⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠉⠙⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣀⣠⣄⣀⣀⠀⢺⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣝⠛⠛⠛⠛⠿⣿⣿⣿⣿⡿ ⠀⠀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠉⣀⡀⠀⠉⢙⣿⠇ ⢠⣾⠟⢉⠠⣀⣬⣙⣷⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⣠⣤⣄⣴⣾⣿⣶⣶⠶⣦⣀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡈⣀⣀⣠⣾⡟⠀ ⢿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣄⡴⠾⢛⣿⠀⠀⢀⣀⣤⣾⣿⣿⢁⣴⠿⣿⣿⣋⠽⣿⣏⣴⣿⣟⣓⣾⣿⡷⢦⣤⡀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠋⠀⠀ ⠈⢻⣿⣿⣿⣿⣿⡿⠟⠛⠛⢀⣴⠟⠁⣠⣶⣿⡿⠛⣻⣿⣿⣿⣥⡶⠻⣿⡦⠒⢻⣿⠜⣿⣯⣭⣿⡟⣃⣼⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀ ⠀⠀⢻⣿⣿⣿⠋⠀⠀⠀⢀⣿⠃⠀⢸⣿⣿⣿⣶⣟⡉⠐⠻⣿⣿⡖⢈⣻⣿⡋⢹⣿⢊⣿⠓⣾⣿⡁⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀ ⠀⠀⠈⢿⡛⠇⠀⠀⠀⢠⣾⠇⣠⡶⣿⠿⢿⣿⣿⣿⣤⠖⢋⣹⣿⣿⣋⡽⣿⣏⣩⣿⣵⣿⣸⣿⠷⣲⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡇⠀⠀ ⠀⠀⠀⠘⢿⣄⣀⣠⣴⣿⣿⣿⢋⣾⠃⣠⡾⠛⠹⣿⣿⣿⣏⣥⠿⣿⣷⠖⢻⣿⣶⣿⣿⡿⣿⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣾⣿⣿⣯⣼⣿⣡⣾⣃⡠⠿⣿⣿⣷⡾⢿⣿⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠙⠛⠛⠛⠛⠻⠿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡿⠛⢋⣭⡀⠀⠀⠀⣿⣿⣿⣷⣶⣌⣿⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⠁⣠⣾⣿⣿⣿⣶⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⣠⣴⣶⣾⡿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡍⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣀⣠⣽⣿⢿⣿⡿⣿⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠛⠋⣁⣀⣼⣿⣿⣿⠀⢀⣼⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣄⠀⠀⢸⣇⠿⢎⣿⣿⣥⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣼⣿⠂⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⠠⢀⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣶⠮⠩⠉⠽⠻⠟⠛⠛⡟⠛⢿⣭⡋⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⢀⡅⠀⠉⠉⠈⢛⣁⣀⣥⣤⣿⡿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣴⣶⠶⠿⠟⠛⠋⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣆⠀⠀⠈⢷⡿⡃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣤⡀⠈⠁⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠉⠉⠛⠿⣶⣦⣸⣇⣠⡶⠖⠛⠉⠉⠉⣻⣿⣿⣷⠶⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠈⠙⠿⠟⠛⠿⢶⣦⣤⣀⠀⠈⠉⠹⣿⣿⣷⣾⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣶⣤⡍⣽⣿⣿⣯⡻⢶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢰⣿⣷⡀⠈⠛⠛⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠋⠉⠉⠙⠻⣷⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠛⠂⠹⢿⣿⣦⣄⠀⠀⠀⠉⠙⠿⢿⣶⣦⣄⡀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣾⣶⣦⣤⣄⡉⠛⠛⢿⣟⣏⡛⠿⣿⣿⣶⣌⠉⠛⢡⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠐⠆⠹⣷⣿⣧⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡈⠻⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣠⡈⠿⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠙⠛⠆⠀⠉⠩⠩⣤⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠿⠟⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠈⠉⠛⠿⣷⣶⣶⣶⣶⠤⠄⢀⣀⣀⣀⠉⠉⠀⠀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⣿⣹⡟⣻⡟⣿⢻⣿⡿⠻⠿⠷⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⣿⣇⣿⣰⣿⡟⠋⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠋⠉⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠱⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠀⠈⠉⠉⠛⠻⠷⢶⣶⣤⣤⣤⣀⡀⡀⠀⠀⣠⡄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⡾⠻⣧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣷⣾⢻⡅⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⢿⠋⠉⠉⠉⠉⢉⣩⡉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠙⠛⠷⠶⣶⣦⣤⣄⡀⠀⠀⢀⣾⠟⠁⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠻⣿⣷⣶⣤⣀⠀⠀⠈⠙⢿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣵⣶⣶⠟⠓⢶⡶⣶⣦⣄⣽⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⠈⠀⠀⠀⠉⠉⠛⠻⢷⣶⣶⣤⣈⡉⠻⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⢿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⠙⢻⣷⣄⢀⣀⠀⠀⠰⡿⠋⠀⠀⠀⢀⣠⣤⣄⣄⣀⡀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠉⠙⠛⠿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⢿⣟⣣⣴⣾⠿⠛⠉⠁⠉⠉⠙⠛⠛⠛⠛⠿⠛⠛⠀⠀⠈⠉⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠶⠶⠤⣴⣶⣶⣶⣴⣤⣄⢨⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣶⠶⣶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠏⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⣰⣄⣠⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣥⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠷⠶⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣽⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠟⠿⢶⣄⣀⣀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠉⠙⠻⠿⢶⣼⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀ ⠀⠀⠀⣠⡿⠿⠿⢶⣤⣀⣀⠀⠀⠀⠀⢹⣿⠀⠉⠛⠛⠳⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀ ⠀⠀⢠⣿⠇⠀⠀⠀⠉⠙⠛⠻⠶⣦⣤⣾⣿⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⡿⠀⠀⠀⠀ ⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⢻⣿⣷⣦⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣼⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣣⣴⠶⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀ ⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠟⠙⣿⡌⠛⠋⠁⠀⠈⠉⠛⠛⠛⠛⠻⠶⣶⣾⣿⣾⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀ ⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡿⠀⠀⠙⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠋⠁⢉⡉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠿⠛⣤⣾⣿⡿⠿⠛⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀ ⠀⣾⠇⠛⢷⣶⣤⣄⠀⠀⠀⣸⡿⢻⡗⠀⠀⠀⠀⠉⠻⢷⣶⣤⣤⣄⣀⣤⣶⡾⠟⠋⠁⠀⠀⠘⣷⣤⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣴⡾⢟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀ ⣾⣋⡀⠀⠀⠀⠉⠉⠉⠃⣴⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣏⠉⠉⠉⠉⠁⠀⠀⠀⣤⠀⠀⠀⠀⠙⠿⣶⣤⣀⡀⠀⠀⣀⣭⣶⡿⠋⢠⣾⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀ ⠿⠻⠿⣶⣦⣄⡀⠀⠀⠀⣿⠀⠀⢸⡇⠲⠶⣶⣤⣤⣄⣀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣍⡉⠙⠛⠛⠋⠉⠀⠀⣠⡿⠁⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠉⠉⠛⠲⠆⢀⡟⠀⠀⠸⣧⠀⠀⠀⠉⠉⠙⠛⠿⠉⠛⠻⠶⠶⣶⣤⣄⣿⣇⣀⣀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠁⣿⣆⠀⠀⠀⠀⠀⣴⡾⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢻⠲⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠉⠉⠻⢿⣾⣬⣿⡿⠙⠻⠿⠟⠛⠻⠛⠿⣿⠃⠀⠀⠀⠀⢹⣿⣶⣤⣦⣴⡿⢻⣤⣴⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠸⣇⠀⠉⠻⣿⣝⠛⠻⠷⣶⣶⣤⣤⣀⣴⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣼⣿⠃⣠⣾⠟⠀⠀⠈⠉⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠙⠻⠷⣶⣦⠄⠀⢀⣿⣿⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⣿⣷⣶⣶⣶⣤⣴⡟⠀⠀⠀⠀⠀⠀⣿⣁⣼⣿⣥⣤⣤⣤⣤⣤⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠆⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢷⣦⣤⣀⡀⣀⣀⣀⣠⣤⣿⠏⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⢰⡿⠿⠋⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡏⠛⠿⣧⣤⣄⣀⣀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⣿⠃⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣹⡁⠀⠉⠈⠉⠉⠀⠀⣿⠢⠠⠤⠄⠀⠀⠀⢀⣀⡀⣼⣅⣀⣀⣀⣀⡀⣀⣀⣸⣧⠀⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⣸⠹⢷⣶⣄⣼⣇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠁⠉⠉⠋⠉⠉⠉⠉⠉⣿⡇⠀⠀⢻⠈⠙⠛⠉⠉⠁⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠛⠿⠷⢦⣤⣤⣠⣶⣾⣿⣀⣀⣠⣀⣀⣀⣀⣀⣀⢀⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⣻⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣿⠉⠀⠈⠉⠉⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⢘⣷⠻⠟⠛⠛⠛⠻⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢁⣷⠀⠀⣼⠇⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀