⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣨⣿⡶⠶⠶⢾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣣⠀⠈⠉⢰⡌⢻⣿⡆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀⢠⣾⡿⣿⠟⠁⠀⠀⠀⢰⣽⣿⣿⡇⠈⣷⠀⠀⠀⣤⣿⣿⢿⣿⣧⣄⠀⠀⣀⣠⣤⣤⣾⡿⡿⣷⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠛⢛⣿⣀⠀⠀⣸⣿⠙⠁⠀⠀⠀⠀⠀⡜⣿⣿⡟⠃⢀⡟⠀⠀⢀⣿⡟⠁⠈⠀⠿⠿⠦⠶⠿⠛⠛⠀⠀⠀⠉⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⣤⠴⠛⢻⣿⣭⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⡀⢠⡞⠁⢀⣰⣿⠿⠁⠀⠀⠀⠀⠀⠀⠐⠚⠂⠀⠀⠀⣠⣶⣾⡿⠇⠀⣶ ⠀⠀⠀⠀⢹⡟⠃⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⡾⠶⠶⢿⣿⣻⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⠏⠀⢀⣴⠟ ⠀⠀⠀⠀⣼⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠻⠟⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⣀⣴⠟⠁⠀ ⢀⣀⣠⣤⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⣰⠾⠁⠀⢀⣀⣀⣀⣀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⡀⠀ ⢸⡿⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⢀⣰⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⡟⣿⣷⣄⠀⠀⠀⠀⠀⢀⣠⣿⣿⡟⠈⢻⠀ ⢸⡇⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠸⣿⣿⠋⠋⣡⣶⣿⣮⣿⣿⣇⢈⣿⣿⡇⠀⣻⣿⣧⣀⣀⣠⣾⣿⣿⡿⠟⠀⢠⡟⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣴⡄⠀⣀⣈⣿⡀⣸⡟⠙⣿⣿⣿⣿⣿⣿⣮⣿⡇⠀⢹⣿⣿⠟⠛⠛⠛⠉⠁⢀⣤⡴⠟⠀⠀ ⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣶⣿⠿⠛⠛⢛⣷⣾⣿⣿⣿⣿⣿⣿⠉⠈⠁⢀⣸⡏⢻⣷⠀⣄⠒⠶⠚⠉⠀⠀⠀⠀⠀ ⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⠁⢠⣴⣾⡟⢿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⣾⣿⡧⠾⣿⡆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⣡⣤⣾⣿⢿⣷⣤⣉⠉⠉⠀⢠⣽⣿⠃⠀⣬⣿⠋⠀⠀⢿⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⣤⣶⣴⣄⠀⠀⠀⠀⢐⣿⣿⣷⣤⣿⡛⠛⠛⠁⠈⠙⠛⣿⣿⣶⣷⣿⠛⠉⠀⢰⣿⡏⠀⠀⠀⠘⢻⣿⣾⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⣷⣾⠯⠉⣿⣤⣤⣤⣭⣿⡏⠀⠀⠀⠉⣿⣤⣤⣤⠀⠀⠀⠈⣿⣇⢰⣾⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠈⣿⣿⡀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⣀⡀⠀⣤⣤⠤⠤⡤⣼⡟⠛⠋⡀⢀⣿⡆⢰⣄⣀⢿⣿⣿⡟⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠛⣿⡌⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣄⣀⣼⣾⠿⠉⠉⠁⠀⠀⠀⠀⣤⡀⠀⣾⡿⠿⠿⠿⠿⠟⣿⠈⢿⡟⠁⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⣀⣿⡇⠙⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣟⠛⠻⣿⠿⠿⠿⢿⣿⣦⣿⣿⡿⠿⣿⣷⡆⠀⠀⠀⣠⣿⣧⣿⣇⠀⠀⠀⠀⠀⠠⠿⣿⡀⠀⠀⠀⠀⣿⣿⡇⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⣿⠀⢠⣤⣬⠉⠉⣿⡟⠁⠀⢸⣿⡇⠀⠀⠀⠉⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠲⢻⡇⠀⠀⠀⣠⣿⣿⠁⢀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣿⣦⠀⢸⣗⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣸⣿⣿⠋⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠆⠀⠀⢹⣿⡆⠈⡿⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⠀⠀⢀⣤⣾⣇⣤⣾⣿⡿⠃⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠸⣿⡇⣄⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣤⣿⣿⣿⣿⠿⡛⠛⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠻⣿⠁⣀⣨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⢹⣿⣿⠋⠁⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠓⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣠⣾⣿⣿⠦⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠏⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⣌⠛⢻⣿⣶⣤⣤⣄⠀⣤⢀⢀⣿⣿⡟⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣷⣄⣀⣀⣀⣀⣶⣾⣿⠟⠉⠙⣿⣷⣤⣀⣹⠛⢻⣯⣵⣶⣿⣿⡿⠿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣛⡛⠛⠛⠛⠛⠁⢀⣴⠞⠉⠛⠿⣟⣛⣿⣿⣿⡟⠛⠛⠉⢀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠓⠲⡆⠀⠰⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀