⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡒⠒⠂⠆⡼⢦⠠⠒⠒⢂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢢⠐⠧⠑⢊⠞⠂⠆⠉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠰⣎⠰⣠⢳⠆⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠈⢣⠀⢯⣷⣱⡟⢀⡜⠁⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⢊⠀⣇⠀⠀⠀⠀⡽⠮⠥⠭⠵⣎⠀⠀⠀⠀⣰⠀⡙⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡅⡇⡨⡂⣉⠠⣀⠀⢴⣓⣒⣀⢒⣒⣛⡆⠀⣀⠔⡉⢀⢇⢰⡰⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠆⡸⠯⠶⢲⠒⠉⠁⠀⢀⡑⠆⢰⠀⢲⠋⠀⠀⠀⠁⢲⡲⠶⠷⠇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡔⣄⡐⠀⠐⣠⠎⠀⠀⠀⠀⠈⣿⣿⣟⢻⣿⣧⠀⠀⠀⠀⠀⠃⢄⠂⠈⢇⡰⢡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⠐⣾⠭⠛⢻⠀⠀⠀⠀⠀⠀⠀⣿⣯⡿⣟⣿⡅⠀⠀⠀⠀⠀⠀⠀⡟⠑⠍⣶⠁⡀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠈⢢⠠⠐⢀⠇⠀⠀⠀⠀⠀⠀⢠⣿⣷⣯⢸⣿⣳⣤⠀⠀⠀⠀⠀⠀⠱⡀⠢⠌⠔⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣁⢾⢠⡶⢣⠀⠀⠀⠀⠀⠀⠒⣶⣶⡞⣟⢸⣻⣶⣶⡂⠀⠀⠀⠀⠀⠀⡾⠦⠀⡷⣂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡈⢳⠈⠠⢸⠀⠀⠀⠀⠀⠀⣾⣿⢯⣿⣧⣼⡿⢷⣻⡆⠀⠀⠀⠀⠀⠀⡇⡀⠙⡏⢀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠚⠀⣁⡾⡄⠀⠀⠀⠀⣸⣿⠃⠈⢳⣿⡝⠁⢘⣿⣻⡂⠀⠀⠀⠀⢠⢧⡈⢂⠑⣁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠍⣯⠝⢠⠨⠀⠀⠀⠀⠉⠉⠁⣴⣶⡿⢾⣶⡌⠉⠉⠉⠀⠀⠀⢀⠃⡄⢫⣯⠨⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠄⠢⠂⢰⠥⡀⠀⠀⠀⠀⢈⡿⣷⢿⣟⣿⡤⠀⠀⠀⠀⠀⢀⢼⡄⠁⡌⠠⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⣠⡕⣿⠠⠘⠄⠀⠀⠀⠸⣷⣤⣟⣽⣯⡯⠀⠀⠀⠀⢀⠃⠈⡵⠮⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠬⠒⢀⠅⠀⠀⠀⠀⠁⠙⡽⢹⠁⠀⠀⠀⠀⠀⢸⡠⠢⠅⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡀⠄⣀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢑⣢⠴⠞⢂⠄⣀⠀⠀⢀⢤⢁⣈⡄⠀⠀⢀⣀⠤⡚⠳⠦⣐⡊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⡄⠀ ⠀⠀⠑⢄⠀⠈⠁⠢⠄⣠⠊⠙⠂⢄⡀⠁⠂⠁⢒⠟⡡⢚⡡⢏⠀⡅⢸⠀⡟⢌⡂⠍⠱⠂⠈⠐⠉⢀⡠⠔⠊⠑⡄⡀⠔⠈⠁⠀⣠⠊⠀⠀ ⢀⠔⠊⠁⠀⠀⠀⠀⠔⠁⠀⠀⢲⢤⣜⡗⠐⠄⡌⡉⠉⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⣑⠃⠄⠐⢀⣡⡤⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠐⠢⡀ ⠀⠀⠈⠁⠒⠤⢀⠘⢦⢄⡀⠀⠹⢥⢣⢫⢵⡶⢤⢤⡁⠈⣁⠒⠒⠒⠒⠒⡂⠈⣉⢁⠤⣄⡖⣞⡟⡄⠛⠙⠄⢀⡠⡴⠃⣀⠤⠒⠈⠁⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⢕⠌⠑⠢⣀⠀⠈⠂⠃⠙⡸⠀⠀⠧⡏⠠⠇⢹⢼⠀⠀⠹⠞⣆⠑⠑⠀⠀⢀⣠⠔⠊⢡⡊⠔⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡔⠁⠉⠁⠒⠂⠄⠬⠀⣀⠀⢀⣀⣁⣀⡀⠀⢀⡀⠨⠅⠅⠒⠒⠁⠁⠈⢢⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀