⣿⣿⡿⠁⠈⠰⣟⢨⡏⠀⠀ ⠀⠀⠀⢳⢡⡗⢀⠠⠀⠈⠈⠉⠻⠯⠁⠀⠀⠀⡀⠀⣀⠐⠀⠀⠀⠀⠈⠙⠁⠀⢀⠈⣱⡟⣾⠁⠀⠀ ⠀⠀⠀⠘⣾⡗⡈⠠⢀⠂⡀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡀⠄⡀⠄⠂⠀⢀⠠⢀⠌⡐⣹⢇⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣴⢃⠢⢁⢂⡐⠠⠐⢀⠠⢀⠁⠌⠀⠡⠐⠀⠄⡀⠂⠄⠊⡀⠢⡐⢄⠢⡽⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡎⡐⠈⡄⡐⠠⢈⠀⠐⠒⠤⢬⣁⣌⠥⠬⠖⠚⢁⠐⡐⢠⠑⡰⢈⢶⡻⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢦⡉⡐⠄⡡⢂⠈⠄⠀⢂⠀⠀⡀⠀⠄⠐⡀⢂⠂⢄⠃⡜⢠⢃⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠣⣦⣁⠆⡐⠌⡐⢀⠀⢂⠀⠡⢈⠡⠒⡄⢊⠤⣣⡼⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠽⢷⢾⣴⣦⣅⢊⣰⡈⡔⣂⣥⣣⣼⣽⣾⠷⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⢁⠀⡈⠄⠀⠉⠀⠈⠌⠙⡭⠿⠝⠽⠙⠋⠁⠉⢀⠂⠌⠐⢈⠑⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠐⠈⡀⠄⠂⠱⡄⠀⠀⠀ ⠀⠀⠀⣠⠃⠀⠀⠀⠀⢂⠠⠁⠀⠀⠀⠀⠀⠀⠤⣀⢀⠤⠂⠀⠀⠀⠐⠠⢈⠂⠀⡀⠂⢀⠘⣆⠀⠀ ⠀⠀⢠⠇⠀⠀⠀⠀⠀⢂⠠⢄⡏⠓⡄⡀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠠⠀⠂⠌⠆⠐⠀⠀⡀⠀⢘⣆⠀ ⠀⠀⢨⠷⠶⣤⣄⠀⡈⠄⢸⡀⠄⠀⡟⠱⠄⢀⣠⣀⣼⣄⣀⡤⠄⠠⠀⠂⠌⡸⢀⢂⣡⣄⣤⣾⣇⠀