⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢥⡀⠐⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⢿⡆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⣦⠀⠀⠀⠉⣢⠀⠀⠀⠀⢸⠃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⢀⠇⠀⠀⠀⢴⣁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⢆⠀⠀⠀⠀⠙⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣤⣀⠀⠈⠢⢤⣤⠶⡒⠋⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡏⠀⠀⠀⠉⠀⠙⠲⢤⡀⠀⠀⠉⡲⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⠖⠂⠀⠀⣤⣀⣄⣀⠀⠈⣷⢤⢰⠿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠀⠀⠀⠀⢠⣹⣷⠣⡼⢃⠀⠸⣯⠎⢉⣹⠷⣄⠀⠀⠀ ⠛⠻⢭⣍⡑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡒⠁⠀⠀⠀⠀⠸⡕⢝⣦⡥⠛⣃⠀⠈⠉⠘⠫⠽⠀⠙⢆⠀ ⠀⠀⠀⠙⢿⣢⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠂⠀⠀⠀⠀⠉⠀⠈⠳⠾⠇⠀⠀⠀⠀⠰⠦⠀⠐⡟⠀ ⠀⠀⠀⠀⠀⢧⢣⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠐⠓⢲⠶⣖⣦⣄⠀⠚⠛⢴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀ ⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢀⠤⠶⣿⣦⣀⠁⠙⢿⣶⣦⣤⣉⣙⡟⠲⠦⢤⠤⠴⢶⣻⠏⠀⠀ ⠀⠀⠀⠀⠀⠸⡇⢇⠀⠀⠀⠱⡀⠀⠀⠀⢰⡇⠒⢄⠈⢿⣿⠆⠠⠤⠬⠝⠻⡟⢻⠉⠉⠓⠒⠒⠚⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠘⡄⠀⠀⠀⠱⡀⠀⠀⣸⡑⠊⠁⢀⣼⡷⠁⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⠈⠢⣀⡀⠀⣨⣴⣶⣿⠁⡔⠚⣿⢹⠓⢄⣤⠒⠀⢻⣾⡃⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣿⣿⢻⢻⡃⠘⠓⠴⣿⠃⢠⣋⣘⣴⡶⣞⣷⠁⢠⠔⣩⠟⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡀⢸⣿⡟⣿⢸⡇⠀⣀⠠⠬⣆⠀⠀⠀⡟⣤⡏⡿⠷⣁⠞⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⡣⠊⣡⠔⠒⠓⡳⡀⠀⢉⠿⠀⡧⠊⠉⢢⢀⠖⠲⢠⣤⣣⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠞⠁⢀⠠⣄⠈⠙⢤⠟⠒⡰⠀⠀⠀⠀⢾⣢⣴⢌⡛⣧⡄⠑⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢏⢆⢴⣁⢸⣍⠲⠀⠀⢱⣔⠉⠲⢄⡀⠀⢸⣿⣟⣲⣏⡬⣿⢦⡘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠱⡜⣶⣿⠟⠉⠀⠀⠀⠀⡜⠙⢗⠒⠀⢈⡭⠟⢧⢈⠹⡽⡀⠈⡆⠹⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡈⠾⣳⡀⣀⠀⢠⠒⢾⡷⡀⠈⣶⣾⣅⣀⡀⠀⠻⣆⠰⡘⢷⢰⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠿⣶⣷⣽⠁⠙⣿⡀⠈⢟⢶⡄⢸⠋⡹⢷⡋⠐⢄⠈⠓⠷⠀⠻⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠟⠳⣦⣤⣤⣾⠁⠙⡆⠀⠸⢷⡄⠘⡦⣿⣄⣀⡧⡀⠘⢤⠤⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⡀⢀⠴⠿⠗⠊⠋⢉⣶⣜⢆⠀⢇⠙⢦⡇⠀⠉⠉⠁⠐⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⠀⠀⣠⡖⣤⡟⡆⠈⢊⠓⣼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣵⣾⠇⡅⠈⡗⠮⢂⡬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠵⣦⣸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀