⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣀⡀⠀⡠⠤⠤⠒⠻⠞⠿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠂⠒⠆⣴⣿⣾⡶⠒⠶⠾⣿⢄⡠⠤⡀⠀⠀⠀⠈⠙⠢⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠉⠀⠀⠀⠀⢜⢿⣿⣿⣿⡿⠓⣁⡬⢗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠁⠘⠉⠒⠒⣛⠓⡠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣿⣯⡭⠛⣉⣀⣼⣀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡆⡄⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡁⠺⠉⠀⠋⣉⡚⢣⢄⡀⠆⠀⠀⠀⠀⠀⠉⠳⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⣄⡄⠸⢃⣻⠀⣤⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣯⠟⠋⣉⣠⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⠒⠺⠋⠵⠦⠙⠒⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡇⠀⠛⠓⠋⢙⡛⠓⡦⡀⢠⠀⡀⠀⠀⠐⢌⠂⠪⢳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣷⣇⣾⡀⢾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣷⣶⣿⣿⠽⠛⣉⣀⣼⣼⡲⠀⠀⢀⠀⠈⠛⢦⡦⠍⡉⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣶⠀⠀⣾⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⢄⢾⠯⠔⠊⠛⠛⠳⣄⡄⠑⠠⠀⣄⠘⠔⠵⠄⠙⠟⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⢰⣎⣢⣄⣝⠀⠀⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣤⣤⣴⣶⡿⠋⣉⣥⣤⣬⣧⡀⢀⠙⠀⠀⠈⠉⠀⠀⡀⠈⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⡟⢇⢘⢿⢴⡿⠨⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⢿⣀⡢⠓⠋⢀⣉⣉⣉⣙⣲⠦⡀⠑⢄⠀⠀⠰⠤⠃⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣶⠄⠿⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠉⠲⠿⢿⣿⠞⢉⣉⡤⠤⣾⣆⣄⠱⡀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣄⢢⢿⡦⣾⠀⡄⠀⣴⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡿⠗⠒⠀⠈⠉⠉⠉⠳⣢⣤⠢⣄⠀⠀⠀⠀⠈⠲⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⢟⣧⡀⢠⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠿⣿⣿⣇⣉⡉⢛⡾⠃⣳⣤⣕⠀⠤⡀⠀⢀⠀⢣⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣻⢁⡏⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⠏⢀⣴⣥⡈⢙⢧⣀⠸⢤⠀⠀⠆⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣄⣲⣄⢀⡀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⢳⣿⣿⣿⣿⣾⣾⣿⣦⡠⡃⠀⢼⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣿⣠⣡⡰⣶⠕⠃⢔⡦⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠈⢿⣿⣿⣿⣿⣿⣿⣯⠁⠁⣠⠆⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⣻⣷⣻⡿⡄⠀⡀⡤⡀⠀⠀⠈⠁⠀⠀⠠⠇⢠⢶⡆⠀⠀⠀⠀⠈⡓⠀⠘⣿⣿⣿⣿⣿⣿⡿⠀⠀⠻⢂⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢽⣿⣽⢿⣾⣽⡉⢁⡀⠀⠀⠀⠀⡤⡄⢰⡺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠄⠀⠂⠀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⡌⠉⢁⣞⠟⣤⣜⡄⠀⢹⣇⠈⠁⣉⠁⠀⠀⠀⠀⠀⠀⠀⣰⡄⢹⣿⣿⣿⠁⠀⣠⣴⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣝⣻⣤⢚⣌⠑⢠⣼⡋⠀⣔⡣⣃⡄⠠⡜⡾⠀⣤⠾⣡⠆⡄⣿⣿⠟⠀⣠⡥⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠛⠽⠯⣷⣾⠀⠀⠀⠀⠰⣿⣷⠋⠁⠀⢿⠼⡄⢻⣋⡤⠖⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⣿⣷⠀⠠⡥⣄⠤⣰⣴⣇⣈⣄⠰⠿⠧⠈⠹⣱⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣻⡼⣾⢻⡻⣿⣜⢾⡿⢉⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀