⠉⠙⠓⠒⠒⠶⣶⡶⠶⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠻⣦⠀⠀ ⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡄⠀⠀⠀⠀⠀⠈⢷⣄ ⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣽⠀⠀⠀⠀⠀⠀⣦⠙ ⣠⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⣸⣿⣿⠻⣆⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣼⡇⠀⠀⠀⠀⢰⣿⣿⡟⢿⠀⠀⢠⣿⣿⢇⡦⢻⡄⠀⠀⢸⠘⣿⣆⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⣿⡇⠀⠀⠀⢠⣿⣿⡟⠀⢸⡄⠀⢸⣿⡏⠐⠀⣀⣿⣀⣀⣸⣦⡈⢿⣧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣼⣿⣿⣷⠀⠀⠀⣾⣿⡿⠁⠀⢸⡄⢀⣿⣿⠷⠛⠛⠉⠙⣯⠉⣹⠉⠻⠈⠻⣿⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠸⣆⠀⠀⠀⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⣿⣿⠇⣷⠀⠀⢸⣿⣿⠃⠀⠀⢸⣧⢸⣿⡇⠀⠀⠀⠀⠀⢹⡇⣿⠀⠀⠀⠆⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣿⣿⣿⣦⡀⢻⡄⠀⠀⢻⣆⠀ ⢀⣀⠀⠀⠀⠀⣤⢠⣏⣿⣿⡏⠀⢹⣄⠀⣼⣿⡏⠀⠀⠀⠘⣿⢸⣿⠀⠀⠀⠀⠀⠀⠈⣧⡇⠀⠀⠀⠀⠀⣄⠙⣿⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⣿⣿⣿⣷⣄⢻⡄⠀⠘⣿⣆ ⣿⣿⠀⠀⠀⣼⡿⣸⣿⣿⣿⣴⠿⠛⣏⠁⣿⣿⠁⠤⠀⠀⠀⣿⢸⡗⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠈⠂⡿⠀⠀⠀⠀⠀⠀⣼⣿⠀⢠⣿⣿⣿⣿⣿⣿⣷⣿⣦⠀⢹⣿ ⣿⡏⠀⠀⣼⣿⡇⣿⣿⣿⡏⠁⠈⠀⢹⣆⣿⡟⢀⠄⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢰⣷⠀⠀⠀⠀⢀⣰⣿⣿⣄⣾⡿⠛⠻⣿⣿⣿⣿⣿⣿⣷⣤⢻ ⡿⡇⠀⢰⣿⣿⡇⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⡇⠈⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢀⣠⢄⣤⣴⣶⣾⣿⣶⣾⣿⠷⠀⠀⠀⢠⣼⣿⣿⡏⣸⢋⡴⠛⢦⠘⣿⣿⣿⣿⣿⣇⠈⠀ ⠁⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣿⠿⠛⠛⠉⠉⠉⠉⢁⡟⠀⠀⠀⣠⡿⣿⣿⣿⣷⢿⡏⠠⣄⢸⡆⢻⣿⣿⣿⣿⣿⡀⠀ ⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣾⣿⠋⠘⣿⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢀⣼⠟⠀⣿⣿⡿⠃⠨⡧⠀⢹⣄⠃⢸⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⢀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣰⠞⠙⠀⢰⣿⠟⠁⠀⠀⣹⠀⢸⠇⢠⣾⣿⣿⣿⣿⣿⣿⡄ ⠀⢸⡀⣿⣿⡿⣷⣿⣿⣿⣿⣿⠿⡎⠙⣦⠀⠈⣿⠹⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠟⠉⠀⠀⢠⡿⠋⠀⠀⢀⣾⠿⠒⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠘⣧⣿⣿⡇⢸⣿⣿⣿⣿⡿⠀⢹⡀⠀⠀⠀⡘⠧⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠘⢿ ⠀⠀⠘⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠈⣧⠀⠀⠀⠁⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠉⣿⣿⣿⣿⣿⣿⢻⣿⡿⠟⠷⣄⠈ ⠀⠀⠀⠘⢿⣧⠀⠈⢿⣿⣿⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣿⣿⣿⣿⣿⠟⠉⠀⢦⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠙⠀⠀⠈⠻⣿⡆⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠐⣂⣭⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢠⣿⣿⣿⣿⠗⠚⠳⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣋⠁⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⢀⢀⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⣾⡟⣿⣷⡀⠀⠀⠀⠀⠸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠚⠓⠚⠳⠦⠤⢤⣄⣀⣀⣿⠁⢻⣿⡙⠳⢤⣀⠀⠀⡇⢠⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠿⠿⣦⣄⠉⡳⣦⡷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿⣿⣿⠀⠈⢷⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⢀⣀⡤⠴⠞⠋⢻⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⠤⠽⠿⠶⠶⢶⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣤⣤⠤⠤⠰⠆⠒⠚⠊⠉⠉⠀⠀⠀⠀⠀⢸⡏⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠠⢂⣀⣤⠴⠛⠉⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⠀⠀⠀⠀⢱⣄⠀⠀⠀⢀⡀⡏⠀⠀⠀⠀⢀⠐⣛⣩⠟⠁⠀⠀⢠⠏⠀⠀⢀⡇⠀⠀⠀⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣄⡀⠀⠀⠘⠆⠀⠀⣾⣾⢃⣤⢤⡄⠀⠈⣡⠟⠁⠀⠀⠀⠀⡾⠀⣰⢀⡾⠁⠀⠀⠀⠀⠉⠛⠶⣄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠠⠤⠶⢶⣹⢿⡶⢦⣤⣀⣤⣯⣿⣟⣤⡞⠃⢀⡴⠋⠀⠀⠀⠀⠀⢠⡇⠼⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉