⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣠⡴⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⡠⢊⡵⠋⠀⠈⠳⡘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠻⣣⡀⠀⠀⠀⣠⠋⠀⡞⠁⠀⠀⠀⠀⠙⠢⠥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢳⡀⠀⣰⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡇⡇⢠⠧⢤⣄⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣦⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⢀⣾⡇⢁⡇⠀⠀⢉⣀⡣⠴⢒⣒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠉⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⠸⢷⣀⣀⠠⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠹⣿⡃⠘⠿⠦⣴⡿⢋⣞⣻⠀⣀⣈⠋⠳⢝⠶⡟⠉⢳⡤⠔⠂⠀⠀⠀⠀⠀⠀⢧⣀⣠⠟⠀⠀⠀⠀⢀⠤ ⣠⠤⠒⢚⠧⢷⠃⠀⠀⠀⣀⡤⠊⠀⠀⠀⢀⣤⣶⢿⣿⣿⣯⢵⣦⣴⣿⠓⠧⢤⣠⣼⢶⠋⠁⠀⢣⡀⡈⠙⡲⣌⣷⠹⣄⡴⠃⠀⠀⠀⠀⣴⣶⣶⣤⣾⡗⠒⠒⠒⠤⣀⠀⡇⠀ ⠀⢀⡴⠁⢀⣸⡠⠤⡶⠯⠷⣵⢴⠋⠑⣾⣿⡿⢛⢿⣯⣏⡝⣧⡙⢿⣿⡋⠉⡎⢰⢃⠏⣠⡾⠿⢍⡻⠙⢾⣇⠉⢿⡇⡇⠘⢆⡠⠊⠑⣼⣿⣿⣿⣿⣿⣿⣯⣶⣦⣄⣈⠳⣹⢦ ⡖⠚⢚⠟⠛⠙⠲⣼⣠⣶⣿⢽⡆⠀⣼⣿⣯⡴⢣⠋⣼⡉⢿⢁⠼⢶⣿⣿⠀⢧⡇⡼⢰⣱⣛⣷⣄⣧⣠⠄⠹⢦⡜⣇⡗⣄⠈⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⢻⠇ ⡇⠀⢸⠖⣾⡿⠛⡟⢯⣀⣈⣽⠅⢴⣿⢩⡿⢡⢧⡞⠛⠻⡾⣧⣶⡾⣷⣸⡆⠈⢻⠡⠸⣧⣀⣀⡹⢫⡓⠿⣿⡝⣷⢣⠳⣸⣠⣴⠎⠈⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡏⢸⠀ ⠸⡄⠀⠓⠾⠤⢚⣿⣿⠿⢷⡎⠀⠀⠓⣻⣇⡎⠀⠉⢙⡩⢄⡱⢄⣀⣽⣸⠇⠀⠈⣷⡀⠀⣤⣶⣶⣦⣷⣄⣮⣿⣧⣾⣴⣿⣿⠏⠀⠀⠀⠀⠸⣽⣻⣿⠿⣿⡿⠿⠃⡼⢀⡞⠀ ⠀⠙⠦⣀⠁⠀⠈⠛⣁⡴⠋⠀⠀⠀⠀⣧⣿⡳⣤⡀⠘⠛⠻⢿⣠⢾⡟⠁⠀⠀⠀⡟⢹⠦⣝⡋⠉⢻⣿⣶⢿⡿⡿⢯⣜⣽⣻⣤⣶⠖⠀⠀⠀⠘⢫⣙⠓⠿⠉⠁⢈⡥⠊⠀⠀ ⠀⠀⠀⠀⠉⡏⠉⠉⠀⣇⠀⠀⠀⠀⠀⠀⠘⡷⠋⠀⠉⠉⣏⣯⡿⠟⠀⠀⠀⢀⡰⣃⠼⣀⠀⠀⠙⣯⡯⠉⡏⠃⡄⠂⢹⣸⡿⢿⣯⠀⠀⠀⠀⠀⡎⠀⠉⠉⢹⡉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠉⠀⠀⠀⠀⠀⠉⡴⠁⠀⡈⠱⡤⠤⡿⣧⣴⣻⣄⣀⣠⡞⠛⡀⢰⣿⣷⡶⠀⠀⠀⡏⠑⠒⠊⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⡴⣧⡐⢦⣉⡾⠷⡖⢿⢺⣿⡿⣶⠟⠛⠳⣴⣖⢤⣽⡇⠀⠀⠀⢨⡗⠦⠤⠴⠺⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢀⢴⠻⠭⠄⢈⠛⠒⢃⣇⠀⠃⠘⠀⠹⣿⡇⠂⡄⠀⣹⣿⣾⣿⣷⣦⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠈⠻⢿⠀⢀⣠⢶⠊⠉⠙⠦⠤⠖⡚⣄⡿⡽⠦⣶⠾⢟⣺⣼⣧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠙⠋⠀⠘⠒⠒⠒⠒⠒⠒⠃⠈⠙⠓⠾⠭⠶⠛⠙⠛⠿⠿⣦⣀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀