⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⢴⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⡩⠟⠉⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠙⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣤⣤⠖⢡⠊⣠⠎⠀⠀⠀⠀⣠⠞⣼⣿⣿⣿⠀⠀⠀⠀⠘⣿⡌⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀ ⠀⠀⠀⠀⢀⣠⠚⣡⠞⣿⣿⣿⠁⠀⢠⣾⠃⠀⠀⠀⠀⣰⠃⣰⣿⣷⣿⡏⠀⠀⠀⠀⠀⣿⣿⠀⢳⣉⢢⠀⠀⢀⣀⣼⣿⣿⠋⠀⠀ ⠀⠀⠈⢉⣽⠁⢰⣿⢟⣿⡟⠀⠀⢀⣿⠏⠀⠀⠀⠀⣰⠁⣰⠋⠈⠊⢻⠇⠀⠀⠀⠀⠀⣿⣿⠐⢠⡋⣈⠴⣾⣿⣿⢿⡿⠃⠀⠀⠀ ⠀⠀⢀⣾⡏⠀⣼⣿⣿⡼⠀⠀⠀⣸⡿⠀⠀⠀⠀⢰⠃⢠⠇⠀⠀⠀⡾⠀⠀⠀⠀⠀⢀⣿⡟⠀⢸⠏⠁⠀⠀⠻⣥⠞⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⣸⠿⣿⣿⠇⡀⠀⠀⣿⡇⠀⠀⠀⠀⡟⢀⡏⠀⠀⣀⠜⣇⣠⣴⠂⠀⠀⣾⠟⠀⠀⡾⠀⠀⢀⣠⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⢀⢿⣶⡇⣿⠀⣇⠀⠀⣿⡇⠀⠀⠀⠀⣿⣻⠒⠒⠛⠋⠉⣉⣩⠀⠀⣠⠞⢹⠉⢳⣴⠃⢶⠒⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⣸⠀⠻⡇⢸⠀⠸⡄⠀⠻⣧⣄⡀⢀⣠⣿⣿⣿⠿⠿⠿⡷⣿⣏⣠⣾⠁⠀⠀⢠⡿⠋⠓⢼⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢸⣇⠘⣧⠀⠱⡀⠀⣯⢻⠙⠓⢿⡟⠉⠀⠀⠐⢿⣿⣧⠉⢱⣇⣠⣴⢠⡿⣿⡷⣶⣼⣞⠁⣸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⡇⠀⠘⡿⣄⣻⣧⠀⠁⢠⠘⣎⣇⠀⡿⢷⣀⣀⣀⡯⠼⠿⠼⠇⠈⠁⠴⠛⢁⣀⣿⣿⡏⠻⣿⢤⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⡇⣠⠴⡿⠿⠷⠶⢵⢤⣈⣣⣈⣻⣦⣣⣠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠻⢧⣰⣏⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⠀⣷⠘⢾⡢⠀⢢⢦⠉⠉⢾⡏⠩⣄⣳⡈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣽⣿⡯⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⢹⡄⠀⢹⡦⣄⠻⣷⣀⡀⢳⠀⣇⠈⠉⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⢰⣧⠀⠀⠀⠀⠀⠀⢸⣷⡿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠆⠸⡷⢄⢸⠀⡇⠳⣄⠀⣉⣻⣆⣻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣿⣷⣯⡿⠹⡦⣄⡀⠀⠀⠀⡼⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⢿⠀⠀⣧⠈⡻⣴⠇⠀⣿⡗⠛⢾⣷⡟⠷⠄⠀⠀⠀⠀⠀⢧⠈⠙⠟⢿⣿⣿⡀⠘⢏⠀⠀⢀⣼⠁⢸⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⡰⣧⣾⠀⠀⣿⢰⣷⣹⠀⠀⢻⣧⣤⣾⣻⠙⣦⡀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⣿⣀⠷⡀⠀⠳⣤⣿⡾⠒⢺⡀⠀⢷⠀⠀⠀⠀⠀⠀ ⢅⠇⡟⠀⠀⣿⣼⠀⣿⡆⠀⠀⠈⢉⡏⡏⠀⢹⡈⠓⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⣦⡜⢁⡞⠀⠀⡴⠳⣄⡌⠣⡀⠀⠀⠀⠀ ⡞⢰⠇⠀⢰⣿⡇⢰⡿⠀⠀⠀⠀⣸⠀⣇⠀⣸⣷⣦⡀⠀⣤⣖⣶⣤⣤⣀⣀⣀⣀⣠⠚⢻⠁⢸⣀⣀⣸⣥⠴⠆⠀⠀⠹⡄⠀⠀⠀ ⠁⣼⢠⢠⡏⡏⠁⣈⠿⠚⠋⠛⠒⢿⠀⠘⢾⣿⡟⠿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣏⡏⢸⡆⠈⡿⠉⠉⢉⣤⡟⢶⠤⢄⠀⠀⠹⡄⠀⠀ ⢀⡏⣿⣿⠀⣧⠞⠁⠀⠀⠀⠀⠀⠈⢧⡀⠀⠙⢳⡖⠀⠉⠡⣙⡿⠿⠋⠻⠟⠁⠉⠻⢿⣿⡁⠒⠲⡖⠋⠙⢟⢦⠀⠀⠀⠀⠘⣆⠀ ⣼⠃⣿⣉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢹⡇⠀⠀⠀⠀⠉⠢⠄⠀⠀⠀⠠⠒⠋⠉⢧⡀⠈⠀⠀⠀⠈⠻⢆⠀⠀⠀⠀⠘⣆ ⠻⢇⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠿⠦⢤⣀⠀⠀⠀⠀⠙⠀⢀⣄⣀⣹ ⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣍⡙⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣦⣤⣤⣶⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⢏⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣻⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢹⣿⣿⡄⠀ ⠀⠀⠀⠀⢰⣿⣟⡗⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣛⣿⣿⠀ ⠀⠀⠀⠀⢸⣿⣿⡓⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠐⣻⣿⣿⡆ ⠀⠀⠀⠀⢸⣿⣿⡷⠖⠋⠻⣄⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⢀⣴⠏⠈⠲⢿⣿⣿⠇ ⠀⠀⠀⠀⠸⣿⣿⣿⣧⠞⠁⠈⠻⢾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡷⠋⡁⠈⢦⣾⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣷⣷⡴⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠱⣴⣷⣯⣿⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣾⣿⢗⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢾⣿⣮⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣽⣿⣿⡍⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢄⣿⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢸⣇⠀⢀⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⠇⠹⣶⣤⣀⣀⠀⠙⢶⣤⡀⠀⠀⠀⣠⣴⠖⠉⢀⣀⣠⣴⡾⠁⢿⣿⡆⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠏⢠⣾⣿⣿⣿⣿⣿⣦⡀⠹⡿⠀⠀⠸⡿⠁⣤⣾⣿⣿⣿⣿⣷⣦⠀⢿⡇⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢿⡀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠆⠀⠀⠀⠀⠀⠞⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⢧⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡷⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⣏⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠙⠻⠿⠿⠿⠟⠁⠀⢠⣿⣿⣧⠀⠀⠙⠿⠿⠿⠿⠛⠁⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⢸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣿⣿⣿⡖⠦⡀⠀⠀⠉⠁⠀⠉⠁⠀⠀⢠⠖⣾⣿⣿⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⢻⣿⣴⣠⢀⠀⡄⠀⡀⢀⡄⢀⣀⣼⣼⣿⠹⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⡇⢸⣿⣿⡇⢹⠒⡟⠙⡟⠉⡗⢹⠁⣿⣿⣿⠀⡧⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠘⢿⣹⠛⠼⣦⣿⣄⣧⣀⣷⣾⠴⢻⣸⠟⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠊⠳⠧⣼⣠⣤⣧⣱⣸⡦⠷⠚⠃⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣠⣴⣶⣤⣄⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀ ⠀⠀⢀⣾⡟⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡙⣿⡄ ⠀⠀⣸⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣹⣿ ⠀⠀⣿⣿⡆⢚⢄⣀⣠⠤⠒⠈⠁⠀⠀⠈⠉⠐⠢⢄⡀⣀⢞⠀⣾⣿ ⠀⠀⠸⣿⣿⣅⠄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠑⣄⣽⣿⡟ ⠀⠀⠀⠘⢿⣿⣟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⣿⠏⠀ ⠀⠀⠀⠀⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢻⠀⠀ ⠀⠀⠀⠀⢿⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢸⠀⠀ ⠀⠀⠀⠀⢸⢰⡿⢘⣦⣤⣀⠑⢦⡀⠀⣠⠖⣁⣤⣴⡊⢸⡇⡼⠀⠀ ⠀⠀⠀⠀⠀⠾⡅⣿⣿⣿⣿⣿⠌⠁⠀⠁⢺⣿⣿⣿⣿⠆⣇⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⠂⠘⢿⣿⣿⡿⠀⣰⣦⠀⠸⣿⣿⡿⠋⠈⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣿⢻⣆⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠶⣶⣦⠤⠀⠘⠋⠘⠋⠀⠠⣴⣶⡶⠞⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣷⠦⢀⠤⡤⡆⡤⣶⣿⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡀⠘⢯⣳⢶⠦⣧⢷⢗⣫⠇⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠋⠛⠛⠋⠉⢀⡠⠒⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⠀⢀⣀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣀⣤⢾⣻⣿⡿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣟⠿⣿⣿⢳⢦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⡌⢣⣻⣿⣴⡿⢚⣽⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣍⠻⣷⡼⣿⣿⠎⣨⢿⣦⠀⠀⠀ ⠀⠀⣴⣿⣮⣷⡙⣆⢳⣿⣿⣾⣿⣯⣿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢿⣮⣟⢿⣮⣿⣿⢃⡞⡹⢋⣼⣷⡀⠀ ⠀⣼⡟⢮⡻⣷⡹⡜⣎⣿⣿⣿⣿⢋⡴⠋⣩⣿⣿⣶⣤⣶⣤⣤⣤⣤⣄⣀⣤⠶⠖⠚⠛⠛⠓⠶⢦⣄⣀⣤⣤⣶⣤⣴⣶⣴⣾⣿⡯⡉⠳⢌⠻⡿⣿⣿⣗⡞⡼⣱⡿⣫⠔⣻⣄ ⣸⣧⣬⣷⣿⣿⣷⡷⠟⠻⣿⣳⢳⠋⢠⠞⣱⢋⡜⣱⢫⠞⠉⡼⢋⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⠱⣌⠙⢎⢳⡙⣌⢳⡘⢦⠈⢳⣹⣹⡿⠙⠳⣿⣿⣟⢕⣫⣄⣿ ⣿⡩⠽⢿⣿⣿⠋⠀⠀⠀⠹⣿⡟⢠⡏⣸⠃⣼⢰⠇⡟⠀⡼⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠘⡆⠈⡇⢷⠸⡆⢻⡈⣧⠘⣿⡿⠁⠀⠀⠈⢻⣿⣿⠿⠭⣙ ⠹⡴⠚⣩⢟⣿⣷⣶⣶⣤⣄⡛⣷⢸⠀⣏⠀⡇⢸⠸⡇⢸⣇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⠀⡿⢸⠀⡇⢈⡇⢸⢠⡟⣁⣤⣴⣶⣶⣿⣟⢯⡉⠲⣼ ⠀⠛⢾⣄⣞⣸⣿⣿⣿⣿⣿⣳⡎⠻⣧⣹⡄⢳⠘⡇⢧⢸⣾⡇⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⣿⣼⢠⠇⡾⢰⠇⣸⣁⡿⠋⣴⣿⣿⣿⣿⣿⣿⣈⣦⣽⠖⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠈⠙⠳⢮⣷⣽⣼⣮⣿⣇⣀⣤⣤⣄⡀⠀⠀⠈⢧⠞⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣞⣼⣡⣯⠴⠟⠉⠀⢰⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⠿⢿⣿⡟⠉⠀⠀⠀⠉⠛⠳⢤⡀⠀⠀⠀⣀⣠⣴⣶⢶⢾⢾⠿⣿⣽⠿⠿⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣦⣄⣀⣀⣀⣤⡶⠞⠛⠉⢀⣀⣠⣤⣤⣬⣿⣆⣀⣲⠶⢦⣀⠀⠀⠉⣷⡗⠋⠙⠂⠉⠈⠀⠀⠀⣶⣿⣦⣤⣤⣀⣀⡈⠙⠛⠶⢦⣤⣀⣀⣀⣤⠴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣥⣤⣤⠴⡶⠿⣟⠉⠻⠇⣿⡀⠉⢿⣟⣄⠀⠀⠙⢷⣤⣴⣫⣻⣤⣀⣠⣤⠴⢶⣶⣿⠏⠁⣽⡆⠿⠉⠙⡿⠷⣶⢤⣤⣤⣽⠿⠿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣄⣀⣀⣟⢶⣤⣿⣷⡀⠀⠉⠺⠽⠿⢿⣿⣿⣎⠉⢉⣿⣿⣻⠷⠶⠽⠚⠁⠀⣰⣿⣧⣴⢞⣦⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣿⢷⣶⣦⣄⣴⣯⣉⠙⠳⠀⠠⠛⢋⣈⣷⣄⣠⣴⣶⢾⡟⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠯⢣⣀⠀⠙⠙⢧⡀⠀⠀⣠⠟⠛⠉⢀⣠⠿⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢿⣿⣶⢤⣤⣽⣶⣿⣥⣤⢴⣾⣿⠃⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⢿⡿⣾⣧⣿⣷⣿⣧⣯⡾⣿⠃⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣷⣾⣟⠛⢿⠛⢙⣿⣤⣯⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣄⡈⣀⣾⣿⣿⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⣿⡏⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⠽⠿⠿⢽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⢿⣿⣿⠟⠉⠻⢶⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⡟⠙⢡⠀⠀⠶⠛⣴⣾⢿⠙⣻⣽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡿⠻⣹⡴⣿⣿⣦⣾⠀⣀⠀⠀⢾⡽⣷⣖⡍⣩⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⣇⢰⣧⣿⣿⡿⢿⣿⣿⣶⢾⡷⣇⣻⣥⣽⣿⣷⣿⣠⠞⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠋⠂⣿⣾⣿⣿⡿⠁⠀⠉⠻⣿⠿⣷⣿⣮⣿⣿⣿⣿⣿⣧⠴⠶⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠻⣄⠴⣷⡾⠋⠉⣿⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠉⢉⡟⣿⠿⣗⠀⠀⢀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣇⣠⣿⣿⣿⠁⠀⣰⣿⣦⣄⣀⣠⡟⠀⠀⠀⠀⠀⠀⣼⠁⠙⣿⣿⣾⣅⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣏⣹⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⣠⠏⠀⢠⠟⢿⣷⣜⣦⣄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⢿⣿⡿⠿⠿⢿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠀⢠⣾⣀⣀⣽⣿⡿⠥⠄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣇⡶⢊⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣴⣿⣿⣿⣿⣿⣿⣷⣶⡆⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣗⣋⠀⠒⠻⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣊⣡⠙⣳⣦⣀⡀⠀⠀⠀ ⠀⠀⠀⠘⣿⣇⣼⣶⣿⣿⣿⣿⣿⣷⣿⣿⣟⣛⠉⣹⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⠶⠆ ⠀⠀⠀⠀⢸⣿⣿⠏⠀⡰⠛⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠿⢤⠽⢿⣟⠅⠀⢿⡁⢀⠘⠟⠛⢻⣤⡶⠾⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣶⣴⠁⠀⢉⡿⠋⠉⠠⠾⠥⢉⣽⣿⠿⣽⣶⡟⠀⠈⣹⢧⣤⠄⠙⠉⣽⣿⣷⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡶⣴⣿⡀⠀⡀⡄⠀⠀⠾⣿⠙⢾⣷⣿⣷⣾⠂⠀⣴⣿⣶⣖⠀⣿⠛⣿⣸⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣇⣻⣯⣧⣀⣀⣦⣉⣀⣾⣼⣺⣿⣿⣧⠀⣿⠟⠋⢻⡀⢹⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠛⠿⠿⣿⣿⣿⣏⣾⣿⣿⣿⠿⠿⠟⣷⠀⣿⠀⠀⢠⣗⣼⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⠇⠀⢀⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠁⠀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣉⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⣮⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣰ ⣇⠈⡕⣄⡴⣶⡉⠉⠉⢉⣷⠦⣠⢎⠃⣸ ⠘⡄⢀⠀⠹⡪⢻⠂⠀⡞⢕⠏⠁⢀⢰⠃ ⠀⡌⠢⣑⣵⡇⠁⠆⠐⠈⢸⣮⣂⠕⢱⠀ ⠀⣷⣒⡚⠲⡈⠐⣄⣠⠂⢁⠔⢓⢲⣾⠀ ⠀⢸⠵⣿⡑⢌⠀⣺⡗⠀⡡⢊⣿⠮⣈⠀ ⠀⢻⠀⠠⠉⠛⢫⠍⠩⠽⡛⠉⠄⠀⡞⠀ ⠀⠀⣳⣦⠴⠒⠃⠂⠀⠘⠂⠤⣼⣞⠁⠀ ⠀⠀⣿⢸⡟⣄⡙⡕⢌⢎⣠⣺⡇⣹⠀⠀ ⠀⠀⠘⡾⣹⣷⣯⣿⣿⣽⣾⡧⢣⠃⠀⠀ ⠀⠀⠀⠉⢧⣿⣿⣿⣿⣿⡏⡴⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⠳⣿⣯⠟⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠱⣞⣳⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠴⠤⠤⠤⠴⠠⠤⠄⠀⠂⠶⠦⠶⠦⠀

⠀⢀⣴⡻⣟⡽⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣽⡿⡢⡀⠀ ⢠⢞⡿⢞⣿⣿⠟⢍⣧⣀⣀⣀⣀⡀⠤⠤⢄⣀⣀⣀⣀⣴⣋⢗⢿⣾⣯⣻⡝⣄ ⣆⠺⣿⠋⠹⣷⠡⡑⡑⠎⣐⡕⠉⠀⠀⠀⠀⠈⠳⡑⠑⡵⠩⢂⢛⡟⠙⢿⠿⢘ ⠱⣝⣿⣷⣶⣝⢄⠇⠇⣠⡼⠀⠀⠀⣀⢀⠀⠀⠀⢹⡁⢇⢀⢠⢜⣶⣶⣟⣪⠽ ⠀⠀⠀⠀⠈⠙⠀⣉⣺⣷⡷⠒⠒⠤⡀⠃⢀⣀⣠⣼⣿⣾⣊⠀⠘⠁⠀⠀⠀⠀ ⠀⠀⠀⠶⣖⣒⣩⢤⠴⡖⢳⣔⠒⢄⣈⣏⣁⣀⢤⡼⢓⡖⠤⣍⣐⣲⡶⠂⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠀⠓⠛⣤⣍⣛⡟⠏⠸⠟⣟⣊⡤⠞⠊⠃⠐⠊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⣤⣉⣢⣔⣉⣥⠊⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⣵⡿⠿⣟⣯⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣼⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀ ⠀⢠⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⠀ ⢠⡏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣘⡆ ⢸⡃⡼⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⡇ ⠘⣧⡇⢣⠀⠀⢀⡤⠖⠊⠉⠉⠀⠀⠈⠉⠉⠒⠤⣀⠀⠀⣸⠁⣿⡇ ⠀⢿⠀⠈⠳⢾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡱⠖⠁⠀⣸⠁ ⠀⠘⡆⢢⡀⠀⢀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡇⠀⠀⡰⢣⡏⠀ ⠀⠀⢸⢦⣙⡶⠞⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠙⢶⣞⡡⣏⠀⠀ ⠀⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡄ ⢀⣇⡹⡀⠀⠀⠀⠀⠀⠀⠀⡼⢠⡟⢳⡀⠀⠀⠀⠀⠀⠀⠀⡜⣡⡇ ⢸⣿⢇⣧⣀⢤⣀⣉⣉⣉⡙⢳⡚⢣⣼⠋⣉⣉⣋⣀⡠⢄⣼⣷⢿⡇ ⠸⣿⣸⡿⢆⠉⣶⣦⣽⣧⢶⡛⣌⢉⠝⡳⢦⣭⣿⣷⡊⢁⠞⡏⣼⡇ ⠀⠹⣿⣧⣄⠙⢿⣬⣿⡿⠀⢘⣮⢸⣏⠀⠸⣿⣭⣿⠗⢁⣴⣿⡟⠀ ⠀⠀⣇⣸⣯⠑⢢⣤⣤⠍⠉⡏⠹⢸⠹⡉⠉⣥⣤⣴⠒⣹⣿⣸⠁⠀ ⠀⠀⡿⢏⣧⣷⣮⣉⣁⡴⠊⠓⠀⠀⠀⠉⢢⣌⣉⣥⡾⣟⡟⢿⠇⠀ ⠀⠀⠹⢿⣿⠀⣿⣖⠒⠻⠄⢶⡀⠀⡴⠦⠜⠓⣲⣿⠃⣸⡿⠾⠀⠀ ⠀⠀⠀⠀⢧⠁⢹⣿⠹⢲⣦⣤⣽⣿⣤⣤⣶⠻⢽⡿⠀⣡⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣀⣿⣴⣿⣤⣯⣬⣧⣽⣷⣾⣧⣼⣁⡴⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡏⢻⡏⡿⣿⣿⣿⣿⣿⡝⡿⢈⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠳⠷⠼⠒⠓⠾⠼⠗⠁⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣠⣤⠶⠶⣦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣦⣼⣿⣿⣅⣀⣁⣀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢫⣾⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠄⠀⠀⣤⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡈⠓⠦⡄⠀⠀⠀⠀⠀⡰⠋⣠⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣞⣵⣿⠿⣓⡦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠓⢤⡀⠀⢊⣠⣾⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠺⠤⠤⢴⣾⣿⡿⣁⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣩⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣥⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⡟⣡⠊⠀⠀⠀⠀ ⠀⠀⠀⠘⢠⣿⣿⣿⡿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢺⣿⣿⣿⢏⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣧⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠤⠤⠒⠓⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⣤⣴⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣄⢸⣿⣿⣿⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉⢀⣩⣉⡛⠿⠿⣹⣿⣿⣿⣿⣿⠿⣅⣀⠈⢹⣿⣿⣿⣿⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⠉⣠⣬⢳⡀⢠⣿⠿⠟⣿⣿⠟⠻⠛⠻⢿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⣀⣀⣀⣿⡄⠙⠛⠾⣧⠀⠀⠀⠞⠋⢁⠀⠐⣻⣿⠀⠘⣿⣿⣿⣿⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠾⢫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⠿⢣⠀⢠⣿⣿⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣏⣯⡀⢸⣆⣖⠉⠛⢿⣿⣿⣿⣿⣯⡉⣿⠡⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠐⠚⢻⣿⣿⡧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⠂⢹⣿⣦⠀⠀⠸⣿⣿⡟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠛⠙⣇⣹⣟⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⠷⠶⣄⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠒⣒⣒⠦⢤⡸⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⠬⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⣿⣶⡅⠸⣗⢶⡄⠀⠀⠀⠀⣼⣿⠇⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡙⠻⢦⠀⠀⠀⠀⠀⠀⠸⣿⠙⠿⢿⠿⣿⣿⣧⠀⠈⢧⡀⠀⠀⢀⣼⣿⣿⡄⠀⢿⢠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⢸⣿⣚⣦⠀⠀⠹⣄⣴⣿⡿⠿⠿⡇⠀⠘⣏⢣⡀⠀⠀⠀⠀⠀⠀ ⢠⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⢤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠺⠛⠁⠈⠳⣄⢠⡎⢉⡿⠁⠀⢀⡻⣄⠀⠸⢆⠙⢦⠀⠀⠀⠀⠀ ⠘⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⡾⠀⠀⢠⡟⠀⠈⠙⠀⠈⢷⠀⠳⡄⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⡟⣶⣿⣿⡓⣦⣤⣤⣤⣤⣾⣿⣿⣄⣠⠿⠤⣤⠴⢻⡟⠉⠀⠀⠀⠈⢧⠀⠹⡄⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠉⠙⣿⣿⣿⣷⣼⣏⠙⠻⢿⣿⡿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣡⢴⣟⢙⣗⠶⠦⠤⠀⠀⢳⡀⢰⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⠶⠀⠩⢤⣌⡛⠿⠟⠁⠻⠟⠋⠀⠉⠻⣿⣿⡅⠀⠒⠲⡶⠋⠙⢿⡿⣇⠀⠀⠀⠀⠀⢱⡄⠁⠀ ⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⣧⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⣀⣠⠔⠛⠛⢷⡀⠀⠞⠀⠀⠀⠀⢻⣽⡄⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠲⠤⣝⣦⣀⠀⠀⠀⠀⠀⠁⠙⠲⠤⠀⡀⠀⠀⣷⠀ ⠈⢂⠹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣀⠀⠀⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡀⠀⠀⠀⢀⢀⣿⣿⣶⣿⡀ ⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠓⠦⠀⠀⠙⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠺⠛⠛⠛⠛⠛⠛⠀ ⠀⠀⠀⠠⣈⠻⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠦⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⢀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀ ⠀⢠⡞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⣦⠀ ⢀⡞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣆ ⣸⡇⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡆⣿ ⣿⡀⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⣿ ⠛⡇⡇⠸⣇⠀⠀⠀⢀⣤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀⠀⠀⠀⢠⡟⢰⣇⡟ ⠀⣧⠙⠀⠙⣆⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⠞⠀⠘⢹⡇ ⠀⢹⡆⢆⠀⠀⠙⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠋⠁⠀⢠⠆⣾⠀ ⠀⠈⢷⡈⢧⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⣰⠋⣼⠇⠀ ⠀⠀⠈⡷⣄⣙⣲⡶⠃⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⠀⠀⠀⠈⠷⣶⣚⣁⡼⡇⠀⠀ ⠀⣀⣸⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢷⢀⡀ ⠀⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡇ ⢰⣇⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⠁⣿⡅⠻⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣤⣿ ⣼⢸⢿⢸⣇⡐⢦⣄⣀⡉⠉⠉⣁⡙⢻⡔⠿⢇⣼⠋⣉⠉⠉⢉⣁⣀⡠⢄⣰⣿⡸⢻⣿ ⣿⢸⡈⣿⣿⡈⠛⢶⣤⣍⣛⣏⣡⡤⢿⡍⠛⢋⡽⢦⣤⣉⣙⣯⣧⡤⠞⠋⣸⢿⡇⣸⣿ ⠙⢟⢧⣿⠁⠻⢄⣿⣿⢻⣿⣿⡄⠙⢦⡝⡄⢾⡥⠚⠁⣿⡿⣿⢻⣿⣄⡼⠁⣼⢠⣯⠏ ⠀⠘⣯⡾⣧⢦⡈⠛⠻⢷⣾⣿⣁⣀⣠⣿⠀⣾⣧⣀⣀⣻⣿⣶⠾⠛⠉⣠⣾⡟⣿⡏⠀ ⠀⠀⣾⡀⡼⣧⠉⠓⣶⣤⣤⡤⠄⠀⣾⢸⠀⡏⠹⡆⠀⠤⣤⣤⡴⡖⠉⣱⣿⣅⣽⠀⠀ ⠀⠀⢿⣿⡏⡏⣷⣤⡙⠛⠛⢁⡤⠖⠿⡈⠀⠀⠠⠗⠶⣀⠉⠛⢋⣡⣼⡋⡏⣯⣿⡆⠀ ⠀⠀⢸⣠⣾⣿⠋⢿⣮⣛⣛⣹⡀⠀⣀⡀⠀⠀⢀⣀⠀⣿⣙⣛⣫⣾⠃⢻⣻⡄⣸⠁⠀ ⠀⠀⠈⠛⢹⠹⡄⢸⣿⣦⣄⡈⠛⠒⠚⢧⣀⣠⠟⠒⠛⠁⣀⣼⣿⣿⠀⡼⣼⠙⠋⠀⠀ ⠀⠀⠀⠀⠈⢷⠙⠈⣿⣿⠸⠙⣶⣶⣤⣤⣿⣧⣤⣴⣶⡏⠫⢼⣿⠏⠘⣡⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡄⠘⣿⢀⣾⣥⣈⣏⡉⣻⣉⣉⣧⣴⣿⣆⢸⡏⠀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢾⠿⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⠻⢷⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⣿⢸⡟⢻⠟⢿⠿⣿⠛⣳⢸⡏⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⠧⠜⠓⠛⠓⠛⠤⠿⠋⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⢀⣠⣤⣶⣦⣤⣀⢀⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡿⡿⡋⠈⣹⣶⣦⣤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣩⣿⣄⣸⠀⠀⠁⣺⣿⣃⠘⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⡇⢸⣼⣷⣿⣿⣿⣶⣥⢶⣻⣡⣿⣧⣿⡤⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⢑⢻⣿⣿⠟⠁⠀⠙⡿⠿⠾⢿⣿⣿⣿⣟⡦⠚⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢛⣦⣿⡟⠁⣸⡀⠀⠀⣰⠃⠀⠀⠀⠀⡼⠿⣯⣅⡤⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⢳⣾⣾⣿⠁⢰⣿⣿⣿⣾⣧⡀⠀⠀⠀⢠⠇⢀⡿⣿⣝⣄⡘⣇⠀⠀⠀⠀⠀⠀⠀ ⠰⢾⣿⠿⠟⢿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⠏⢀⣼⣀⣹⣿⡿⠥⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡾⣪⠽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣷⣶⣀⡿⣄⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⡶⢠⣠⣽⣿⣷⣌⣻⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣟⣶⣤⣀⡀ ⠀⠀⠀⠸⣿⣿⠟⢉⠾⣿⢿⣿⡿⣿⣶⣿⣿⣿⡿⣉⣿⡿⠋⠹⡏⠉⠻⠿⢿⣩⡽⠟⠛⠉⠁ ⠀⠀⠀⠈⢿⣷⣶⡎⠀⣩⠋⠉⠰⠫⢉⣽⡿⣯⣶⡇⠀⡭⢧⡤⠙⠩⣿⣷⢸⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣺⣯⢀⡄⡆⠀⡘⡯⢙⡿⣿⣿⣏⠀⣾⣿⣯⠐⡏⣿⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣷⠛⠿⢾⣽⣷⣶⡿⣲⣾⣿⣿⣿⢿⡇⡏⠀⠘⡆⡧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⢸⣡⠇⠀⣼⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀ ⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀ ⠀⢀⡟⢸⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡏⢹⡄⠀⠀ ⠀⢸⣷⠀⣏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠁⣼⡇⠀⠀ ⠀⢸⡏⡆⠸⡎⢷⡀⠀⠀⠀⢀⣀⣤⣶⠶⠾⢿⣿⡿⠶⠶⣶⣤⣀⡀⠀⠀⠀⢀⣼⢣⡏⢠⠋⡇⠀⠀ ⠀⢸⣧⠀⠀⠹⡈⢻⣦⣤⠾⢿⣟⡷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠷⣦⣴⡟⢁⠏⠀⠀⣸⡇⠀⠀ ⠀⠈⣯⢦⠀⠀⠉⠀⠉⠙⠻⣶⢌⠛⣿⣧⡀⠀⠀⠀⢀⣰⣿⠟⡡⣶⡞⠛⠋⠀⠊⠀⠀⣰⣽⠃⠀⠀ ⠀⠀⠈⢷⡀⠰⣀⠀⠀⠀⠀⢻⣆⢳⡈⢳⡉⠁⠀⠀⠉⡼⢁⡼⢡⡟⠀⠀⠀⠀⢀⡔⢀⣼⠁⠀⠀⠀ ⠀⠀⠀⠈⣻⣄⠈⠳⣄⠀⠣⣌⣿⠀⢣⠀⢧⠀⠀⠀⡸⠁⡼⠁⣿⣣⠔⠀⣠⠜⠋⣠⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠈⠳⢦⣌⡙⢲⣬⣿⡀⠀⠀⠘⠆⠀⠀⠇⠀⠁⠀⣿⣥⡴⢚⣁⣴⠞⠁⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⢸⢠⠀⣀⣀⣙⣿⣉⡉⠉⠳⢤⣀⠀⠀⠀⠀⠀⢀⡠⠞⠋⢉⣉⣽⣋⣀⣀⠀⡀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⣾⡄⣿⡉⠉⠉⠛⢧⡀⠀⠀⠈⢳⡄⣤⢀⡞⠉⠀⠀⠀⣨⠟⠉⠉⠉⣹⠁⣧⡿⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠃⣿⠹⣷⠲⢤⡀⠹⢦⣀⣀⡀⢻⣿⡿⢁⣀⣀⣠⠞⠁⣠⠶⣾⡆⣸⠀⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣀⣼⢧⣳⣧⡀⠙⢦⡀⠀⠀⠈⠹⣿⡟⠉⠀⠀⠀⣠⠎⠁⣴⣟⡴⢷⡀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠋⠀⠀⠓⠽⢿⣦⡤⠿⣦⣄⣴⣾⠿⣧⣦⣀⣤⡾⢥⣴⡿⠻⠚⠁⠀⠉⣻⡄⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⡇⠀⠀⠀⡶⠁⠈⠉⡛⠺⣧⣤⡖⠀⢲⣤⣼⠗⠛⠋⠁⠀⢲⡀⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣄⠀⣸⠁⠀⠀⠀⠈⢳⡈⢀⠃⠀⠈⠁⠁⡔⠃⠀⠀⠀⠀⢷⠀⣠⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣧⣧⣀⣤⣴⠶⢲⡾⠃⠘⡆⠀⠀⠃⠀⢻⡖⠶⢦⣤⣀⣸⣶⣿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡟⢻⣿⢅⣀⠀⠈⢧⣀⠠⡅⠀⢀⡄⣀⣸⠇⠀⡀⣨⢿⡟⢻⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣏⡇⢸⣿⠻⢿⣧⠀⠈⠻⣇⠸⣤⠏⢰⡿⠁⠀⣰⡿⢿⣿⡗⢸⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡅⠀⣿⡇⢸⣾⠛⣶⣤⣘⣦⣀⡴⣋⣠⣶⠛⣿⡇⢸⣿⠁⢨⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣤⡏⢁⣻⣿⣾⣿⣀⣿⠉⣿⠋⣻⣀⣽⣷⣿⣧⡀⠿⣦⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣟⣴⡎⢹⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠙⣦⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣧⡀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣀⣼⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣗⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⢳⡗⢫⢯⣿⡽⢹⢻⡽⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠿⣿⣿⣿⠿⠋⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡶⠟⠿⠫⢴⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠴⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⢀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀⣀⡀⠀⣀⣀⢀⣀⡀⢀⠀⢤⢠⣄⡤⣠⡄⣠⢠⢄⣤⢀⠄⠠⠀⠀ ⠂⠃⠛⠛⠓⠓⠓⠚⠘⠚⠛⢚⠛⠛⠓⠘⠚⠓⠛⠃⠃⠀⠀⠒⠐⠃⠘⠙⠊⠙⠁⠋⠛⠐⠁⠒⠀⠃

⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀ ⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀ ⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣇⠀⠀ ⠀⠀⣾⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⠀⠀ ⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⠉⠉⠀⠀⠀⠀⠉⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣿⡇⠀ ⠀⠘⣿⠀⠀⠹⡄⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⢠⠎⠀⠀⣿⡇⠀ ⠀⠀⣿⡤⠼⠁⠈⢢⣄⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⡔⠃⠀⠣⣤⣿⠃⠀ ⠀⠀⢻⣷⣀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⡀⣀⣼⡟⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⡟⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢻⣿⣿⣿⣿⡿⠁⠀⠀ ⣄⠀⠀⠀⠻⣿⣿⣿⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣿⣿⣿⠟⠁⠀⠀⣠ ⠘⣧⡀⠀⠀⣾⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣷⠀⠀⢀⣼⠇ ⠀⢹⣳⡀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢀⣾⡟⠀ ⠀⠘⣿⢳⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡞⣼⠃⠀ ⠀⠀⣿⡄⢣⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡜⢠⣿⠀⠀ ⠀⠀⢻⣇⠈⢻⡀⠀⢹⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡏⠀⢀⡿⠁⢸⡟⠀⠀ ⠀⠀⠀⢻⠀⠈⡇⠀⠀⠉⠫⢯⠙⠻⢄⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠞⠋⣩⠍⠉⠀⠀⢸⠁⠀⡟⠀⠀⠀ ⠀⠀⠀⣼⠀⢸⣇⠀⠀⠀⠀⠈⠳⠤⠤⣵⣤⡔⠃⠀⠀⠀⠀⠈⠢⣤⣮⠤⠤⠞⠁⠀⠀⠀⠀⢸⡇⠀⣷⠀⠀⠀ ⠀⠀⠀⢻⡀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⡿⠀⠀⠀ ⠀⠀⠀⠘⣷⣼⣿⡿⠲⣄⡀⠀⠀⠀⣀⡜⠁⠀⢠⠇⠀⠀⠸⡀⠀⠈⢣⣀⡀⠀⠀⠀⣠⡖⢻⣿⣧⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⣿⣿⠀⣧⠉⠛⠛⠉⠘⠳⢤⣀⢸⡀⠀⠀⠀⡇⣀⡤⠞⠁⠉⠛⠛⠉⣼⠀⣾⣿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⡀⢸⡆⢀⡞⡏⠑⠦⣀⠀⠙⢧⣤⣤⡼⠋⠁⣀⢴⠊⢹⠳⡀⢠⡏⠀⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣇⠈⣧⡼⣾⣿⣴⡇⠀⣍⠒⠦⠭⠭⠴⠒⣹⠀⢸⣦⣿⣗⠳⢸⠁⣸⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢿⢀⡿⣿⣿⣿⣼⣿⣦⣷⣴⣦⣾⣶⣿⣧⣿⣿⣿⢷⡀⣿⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢸⠘⣅⡙⠀⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠁⢃⣨⠇⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⡆⠈⢧⠀⠙⠀⠻⠃⠏⠹⠏⠹⠈⠏⠀⠋⠀⡼⠁⢠⢣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⠀⠈⣿⢿⣤⣆⣰⣦⣰⣆⣴⣆⣰⣄⡾⣿⠁⠀⠈⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢸⡆⠉⢁⣤⠤⠤⠴⠤⣤⣈⠉⢠⡏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡤⣶⣿⣿⢛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣟⢿⣿⡗⡦⣄⠀⠀⠀ ⠀⠀⣰⡿⡷⡜⢟⣷⣟⣽⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣝⣿⣿⢟⡴⡽⣧⡀⠀ ⠀⡼⢟⢿⡟⡜⡜⣿⣿⣿⢟⡭⢛⣿⣦⣀⣀⣀⣀⣀⠀⢀⣠⡤⠤⠤⠤⣄⣀⠀⣀⣀⣀⣀⣀⣠⣾⣟⠫⣛⢿⣿⣿⣏⡎⣜⣼⢟⠷⡀ ⣸⣭⣿⣿⣿⣾⠟⢻⣟⣯⠋⡰⢫⢋⢟⣟⠝⢉⠟⣩⠟⠉⠀⠀⠀⠀⠀⠀⠉⠙⢯⡙⢍⠛⡝⡟⣌⢫⠳⡈⢪⣟⣿⠛⢿⣿⣿⣟⣯⣿ ⡯⠐⣛⣿⣏⠁⠀⠀⢻⡏⢰⢁⠇⡜⡜⡸⢀⣮⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⡆⠸⠸⠸⡌⠇⢡⠘⡿⠃⠀⠀⢙⣿⣟⡓⢬ ⠘⣍⡔⡻⣿⣿⣿⣶⣦⡻⣼⠸⡀⠇⢣⢡⢸⣺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⢰⢠⢀⠇⡘⢸⡼⣡⣶⣿⣿⣿⠻⡑⣌⡟ ⠀⠀⠉⠉⠉⠉⠉⠛⠿⣧⠈⠓⢷⣜⣜⣌⣞⣿⠀⣀⣀⠀⠀⠈⢣⡰⠋⠀⠀⠀⠀⠀⢸⣿⣎⣎⣜⣰⠗⠁⢰⡿⠛⠋⠉⠉⠁⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠾⠿⣿⡟⠉⠀⠈⠙⠳⢤⡀⠀⠀⣀⣤⣤⠴⡶⠿⣿⡿⠿⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⢦⣤⣤⠴⠖⠋⢁⣀⡤⣴⢶⠼⢿⣤⡼⠓⢦⡀⠀⢩⣿⠉⠉⠀⠀⠀⣀⣸⠿⣶⢶⡤⣤⣈⠉⠓⠶⢤⣤⣤⠖⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠙⠿⣟⡛⠉⠙⣤⡉⢸⣆⠈⠻⢷⣤⣤⣼⣷⡻⠿⣷⣶⣖⣉⣽⠿⠁⢀⣿⢈⣠⡘⠉⠙⣙⡿⠟⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠉⠉⠹⣶⣤⣄⣀⣼⡛⠻⠇⠀⠿⠛⢻⣌⣁⣤⣴⡾⠉⠉⠀⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⠳⣀⠈⠛⢧⡀⠀⡠⠛⠋⢀⡼⠻⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢻⣿⣷⡶⣿⣿⡶⡖⣿⡿⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣿⣹⡿⢿⣿⠿⣟⣹⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣀⢃⣸⣿⣟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣽⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡉⢉⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣾⣿⣿⣿⣿⣶⣶⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡅⠠⣄⠀⠀⠀⠀⢀⠔⣱⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⢐⣵⡿⢷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡑⠢⡀⠀⣡⣾⣿⠏⠀⠀ ⠀⠀⠀⠓⠒⣺⣿⣿⠄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢹⣿⣿⡿⡧⠁⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡏⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⣄⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⣒⡛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⠉⠓⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⡀⢉⣽⢆⠀⣾⠿⢿⣿⠟⠟⠛⢷⣿⣿⣿⣿⡷⡄⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠛⠤⣤⠤⠧⠘⠛⠚⠆⠀⠀⠋⠁⣄⣨⡿⠀⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣟⡟⠛⣟⣹⠿⣿⣿⣿⣿⣿⠿⣷⢛⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠁⡠⢼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣦⠘⣿⣄⠀⠙⣿⣿⠿⠷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠚⢻⣳⡟⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣜⠛⠒⠤⣽⣿⡄⠀⠀⠀⠀⠀⠀⣰⣖⢒⣶⣢⠤⠿⣄⠀⠀⠀⠀⠀⣼⡟⢱⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⢷⣄⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⡀⠻⡟⠀⠀⠀⣰⣿⡇⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠀⠀⠀⠀⠀⠙⢄⡈⠉⠹⣿⣧⠀⠘⢦⣠⣾⡿⠿⡇⠀⢻⠢⠀⠀⠀⠀⠀ ⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠲⠄⠀⠀⠀⠀⠀⠈⠉⠚⠋⠁⠳⣄⡸⠉⡟⠀⢀⡜⣄⡀⠧⡑⢄⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣠⣄⣤⣄⣀⡀⠀⠀⢀⣴⣿⠁⢸⠀⠀⣸⣤⠤⠀⠀⢱⡀⢢⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⢿⣿⣿⣻⡟⠻⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⡗⠉⠉⣋⣵⠓⡤⠄⠀⠀⠱⡀⠃⠀ ⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡶⠆⠩⠥⣙⡿⠟⠉⠿⠋⠉⠙⢿⣿⠀⠐⢲⠗⠙⠻⣿⡄⠀⠀⠀⠑⡄⠀ ⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣇⠀⠀⠀⠀⠉⠢⠀⠀⠀⠠⠒⠉⠉⢣⡀⠊⠀⠀⠀⠹⠷⡀⠀⠀⠀⠸⡀ ⠀⠌⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠤⣄⡀⠀⠀⠈⠁⢠⣤⣤⣧ ⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠲⠈⠈⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠶⠞⠛⠛⠛⠛ ⠀⠀⠀⠀⠙⡦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⣇⣀⠤⠀⠀⠀⠀⠀⠀⠀⢠⠄ ⠀⠀⠀⠀⢀⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣔⠀⠀⠀⡀⣪⡟⠀ ⠀⠀⠤⣴⣾⠉⣹⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣷⣮⣴⣾⡟⠁⠀ ⠀⠀⣰⣿⠿⣾⣿⣿⣿⣿⣿⣿⡿⠀⢀⣾⣿⣿⣿⣿⣿⠋⠘⢿⠯⠂⠀⠀ ⠀⢠⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣇⣒⡚⣿⣿⣿⣿⣿⣏⢠⣶⣷⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢭⡝⢫⣿⣿⠿⢤⣽⣿⣿⡄⠀⠀⠀ ⠀⢸⣿⣿⣿⣟⣻⣿⣿⣿⣿⣓⢠⠐⠈⠚⠀⠈⠡⣤⠇⢸⣿⠋⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⡌⢾⡉⢻⣿⠯⠗⠀⠀⠀⠀⠀⢀⠀⠁⠈⠹⣣⡦⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣯⡉⣰⣿⡀⠀⠀⠀⣾⣽⣧⡜⢧⡄⠀⢀⡏⢃⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣍⠀⠀⠀⠫⢉⡙⣟⡄⠢⣠⡿⢇⠘⡀⠀⠀⠀ ⠘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠀⣀⣀⡀⠈⠀⣨⡞⠘⠀⣎⡒⠑⡄⠄⠀ ⠀⣿⣿⣿⡿⠟⠉⠙⢻⣿⣿⣛⠿⠿⣿⢾⣿⢿⣿⡟⣉⣩⣞⡆⠀⠘⠌⠀ ⠀⣿⣿⠟⠀⠀⠀⠀⠀⠙⠛⡇⠀⠈⠂⠄⠀⠤⠚⡣⡐⠁⠀⠻⣀⠀⠈⠄ ⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⠀⢄⠀⠀⠀⠀⠉⠐⠂⣄⣀⣤⣶⡇ ⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠤⠐⢂⣿⡧⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡆ ⠀⠀⠀⠀⠀⣀⣀⣠⡄⠊⣩⠊⠀⠀⡔⣽⣿⡇⠀⠀⢻⡐⣄⠀⠀⠀⠀⣠⡿⠀ ⠀⠀⠤⡴⢡⡮⣿⠋⠀⣼⠁⠀⠀⠌⡰⠛⢿⠀⠀⠀⢸⡇⠐⠐⣀⣤⣾⡿⠁⠀ ⠀⠀⡴⠃⣼⣿⡄⠀⢰⡇⠀⠀⡈⠠⠁⠀⡌⠀⠀⠀⣸⠇⢸⠈⠀⢙⠝⠀⠀⠀ ⠀⠰⠀⠰⣭⢹⢰⠀⢸⠀⠀⠀⡷⠥⠄⠚⢒⡋⢀⠔⡗⢄⠇⡤⠒⡅⠀⠀⠀⠀ ⠀⠀⠀⡄⢹⠘⡀⢆⠈⡷⠤⣠⡿⠟⠋⣿⡟⠔⡇⢀⢠⣏⣁⣧⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⡇⠘⣇⠷⡀⠀⠡⣆⠸⠇⡀⠰⠜⠹⠈⠉⠛⢁⣿⡟⢻⣼⡟⠀⠀⠀⠀ ⠀⠐⠀⡇⢬⡉⢭⠙⢲⠓⡘⡒⠆⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⣷⣮⡀⠀⠀⠀⠀ ⠀⠀⡇⢡⠀⡗⣌⠣⠤⣁⠃⠈⠀⠀⠀⣠⡤⣤⣀⢦⠀⠀⠀⢠⠞⡆⠀⠀⠀⠀ ⠀⠀⡇⢸⠐⢧⠃⣵⠘⢿⡟⠄⠀⠀⠀⢏⠛⠻⡿⡀⠋⠀⢀⡆⠀⠰⠀⠀⠀⠀ ⢀⠗⠇⢸⡸⢻⠀⠘⠒⣧⠈⡆⠄⠀⠀⠀⠁⠂⠇⠃⢄⡑⡻⠉⡡⡀⠇⠀⠀⠀ ⢰⢰⠀⣸⠇⢾⣀⣀⣰⠸⣀⣷⣦⣀⣴⣦⡤⣄⣀⢴⠻⣀⠄⠴⣄⠂⠀⠡⠀⠀ ⠀⡄⣷⢹⠔⠈⠀⠀⠈⢄⠈⢧⠍⠛⢙⡿⠟⠿⠛⠺⣶⠁⠤⠜⠳⣍⠀⠀⠱⡀ ⠰⡅⣧⠂⠀⠀⠀⠀⠀⠀⠈⠈⡄⠀⠀⠈⠀⠀⠀⠈⠀⢣⣀⠀⠀⠉⠢⠀⠀⢡ ⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠤⠐⠂⠄⠀⠀⠀⠀⠀⠈⠐⠦⠤⠦⠿⠿

⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀ ⢠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡄ ⢸⠀⡄⠀⠀⣀⠤⠄⠠⠤⢀⡀⠀⢀⢹⡇ ⠀⡇⠐⠴⢁⠀⠀⠀⠀⠀⠀⢈⠰⠊⣈⠃ ⠀⢑⢕⣤⠎⠀⠀⢠⡆⠀⠀⠘⢤⣌⡎⠀ ⢀⢾⠀⠀⠀⠀⠀⡜⡷⠀⠀⠀⠀⠀⡱⡆ ⢸⣧⡦⣤⠀⣂⠜⣖⣣⡃⢐⣂⢠⢴⡹⡇ ⠘⢷⣏⠰⣟⣿⠑⣵⢨⠊⢿⣻⠧⣢⣿⠃ ⠀⢰⣼⣍⠶⠖⡠⡙⠈⠇⡰⠶⣨⠿⣄⠀ ⠀⠸⢺⡉⣿⡛⠤⢆⡠⠦⢛⣻⡇⠿⠆⠀ ⠀⠀⠈⢂⢻⣰⣽⣛⣟⣯⣏⡟⡠⠃⠀⠀ ⠀⠀⠀⠀⢩⠹⡟⣟⣟⢻⡙⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⠤⠴⠦⠤⠔⠁⠀⠀⠀⠀

⠀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⣴⡟⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣶⠿⠟⢿⣆⠀⢀⣼⠿⠿⣷⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣄⠀ ⣿⣰⣧⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠉⠉⠁⠀⠀⠘⢿⣶⣿⠏⠀⠀⠈⠛⠋⠛⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣌⣿⡄ ⠻⣿⡏⣠⣿⣿⣦⣤⣀⠀⠀⣀⣀⣀⣀⢀⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣯⢿⣿⣼⠇ ⠀⢿⣷⣿⡄⠘⣡⡾⢛⡿⣿⠿⣿⠟⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢿⣿⣷⣶⣶⡾⣿⡛⢿⣁⢷⣬⣿⠏⠀ ⠀⠈⠻⣿⣇⣸⣧⣿⢩⡴⢇⠐⠁⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠘⢦⡹⣦⡳⢦⡓⣆⢸⣾⣿⠟⠀⠀ ⠀⠀⠀⠈⢙⣿⠿⣿⣿⣧⣸⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣇⢡⣿⣾⣿⣿⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣦⣌⡛⠿⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣠⣿⡿⢟⣉⣵⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣭⣛⢿⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣟⣥⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⢻⣧⡇⣟⠉⣉⡅⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⢿⣾⣡⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⡀⢠⣿⢀⣼⣏⣷⠶⣦⣤⣤⣀⠀⠀⠀⢠⡘⠿⣿⠿⠇⡄⠀⠀⠀⢀⣀⣀⣤⣾⣯⡳⣌⣸⣿⡁⠀⢀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣙⠿⢿⡟⠘⣿⡿⠀⣀⣀⣀⠰⣌⠁⠀⠀⠀⢱⡄⠀⢠⡞⠀⠀⠀⠘⣹⠉⢉⣁⠀⠘⣿⡿⠇⣻⣷⣶⠟⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⡟⠙⣻⠗⡶⢛⣡⣾⣿⢿⣿⣿⣿⣆⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⡘⠷⣤⢹⡿⠖⣷⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⣇⠀⠁⠀⣿⡘⣿⡿⣯⠸⣧⠛⢛⣿⣷⡀⠀⢰⣿⠀⣿⡆⠀⢀⣾⣿⠻⠟⣽⠇⣿⣿⣿⠇⣾⠀⠑⠀⢸⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢻⣆⠀⠀⠈⠙⢻⣷⣜⠦⠈⠁⠀⠀⣹⡿⣿⣿⠿⠿⠿⣿⣿⣿⣋⠈⠀⠈⢁⣰⢏⣿⡿⠟⠁⠀⠀⢀⡿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡙⢇⣀⣀⣀⠀⠙⠛⠳⠶⠒⠂⢀⣀⣼⠇⠀⠀⠀⠀⠀⠹⣦⣉⡀⠢⠤⠤⠶⠿⠛⠀⠀⠀⠀⢰⠛⣡⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢉⣭⣭⣤⣤⣀⠀⠀⠀⣴⠟⢉⠻⣄⠀⠀⠀⠀⠀⣠⠟⠙⢿⡆⠀⠀⠀⠀⣀⣨⣝⡒⠒⢷⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⣿⡿⠿⣿⣮⣍⠉⠉⠁⠘⢦⠙⠿⠷⠦⠄⠀⠤⠴⠶⡿⠗⠼⠃⠙⠓⠛⣉⣽⣿⣿⣿⣦⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣄⣀⣤⣴⣿⡟⠁⠀⠀⠈⢻⣿⣿⣶⣤⣤⣤⣴⣶⣶⣧⣀⣀⣠⣶⣦⣤⣤⣄⣤⣤⣴⣾⣿⡟⠁⠀⠈⠻⣿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣧⣤⣤⠴⠂⢸⡟⢹⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠙⣿⠓⠶⣤⣀⣀⣽⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠘⠀⢸⡇⠀⣿⡟⢁⠹⣿⡟⠉⠛⠙⣿⣿⢉⠙⣿⡇⠀⢻⡇⠘⠇⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⣶⢿⡁⠀⠀⠀⢸⢿⡏⢷⣿⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠟⠁⠀⢻⡀⠁⠀⠀⠀⠉⢸⠃⠈⠻⠿⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⡄⠀⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣾⢁⠀⣸⣦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣦⠀⠀⢰⣦⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀ ⢸⣵⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠛⠛⠋⠀⠹⣷⣴⡟⠀⠉⠛⠛⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣘⣧ ⠘⣿⢁⡾⣷⣦⣄⣀⣀⣀⣀⣀⣤⡶⠟⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠿⣦⣄⡀⠀⠀⠀⠀⢀⣀⣴⣿⠿⣿⡿ ⠀⠻⣿⣷⢠⣼⡩⢛⡟⠻⠋⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠛⣟⢿⠻⣟⣯⡙⢦⣷⣿⠁ ⠀⠀⠈⠻⣾⣿⣷⣏⣟⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢢⢻⣮⣿⣷⣾⠟⠁⠀ ⠀⠀⠀⠀⠙⠺⣭⣿⣿⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣿⠿⣛⣿⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣽⣦⡤⠤⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⣀⣄⣠⣟⣿⡷⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⣻⠋⣧⣴⣦⣀⣀⠀⠀⠀⠀⢸⣧⣼⡏⠀⠀⠀⠀⠀⢀⣸⣦⣈⢻⣿⠁⠀⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⣛⣿⡿⠘⣿⠋⣀⣉⡉⣏⠀⠀⠀⢳⡀⢀⡞⠁⠀⠐⣻⠉⣉⡉⠻⣿⠏⣿⣶⠞⢻⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠇⡏⠉⠟⣟⣯⣾⣿⢿⣿⣿⣦⡀⠀⢈⡇⢸⡀⠀⢀⣰⣿⣿⣿⣿⣦⣙⢶⢻⠛⢻⢴⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⣧⠀⠀⠻⢼⣿⣻⡈⠂⠁⠛⢷⣤⣼⣧⣼⣧⣤⡾⠻⠉⠹⢃⣿⣿⣧⠟⠀⠀⣸⢠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣌⠳⠀⠀⡀⠙⠻⠦⠤⠀⢀⣩⡟⠉⠀⠀⠉⢻⣙⡀⠤⠤⣼⠿⠋⠀⠀⠀⠴⢃⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢉⣽⣷⣤⣄⣀⣀⢰⠛⣙⡧⠀⠀⠀⠀⢸⣋⢻⡆⣀⢀⣀⣤⣭⣍⠛⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⠟⠛⠙⢿⣶⣤⣀⡈⠁⣉⣉⡁⠀⠀⣈⣉⠉⠈⠀⣈⣡⣴⡿⠛⠻⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣄⣀⡤⠀⡿⢻⡿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⣿⠢⣄⣀⣈⣿⣿⣶⠶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠁⠸⠀⣸⡏⡉⣿⡟⠙⠛⢿⡟⡉⣿⡇⠘⡇⠘⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠹⡟⠄⠀⠀⠸⢻⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⢀⠀⠀⠀⣆⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣾⡀⣸⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣽⣆⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⢧⡴⠉⠓⠲⢦⡀⠀⠀⠀⠀⠀⢀⣏⢆ ⠈⣧⡟⡳⡶⡶⠖⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⢤⢤⢤⠖⢟⣽⠏ ⠀⠈⠳⡿⢮⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢱⣱⡿⡾⠋⠀ ⠀⠀⠀⠈⠑⠾⣳⣠⠄⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⣀⣀⣼⡯⠗⠋⠀⠀⠀ ⠀⠀⠀⠀⡼⢤⡽⣵⠟⠢⠤⠀⠠⡛⢚⠄⠀⡤⠤⢷⣮⣯⣠⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⡏⠓⣮⣾⢻⠿⣄⠀⡁⢈⠀⣠⡷⡟⣦⣗⠹⢳⢼⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡳⡀⠉⠳⠆⠀⢈⡟⠛⠛⢛⡉⠀⣱⠿⠋⠀⠜⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣹⠷⣖⠠⠰⠩⠧⠀⠀⠼⠝⠢⠤⣴⣿⣝⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠲⢿⣅⠠⢸⢻⢷⣶⣿⣶⣶⣷⣶⡶⡿⡧⢀⣸⣷⠦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡗⣽⠀⠈⢧⢼⡇⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⡄⢀⢀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀ ⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄ ⣜⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢣ ⡿⡀⢿⣆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣰⣿⠀⣿ ⣇⠁⠘⡌⢷⣀⣠⣴⣾⣟⠉⠉⠉⠉⠉⠉⣻⣷⣦⣄⣀⡴⢫⠃⠈⣸ ⢻⡆⠀⠀⠀⠙⠻⣶⢝⢻⣧⡀⠀⠀⢀⣴⡿⡫⣶⠞⠛⠁⠀⠀⣰⡿ ⠀⠳⡀⠢⡀⠀⠀⠸⡇⢢⠹⡌⠀⠀⢉⠏⡰⢱⡏⠀⠀⢀⡰⢀⡞⠁ ⠀⢀⠟⢦⣈⠲⢌⣲⣿⠀⠀⢱⠀⠀⠜⠀⠁⣾⢒⣡⠔⢉⡴⠻⡄⠀ ⠀⢸⠀⠀⣈⣻⣞⡛⠛⢤⡀⠀⠀⠀⠀⢀⡠⠟⢛⣓⣟⣉⠀⠀⣧⠀ ⠀⢸⣶⢸⣍⡉⠉⠣⡀⠀⠈⢳⣠⣄⡜⠁⠀⢀⡴⠋⠉⠉⡏⢸⡿⠀ ⠀⠈⡏⢸⡜⣿⠑⢤⡘⠲⠤⠤⣿⣿⠤⠤⠔⠋⡠⠊⣿⣃⡆⢸⠁⠀ ⠀⢀⡿⠋⠙⠿⢷⣤⣹⣦⣀⣠⣼⣧⣄⣀⣠⣎⣤⡾⠿⠋⠙⢺⡄⠀ ⠀⠘⣷⠀⠀⢠⠆⠈⢙⡛⢯⣤⠀⠐⣤⡽⠛⠋⠁⠐⡄⠀⢀⣾⠇⠀ ⠀⠀⠘⣷⣀⡇⠀⢀⡀⣈⡆⢠⠀⠀⠀⢰⣇⡀⠀⠀⢸⣀⣼⠏⠀⠀ ⠀⠀⠀⣸⡿⣷⣞⠋⠉⢹⠁⢈⠀⠀⠀⠀⡏⠉⠙⣲⣾⢿⣇⠀⠀⠀ ⠀⠀⠀⣿⡇⣿⣿⢿⣆⠈⠻⣆⢣⡴⢱⠟⠁⣰⡶⣿⣿⠘⣿⠀⠀⠀ ⠀⠀⠀⠹⣆⢈⡿⢸⣿⣻⠦⣼⣦⣴⣯⠴⣞⣿⡇⢻⡇⢸⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣞⣠⢾⣿⣿⣶⣿⣼⣧⣼⣶⣿⣿⡷⢌⢻⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠉⢿⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⢏⢁⡼⠋⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡟⢿⣿⣿⣿⣿⣿⣿⡿⢸⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢿⣿⣿⣿⣽⡿⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣬⠿⠿⣡⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀ ⠚⠞⠛⠛⠛⠓⠓⠟⠻⠓⠐⠛⠚⠛⠃⠀⠀⠈⠋⠛⠟⠛⠛⠛⠚⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣆⠀⠀⠀⠀⢠⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠁⠀⠉⢳⢿⣿⠗⠀⠆⠲⢿⣿⢻⠉⠀⠀⠁⠀⠀⡀⠀⠀ ⢀⠎⠀⠀⠀⠀⠀⠀⣼⠽⠁⠀⠀⠇⠀⠈⠽⢾⡀⠀⠀⠀⠀⠀⠐⡄⠀ ⡎⠀⠀⢄⣠⠒⠀⢱⣿⠞⢀⡀⠀⠀⠀⣀⠘⣾⡿⠁⠐⢆⣠⠀⠀⠸⡄ ⣇⠀⠀⠀⠙⢄⠀⠀⢨⡘⠛⠛⣨⢧⠚⠓⠛⡨⠀⠀⡀⠞⠁⠀⠀⢀⡇ ⢧⡃⠀⠀⠀⠈⠉⠂⠀⢰⣰⣎⣓⣔⣉⣆⣼⣀⡄⠊⠁⠀⠀⠀⠔⡵⠃ ⠀⠀⠀⣩⠟⠋⠐⠄⢏⠾⢳⠻⠿⠟⠿⠙⣧⢆⡇⣴⠜⠋⠛⠁⣀⠀⠀ ⠀⣄⠊⠁⢀⠠⠔⠊⠀⠀⠁⢣⠀⠀⡰⣧⠇⠀⠙⠀⠀⡀⠀⠀⠀⠉⠀ ⠀⠀⠀⠈⠉⠀⠐⠀⠀⠀⠀⢧⣦⣄⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠈⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠶⠦⡴⣞⢦⣘⡿⣦⣀⠀⠀⠀⠀⣀⣠⡾⣇⣠⣞⡶⡤⠶⠶⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠂⠈⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣷⢻⡟⠋⠑⡖⠉⠛⣿⢱⣿⡿⢻⠃⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀ ⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⣿⠞⠃⠀⠀⠀⡿⠀⠀⠀⠻⢿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⡏⡉⠃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠋⡉⣿⣆⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⢠⠃⠀⠀⠀⠠⡀⠀⡤⠞⠛⠒⠦⣶⣯⡿⠋⣂⠀⠀⢄⠀⠀⠀⠀⠀⢀⡊⢻⣾⣷⡵⠖⠒⠚⢦⡄⠀⣠⠀⠀⠀⠀⣷⠀ ⣾⠀⠀⠀⠀⠀⠻⣾⡇⠀⠀⠀⠀⠙⢻⠃⣦⣨⣳⣦⡀⢱⣶⠂⣠⣶⣫⣠⣆⢿⠛⠀⠀⠀⠀⠀⣽⡶⠃⠀⠀⠀⠀⢸⡀ ⣿⣄⡀⠀⠀⠀⠀⠈⠛⠦⣀⠀⠀⠀⠸⣄⣈⠙⠉⠉⢙⠾⠿⣞⠉⠉⠉⢉⣀⡼⠁⠀⠀⢀⡠⠞⠋⠀⠀⠀⠀⠀⢀⢾⡇ ⢻⣎⠣⣀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠈⢣⠀⣴⡖⠻⢆⢠⠾⠑⢶⡄⢠⡇⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢀⡠⢋⣾⠁ ⠀⠙⠧⣈⠑⠢⢤⣤⣀⣀⣀⠀⠀⠹⡤⠴⣿⣷⠻⣿⣷⣶⣿⣶⣿⡿⣣⣿⢻⠊⡾⠁⠀⢀⣀⣀⣠⡤⠤⠖⢉⡠⠟⠁⠀ ⠀⠀⠀⠀⠉⠉⣩⠟⠋⠉⠉⠙⣆⠀⡇⡼⢿⠙⣧⠻⠿⠿⠿⠻⠿⢃⡏⢹⡼⡆⡇⢀⣾⣯⠽⠋⠉⠉⠛⠯⣁⡄⠀⠀⠀ ⠀⠀⠀⣀⠴⠞⠋⠀⠀⠀⠀⣀⠼⡼⠋⠀⠘⡆⢻⣆⠀⠀⡆⠀⢀⣾⠀⡿⠁⠈⠻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀ ⠀⠐⠿⠄⢀⣀⣀⣠⡐⠚⠉⠁⠀⠀⠀⠀⠀⢹⢸⠙⡄⠀⡇⠀⣾⢻⡆⠇⠀⠀⠀⠀⠀⠀⣠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠤⠄⣀⣀⣀⠈⢧⣷⣀⡇⢠⠇⠀⠇⠀⠀⣀⡠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠙⢏⣙⡵⠒⠈⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠈⠈⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣈⡶⠒⠊⠉⠉⠉⠉⠉⠒⠶⣊⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢐⣶⠦⠤⣤⣤⠇⠀⠀⠘⢧⣤⡤⠤⢶⣖⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡀ ⠈⠙⣗⠢⣄⠀⢀⡜⠁⢀⡔⠁⣠⠶⢶⣴⣍⠳⡄⢀⡴⢉⠿⢿⣦⣤⡈⠑⡄⠀⠱⡄⠀⢀⠤⢲⠟⠁ ⠀⠀⠈⢣⠀⠑⡞⠀⠀⡞⠀⠘⠁⠀⠳⣄⡹⡇⢹⡼⢱⠃⠀⠘⢄⣸⢷⠀⠸⡀⠀⠹⡖⠁⡴⠃⠀⠀ ⠀⠀⠀⢸⠀⡸⠀⠀⠀⢧⠀⠰⡀⠀⠀⠀⢀⠇⡸⢱⠘⣄⠀⠀⠀⠀⡼⠀⢸⠀⠀⠀⢻⠀⡇⠀⠀⠀ ⠀⠀⠀⢸⡀⡇⠀⠀⠀⠈⠣⣀⠉⠒⠒⠒⢉⡴⠁⠀⠳⣌⠓⠒⠒⠊⢀⡴⠃⠀⠀⠀⠈⡆⡇⠀⠀⠀ ⠀⠀⠀⠀⠑⢧⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⠁⡀⠀⠀⠀⠀⠉⠒⠒⠊⠉⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡀⠀⠑⠢⢀⡀⠀⠀⠀⠀⠈⠒⠒⠋⠀⠀⠀⠀⠀⣀⠤⠊⠁⢀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠈⠉⠒⠒⠢⠤⠤⠤⠤⠤⠒⠒⠈⠉⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠛⡖⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠲⡖⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⠞⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⢾⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸⡄⠸⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣠⠦⣌⠻⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⢁⡤⢦⣤⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⠿⣿⠀⠈⢳⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⠃⠀⢺⡿⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⡇⠀⢀⣀⣀⣀⣀⣀⠀⢠⠇⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⣹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠛⠸⡄⠀⠀⠀⠀⠀⣏⠘⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠈⠛⠒⠒⠒⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀ ⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀ ⠀⢸⠁⠇⠀⠀⠀⠀⢀⠠⠔⠂⠀⠀⠒⠂⠤⡀⠀⠀⠀⠀⠸⠁⡇⠀ ⠀⢸⣀⡌⠀⡀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⢁⣀⡇⠀ ⠀⠘⣧⣀⣠⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣦⣀⣼⠃⠀ ⢀⠀⠘⢿⣿⣃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⣿⣿⠋⠀⡀ ⠈⣧⠀⢸⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⡇⠀⣴⠁ ⠀⢸⢃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡘⡇⠀ ⠀⠸⡇⢻⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡟⢸⠇⠀ ⠀⠀⠱⠀⡂⠈⠉⢏⠓⢄⠀⡀⠀⠀⢀⠀⡠⠚⡩⠉⠁⢸⠁⠈⠀⠀ ⠀⠀⢂⢰⣧⠀⠀⠀⠉⠉⠉⢀⠀⠀⡀⠉⠉⠉⠀⠀⠀⣼⡇⡸⠀⠀ ⠀⠀⠘⢾⣿⠱⠤⣄⠤⢾⠀⢸⠀⠀⡇⠀⡷⠤⣠⠤⠎⣿⡷⠃⠀⠀ ⠀⠀⠀⠀⢻⡆⡇⠠⡆⠢⢈⠙⢤⡤⠃⡁⠔⢲⠄⢸⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣧⢸⢻⣿⣷⣰⣬⣍⣩⣥⣇⣾⣿⡏⡇⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣼⠨⡌⢸⢻⣿⣿⣿⣿⠟⡏⢡⠅⣧⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠃⠘⣶⣠⡠⣠⣄⢄⣄⣴⠃⠐⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠣⠤⠒⠒⠓⠒⠤⠜⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⢄⠀⢀⣀⣀⡀⠀⡠⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡨⠆⠋⠀⠀⠀⠀⠈⠂⠇⡀⠀⠀⠀⠀⠀ ⢄⡀⠀⠀⡠⠊⡠⢖⡲⣖⡀⠀⣣⣖⠒⠦⡈⢢⠀⠀⢀⣠ ⠀⢢⠑⡜⠀⡎⠐⠁⠏⡳⢱⡜⠎⠘⢉⢦⠰⠀⠡⠔⡕⠁ ⠀⢸⢰⠀⠀⢣⠐⢄⣀⠔⡘⠡⠣⢀⡠⠎⡸⠀⠀⠇⡇⠀ ⠀⠈⠺⡄⠀⡀⠉⠐⠒⠨⣀⢀⠈⠐⠒⠈⢀⠀⢀⠗⠁⠀ ⠀⠀⠀⠈⠢⢈⠐⠂⠤⠄⠀⠀⠠⠤⠀⠂⣁⠄⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⢑⠒⠒⠒⠒⠒⠒⣰⠙⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠁⠔⢹⠀⠀⠀⠀⠀⠀⠈⠳⡀⢃⠀⠀⠀⠀ ⠀⠀⠀⣰⣇⣌⢦⢸⠀⠀⠀⠀⠀⠀⡇⡠⢃⣘⣦⠀⠀⠀ ⠀⠀⠀⠙⢻⠀⠱⠐⡄⠀⠀⠀⠀⠀⠇⠗⠁⡾⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠂⠀⠀⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠖⠀⠁⠆⠀⠀⠠⠎⠁⠒⡄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣤⣤⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⢀⡤⣄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠉⠉⠉⠉⠛⠋⣿⣌⣿⣾⣏⢻⣷⣤⡤⣄⡀⢀⡠⣤⣶⣿⠏⣿⣴⣿⣼⡟⠛⠋⠉⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡿⢿⣌⣿⠏⠁⠀⢻⠋⠀⠉⠻⣏⣸⠿⣿⠟⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⢺⣿⡾⠓⠀⠀⠀⠀⢸⡇⠀⠀⠀⠐⠻⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠞⠻⣦⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡼⠿⢺⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠐⠒⡸⣿⣿⣰⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣴⣎⣿⣟⢘⠓⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⢰⡇⠀⠀⠀⠀⠀⢲⡀⠀⣴⠟⠉⠉⠉⠙⠻⣿⣿⣿⡏⠀⢀⡀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣀⡄⠈⢿⣿⣿⡾⠛⠉⠉⠉⠙⢷⡆⠀⣰⠆⠀⠀⠀⠀⠘⣿⡀ ⣾⡇⠀⠀⠀⠀⠀⠈⠻⣾⣇⠀⠀⠀⠀⠀⠀⠙⢻⡟⢠⣦⣀⣸⣷⣄⠀⠙⣶⡴⠀⢀⣴⣿⣁⣀⣤⡘⣿⠛⠃⠀⠀⠀⠀⠀⠀⣿⣶⠏⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠸⣄⠀⠙⠻⠙⠛⠛⠳⣤⣿⣧⡴⠛⠛⠛⠿⠟⠋⠀⣸⠂⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣼⡇ ⣿⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣤⡀⠀⠀⠀⠙⢷⡒⠂⠀⢀⣠⣶⡋⠉⠉⣛⣦⣀⡀⠀⠐⣶⠞⠁⠀⠀⠀⣀⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⡇ ⠸⣷⣌⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⣷⡀⢸⣿⡁⠘⠹⣄⡰⠛⠀⣙⣿⡆⣰⣿⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣴⡿⠁ ⠀⠈⠻⢤⣀⠉⠳⢤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠹⣦⡴⢾⣿⣷⡟⢿⣿⣿⣶⣾⣿⣾⣿⣿⠟⣳⣿⡿⡟⠉⣿⠁⠀⠀⠀⣀⣀⣀⣤⣤⣤⠴⠞⠁⣀⡼⠋⠁⠀ ⠀⠀⠀⠀⠈⠉⠙⠚⢛⣿⠿⠋⠉⠉⠓⢦⡄⠀⡏⢀⣾⣿⠛⣷⡈⣿⣿⣿⣿⣿⢿⣿⡟⢰⡟⢹⣃⣷⠀⡇⠀⢠⣶⣟⣋⡽⠋⠉⠛⠿⢿⣋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠙⣧⢠⣧⠞⠁⢹⡄⢸⣧⠈⠉⠉⢉⡅⠀⠉⢁⡞⠀⣸⡟⠙⢧⣿⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⢶⣆⣀⠀⠀ ⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⢀⣠⣤⠖⠙⠟⠀⠀⠀⠈⣧⠀⣿⣧⠀⠀⢸⠀⠀⢀⣾⣿⠀⣿⠃⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀ ⠀⠀⠹⠶⠤⠤⣄⣀⣀⣀⣔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣧⠸⡄⠀⢸⠀⠀⣼⠉⢿⡄⠯⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠤⢄⣀⡀⠀⠀⠀⠀⠁⠹⡄⣧⡀⢸⠀⢀⡿⠀⢸⡇⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠢⠿⢽⣿⠿⢧⢞⣡⠤⠤⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠹⡦⠴⠋⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀