⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠈⠉⠛⢲⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⣢⡶⠶⠶⣿⣤⣄⠀⠀⠀⠀⠀⠀⠠⠤⠤⠖⠒⠒⠒⠲⣄⡀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠠⣿⠀⠀⠀⠀⠈⠉⠻⢶⣄⠀⠀⠀⠀⠀⠒⢄⡀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣆⡀⢀⡤⠔⢦⡀⠀⠙⢷⣄⠀⠀⠀⠀⠦⠼⠀⢸⡃⠀⠀⠈⡇⠒⠦⣄⠀⠀⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠂⣀⣀⣀⣴⠿⣿⡉⠁⠀⠀⠀⡇⠀⠀⢀⣹⣷⣤⣤⣄⣀⠀⠀⠀⠙⠒⠒⠒⠃⠀⠀⠀⢳⠐⢿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠋⡁⠀⣼⠃⠀⠘⣿⡀⠀⠀⠀⡇⠀⣠⣄⡀⠀⢠⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡇⢸⡇⠀⠀⠀⠈⢻⣆⠀⠀⠑⠚⠁⠀⢣⠀⢸⠀⠀⠀⠀⠀⠘⠻⣷⣄⠀⠀⠀⠀⠓⣆⠀⠀⢈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡇⠘⣿⡀⠀⠀⠀⠀⠹⡷⣄⣀⠀⠀⠀⠈⡇⡼⠀⠀⠀⠀⢀⡀⠀⠈⠻⣷⡀⠀⣀⠀⢀⢳⣰⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⣸⣧⡀⠀⠀⠀⠀⢿⡀⠈⠀⠀⠀⠀⡿⠅⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣆⠈⠓⠒⠚⢋⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠤⡄⠀⠀⠀⡾⣆⠀⠀⢸⢸⡏⠘⢷⣄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⠇⠀⠀⠀⢸⠀⢻⣆⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠉⠳⢠⠇⢿⣧⠀⠈⠙⢷⣤⣀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⢸⠀⠀⢿⡆⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇⣿⠀⢀⠇⠀⠈⣿⣄⠀⠀⢸⡄⠉⠙⠛⠛⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⢀⣿⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠞⠀⣟⠀⡊⠀⠀⠀⢸⣿⢧⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣿⠃⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢧⠁⠀⠀⠀⠀⢻⣆⡽⠷⣬⣷⡀⠀⠀⢀⠀⠀⠀⠀⠀⢌⡟⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠉⠀⢠⢽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢤⠉⠓⠒⢲⡗⠊⠹⣦⡀⠠⠞⣷⠀⠀⠀⠀⡞⠙⠒⡚⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡇⠀⠀⡜⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢝⠀⠀⠀⡇⠈⠀⠀⠛⢿⣦⠀⣹⣧⠀⢀⠮⠀⠀⠐⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⠁⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣧⢏⣀⡶⠎⠁⢀⣠⡤⢴⣶⡿⠿⣦⢻⡄⣏⠀⢸⡉⢳⠘⠰⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣤⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⠓⢹⠕⣥⡴⣞⡯⠖⠋⠁⠀⠀⠀⠈⠻⡷⠈⠧⠤⠤⠋⠀⠀⠙⢿⡛⠷⢦⣤⣄⣀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣤⣯⣼⠿⣇⣰⠙⠆⡀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢀⢠⢄⣀⣈⣿⣆⠀⠈⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⠷⣶⡿⠫⢄⣴⡞⠛⠒⢾⣃⣠⣤⢆⣠⠶⣶⣤⣀⠀⢠⠀⠀⢸⠧⠄⠀⡏⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⣉⠀⠀⣼⠏⠉⠁⠈⠉⠉⢧⠀⠀⣹⠃⠙⠉⠁⠀⠘⡂⠉⠙⠀⠀⠀⠈⠒⠒⠋⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⡇⠀⣼⡟⠀⡆⠀⢠⠀⠀⠈⢧⣠⡏⠀⠀⠀⠀⠠⣀⠤⢤⡀⢀⡔⡉⢧⡄⠀⠀⢀⣠⣼⣗⣚⠛⠛⠛⠶⣦⣤⡀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⠀⡼⠀⠀⣿⡇⠀⡇⠀⢸⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⢰⠃⠀⠀⢣⡏⠀⠀⢸⢠⡴⠞⠛⠉⠉⠉⠛⢷⣦⡀⢀⠀⠈⣿⡄⠀⠀⢸⠀⢠⠀⠀ ⠀⠀⠀⢸⣿⠀⢀⡇⠀⠀⢿⣇⠀⡇⠀⢸⠀⢠⠀⠀⠀⠸⣧⠀⠀⠀⢸⠀⠀⠀⠈⠇⠀⠀⢸⠁⠀⠀⠀⠀⢸⠀⢠⠀⠙⣷⡌⠀⢸⢸⣷⠀⠀⢸⣠⠏⠀⠀ ⠀⠀⠀⠈⣿⡄⡞⠀⣏⡇⠈⣿⣄⠀⠀⢸⠀⠸⠀⠀⠀⠀⢹⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣸⢀⣀⣠⣴⣦⠸⠀⢸⠀⠀⠙⣿⠀⠈⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠈⠉⡏⠀⠀⣿⢿⣆⠀⢸⠀⠀⠀⠀⠀⠀⣠⣿⣦⣤⣤⣧⣤⣤⣤⡶⠶⠶⠿⠛⠋⠉⠈⢿⣆⡀⠘⠀⠀⣀⣿⡉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⣰⠃⠀⣼⡟⢠⣿⠀⠘⠀⣠⣤⣴⣶⡾⠛⠁⢀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⠚⠛⠁⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣄⣀⣠⣴⢿⣁⡇⣠⣾⠟⠀⣾⣧⡀⠀⠀⢸⣇⠀⠀⠠⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠻⠿⠤⠶⠾⠟⠋⠁⠀⠀⢿⣦⣉⠛⠛⢋⣿⠦⠤⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀