⣿⣿⡅⠀⠀⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣷⡘⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⠷⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣼⣷⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣯⡜⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡅⠀⠀⣠⣴⠾⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⡄⡌⡍⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⣶⠾⠋⢀⣠⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⠀⠀⠀⠑⠠⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣻⡏⢠⣾⣿⠋⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠵⠶⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⢻⣤⣿⣿⠏⠀⢀⣸⣿⣄⠀⠀⠀⠀⠀⠀⣠⡾⠇⠀⣰⠶⣤⣀⠀⠀⠀⠀⠀⣠⣤⡝⢦⡀⠀⢀⣾⡿⠋⣠⡆⠀⠀⠀⣙⣦⠀⠀ ⠀⠀⠀⠀⠀⠉⣿⡿⠶⣶⢾⠉⠀⣨⡇⠀⠀⠀⠀⣼⠟⠁⠀⠀⡏⠀⡆⠈⠓⢦⣀⣠⠞⠋⠀⠹⣆⢳⣤⡿⢼⠁⠀⠀⠙⠒⠒⠚⠉⢱⣣⠀ ⠀⠀⠀⠀⠀⠀⣟⢀⡾⠃⢠⣶⠛⠙⠳⣄⠀⠀⢰⡟⠀⠀⠀⣸⠃⢀⣭⢦⣄⠀⠉⠁⢠⣶⣦⡄⢹⣶⣿⡀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠙⢻⠃⢠⣿⡿⠛⠳⣦⣈⡇⠀⢸⠃⣀⣤⠾⠋⢰⡟⠁⠀⢹⡀⠀⢰⠟⠿⣿⣿⣸⣿⣿⣧⠘⣦⠀⠀⠀⠀⠀⠀⠀⠘⣽⠇ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⣿⠁⠀⠀⠀⢿⡅⠀⠸⡇⠉⣲⠇⠀⣿⡤⠶⠛⢉⡿⠀⠘⣷⣷⣦⣼⣿⣇⢻⣿⣧⡈⠳⢤⣀⠀⢀⣀⣴⣾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⣀⠀⠀⠀⢸⣿⢤⣀⣿⣠⡟⠀⣸⣃⣠⡴⠚⣯⣠⣤⣄⣿⡹⠾⢻⣿⣿⣷⣿⠿⠿⠶⠤⢬⣉⣉⠴⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⠉⠛⠶⠶⠾⠷⣄⠀⠹⣿⣧⡀⠀⠉⠀⠀⠀⢾⠀⠀⣸⠏⠉⠉⠁⣠⡿⣿⣧⠀⠀⠀⠀⠀⢀⣹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣦⣤⣄⣠⣮⣷⣦⣍⣿⣿⣦⡀⠀⠀⠀⠸⣆⣴⠋⠀⠀⣠⡾⠋⠀⣿⣿⣤⣴⡶⠶⠖⠚⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠀⠉⢹⣏⡾⠁⠙⠛⠛⢻⣿⣷⠶⣦⣤⣽⣧⣶⣾⣿⠿⠂⠀⣠⣿⣿⠁⠀⣀⣖⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢠⣤⣾⣿⡁⢀⠀⠀⠀⢸⣿⣿⣗⢿⣿⡟⢣⣿⣿⣿⣶⣌⣷⣦⣀⠙⢧⣀⢉⡿⠃⠀⢀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⢻⣏⠿⠿⣿⣶⠚⠉⢹⣿⣿⣿⣦⣄⣠⣿⠻⠏⢁⣸⡏⠛⢦⣼⣿⣷⣭⣛⡷⠟⠉⢉⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⠀⠀⠀⠀⡼⢷⢶⣿⣿⣿⣛⣉⣀⣈⣿⣷⣤⡀⠈⠙⠿⠶⣿⣿⡏⠁⠁⢀⣰⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢐⢶⣄⣤⣿⣿⣷⣾⣭⣿⣿⣿⣿⣏⣹⣿⣯⣿⣄⣠⡶⠿⣿⣿⡟⠻⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⣧⣤⣶⣾⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣷⣭⣛⡋⠿⢋⣼⡏⢀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣄⠀⠀⠉⢛⡻⢿⣥⣿⡋⠉⠀⣈⣿⣿⣿⡿⠟⠛⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠴⠾⠛⢻⣍⣟⣿⣿⣿⣦⣄⠀⠈⠛⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠾⣿⣿⡛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣾⣿⠛⠻⣦⣤⣼⣿⡦⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠙⠻⠶⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠳⣄⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⡿⠟⠛⠉⠻⢦⣤⣴⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣄⡈⠀⠀⠀⢠⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⢹⡆⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠓⠦⠴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠆⢻⡀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢿⣦⣿⣧⡀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀