⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣾⠟⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⣾⣣⠴⠛⠛⠛⠳⢦⡢⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣄⡶⠤⠤⠤⠤⣴⡀⠰⣆⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⡿⡀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠙⢯⡈⠃ ⠀⠀⠀⠀⠀⣺⠇⠀⠀⠀⠀⢀⣠⣴⠺⣺⣤⣄⣴⣦⠦⠷⠵⠶⣦⣄⣠⡚⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡥ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠖⠏⣈⣰⠗⠋⠉⠀⠀⠀⢴⡀⠀⠀⠀⠀⠉⠙⠾⣌⢍⠷⣤⡀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⠈⠷⣄⡾⠑⠁⣲⠋⠁⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⣀⣀⣀⡀⠀⠈⠳⣖⠁⠛⢦⡀⣠⢴⠟⠁ ⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⡽⠁⠀⢠⡞⢫⡍⢻⡄⠀⣻⠀⠀⣾⠋⢴⠈⣿⠀⠀⠀⠘⢧⡂⠀⠛⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠈⠓⠖⠒⠋⠀⠀⠽⠀⠀⠉⠓⠒⠚⠋⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⣤⣀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡄⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠟⠿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠖⠀⢠⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⣻⡏⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⣿⠿⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠿⢻⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀ ⢘⢿⡄⢸⠛⠾⣦⠂⠈⣿⠀⠀⠀⠀⠙⠻⣿⣷⣶⣶⣶⣶⣶⣿⠿⠋⠁⠀⠀⠀⠀⢀⡼⡀⠀⠀⠀⠀⠀⠀ ⠀⠾⠷⠻⠀⣾⡏⠃⠀⠉⣆⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠷⠴⠶⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼⢻⣤⣤⠶⠚⢶⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡶⠶⣤⠶⠟⣩⢟⠟⢲⣤⣄⣀⣀⠀⣀⣀⣀⣀⣤⣶⡟⠛⠋⠛⣦⡈⠁⠀⠀⠚⠯⡆⠀⠀ ⠀⠀⠀⠀⠀⢨⣹⠗⠀⠀⠘⡛⣦⡄⠀⠈⠁⡏⠉⣿⠉⠁⣽⠀⣿⠂⠀⠀⠀⣴⠟⣡⣄⠀⢿⡉⠉⠑⠀⠀ ⠀⠀⠀⠀⠀⠸⠧⠴⢷⡀⠀⡟⠏⠁⠀⠀⠀⡇⢸⠓⠀⠀⣿⡅⠹⣖⡀⢀⠀⠙⠉⠉⠈⠳⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢠⡾⠛⠛⠃⢸⠀⠀⠀⠿⡇⠀⠈⠙⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣤⣤⡞⠀⠀⠀⠈⠙⢲⣶⣤⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀