Cursed Dot Art

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⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⡡⢫⣿⣟⣿⠏⠈⢏⠙⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⠏⣰⢡⣿⣿⢟⣸⠀⡀⠈⡆⠈⢿⣿⣾⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣏⣽⣟⣾⣿⡏⢀⣧⣿⣿⠏⡜⡇⠀⠘⢆⠈⡄⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⡟⣾⣿⣿⠀⢸⢿⣿⣿⡄⢰⠁⠀⠀⠀⢧⠘⡄⢸⣿⣿⣿⣿⣿⣴⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠁⠋⣸⢿⠔⢻⡿⣿⠋⠀⡞⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠇⠀⣀⣿⣠⣔⠉⠠⠃⠀⢰⠃⠀⢀⣀⣤⣤⣆⠀⣼⢿⣿⣿⣿⣿⣾⡀⠀ ⠀⠀⠀⠀⢾⣿⠏⣴⣿⠟⠛⠿⣿⣿⣆⠀⠀⠈⠀⣶⣿⠿⠛⠛⠻⣷⣴⠀⢹⣿⣿⣿⡿⠵⠀ ⠀⠀⠀⠀⢸⣿⠀⣿⣇⢸⣿⣿⠎⣿⣿⠀⠀⠀⢸⣿⡏⣠⣶⣶⡀⢸⣿⠀⠀⣿⣿⣿⣿⠀⠀ ⠠⠤⠤⠤⢼⣿⡄⠘⣿⣦⣭⣽⣿⡿⠟⠀⠀⠀⠸⣿⣿⣼⣿⣟⣽⣿⠏⠀⢰⣿⣿⣿⣿⡘⠀ ⠀⠀⠀⠀⢸⣿⣧⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⢀⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣰⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⣰⡶⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣷⢦⡀⠀⠀⠀⠻⠟⠛⠿⠙⠂⠀⣠⠞⣉⡴⣫⣿⣿⣿⣿⣿⣿⣿⡇⡆ ⠀⠀⠀⢠⣸⣿⣿⣿⣿⣄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠇ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡈⠻⣦⣄⣠⣄⣀⣠⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⠛⠛⢛⣉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣠⡶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀ ⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⠀ ⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⡿⠛⠾⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡄ ⠰⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠹⢷⣤⣤⠴⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡇ ⠀⠑⡄⠀⣿⡇⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢷⢃⢙⡇ ⠀⠀⠀⠀⠘⠧⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠘⢿⡾⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠁⠀⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⢿⠖⠃⣐⡒⠤⢄⡀⠀⠀⢀⣀⡙⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠃⠈⢀⡾⠿⠿⣷⣦⣈⣦⠸⡉⠀⠀⡈⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠣⠀⠀⠀⠁⠀⢀⣼⣿⣿⣿⣿⣷⣶⣿⣿⣏⢧⠀⠀⠀⠀ ⠀⠀⣰⢣⡶⢶⣶⣦⣠⣾⡿⣿⣿⣿⣿⡿⠿⣿⣹⣿⠛⠉⢣⡀⠀⠀ ⠀⡴⠃⠟⠁⠀⠀⠀⠀⠉⣹⣿⡋⣉⣥⣤⢀⣀⣴⣮⣷⣤⣀⠑⡄⠀ ⡼⣱⠀⢠⣾⣿⣿⣾⣿⣿⣟⣿⣷⣿⣛⣯⣽⣿⣿⣭⣼⣿⣿⡆⠘⡆ ⣷⠀⠀⠸⠿⣿⣿⣿⣿⠿⢿⣟⣛⠿⠿⠿⢿⣻⣟⣋⠁⠀⠀⡅⠀⣧ ⣇⠀⠀⠀⠀⣿⣿⡟⠁⠀⠘⣿⣿⣿⣿⣿⣿⠿⠛⠃⠀⠀⠀⠀⢀⡇ ⠈⢦⡀⠀⠀⠸⠿⠻⣧⣀⣠⣎⡿⣟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠈⠙⠲⠤⢤⣤⣌⣉⣉⣉⣁⣀⣠⣤⣴⡖⠒⠛⠛⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡸⢿⠉⠉⠉⠉⠀⠀⠀⣀⣿⣠⣴⠖⠛⠛⠲⣄⠀ ⠀⠀⠀⢀⣤⣶⣶⡇⠠⡄⠀⠀⠀⠀⠀⣠⣿⣿⣿⠇⢒⣠⠴⠛⣿⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣄⡙⣄⠀⠀⠀⣸⣿⣿⣿⣿⡷⠛⠁⠀⣠⠏⠀ ⠀⣼⣿⠛⠋⠙⠻⣿⣿⣿⡏⠉⠉⠉⠡⣿⡏⡼⠋⠀⠀⣠⠞⠁⠀⠀ ⠀⣿⡟⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠘⠿⢇⡠⠴⠊⠀⠀⠀⠀⠀ ⠀⠘⢷⣤⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢉⠙⠛⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⠶⠶⠛⠳⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⣶⣶⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⠻⣿⣿⣿⣿⣦⡀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣃⠀⠀⠀⠀⠀⡈⣙⣳⣤⣀⠀⢀⣼⣦⣤⣀ ⠀⠀⠀⠘⣿⣴⣦⣻⣿⣿⣿⣿⣷⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡶⢛⣉⣠⣤⣤⣉⡙⠻⠶⣶⣦⣶⣿⢿⣭⣙⣿⣴⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⣹⡏⢁⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠿⠿⣿⣿⣿⣾⡀⠀⠉⣻⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⡏⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⢀⣠⣤⣠⡈⠙⢿⣿⠀⠀⣿⡟⢋⣥⣹⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⠀⠀⠀⠀⠀⢘⣿⡟⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⣿⡆⢠⡿⠀⣼⣿⣿⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠇⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⢿⣿⣿⣿⣿⡿⠁⣀⣿⡇⢸⡇⠀⢿⣿⡿⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠉⠉⠉⠉⢁⣀⣿⣿⠁⠀⣿⣄⡜⢉⣤⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣅⠀⠀⠀⠀⠘⠙⢿⣿⣶⣶⣶⣶⣶⣾⣿⡿⠟⠀⠀⣻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠈⢻⣿⣷⣤⡀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⢀⣴⣿⣿⣿⠋⠀⣹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣤⣤⣶⣿⡿⠷⣿⣿⣷⣤⣀⣀⡞⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⢀⣴⣟⣷⡶⠶⢶⣒⠀⠀ ⢀⣀⣀⣀⣀⣤⣴⠿⠛⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠠⠄⠀⠀⠀⠀⠀⠀⠈⠩⠀⠀⣸⠋⠉⠀⠀⠀⠀⠈⠁⠀ ⠈⠉⠉⠽⠛⣿⣿⣶⣶⣶⣶⣶⣤⣤⣠⣦⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠈⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⡇⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣤⣤⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠋⠉⠉⠙⢿⣿⣴⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⠤⠒⠋⠉⠀⠀⠀⠀⠀⠙⠦⣀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠀⠉⠆ ⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⣤⠾⣿⣝⣷⡴⠂ ⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⠋⠁⠀⠀⠈⠻⢿⣇⠀ ⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⡀⠀⣴⡾⠛⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠹⡀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠛⠆ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠉⠻⣶⡟⠀⠀⠀⠀⠀⣠⣽⣿⡄⠀⠀⠀⠀⠀⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⢀⣶⣿⣿⣷⡜⠇⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⢿⡌⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⡀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⢉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡿⣷⡀⠙⠈⢿⣿⣿⡿⢃⣠⣧⡀⠀⠘⠿⣿⡟⠁⢠⣄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣂⠙⠲⠤⣤⣀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⢸⣿⣩⢷⣶⣶⣦⠀⠀⠙⠷⢀⡀⠀⡈⠉⢰⣿⣿⣿⡗⠷⠶⠖⠈⣻⣷⣿⣿⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣙⢿⣾⡶⠃⠈⡉⠓⢦⡀ ⠘⡇⠀⠀⠀⠀⠈⢷⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠀⠀⣹⣿⡿⣿⣣⠀⠀⠀⢸⡇⠀⠀⣰⡶⠶⠶⠾⠷⠶⠒⠛⠓⠚⠛⠛⠛⠿⠧⢶⣯⣭⣴⣄⠁ ⠀⢻⡀⠀⠀⠀⠀⠉⣿⣿⣿⣿⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⣿⣿⣿⣿⣿⡶⠀⢠⣿⣴⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣇ ⠀⠀⢳⡀⢻⣩⠇⠐⢿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠿⠿⠿⠛⣿⣿⣿⣿⣿⠿⠛⠋⠁⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⣄⠀⠀⠀⠈⠛⠻⠿⠿⢿⣿⣿⣯⣥⣤⠤⠶⠶⠶⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⢤⠀⠀⠀⠀⠠⠤⠤⠴⠒⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⡁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⣿⣿⣿⠋⠀⠀⠞⢃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡋⠉⣿⣷⣷⣟⠟⠁⠀⢀⠰⢡⡂⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠑⢿⣿⣿⣿⣿⣇⣠⣿⣿⣁⢛⣰⠄⣴⡎⢀⡴⢧⢖⣀⠀⠀ ⣿⣿⣿⣿⣿⣿⠃⣀⣀⠘⢿⣿⣷⣿⣿⡇⢸⢍⣼⣇⠰⣠⡊⠁⠀⠸⡰⠋⠀⠀ ⣿⣿⣿⣿⣿⣇⢼⣿⣿⡇⠈⠛⠛⠛⠻⢷⢦⣦⣽⣟⡾⢫⣴⣶⣄⢸⡻⣆⣠⠀ ⣿⣿⣿⣿⣿⣿⡧⠍⠉⠁⠊⠀⠀⠀⠤⠀⠈⠿⢿⣿⣇⠿⢿⣿⠝⡾⠐⡴⠉⠂ ⣿⣿⣿⣿⣿⡿⠇⠁⠀⠀⣀⣤⠄⠀⠀⠀⢠⠀⠀⠛⣿⣷⡄⠀⢸⢥⡌⠀⠀⠀ ⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⢿⣟⠀⠀⢶⡽⠟⠀⠀⠀⠙⢳⣤⠾⠿⠃⠀⠀⣤ ⣿⣿⣿⣿⣇⠠⣀⣀⠄⠀⠀⡀⢉⣬⠐⠋⠠⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠘ ⣿⣿⡿⣿⡏⠈⠿⠛⡗⠲⠿⠶⣮⡿⠦⣴⡤⣂⣀⣤⡀⠀⠀⢀⠟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣴⠿⠋⠉⠙⢿⣧⠀⠀⠀⠀⠀⣀⣤⠶⠶⢶⣤⡀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠏⠀⠀⠀⠀⠀⢹⡆⠀⠀⢠⣾⠋⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⣾⠃⠀⡀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⢀⣷⠀⢸⡇⠀⢸⡏⠀⣶⣧⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠸⣇⠀⠀⠀⠈⠟⠀⢸⡇⠀⣿⡇⠀⢿⡟⠀⠀⠀⠀⠀⢠⡿⠀⠀⢰⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣹⣷⣄⣀⣀⣀⣀⣾⠁⠀⠟⣿⡄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣰⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⠿⣿⣿⣿⠟⠃⠀⠀⠀⠘⠻⣶⣤⣤⣤⣴⡾⠋⠀⢀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡈⠀⠀⠀⠀⠀⠀⠀⠉⠒⠯⣿⣿⠁⢁⣠⡶⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡦⣤⣀⡀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣄⣀⣾⡯⢴⣿⠯⣽⠿⢶⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡟⢻⠀⠸⡅⠘⠋⠀⠀⢰⣬⣧⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠿⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣬⡏⠀⠀⠉⠉⠉⠓⠒⠲⠦⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣌⠉⢙⠒⣶⡦⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⡿⠷⠶⠦⢭⣭⣍⣛⣓⣲⣗⣶⣶⣚⣩⠴⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠻⢦⣄⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣤⠤⢤⣤⠿⠓⢲⣤⣤⣎⣥⣠⣤⣼⡿⠆⣀⣤⣤⣶⣶⣶⣾⣶⣴⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣀⠀⠰⠂⢀⣠⢤⣀⠠⠄⢐⣒⣒⣂⣀⣂⡐⠤⠤⣤⣀⠀⠐ ⠀⠀⢀⠞⠑⠛⠉⠉⢀⣴⡿⣫⠞⣡⠞⠁⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⣀⣭⡵⠞⠛⠉⠉⠉⠉⠙⠛⠉⠛⠓⢮⣭⡓⢰ ⠀⢀⠎⠀⠠⠀⢀⠀⣾⡟⢠⡏⠞⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢸ ⠀⠀⠀⠀⠀⠀⠃⢸⠙⢀⡏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠃⠀⠀⢰⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠸⠿⠛⠉⠁⠀⠈⠻⠿⠟⠁⠀⠈⠻⠋⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸ ⠀⠀⠀⠀⠀⠀⢸⡟⡐⢀⠀⢀⣿⣿⣿⣿⡟⢁⣠⠴⠞⠛⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠛⢦⡘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢠⠇⣼⣿⣿⣿⣿⡴⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡤⠤⠀⠤⡼⡇⢀ ⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⣼⣿⣿⣿⡿⠉⠀⠀⣠⢴⣶⣶⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⠘⣿⣿⣿⣿⣏⠉⠉⠉⠉⠀⠀⠀⠀⢘⡇⠸ ⠀⠀⠀⠀⠀⠀⢸⣧⣇⣸⢣⣿⣿⡿⠁⠀⢠⣾⠃⣿⣿⣿⣿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⣿⣿⡟⣷⡀⠀⠀⠸⢿⣿⡟⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠰⠤⣴⣶⣶⣶⡾⣿⡿⢋⠎⠙⠛⠁⠀⠀⠈⠹⢦⣿⡟⠛⠋⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⠿⠃⣼⠃⠀⠀⠀⠈⢿⠁⠀⠙⣦⡀⠀⠀⠀⠀⣀⣤⡇⠀ ⣶⣤⣤⣤⣤⣤⣼⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠹⣿⣿⡇⠀ ⣿⣿⠁⠀⢰⣿⠇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠐⡏⠾⠇⠀ ⣿⣥⣴⣶⣾⣿⢰⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢸⣷⠶⣶⣧⣤⣴⣾ ⣿⣿⣿⣿⣿⡿⢸⢧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠠⠀⠀⠀⠀ ⠈⠉⠉⠉⣹⠇⣼⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⢻⡀⠀⠀⢀⣀⣀ ⠶⠤⠤⠬⣿⢠⣷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⢸⣟⠛⠛⠛⠛⠛ ⠀⠀⠀⢠⣯⣿⣯⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣖⡸⣧⠀⠀⣿⡄⢀⣄⣀⣀ ⠀⠀⠀⣿⢻⡿⣿⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣭⣉⣛⢿⣆⠀⢻⡝⠓⠒⠚⠚ ⠉⠉⢻⣿⣾⢿⡿⠒⠒⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⣼⢛⣆⡀⡇⠀⠀⠀⠀ ⠀⠀⢈⡏⣿⢱⡇⠀⠀⠀⠉⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⡀⣸⠋⠁⠀⡇⠀⠀⠀⠀ ⠀⠀⢸⠏⡇⣾⡇⠃⠀⠀⠀⠀⠘⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡾⠟⠁⠀⠀⠀⠀⢀⣼⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⢸⠀⠇⣿⡇⠂⠀⠀⠀⠀⠀⠀⠰⡏⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⢸⢸⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡌⠀⣿⣿⠆⠀⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣾⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠨⡇⡇⢠⣿⡟⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣼⡇⠒⠤⠤⠤⠤⠤⠀⠀⣴⢡⡇⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⢰⣿⠹⣇⢦⣄⣄⣀⣀⡀⠀⢀⣨⡸⡇⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⢸⣿⠀⠹⣦⢻⡀⠀⠐⠋⠉⠉⢹⢁⣷⣿⡇⠐⠒⠒⣶⣶⡶⠶⠶⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢻⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠸⣿⠀⠠⣞⣇⢷⣶⣶⣶⣤⣤⣤⣼⣿⣿⣧⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⢰⡶⠋⠀⠈⠀⠈⠉⠉⠉⠛⠛⣻⣧⣿⣷⣼⠶⠲⠶⠶⠶⠶⣶⣶⡞⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀ ⣿⣧⣰⣿⡇⠰⣿⣿⡛⢿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⡇⠀⠀⣷⣶⣦⣤⣄⣀⣀⣀⣀⣈⣹⡿⢿⣇⡀⠀⠀⠀⠀⠀⣠⡟⠁⣠⡄⠀⢀⠀⡆⣿⠀⠀⠉ ⡀⠸⣿⣿⣷⣀⢾⣿⣷⡾⣟⠛⠛⠛⣿⣸⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⢻⡇⢀⣿⣿⣿⣿⣿⣷⣾⡟⠤⢰⣿⠇⠀⣼⠀⡟⣷⣀⣀⣀ ⠿⣾⣿⣷⣿⣟⠷⠾⠿⠇⣿⡛⠛⠛⣿⢹⡿⢹⡇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠛⣿⣛⣛⠛⠿⠿⠿⢿⢸⠇⢈⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⠀⣰⠟⣼⣷⣿⣿⣿⣿ ⠀⠀⠀⠙⠻⣿⣦⣘⠛⠚⠋⠛⠛⠛⠛⣿⡁⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢈⢶⢶⣦⡤⠈⠉⠙⠛⠶⣶⣤⣿⠸⠀⠘⣦⡀⠀⠀⠉⠉⠉⠸⢿⡿⠉⢀⠃⣸⣱⢿⡿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣴⣷⡄⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⠴⠶⢤⡀⢠⡴⠋⠁⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠈⠹⡟⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⣿⡇⢰⣇⠀⢀⣀⣸⣀⠀⣾⣆⡀⢀⣿⣇⣰⣿⢿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣿⣿⣿⣿⣿⣸⣿⣿⣽⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⠟⠀⠀⠀⠀⢀⣶⡗⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣼⠁⠉⠙⢯⠙⠿⠏⠉⠉⠉⠹⡙⠿⠏⠀⠀⠀⠀⠉⠉⢰⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠻⣄⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠲⢦⣀⡾⠁⠀⣴⠃⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣹⣄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⣆⠀⠀⠀⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠙⢿⡄⠀⠀⠙⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣠⠴⠃⠈⠳⢤⣀⠀⣀⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡟⠁⠀⢀⣴⠃ ⠀⠀⠀⠀⠀⣠⠶⠚⢿⡆⠀⠀⠀⢻⡄⠀⠀⠘⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣰⡴⠋⠑⠒⠒⠒⠓⠦⣌⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⢀⣀⣀⣼⠃⠀ ⠀⠀⢀⡀⣸⡇⠀⠀⠈⢿⣆⠀⠀⠈⢿⣦⡟⣗⠀⠀⠈⣧⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣴⠛⣿⣿⠃⠀⠀ ⠀⣴⡟⠛⠛⢿⣦⠀⠀⠈⢿⣧⡀⠀⠈⢿⣧⠈⠱⡄⠀⢸⡄⠀⠀⢠⢟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡴⡃⢠⣿⠏⠀⠀⠀ ⢰⣿⣶⡀⠀⠀⠹⣷⡀⠀⠈⢿⣧⣠⡤⠾⢿⣷⣶⣸⠀⠸⡇⠀⢠⡏⠈⠀⢀⣠⣾⣿⣟⣻⡟⢛⣶⣤⡀⠀⠈⠳⣝⣦⠀⠀⠀⠀⠀⠀⢸⠀⠸⣡⣧⣿⠏⠀⠀⠀⣼ ⢸⣿⣿⣿⣷⡄⠀⠙⢿⡄⣠⠜⢿⣿⣧⠀⠈⠿⣿⣿⠆⢠⡇⠀⢸⡧⠶⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣽⣿⠇⠀⠀⠀⠀⠀⢸⢠⣞⣿⡿⠋⠀⣠⣶⣾⠃ ⢸⡿⢿⣿⣿⣿⣾⣧⡈⢿⣿⣧⠀⢹⣿⣟⣄⢂⠈⠛⠋⠙⡇⠀⠀⢳⡈⠁⠀⠀⠀⢀⣉⡷⠀⠀⠀⠀⠀⠀⣠⢴⡿⠋⠀⠀⠀⠀⠀⠀⢸⠈⠙⠉⠀⠀⣼⣿⡟⠁⠀ ⠈⣿⢀⡽⠛⠿⠿⣿⣿⣮⣿⣿⣷⠀⠹⣿⣎⠀⢧⡀⠀⠀⡇⠀⠀⢀⡇⠀⠀⠀⠴⠶⠭⠤⠤⠄⠠⠤⠤⠽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⣠⠀⢘⣿⡟⠀⢠⣶ ⠀⠺⠿⠶⠀⠀⠀⠀⠉⠙⠻⠿⠿⡷⠀⠘⠻⢷⠚⠉⠉⠉⢳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠁⠠⢧⡿⠋⠀⡰⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠙⢧⡀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢡⠂⠀⠀⠀⢠⠃⢠⠏⠀⠀⣠⠤⡟⠀⣠⠆⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⢣⡏⠀⠀⣀⠴⠋⢠⠏⠀⢀⡼⠁⢰⣇⡼⠁⣾⣴⣿⣿⣿⡿⠿⠿⣿⣷⣦⣤⡀⠀⠀⠈⣷⣜⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⡞⡞⠀⢀⡼⠁⠀⢠⣟⢀⣠⢏⣤⣶⣿⠟⠀⣸⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⡀⠀⢹⣿⡟⠀⠀⠀ ⠀⠀⠀⡀⠀⣷⣼⣿⠁⡆⠀⠁⣠⣎⣀⣤⣴⣾⣿⣿⡿⠿⠟⠛⠃⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡆⠀⣿⠀⠀⠀⠀ ⠀⠰⡀⣧⢠⠏⠘⣿⠐⣷⢀⣼⣿⠿⠿⠛⠋⣿⠟⠛⠓⠛⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠤⠰⣄⣀⣀⣀⠀⠀⠀⠘⢿⠀⢷⡄⠀⠀⠀ ⠀⠀⢣⢹⣠⢠⠀⢿⠀⣿⣾⢿⣡⡴⠶⣾⣿⣿⣷⣶⣤⣢⢄⠀⠀⠀⠀⠀⠀⠀⣴⣋⡵⢾⣿⣿⣿⣿⠛⠻⢷⣦⡄⣀⠀⢀⡇⡴⡸⠀ ⠀⠀⠀⢧⢫⠘⣆⠘⠀⠸⠇⠸⣏⠀⠀⣯⣿⣿⣿⣿⠈⠙⣿⡆⠀⠀⠀⠀⢠⣾⡿⠋⠀⢾⣿⣿⣿⣿⠇⠀⠀⢸⢿⡇⢀⣾⡿⣳⠁⠀ ⠀⠀⠀⠀⢻⣷⠾⣦⠀⡀⠀⠀⢻⣄⠀⠘⠻⠿⠟⠃⢀⣠⠾⠁⠀⠀⠀⠀⠀⠙⢷⣄⠀⠘⠻⠿⠿⠋⠀⠀⣠⣛⡼⠁⡼⠋⡱⠃⠀⠀ ⠀⠀⠀⠀⠀⠙⣄⠈⣆⠱⡄⠀⠀⠙⠳⣶⣖⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⠤⠤⠴⣖⣫⠖⢻⠀⢠⣧⠜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠻⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⡾⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⣇⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠘⡄⠀⠀⠿⠛⢿⣦⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣶⣦⠀⠀⠀⠀⢠⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⢦⡀⠘⡄⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣉⣉⣉⣭⠿⠛⠁⠀⠀⠀⠀⣰⠋⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡄⢻⣄⠙⣆⠀⠀⠀⠀⠀⠠⣄⣉⣉⠉⣉⣉⣤⠶⠀⠀⠀⠀⢀⡜⢡⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⣄⠹⣷⣌⠳⣄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⣠⢋⡴⢫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠀⠘⣆⠈⢻⣷⣬⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠞⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⣉⠼⡇⠀⠸⡄⠀⠙⢿⣿⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⠃⣰⠃⣏⠳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠚⣻⣿⠓⠋⠁⠀⠇⠀⠀⡇⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣴⣿⠏⠀⢠⠇⢸⠁⠉⠲⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀ ⢈⣴⣾⣷⣤⣴⣿⣿⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⢻⡄⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⠀⢸⠀⠀⠀⢻⣿⣿⣿⣿⣷⡦⣤⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠞⣇⠀⣿⠀⠀⠀⠹⣄⢀⡀⠀⠉⠛⠿⠿⠟⠁⠀⠀⡴⠃⡾⠀⡾⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⡄⠸⡇⠀⠀⠀⠘⣦⠱⣄⠀⠀⠀⠀⠀⠀⢀⡞⠁⣰⠃⣰⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠹⠄⢻⡤⠤⠀⠀⠘⠧⠈⠧⠀⠀⠀⠤⠤⠏⢀⣤⢏⡴⡋⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣾⣿⣿⡿⠋⡴⢫⣾⡿⣻⣿⠋⠉⢹⡉⢻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⢿⣿⢿⡿⠁⡜⢠⣟⣿⣽⠟⡼⠀⡀⠀⢣⠀⠙⣿⣿⣷⡻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⢫⣿⣿⡟⠁⡼⢡⣿⣿⣿⠏⣟⡇⠀⢰⡀⠈⢧⠀⠘⣿⣿⣿⡽⣿⣿⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⣸⣿⢣⣿⣿⣿⠁⢠⣧⣾⣿⣿⠏⡼⣸⠁⠀⠀⠙⣄⠈⣦⠀⠘⣿⣿⣷⣿⣿⣿⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⢳⣿⢧⣿⣿⣿⠇⠀⣼⣿⣿⣿⣏⡤⠀⡿⠀⠀⠀⠀⠸⣆⠈⣆⠀⢻⣿⣿⣿⣿⣿⣞⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⢠⡏⣽⣿⢀⣠⣿⣹⣿⣿⠟⠁⢰⠃⠀⠀⠀⠀⠀⠘⠀⠘⢦⣸⣿⣿⣿⣿⣿⣿⢵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⡀⣿⠘⠋⢁⣿⠋⢱⠃⠀⠀⡼⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⣿⠁⠀⣀⣼⣿⣴⣶⡉⠀⠠⠏⠀⠀⢠⡇⠀⠀⣀⣤⣴⣶⣾⣍⡀⠀⡟⠿⣟⣿⣿⣿⣿⣯⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⣿⠁⣄⣾⡿⠿⠿⢿⣿⣿⣿⣆⠀⠀⠀⠈⠁⢲⣾⣿⣿⠟⠛⠛⠿⣿⣆⣇⠀⠙⣿⣿⣿⣿⣿⠣⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⣿⣿⠁⣴⣶⣶⣌⠻⣿⣿⡆⠀⠀⠀⠀⣿⣿⡟⠁⣠⣤⣄⠀⠘⣿⢻⠀⠀⢹⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡇⠀⢻⣿⣄⠻⣿⣿⢯⣴⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⣿⣿⠦⣰⣿⡼⠀⠀⣸⣿⣿⣿⣿⡏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠒⠒⠒⠒⠾⣿⣿⠀⠀⠻⣿⡷⣶⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣻⣥⣶⣿⡟⠁⠀⢰⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⣿⣇⠀⠀⠘⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠀⣴⣷⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⠟⢩⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⣿⣿⣿⣿⣿⡼⣆⠀⠀⠀⠀⠀⢻⡿⠙⠹⢿⠏⠛⠀⠀⢀⣴⠟⣁⡴⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠃⣿⣿⣿⣿⣿⣆⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣡⣾⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣸⣿⣿⣿⣿⣿⣿⣧⡀⠙⣷⣄⠀⡀⠀⠀⠀⠀⢀⢠⣴⣴⡿⠛⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠻⣿⣦⣴⣲⢖⣠⣴⣿⠟⠉⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠙⠛⠛⠋⢉⣠⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡛⠷⠶⠟⠉⣠⣴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠶⠶⠟⠋⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣧⠀⠀⠀⠀⠀⢘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⠶⢿⣿⣦⡀⠀⠀⠀⠒⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡄⠀⠀⠀⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢿⣧⣤⣄⣀⣠⣾⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣏⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠳⡀⠀⠀⣧⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠿⡏⠉⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢹⠛⢦⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠑⠀⠀⢻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⡸⣞⣆⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠻⣻⡿⠋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠛⢶⣄⠀⠀⠀⣠⣴⣤⡄⠀⠀⡼⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡀⠸⡇⠀⠀⠉⠓⣦⣾⠏⠀⠈⣷⠀⣼⠃⠀⠸⣆⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠙⢳⣌⠉⠛⠛⠻⠷⢿⣿⣿⣿⣀⣀⠀⣰⣿⠃⠀⠀⠀⢻⡾⠃⠀⠀⠀⢹⢠⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣧⣤⣀⡀⠀⣿⡇⠀⠀⠀⠀⠸⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⣰⣆⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⣿⠛⠿⣷⣿⣄⡀⠀⠀⠀⠀⠀⠀⣼⣤⠾⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⢼⡿⠏⠀⢠⣴⣧⠀⠀⣼⡇⠀⠀⠀⠀⢀⣴⡿⠟⠋⠙⠻⣶⣿⡄⠀⠀⠉⠻⢿⣶⣄⡀⠀⣠⣾⠋⠁⠀⠀⠀⠈⣿⠀⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠻⠿⠃⠀⢠⣿⠃⠀⠀⠀⠀⣾⡟⠀⢠⣶⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣾⡏⠀⠀⠀⠀⠀⠀⣸⣿⡤⠞⢡⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⢻⣷⡄⠈⠋⠀⢀⣾⡏⠀⠀⢀⣤⣶⣶⣿⣿⠛⠙⢿⣦⡀⠀⠀⠀⣰⣿⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣀⣀⣀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣶⣶⠿⠋⠀⠀⣰⡿⠋⠉⠀⠀⠈⠳⣆⠀⠙⣿⣦⣀⣼⡿⠃⠀⠀⣸⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⠛⠋⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⡷⠀⠀⣿⠀⠀⠈⢿⣿⠛⠀⠀⠀⣼⡧⠒⣲⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠉⠀⢀⣼⡿⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⣀⣀⡄⠀⠀⠀⠀⣼⣿⣀⣀⣀⣀⣀⣈⣹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣼⡿⢷⡉⠀⠀⠀⠀⢰⣿⠇⣿⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠉⠻⢷⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠉⠲⠄⠀⠀⠀⠀⣰⣿⣯⣀⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠾⠷⠝⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣄⣤⢤⣤⣀⡀⠀⢀⣠⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀ ⠀⠤⠐⠉⠉⣉⣀⣠⣴⣾⣟⣿⣿⣿⣽⣿⣿⣿⣿⣯⡙⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠟⠋⠁⠀⠀⠹⣷⡄⠀⢀⣤⣴⣶⣿⠿⠷⠶⣶⣦⡍⠙⠓⠦ ⠀⠀⢿⡉⠉⣩⣾⣏⣡⡶⠛⠻⣆⣸⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠙⠻⠿⢿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⣠⣾⣿⣯⣩⡏⢀⡿⠛⣿⠶⣦⣤⡀⠀⠀⢸⠧⠴ ⠉⠉⠉⢁⣾⡋⣨⡿⢷⣄⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⢀⣿⢷⣾⣇⠀⣠⡾⠻⣷⣄⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣇⠀⠈⣹⣷⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠻⣿⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⠏⠙⣻⣿⣄⢀⡾⢻⣷⡀⠀ ⠀⠀⠀⠈⠻⣿⣿⣷⡾⠋⢉⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⠿⢶⣼⣟⡀⢹⡿⣧⡞⡜⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⢟⣩⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⣷⣄⣼⠋⠙⣿⣿⣤⡟⣱⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠙⠻⠷⣾⣿⣴⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⣿⠀⠀⠙⣿⣿⣿⠿⣿⣄⠀⠀⣼⠏⠁⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣦⡀⠀⠀⣿⠀⣠⣴⣿⠟⠁⠀⠈⠛⠳⠶⢿⣷⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠻⢿⣶⣦⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⣤⣀⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢿⣿⣿⣿⣿⣿⡿⡿⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣒⣒⠠⠄⡀⠀⠀⣀⠀⠙⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⣴⠟⠛⢿⣷⣦⣈⣆⠈⠀⠀⢀⣀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣠⣴⣮⣿⣿⣿⣿⣶⣶⣿⣿⣆⢣⠀⠀⠀⠀ ⠀⠀⢠⡎⠀⠐⠲⠿⢾⣿⣿⠛⣿⣿⣿⡿⠿⠿⠿⡽⣟⠉⠀⠣⡀⠀⠀ ⠀⡰⡟⠂⣀⣀⡀⣀⠀⠀⠈⣹⣟⡉⣀⣤⣆⣀⣠⣴⣦⢷⣤⣄⠈⢄⠀ ⡰⠁⠁⢸⣿⣿⣿⣿⣿⣿⣿⣋⣿⣿⣻⣭⣽⣶⣶⣶⣾⡾⢿⣿⣆⠈⡆ ⡇⠀⠀⢻⣿⣿⣿⣿⣿⡿⢻⣯⣽⣛⣛⣛⣛⣛⣛⣋⠉⠀⠀⠀⠈⠀⡅ ⢳⡄⠀⠈⢻⣿⣿⣿⣏⠀⠀⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⢠⠇ ⠀⠑⢄⡀⠀⠙⢿⣿⣿⣿⣷⣿⣿⣿⣿⡁⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀ ⠀⠀⠀⠈⠑⠒⠠⠤⢭⠉⣛⠉⡉⠀⠀⠠⠤⠶⡟⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣤⡶⠋⠉⠉⠑⣄⠀ ⠀⠀⠀⢀⣤⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢐⡠⠖⠊⣻⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠞⠉⠀⠀⡠⠃⠀

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⠀⠀⠀⠀⢀⡀⠤⠀⠤⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⢴⠝⢠⡠⠄⡀⢀⣈⢢⠀⠀⠀ ⠀⠀⢠⠀⠰⠛⠛⣷⣮⣇⣤⣤⡣⠀⠀ ⠀⡠⡱⠲⠤⢴⣟⣿⣿⠿⠿⢿⡃⠡⡀ ⡐⠅⣡⣤⣤⣤⡾⣧⢶⣗⣲⣛⣻⣶⠀ ⡇⠀⠛⣿⣿⠛⢯⣿⣿⣿⣿⡯⠀⠀⠀ ⠣⡀⠀⠿⠷⣀⣸⡻⡛⠋⠁⠀⠀⢀⡴ ⠀⠀⠉⠒⢲⡤⠥⠤⠔⠒⡏⢉⣩⢀⡀ ⠀⠀⣠⣴⡇⢅⠀⠀⠀⣼⣿⡏⣂⠴⢺ ⠀⣼⠿⠿⣿⣦⠦⠤⠐⡟⣻⠟⠁⡠⠊ ⠘⡟⠀⠀⢸⡟⠀⠀⠀⠙⠧⠔⠈⠀⠀ ⠀⠈⠃⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⢀⣯⢀⣤⢄⣀⠀⠀⠀⠀⡈⠹⣿⣿⡟⠡⠘⢿⣿⣿⣷⣾⣠⣤⣼⣿⡋⣠⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠘⢣⣄⠀⠀⠸⣟⠀⠀⠒⠀⠉⠋⠙⠲⣟⠣⡸⣯⣀⡈⠀⠈⢙⣿⣿⣿⣿⣿⢿⣿⡏⠙⠋⣩⠀⠀⢀⡶⣤⣖⡄⢀⠀⠀⠀⠀⠀⠀ ⠗⠠⠤⠌⠀⠀⠀⠻⢷⡶⠒⠁⠒⠠⠀⢰⢻⣷⣀⠈⣉⣙⣶⠀⣈⣴⣿⡷⠋⠀⠀⠀⠀⠀⣬⡵⠾⣦⣸⣷⣿⣯⣼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣦⡀⠀⠀⢸⢼⠉⠻⢷⣄⠙⣿⠰⠟⠑⠋⠀⠀⠀⢠⣠⠶⢛⣡⣿⠀⣿⠛⠁⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⣿⣷⣄⡄⢸⠀⠀⠀⢹⣷⡈⢿⠛⠛⠛⠛⢷⣾⢏⣤⠾⠛⢿⡟⢸⠏⢀⠀⢰⡈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠸⡄⠀⣀⡼⠿⣿⡄⠀⠀⠀⢀⡾⣱⠋⠀⠀⠀⣼⡇⣼⣤⠟⠀⢰⣇⣀⣀⣤⠶⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⢸⣿⡿⠿⠿⢿⡄⢻⠋⠁⠀⠀⠘⠋⠀⠀⠀⠸⠷⠋⠉⠻⢷⣾⣿⣰⠉⠻⣾⠆⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⣀⣠⡤⠖⠛⠛⠁⠀⠀⠀⢸⣿⣤⡴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠙⢷⡶⠤⠤⠬⠀⠈⠉⠁⠒⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢰⣿⣿⣉⡙⠲⡜⢆⠀⠀⠀⠀⢀⣤⣶⣒⡀⠀⣾⡿⠃⠈⠓⠂⠀⠈⢻⣧⣴⣒⠀⠠⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⢴⣾⡿⠋⢱⣿⣿⣧⣘⠻⢷⣾⣜⡇⠀⢀⣴⣿⣋⣥⢤⣍⡓⢄⠑⢴⠀⣶⡀⠀⢀⡜⠀⠀⠈⠙⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⢸⣿⣿⠿⠿⣿⣻⣿⣿⠇⢰⣿⣿⣿⣿⣧⣄⣚⣿⣿⣧⠈⠀⠸⣿⣿⣿⣿⣿⡆⠀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢸⣿⣭⣋⣉⡭⢟⣿⣏⡀⣸⣿⣿⣧⣛⠺⠿⣿⠿⣿⡇⠀⠀⠀⠉⠁⠀⠈⠉⢿⠁⠈⠛⠿⠿⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠈⠻⣮⣭⣥⣴⠿⣿⣇⣇⢻⣿⣯⠳⣬⣍⣁⣲⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⡀⠀⠈⠉⢉⡽⠶⠛⠛⠿⢿⡏⠻⢷⣦⣤⣩⡴⠞⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⣀⣀⣀⠀⠈⠑⠒⠒⠒⠢⢄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⣸⠛⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⣾⠿⠟⠛⠻⢦⣤⣤⣤⣠⠠⠀⠳⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢣⠇⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢴⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡼⠃⢀⡾⣱⠂⠀⠀⠀⠀⢠⡾⠁⢰⡇⠀⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⣴⠏⠀⠀⠀⠀⣰⡿⠇⠀⣾⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⡆⠈⣹⡿⠛⠛⠻⠿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⣦⣀⣀⣼⣿⣿⣷⣄⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠐⣿⣿⡇⠀⡿⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀ ⠚⠉⠀⠀⠀⣿⣿⡇⢸⣷⠀⠀⠀⠀⠀⢀⣀⣠⣾⠋⠀⠀⠈⠉⠉⠉⠉⠉⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡴⣦⣤⠟⢓⣶⣴⣯⣤⢴⡼⠟⣀⣤⣴⣶⣿⣷⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⠒⢀⠠⢄⠀⣄⣐⣀⣀⣤⣀⣒⡦⣤⣄⠐ ⠀⢀⠌⠈⠁⠀⢠⡿⢻⢫⠟⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⡖⠋⠁⠀⠀⠀⠀⠁⠈⠉⠳⣮⢸ ⠀⠀⠀⠀⠀⠀⡟⢁⠋⠁⢠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠘ ⠀⠀⠀⠀⠀⢸⡀⠁⠀⢠⣿⣿⣿⡿⠟⠉⠁⠀⠀⠟⠛⠉⠁⠘⠻⠟⠁⠀⠙⠋⠁⠀⢀⣉⠻⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⢠⠀⣾⣿⣿⡟⣠⠖⠋⠉⠛⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⢦⣻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣦⠀ ⠀⠀⠀⠀⠀⣿⠀⢸⣼⣿⣿⡿⠋⠁⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠶⠶⠒⠒⠉⠀⠉⣿⠀ ⠀⠀⠀⠀⠀⣿⣄⡼⣹⣿⡿⠀⠀⣴⢩⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠀⢿⣿⡿⣅⡀⠀⠀⠀⠀⠀⢸⠀ ⠐⠴⠶⠶⠶⢿⡟⠱⠉⠛⠀⠀⠀⠙⠾⠿⠛⠁⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠟⠠⠏⠀⠀⠀⠻⠀⠈⠳⣀⠀⠀⣀⣤⡾⠀ ⣷⡶⠶⢶⣶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⡿⣇⠀ ⣿⣁⣠⣼⡏⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢻⣄⣠⣇⣁⣠ ⣿⣿⣿⣿⡇⣶⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢸⡇⠀⠀⠀⠀ ⠀⠈⠉⣿⢠⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣧⣀⣀⣤⣤ ⠉⠁⠈⡟⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣒⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⡇⠀⢻⡅⠀⠀⠀ ⠀⠀⢼⢻⣿⡿⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣛⣲⣿⡀⠸⡟⠯⠿⠿ ⠉⠙⣿⣿⢿⠗⠒⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢼⣳⡄⡇⠀⠀⠀ ⠀⠀⣷⡟⣼⢀⠀⠀⠈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢸⠁⠀⡇⠀⠀⠀ ⠀⠀⡿⠇⣿⠀⠀⠀⠀⠀⠈⣽⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⠞⠋⠀⠀⠀⠀⠀⠛⠀⠀⠇⠀⠀⠀ ⠀⠀⢰⣶⡏⠀⠀⠀⠀⠀⠀⣸⠈⠉⣷⡆⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠹⠆⢰⣿⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣜⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⢉⡉⠉⠀⠀⠀⠀⢃⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠁⠀⣿⠈⢧⣻⡛⠛⠷⠒⠒⡟⣷⣿⡇⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠳⣿⠀⡆⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⣿⡇⢿⠀⢰⣿⣳⣶⣶⣤⣤⣤⣿⣿⣤⣀⣀⣉⣀⠀⠀⠀⢩⠟⠋⠉⠉⠉⠉⠉⠛⠻⣷⣿⣷⠗⠒⠒⠒⠶⣶⣶⠃⠀⠀⠀⢠⡀⠀⠀ ⠿⢧⣼⡇⠘⣿⣏⣿⣿⣿⣿⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣷⣶⣶⣦⣤⣤⣤⣴⡟⠻⣤⣀⣀⣀⣀⡼⠃⣴⡆⠀⡄⣾⡇⠀⠈ ⣦⣼⣿⣿⣦⣹⣿⡋⡧⠤⢬⣿⣿⢿⡏⢉⠉⠙⠛⠛⠛⠛⠃⠀⠀⠿⣿⣿⠷⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠁⣰⣿⠁⣸⣇⣏⣿⣶⣶ ⠈⠉⠙⠿⣷⣐⠳⠚⠓⠒⠒⢿⡏⠘⠀⠈⠀⠀⠀⠀⢀⡀⠀⣤⣤⣤⠉⠛⠳⠶⣤⣼⠘⠃⢺⡍⠉⠉⠉⠋⠼⣿⠛⠀⠃⣯⣿⠿⠿⢿

⣿⠏⠀⠀⠀⠀⣼⣿⣿⣿⡏⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⡟⢷⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⠀⢀⢱ ⠏⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣠⡟⠀⠘⣧⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣿⣿⣿⣇⡐⠁⠀ ⢀⠀⠀⠀⣠⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣘⣷⣀⣀⣀⣴⣋⣀⣀⣀⣹⣆⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣷⣦⣶ ⣿⣷⣶⣶⣿⣿⣿⣟⠙⠛⠛⠛⠘⣿⣿⣿⣿⣿⣿⣯⣭⢩⢀⣼⣿⣽⣟⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠳⢿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣻⢳⣿⡿⣦⣾⣿⣿⣷⣿⣿⣿⣿⣿⣧⣄⣹⣾⣿⣿⣷⣤⠈⠻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣀⣩⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⠛⠻⠿⣿⠻⠿⣿⣿⣿⠋⠙⠛⣿⣿⣿⣿⣿⡇⠀⠈⠋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣤⣨⡟⢻⣿⣿⣿⣿⣷⣶⣶⢶⣶⣶⣿⣶⣶⣿⣿⣿⣿⣷⡾⠛⢻⡿⣿⣿⣿⡄⠀⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣩⡵⠞⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣷⣀⣾⠃⠘⢻⣿⣿⣦⠠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⣏⠻⢿⣿⣿⣿⠁⠀⠀⠈⠻⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣿⣿⠟⠁⠁⠀⠀⠈⢑⣶⣾⣶⡀⠀⠀⠀⣀⠀⢿⣿⡿⠀⠀⠈⢻⣦⡙⠛⠛⠷⠦⣤⣀⡀⠘⠻⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⣠⠋⢠⠾⢳⡀⠀⠀⠀⠻⠿⠟⠀⢀⠀⣡⣾⣿⣿⣷⣦⡄⠀⠀⢸⠝⠿⣦⡀⠀⠀⠀⠉⠙⠋⠘⠑ ⢻⣿⣿⣿⣿⣿⠋⠀⠀⢀⣤⣤⣴⡇⣰⠃⠠⣴⣷⡀⠀⠓⠄⠀⠀⠞⢁⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⢹⡀⠈⠉⠙⠲⠤⣤⣤⠀⠀⠀⠀ ⣿⣿⣿⠿⠋⠀⢀⠀⣶⡾⠛⠋⢸⣶⠏⠀⠀⣠⣿⣝⣆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣻⣿⣿⣿⣿⠇⠀⣼⠙⠲⣤⡀⠀⠀⠈⠉⠀⠀⠀⠀ ⣿⣿⣏⠀⠀⠀⠘⠶⣗⣀⣠⠴⠛⠃⠀⢠⡿⠁⠈⠻⢿⣷⣤⡆⠀⠀⠀⠀⢉⣿⣫⣽⣿⣿⠟⣀⡼⢯⠀⠀⡟⠻⣦⣀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢠⠋⠀⠀⠀⠀⠀⢹⡋⠉⠑⣶⣦⣦⣼⠿⠖⢋⣉⣹⣿⡿⢁⠎⠀⣰⠧⢤⣈⣿⡄⠀⠀⠀⠀⠀ ⣿⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠙⠶⠼⡯⠛⠛⠻⠶⠞⠛⠉⠿⠋⠀⠈⠀⢠⡇⠀⠀⠈⠋⠻⣄⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣦⣴⣄⡰⠩⠳⠦⠀⠀ ⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⣾⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⠃⣾⣿⡇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠙⣧⠈⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣆⠀⠙⠻⣿⣿⣿⣿⣿⣶⣄

⠀⠀⠀⠀⣼⣿⣿⣿⠫⣱⣿⠟⠈⠌⢿⣿⢿⣦⠀⠀⠀ ⠀⠀⠀⣾⣹⢿⣿⠁⣷⣿⠙⠇⠐⠌⡄⢻⣿⣿⡆⠀⠀ ⠀⠀⢸⣿⠏⢟⣏⢼⣽⠟⠸⠀⠀⠘⠘⢼⣿⣿⣿⡇⠀ ⠀⠀⣰⡟⣠⣼⣴⣭⠈⠀⠆⣠⣴⣶⣤⠘⢿⣿⣿⣧⠀ ⠀⠀⢺⠁⣯⢴⣶⣹⡇⠀⢠⣿⢡⣦⣈⣿⠀⣿⣿⣆⠀ ⠉⠉⢻⣇⠘⢿⡿⠋⠁⠀⠈⠻⣿⣷⠟⠁⣸⣿⣿⡇⠀ ⠀⠀⣼⣿⠂⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣏⠀ ⠀⠀⢿⣿⣷⢆⠀⠀⠛⠛⠓⠀⡠⣪⢔⣽⣿⣿⣿⡇⡄ ⠀⠘⢾⣿⣿⣦⡙⣤⣀⡀⢀⡴⠞⣵⣿⣿⣿⣿⣿⡗⠁ ⠀⠀⣸⣿⣿⣿⣿⣦⡩⣉⠭⣠⢾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⡏⠉⠉⠀⢾⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣾⣧⠀⠀⠀⣾⡯⣿⣿⣿⣿⣇⠀⠀ ⠀⠐⣻⣿⣿⣿⣿⡿⣻⡄⠀⠀⢹⣿⣿⣿⣿⣿⣿⢦⠀ ⠄⠀⣷⢿⣿⣿⣿⡀⠈⠻⢤⠤⠞⢛⣿⣿⣿⣿⣿⢟⡇ ⠈⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠹⣶⠇

⠀⠀⢰⢷⠀⢠⡿⡇⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣾⣆⠀⣧⡇⢠⠏⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⣄⣈⡿⠲⠛⠧⠋⡘⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠉⠉⠉⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠷⡅⠀⠀⡠⠀⠴⣀⠤⣤⡀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣀⠜⢁⣤⡶⠛⠓⠦⠟⠀⠀⢀⡞⡠⢶⡄⠀⠀⢠⡤⡄⠀⠀⢸⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡽⠿⡟⠁⠀⠀⠀⠀⠀⠀⢀⡞⢀⣇⠸⠃⠀⠀⣿⠠⡇⠀⠀⠈⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⣸⣳⠀⢍⡁⠀⠀⠀⢈⣱⠇⢀⡤⢦⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠈⢿⣿⣿⣿⣿⣟⠀⡎⢀⣼⣿⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⡄⠈⠁⠒⠢⠤⠄⣀⡀⠀⠀⠈⠓⢤⣀⠙⠒⠤⠞⠻⣄⠹⣿⣿⣿⣞⣁⡠⠤⠤⠤⠒⠒⠒⠒⢒⠚⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠒⠒⠤⢖⣀⡀⠈⠉⠑⠒⠒⠉⢉⡿⠒⠒⠒⠒⠿⠿⠟⠉⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠚⠙⡆⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠠⣄⡾⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⢹⡀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠛⣢⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠉⠁⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⠿⢤⣠⣤⣾⣿⣿⡟⠿⠗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⠉⢿⣆⠙⠻⠷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⣰⡤⣀⣀⡀⠀⠀⠐⠀⠺⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠘⠿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⣠⠔⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⣁⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⡀⠈⠑⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣏⠀⢀⣴⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡠⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣍⠁⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅⢐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡄⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣤⣶⣁⠴⠻⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢗⡀⠀⠀⢱⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣈⣀⣩⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠖⠋⠉⠉⠉⣷⡦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⣠⠔⣾⣟⠁⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠶⠶⢚⣍⠀⠀⠀⣀⣀⡀⠈⠙⠒⢤⣀⡄⠀⣠⠞⠁⠉⠙⢦⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⠖⠛⣇⠀⠀⣿⡿⢀⡴⠋⠁⠀⠈⠉⠉⠳⢶⡋⣷⠋⠀⢀⡴⣶⣾⠋⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠁⢀⣀⡈⣧⣀⡉⣠⢞⣧⠴⠚⠿⢿⣓⡶⣄⡠⣿⣷⡠⡞⠟⠋⠁⢀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⢠⣿⣿⣟⡇⠈⠂⣿⡉⠒⠀⠀⠀⠀⠈⠑⢮⣙⣿⣿⡟⠁⣀⣠⠔⠋⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡆⠘⠿⠛⠁⠸⡄⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⣠⠿⠋⠀⠙⠛⢉⣀⣤⠴⠚⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⠀⣀⠀⠀⡷⠀⠀⠀⠀⠈⠉⠓⠒⣶⣿⡿⠶⢺⣶⠒⠲⢿⢥⣀⡀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡆⠰⣿⠀⠀⣧⠀⠀⠀⠀⠀⣀⠴⠛⠁⣿⠁⠀⢸⣿⣀⣀⣼⡳⣄⣙⢓⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⢀⣤⡀⢘⡄⣠⢀⡤⠚⠁⠀⠀⢀⣿⠻⡏⠙⣟⢧⠙⠆⠹⠄⠙⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⣀⣾⣿⣿⣾⡟⠡⠋⢠⠀⠀⠀⠀⠉⡟⠀⢿⡄⠋⠙⢷⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠙⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠟⢿⣿⣁⣿⣽⣖⠚⠉⠀⠀⠀⠀⡼⠁⠀⡸⠁⠀⠀⣼⣀⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀ ⠀⠀⠀⠘⣦⣘⣯⡀⠀⠀⠈⣉⣢⡀⠀⠀⠞⠁⠀⡰⠃⠀⠀⠀⢹⣷⠏⣸⠗⢶⣄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀ ⠀⠀⠀⢸⠿⡿⠀⠛⢦⣀⣸⣧⠭⣽⣻⣒⠦⠤⢄⣀⡀⠀⣠⡄⠀⠀⣰⠃⢀⣾⣿⡧⢄⣀⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢠⢃⣼⠇⠀⠀⠀ ⠀⠀⠀⣸⣄⡀⠀⠀⢸⡀⠉⢿⣤⠿⠀⠉⠉⠛⠒⢮⣭⣭⣻⣳⣦⠤⣏⣙⣛⠚⠃⠈⠙⠛⠻⠿⢷⣲⣧⡄⢠⡄⣼⢀⣾⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⣿⣤⡉⠓⠒⣾⠷⠒⠛⠲⠤⠖⢻⡽⣷⣶⣯⠟⣙⣚⣋⣩⡟⠛⠿⢿⣿⣒⡒⠦⢤⣄⣀⠀⢸⠛⢷⣼⣷⡷⢾⣿⣾⡀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣶⣿⣶⣶⣶⣶⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠉⠉⠓⠶⠾⢽⣟⣀⠀⠀⠀⠀⢉⣾⣻⠇⠀⠀⠀⠀ ⠀⠀⠙⠿⢿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠓⢲⠶⢾⡏⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡉⠉⠉⠁⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠀⢸⠀⠹⠛⢦⡘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠿⣯⢹⠟⠁⠀⠀⠀⠘⠛⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠀⠈⣧⠀⠀⠀⠑⠘⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢸⣾⡀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠀⠀⠹⠀⠀⠀⠀⠀⠸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢧⢀⣴⣶⣶⡆⠀⠀⢳⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠒⠛⠛⠛⠛⠋⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠀⠀⠀⠙⠛⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⠒⢦⣀⡴⠋⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡇⢠⡄⠀⢀⣈⠀⢠⡄⠀⣰⡆⣸⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣾⣿⣿⣧⣾⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣷⡿⠃⠀⠀⠀⣴⡆⠀⠀⠀⠀⠘⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢻⠿⠿⣿⢿⣿⠿⠿⠿⡿⣿⡿⠿⠿⠿⠿⠿⡟⠁⠀⠀⠀⠘⡟⠳⡄⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⡰⠋⢀⡎⠀⠀⠘⣆⠉⠀⠀⠀⢱⡌⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢳⡀⠘⣆⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⣄⠀⠙⢷⠀⠸⡅⠀⠀⠀⠈⠳⠄⣀⠠⠞⠙⠢⢄⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⡿⠁⠀⣠⠏ ⠀⠀⠀⢀⡖⠋⠻⣆⠀⠀⠹⡄⢀⡈⠀⠀⡇⠀⠀⠀⠀⢠⠗⠉⠉⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⣤⣠⠏⠀ ⠀⣠⠶⠼⣇⡀⠀⠹⣶⠀⠀⢻⣯⠑⢄⠀⢹⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠠⠀⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⡏⠀⡰⠁⣿⠏⠀⠀ ⢰⣿⣄⠀⠈⢷⡀⠀⠹⣷⣠⠤⢿⣧⢮⡆⠈⡆⠀⡼⠈⠀⣀⣼⣶⣒⡖⢲⣦⣄⠀⠐⢝⣆⠀⠀⠀⠀⢸⠁⠸⣹⣾⠟⠀⠀⣰ ⢸⣿⣿⣿⣄⣈⠻⣦⣔⠛⣿⣇⡀⡛⢷⣗⣠⡇⠀⢗⢒⠏⠁⢀⢀⣀⠀⠀⠀⠀⠉⠑⣺⣿⠀⠀⠀⠀⢸⠠⣮⡿⠋⢀⣴⡾⠃ ⠸⡏⢻⣿⣿⣿⣧⣹⣿⣆⠘⣿⣗⠐⡀⠀⠀⡇⠀⠈⡆⠀⠀⣀⣐⠚⠀⠀⡀⠀⢤⡺⠟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠠⣾⡟⠁⣠ ⠀⠿⠯⠄⠀⠈⠙⠻⠿⠿⡦⠈⠻⢦⠜⠒⠒⢧⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠉⠱⡶⠟⠀⡴⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣤⣤⣤⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣿⣶⣽⣷⡀⠀⠀⠀⠀⣴⡾⣿⣿⣿⣷⣦⣉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣿⣿⣿⣏⣧⠀⠀⠀⢰⡿⢰⣿⣿⣿⣿⣿⣿⣧⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢿⣿⣿⣿⡟⣿⠀⠀⠀⠸⣷⡸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢷⣌⠻⢿⢿⣷⠏⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⠟⠁⣠⡾⠃⠈⠓⢤⡀⠀⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠙⠛⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠯⠷⠶⠟⠋⡀⢀⠀⠀⠀⠹⠀⠀⠀⢠⣿⠏⠀ ⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠹⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢱⡈⢧⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀ ⠀⠀⢀⣿⠀⣼⡿⠿⠶⣦⣄⠘⢿⡶⠿⣦⣜⠛⠛⠿⠷⠶⠶⠶⠆⠀⠀⢄⠀⠀⠀⠀⠈⢧⠙⠆⠀⢀⣰⣴⡾⠟⠁⠀⠀⠀ ⢠⡞⢹⣿⣷⣿⣇⠀⠀⠐⠿⢷⣿⠁⠀⢨⡿⠛⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⢀⣀⣤⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⢹⣄⣿⠋⠈⠙⠛⢦⣄⠀⠀⠀⠙⠷⣦⣟⡅⠀⠀⢹⡿⠶⠶⠶⢶⡶⠶⠶⠶⠶⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠟⢿⣧⡀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣼⡁⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣟⣻⣦⡀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⣿⠛⠲⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠖⠈⠁⠀⠀⢠⣌⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣄⡀⠀⠀⠣⠀⡀⠔⠀⠀⠀⢠⡰⠈⠈⠻⡇ ⠈⠀⠀⠀⠀⠀⢠⠊⢉⣭⣕⠇⠀⣠⣼⡆⠀⠀⢋⠀⠀⠀⠀⢠⡾⡀⠀⠀⠀⠀ ⡇⠀⠀⢀⠀⠀⣸⡈⠸⣿⡿⣠⠀⠿⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣕⠠⣀⡀⠀ ⢀⠀⠀⢿⣿⣿⠀⠉⠀⠀⠸⠿⠉⠁⢸⣿⣇⠀⡰⢀⠄⠀⠄⠤⠴⠿⠷⠡⣬⣠ ⠀⠀⠶⠸⣿⣥⣤⣤⡶⠶⠶⠖⢛⣿⠿⠟⠋⡰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠡⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⢀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣷⣶⣿⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣷⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀ ⣿⠛⢻⣿⠀⠀⠀⠀⠀⠀⣼⡀⢀⡞⠁⠀⠀⡄⢠⠐⠤⣄⡀⠀⠀⠀⠀⠀⠀⢠⡄⠈⢳⡝⣷⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠚ ⢁⣤⣥⡆⠀⠀⠀⠀⠀⢀⡿⢽⡞⠀⠀⠀⠀⢧⣈⣶⠚⠿⠿⠓⢀⡤⠒⠚⠒⠪⣷⡀⠀⢻⡜⢿⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀ ⢘⣿⣿⡇⠀⠀⠀⠀⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠙⠿⠓⠀⢀⡴⢋⡴⠊⠉⠉⠉⠛⠷⠀⠀⠹⣦⠻⣄⠀⠀⠀⠀⠀⠀⢣⠀⠲⣶⢾⡦ ⠟⠛⢻⡇⠀⠀⣀⣀⠀⣼⠀⢸⠀⠔⣊⣉⣉⠉⠒⠠⠤⡶⢟⡴⠋⣠⡴⠞⠛⠓⠂⠀⠀⠀⠀⠙⣧⡈⢦⠀⠀⠀⠀⠀⠈⣇⠀⠉⠉⠁ ⠀⠀⣸⠀⡴⣻⡿⠃⢠⡿⠀⠈⡇⠚⠁⠀⢀⠈⠉⠒⠒⠒⠋⠀⠺⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠳⣄⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⡸⢻⢀⡿⠃⠀⢀⡎⠁⠀⠀⣳⠀⠴⠋⠉⢹⣶⣄⠀⠀⠀⠀⠀⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣿⣦⡀⠀⠀⠀⢏⠀⠀⠀ ⠀⠋⢹⡼⠁⠀⠀⡼⠁⠀⣶⣿⣿⣧⠀⠀⠀⠀⠀⡈⢳⡀⠀⠀⠀⣞⣫⣭⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⣿⣦⡀⠀⢸⡂⠀⠀ ⣀⡀⡸⠀⠀⠀⣼⣥⣄⠀⠈⢿⣿⣿⣧⣄⠀⣶⣿⣿⡆⢣⠀⠀⠀⠘⠳⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣄⣿⠈⠓⣴⠏⠀⠀ ⠙⣿⠃⠀⢀⣼⣥⣿⣿⣿⣆⠈⠙⢿⣿⣯⠘⠛⠛⠛⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣟⣿⠟⠻⣶⡁⠀⠀⠀ ⢸⡏⠀⢠⠾⢿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⡆⠀⠀⠀⠀⣸⡤⣤⣶⣶⡴⠒⠒⢶⣪⠟⠋⠁⠀⠀⢀⡀⠀⠀⢀⣷⠁⠀⠀⠘⢷⣀⡀⠀ ⣿⣇⡴⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⡜⠻⣶⣿⣿⡿⠃⠀⠀⠀⢹⣖⣶⡶⠶⣞⣷⣤⣄⣀⣸⢿⠀⠀⠀⠀⠀⠻⡗⠀ ⠿⠿⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣇⠀⠀⠉⣯⣀⠀⠀⣀⣤⣿⡿⠻⣯⠁⠀⠀⠀⠉⢑⡇⠈⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠀⠀⠀⠛⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠷⣶⣾⣛⣿⢏⣩⢽⣻⡿⠃⠀⣹⡇⠀⠀⠀⠀⣼⢠⠀⠈⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⣍⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⣯⠻⣟⣒⣛⣭⣾⠁⠀⠀⡇⡇⠀⠀⠀⣼⠃⡜⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⢉⠃⠀⠀⠀⠈⠁⠀⠛⠿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠓⠒⠒⠀⠀⠀⣰⠃⡇⠀⣠⣾⠏⢠⠃⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⡴⢤⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣽⠀⢿⠸⣆⠀⠀⠈⠓⠒⠚⠁⠀⣧⢾⡽⠃⠀⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡆⢈⠳⢦⣤⣤⣤⣔⣲⡿⠞⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢦⣴⣾⣿⠄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⠹⠌⢢⡀⠀⠈⣉⡁⠀⠀⠀⠀⢠⠜⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡎⠀⡀⣠⢞⠥⢺⡇⠀⠀⢻⡄⠙⢶⣼⣏⠲⣄⠈⢿⣦⠑⡀⠀⣠⠀⠀ ⠀⠀⡼⠀⣼⢟⠕⠁⠀⠀⠙⠲⣤⡁⠹⣦⠀⠉⠛⠧⡈⠙⠮⣷⡳⣄⠀⢸⣦⠀ ⣠⣾⣣⠞⠱⠁⠀⠀⡀⠀⢃⠀⠀⠉⠓⠯⣷⡀⠀⠀⠑⠀⠀⠈⠉⢈⣷⢦⣿⢳ ⣽⡟⣃⣀⠀⠀⠀⠀⠁⢸⢈⠀⠐⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠙⡆ ⠋⠉⢀⡈⠙⠲⣤⣀⡀⠈⠚⢠⠀⢇⢀⡀⠈⠀⠀⠀⣠⣴⣿⠿⠾⠿⢿⣿⣷⡄ ⣠⣼⣾⠾⠿⠿⠿⠿⣿⣷⣦⣄⣀⣸⡀⢻⣦⣤⣴⣿⢟⠥⠠⡀⠀⠀⠀⢸⣿⠁ ⢹⣯⠀⠀⠀⢠⠊⠉⢂⠙⣿⠝⠉⠡⢝⡥⠠⠕⢻⠇⠘⠄⠠⠂⠀⠀⣠⡾⠃⠀ ⡎⢿⣦⡀⠀⠀⠑⠒⠂⠀⠘⣂⣀⣀⠀⠀⠀⠤⠭⣁⠀⠐⠒⠒⠚⠉⠁⠀⠀⢠ ⢻⡀⠈⠙⠛⠛⠛⠉⠁⢠⣎⠀⠀⠀⠀⠀⠀⢀⣠⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠾⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾ ⢢⣜⣧⠀⠀⠀⠀⠀⠀⢿⡿⠟⠛⠛⠛⠏⠉⠉⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⣰⡇ ⡞⢹⡼⣧⡀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡴⠃⢳ ⠀⠀⠱⣘⣷⣄⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⣠⡞⢳⠀⠸ ⠀⠀⠀⢻⣸⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠀⠈⣧⣀ ⢶⡾⡩⠋⣿⠀⠀⢿⢷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠸⡇⠀⠀⢹⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠛⠓⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣤⡄⢀⣀⣄⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢹⣿⣴⡿⣿⣄⣼⡆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣷⠞⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣠⠴⠒⠐⠛⠘⠋⠀⢸⡿⠋⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠛⠛⠁⠀⠀⠠⣀⠐⢿⣠⣾⣉⣀⣀⣀⣍⣥⣤⣤⣄⣐⡀⠄⠀⣠⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣾⠏⠹⣿⠿⠛⠻⢿⣷⣄⠀⠀⢈⣽⣿⣦⣌⣱⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⡟⠀⠐⠾⢦⣀⣠⡆⢙⡿⠂⠸⣿⡋⠉⢻⡿⣿⡿⠁⣸⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⢹⣄⠀⠈⠢⣀⠀⠀⠀⠀⣀⣤⠞⢦⣤⣾⣧⣶⣄⠀⣀⣠⠉⠉⡏⠀⠀⠀⠈⠇⠤⠞⠀⣿⣠⣿⠁⢘⡃⡤⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠙⢶⣄⡀⠈⠓⣢⠖⠋⠁⢻⡀⢘⡟⠻⢿⡿⢿⣿⣿⣿⣦⣼⠁⠀⠀⠀⠀⠀⢀⣄⠀⣸⣏⡸⠓⠚⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⣯⠀⠀⠀⠀⠀⠉⠉⠹⣧⠤⡤⣄⣀⠉⠛⣧⠀⢸⡇⠈⠉⠀⠉⠻⠟⠳⠦⣤⣤⣴⣿⣿⣿⣿⢿⡿⠥⣀⣀⣼⣿⠧⣤⣀⣀⡤⡂ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡤⠖⠈⢉⡩⠿⠟⢷⣌⠙⠢⣄⡀⠀⠉⠀⠀⠲⠂⠀⠀⠁⠠⢼⣿⣆⠀⠀⠀⠈⠉⢿⡟⢲⠶⠛⠉⣿ ⢸⣇⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⡰⠋⠀⠀⠀⠀⢻⣷⣦⣀⠈⠉⠙⠲⢦⣤⣄⣠⡤⠠⠴⠋⢀⠎⠁⠀⠀⠀⠀⠀⠻⠁⠀⣠⣤⡇ ⠀⣿⡀⠀⡀⠀⠠⠖⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠻⡝⢿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣴⣤⠞⠀⠀⢰⣾⣿⠟⠀ ⠀⠘⣧⡀⠈⢳⣦⣀⠀⠀⠀⠀⠀⠸⣶⣆⠀⠀⠀⠀⠀⢱⡀⠈⠉⠉⢉⣹⡛⠳⠶⣴⡶⠋⠀⠀⠀⠀⢠⣿⠇⠀⠀⣠⠼⠟⠋⠀⠀ ⠀⠀⠈⠛⠧⣄⡻⣿⣿⣷⣦⡀⠀⢠⣿⣿⣷⣦⣄⠀⠀⠀⠉⠑⠒⠚⠉⠉⢻⣞⠒⠋⠀⠀⠀⠀⢀⣠⣾⣿⣖⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⢿⣾⣿⣿⣿⣿⣿⣷⣄⢀⣀⠀⠀⠀⢀⣴⣿⠉⢻⣄⣀⣀⣠⣴⣿⣿⣿⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⡉⠙⠻⣿⠿⣿⣿⣿⣧⠤⡴⠟⠉⠀⢰⠀⠀⠉⢙⣿⣟⣿⣿⣿⣇⡠⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣙⠒⠦⢬⡁⠸⠻⣄⠙⣷⠦⠤⠤⠤⢾⡷⠒⠛⠛⢻⣯⣼⡟⣸⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢿⠙⠛⠶⠦⣿⡆⢸⣏⠓⢬⡀⠀⠀⠀⢸⡇⠀⢀⣤⣼⣿⣿⡇⣸⣿⣛⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣀⣘⣷⣘⡍⠻⢾⡿⠶⠶⢶⣾⣷⡞⠉⠉⣿⣿⣿⡿⠿⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠿⠛⠛⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣛⣿⣿⣏⡓⠀⢀⣠⡿⢋⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⣳⡀⠉⠀⠀⠐⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠘⣩⡅⠀⠀⣹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⢿⡒⢀⠀⠀⡀⠘⣟⠟⠁⠈⠉⠙⠛⠛⠛⠋⠉⣉⣡⢿⣯⠜⠋⢀⣀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠁⠈⠙⠳⢬⡗⠦⠄⠀⠀⠀⠀⢤⠤⠴⠒⠊⠉⣠⣾⣯⣤⣤⣾⠟⣁⣀⣀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠃⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⡟⣹⣿⣿⣿⠋⠀⠀⠀⠀⡞⠛⢁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣷⣦⣤⣥⣭⣿⣿⣿⡟⠁⠀⠀⠀⠀⣠⠖⢀⠉⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣾⣿⣿⣿⣿⣿⣽⠃⠀⠠⠀⠀⢠⡄⠛⢠⡟⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠱⣝⣿⣿⣿⣿⣿⣿⣿⣿⡃⠂⣠⣿⣿⣿⡏⠒⠭⠿⢰⣄⡀⣠⣤⠟⠀⠀⢀⣾⣃⣤⡤⠀⢀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠘⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠟⠻⢿⣿⢀⣶⣿⠋⠙⠋⠙⣢⣴⠚⠋⠉⢹⡇⠂⣶⠟⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣀⣤⣄⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠢⣤⣼⣿⣧⡀⠙⣠⣾⡉⠀⠀⠀⠀⠀⣧⡾⠃⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣷⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣤⣇⣤⠏⣹⣿⣿⣯⣿⡿⠛⣁⣀⣀⠀⠀⢰⣿⣷⡄⠀⠀⠀⠊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣿⣿⣟⣽⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢩⣿⣿⣿⣿⣿⣾⡏⢰⣿⣿⣿⣿⣿⡦⢸⣧⠈⠻⢶⣴⡃⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣀⠀⠀⠁⠐⠃⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣹⢁⣿⠁⠶⣦⠟⠁⠙⠂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣬⡀⠉⠉⠉⠁⣾⠇⠀⠰⠋⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠂⠀⢀⣤⣴⣿⠂⢀⠀⠀⠀⠀⠀⢒⡠⠀⠀⠀⠀⠿⣿⣿⣿⡦⠄⠀⠀⣿⢻⣶⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡆⠀⠀⠀⣠⣴⣻⣿⡷⠀⠀⠀⠀⠈⠻⣿⣷⣄⢀⣼⣿⣿⣿⡆⠀⠀⠀⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⡆⢠⠀⠀⣹⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡋⠉⠉⠀⠀⠀⠀⠀⠸⣿ ⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⡄⢠⠀⠤⠀⠀⠀⠀⠐⠂⠀⠱⣮⠄⠘⠁⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣿⣿⣯⣿⠀⠐⣿⣿⣿⣷⣤⣀⣀⣶⣬⣤⣨⢿⣿⣤⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣟⣿⣿⣧⠀⠀⠙⠃⠁⠩⠀⠘⠛⠛⠛⠹⠿⠿⣿⠛⠛⢿⣿⡿⠷⠤⠴⣶⡿⠦⠀⠀⠀⠀⠀⢆⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢰⡄⠀⠀⠀⠀ ⠀⠀⠀⡠⡔⣖⣆⣀⣲⢒⢒⠪⣀⣀⠀⢇⠀⠀⠀⠀ ⠀⠀⠀⡞⣩⣣⠀⠀⠈⠉⠛⠲⢧⡎⠦⡀⠣⢄⡀⠀ ⠀⠀⢸⠈⠸⠍⠀⠀⠀⠀⠀⠀⠀⠙⢥⢴⠀⠀⣷⠀ ⠀⠀⠸⠀⠀⡷⣆⡔⠰⠀⢦⣤⣶⡀⠘⣌⠖⠊⢣⠀ ⠀⠀⠀⡳⠀⠳⠧⣼⣀⢀⡀⣭⡤⠴⠄⠈⢩⢢⠀⢃ ⠀⠀⡎⠀⠀⡆⠀⠈⠝⡄⠙⠀⠀⣀⠀⠀⢸⠀⠧⢸ ⠀⠀⢰⠀⠀⠙⠀⣀⡀⣀⠀⠀⠰⠇⠀⣠⠀⣼⠀⢛ ⠀⠀⠀⠹⣎⠔⠀⠉⡞⠀⠉⠀⢀⠔⡡⠛⣿⠁⠰⠈ ⠀⠀⠀⠀⠀⠁⢒⠀⠀⠀⠐⡖⠒⠈⠀⠀⡇⢰⢀⢠ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⣦⡀⡇⠀⠀⠀⢀⠃⠇⡄⡆ ⠀⠀⠀⠀⣀⡤⢧⠤⠀⢏⢹⣃⠀⠀⠀⠸⡀⠐⢠⠀ ⣀⣤⣶⣋⡍⠛⢦⣄⣀⡬⢓⡒⠋⢙⢱⣢⣌⡁⠚⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡟⠀⠉⠈⠙⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣿⣿⣿⡿⠋⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⡏⢹⠻⣿⡟⣥⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠟⠁⢁⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠻⢿⣷⣦⣄⣨⣤⣭⣿⣿⣿⣿⡿⠋⠀⠀⢀⠀⠀⠀⣰⡖⠂⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠀⠀⢠⡻⣯⣿⢿⣿⣿⣿⢙⣿⠈⠀⠀⡀⠀⠀⠀⢀⡠⣿⠇⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠀⢩⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣁⠀⢸⣿⣿⣿⣿⠿⡻⠿⣿⡇⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠘⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠙⢦⡽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣁⣉⣤⣿⣿⣿⣿⣿⡆⡁⠚⠘⠃⠻⣧⣄⢠⡴⣾⠏⠀⠀⠀⣀⣾⣭⣤⡶⠾⠁⠀⣤⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠀⡀⠀⠀⠑⠚⢿⣿⣿⣿⢻⡿⣿⠾⢿⣿⣿⣿⣿⣿⠛⠿⢿⣿⣷⠀⣿⢸⣟⠃⠀⠻⠁⠛⢇⣠⡶⢛⠉⠉⠀⢻⡇⠘⢈⣿⠟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⡀⠀⠻⠻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠉⠀⣿⡦⢀⡋⢠⣿⣿⡏⠀⠰⡆⣀⣴⠟⠁⠈⠁⠀⠀⠀⠈⡇⣠⡿⠃⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣠⣶⣿⣿⣿⣦⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣼⠃⠘⡿⢻⣿⣟⣾⡧⣤⣾⣿⣵⠯⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⠀⠀⠀⢀⡴ ⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣾⣼⣿⣋⣼⣿⣿⡟⢼⣿⣿⠋⣀⣤⣶⣶⣶⣄⠀⠀⢸⡿⢾⣿⡀⠀⠀⢀⠘⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡜⠚⣿⣿⣿⣿⣃⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣼⣿⣽⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⣿⣿⣿⣿⣷⠇⣼⣧⠄⠙⠻⠷⣴⡏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠈⠀⠉⠁⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⢹⡟⢰⣿⠁⢤⣤⣠⡿⠃⠙⠳⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣍⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠛⠩⣿⣿⣿⣿⣷⣀⠟⠘⠛⠿⠿⠿⠚⢀⣾⡏⠀⢨⣬⡟⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣷⣒⠀⠀⠀⠀⠀⣾⣟⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠑⠀⠀⢀⣶⡶⣿⣻⠃⡀⡀⠀⠀⠀⠀⠀⠀⠮⣗⠤⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣷⠤⠄⠀⠀⣽⡟⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣿⣿⣷⣶⠠⠀⠀⠀⠀⣄⣒⡚⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⣴⣿⣶⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣉⠀⠀⠠⠀⠸⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⣙⣻⣷⣿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠠⣶⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠳⠴⡃⣾⠀⠀⣴⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢆⣄⠀⣆⡀⠂⠄⠀⠀⠀⠀⠈⠉⠁⠀⣀⣻⣶⠂⠈⠁⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣿⣿⣿⣿⣿⣿⣿⣿⣉⣽⡇⠀⡼⣿⣿⣿⣿⣷⣦⣀⡀⠘⢷⣬⣅⣠⠠⠭⢿⣿⣄⡀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠐⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣧⠙⠋⢿⠉⠉⢿⣿⡿⢿⡿⢿⣻⠿⣿⡿⠷⣶⣶⣭⣗⣶⣾⣍⣀⣀⣀⣰⣶⣂⠀⠀⠀⠀⠀⠀⠀⡀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠐⠂⠀⠈⠉⠉⠙⠓⠀⠀⠀⢛⣷⢧⣬⡍⠉⠉⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠉⠀⠀⠉⠁⠀⠀⠀⠀⣯⡁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠬⠛⣿⣿⣿⣿⠏⡄⢙⢿⣿⣿⣿⣶⣮⣍⣤⣤⣰⣿⣷⠋⢀⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠄⠀⠀⠀⠀⢸⡟⡟⠋⠩⢍⡙⠒⠦⠤⠴⢦⣀⡷⢤⠙⣿⣟⠁⠀⠅⠠⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠿⡿⠇⠞⠀⡄⢠⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠘⢳⡆⠀⠀⢨⣻⣄⠀⡀⣀⣀⣀⠀⠀⠀⠀⢸⣷⣈⠳⠭⠿⠶⢧⣄⠀⠀⢠⡿⢻⣿⡟⣻⠿⠟⠘⠛⠛⠁⠀⠀⣴⠷⢠⠁⠀⣼⠃⣿⣿⡾⢡⡴⠆⠀⠀⠀⠀⠀⠀⠀ ⠟⠰⠶⠖⠃⠀⠀⠀⠀⠘⠻⣿⡟⠁⠀⠀⠉⠓⠒⠀⣼⢠⣿⣦⣀⠠⠤⣄⣨⣿⠀⢚⣠⡿⣫⡾⠃⠀⠀⠀⠀⠀⠆⢀⣤⡴⠞⠛⣷⣄⣟⣼⣷⠿⠶⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡻⣶⣄⠀⠀⠀⠀⡇⣼⠁⠹⣿⣷⡀⠈⢷⡟⠠⠾⠏⠸⠛⠀⠀⠠⠀⠠⣀⣤⠶⠛⣁⣴⡿⠀⣿⡿⢛⣁⡀⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⣿⣿⣷⣤⡀⠀⡇⣿⠀⠀⠀⠈⢻⣦⡀⠻⣦⣤⣤⣤⣤⣤⣤⣤⣴⡟⠋⣀⣴⣾⣿⣿⡇⢰⣿⠁⠀⠀⢠⡈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠀⣿⣿⣿⣿⣿⣿⡇⢻⠀⠀⠀⠀⠸⣿⣿⣄⠘⠃⠀⠀⠀⠀⢀⣼⠟⣵⠟⠋⠁⠀⠀⣿⠇⢸⠃⢀⡆⠀⠈⣷⡄⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⣿⣿⣿⣿⣻⣧⠈⣇⠀⣠⡴⠶⠟⠻⣿⡆⠀⠀⠀⠀⢀⣾⢃⣼⣁⡀⠀⠀⠀⣿⣿⠀⣿⣶⠟⠁⠀⣀⣿⣁⣀⣤⡶⡟⠛⠁⠐⠂⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣾⠀⣿⣿⡿⠿⠿⠿⣿⡄⢸⡟⠉⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠸⢿⠟⠉⠉⠙⠿⣷⣾⣿⠇⣾⠉⠻⣿⡿⠆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠀⠒⠒⠒⠒⠂⠀⣀⣠⡶⠿⠾⠛⠁⠀⠀⠀⠀⢻⣿⣀⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⣾⠃⠀⠀⠈⢻⣦⣤⣤⣀⣀⣒⠒⠀⠹⠚⠳⢤⣤⣀ ⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢷⣬⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣿⣿⠃⢰⣤⣀⠀⠉⠻⣶⣬⠉⣭⣉⡉⠁⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⡀⣠⣿⣿⡶⢶⣶⣄⡙⢧⡘⣆⠀⠀⠀⠀⠀⣤⣾⣯⣭⣥⣤⡀⠀⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠳⠶⣮⣅⠈⠉⠁⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⢶⣿⣿⠛⠉⢸⣿⣿⣿⣭⣅⡓⠺⣽⣮⣷⢸⠀⠀⢠⣠⣾⣿⣯⣥⣤⣤⣤⡉⠳⣄⠉⢢⡇⠸⣷⣄⠀⠀⣠⣄⢃⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀ ⠤⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠀⢸⣿⢿⣿⣿⣿⣹⡟⠻⣿⣿⣾⢀⢠⣻⣿⣿⣿⣗⣒⣒⡒⠪⢽⣷⣿⣦⠈⠁⢠⢹⣿⣿⣷⣿⣿⣿⣷⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣼⣿⣿⠀⠀⠀⢸⣿⡷⠯⠭⠤⠶⢗⣻⣽⣿⠏⠀⢼⣿⣿⣿⡉⣿⡏⣿⣿⣿⣶⣽⣿⣿⠀⠀⠀⠠⠿⠟⠛⠛⠛⠻⢿⣷⠄⠛⢿⣿⣾⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠄⠀⠀⠸⣿⡻⠷⠶⠶⠞⢋⣥⣾⣿⢦⢠⣴⣿⣿⢮⡛⠶⣥⣙⣋⣚⣋⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠉⠛⠛⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠠⠀⠛⢿⣶⣶⣶⣶⣿⠟⣿⣯⣼⣆⠹⣾⣿⣎⠻⢷⣦⣭⣍⣭⡭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣤⠀⠀⠀⠈⠉⠉⣉⣽⠦⠿⠿⠿⢿⣿⡟⠛⣿⣷⣤⣤⣀⣀⣤⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠤⣀⡀⣀⣀⣀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠁⣠⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡿⢰⡏⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⡿⠿⠿⠻⠿⣶⣄⣀⣀⣀⣠⠀⣄⠈⢳⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⢃⡞⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣇⣽⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⣦⣀⣀⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣼⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡿⠀⠀⣸⢇⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⣿⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⡀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⣰⠏⣼⠃⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⣼⡏⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢃⣴⠏⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⣿⡇⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⠈⠋⣿⣿⡿⢿⠿⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢋⣤⠀⠀⠀⣸⣶⣿⣿⣧⡀⠀⢰⣿⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⣿⠏⠀⠀⠀⠀⠉⠈⠙⠻⢿⣿⣿⣿⣆⣐⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢀⣠⠤⠖⠂⠈⢹⣿⣿⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⠛⠿⠿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠋⠁⠀⠀⠀⠀⢸⣿⣿⡧⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣼⡿⠃⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⣀⡀⣀⣀⠀⠀⣰⡂⡆⢀⣀⠀⡆⢀⡀⣀⣀ ⠀⠀⠀⠀⢸⡀⡁⣇⢈⡇⡏⠀⡇⢘⡇⠀⣼⠀⡇⣨⢚⡇⡿⢯⠰⡗⢚ ⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠁⠀⠁⠈⠁⠀⠉⠀⠁⠈⠉⠁⠁⠀⠁⠈⠉ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⠲⣒⠢⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠉⠉⢷⡿⠛⠋⠑⣀⣤⡶⢶⣮⡁⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⢃⠀⠀⠀⠀⢻⡄⢠⡾⠋⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⠇⠁⠀⠀⠀⠀⠈⡧⣿⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⣀⣀⣀⠀⠀⣿⣁⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠀⠀⠀⢸⡇⢤⠜⣧⠀⢸⠋⣉⠙⣧⠀⠀⠉⠛⢷⣄⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠈⠈⠷⠤⠼⠋⠈⠹⣆⣉⣠⡿⠀⠀⠀⠀⠑⠙⣧⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠠⣄⠀⠀⠀⢈⣯⠑⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⠳⢦⣄⣀⡀⠈⣳⣦⠾⠛⠁⠀⠀⠀⠀⢀⣀⣤⡼⠃⠀⠀

⠀⠀⠀⠀⠀⠀⣠⠞⠉⣩⣅⠀⠀⠀⠈⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠁⠀⠀⠙⢿⣿⣾⣿⠆⠀⠀⠀⠀⠀⢈⣉⠙⠲⠤⣄⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠺⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣤⡈⠳⡄ ⠀⠀⢠⡇⠀⠀⠀⢠⠄⠈⠉⠋⠫⢀⠀⠀⠀⠀⠐⣿⣦⣬⣭⡉⠉⠀⠀⢿ ⠀⠀⠈⣇⠀⠀⠀⠘⣷⣦⡀⠀⠀⠀⠈⠑⠠⢀⠀⠈⠙⠛⠛⠃⠀⠀⢀⡞ ⠀⠀⠀⢹⡄⠀⠀⠀⠉⠾⠛⢦⣤⣀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⡴⠋⠀ ⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣦⣤⣐⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⡠⠴⠚⠁⠈⠳⢤⠀⠀⡴⣍⠉⠛⠛⠻⠛⠁⠀⠀⠀⣠⠇⠀⠀⠀ ⠀⢠⠎⣠⠖⠒⠲⢢⠴⢯⣙⠚⢧⡘⢦⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀ ⠀⢯⡞⠁⠀⠀⣠⠞⠓⠦⡌⠁⠀⠉⠈⠻⣟⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀ ⢠⡎⡴⢠⢀⢰⠃⠀⠀⠘⢧⣀⣀⣄⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠳⠾⠞⠞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢄⡀⢀⣀⡀⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠖⠒⢖⠒⠢⠶⣶⣀⣸⠏⠀⡧⠁⠈⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⣴⠀⡀⠈⡆⠀⠀⣀⣬⣉⣳⠲⢧⣀⠀⢁⡠⠔⠲⡄⠀⡀⠀⠀⠀ ⠀⠀⠀⢼⠀⠁⠘⠃⣰⠃⠀⢰⡃⠶⠈⡿⠀⢀⣉⡷⢎⠀⠀⢠⠇⢪⠃⠀⠀⠀ ⠀⠀⠀⠘⠢⣤⠤⠞⠁⠀⠀⠀⠙⠒⠚⠁⣴⠉⣄⠑⡌⠳⡴⠋⢠⡃⡤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠁⠀⢻⠀⢠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠎⢃⠀⠀⠀⠀⠠⣀⣀⠀⠀⣸⡀⠀⠑⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⠦⠼⠀⠀⠀⠠⠞⠋⠁⠀⣰⣯⣵⠀⠀⠀⠀⠀⠀ ⢀⠠⠤⢄⣠⣄⣤⣿⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠳⡄⠀⢀⣠⣤⣤⡤⢀ ⠤⢏⡝⣯⡊⢳⣿⣿⣿⣷⣌⠉⠛⠒⢶⣶⣾⠟⠉⠀⢀⣴⣿⡝⣼⡝⢒⢤⡀⠂ ⠀⠘⢿⣤⠝⣧⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠁⠀⢀⣴⣿⣿⣿⣟⡼⣭⡛⡶⣽⠀ ⠀⠀⠀⠙⠿⠊⠙⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠐⠻⣿⣿⣿⣿⠋⠓⠧⠿⠿⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⣠⣄⠀⢸⠈⣻⡿⢧⣀⣖⡩⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡓⠦⢤⣾⣿⣿⠷⢾⠚⠁⠀⠀⠀⠉⠑⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣬⡇⠀⠀⢀⣤⣴⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠢⣈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢠⠢⠀⠀⡐⢀⠃⢀⠤⡆⡠⡀⣠⣊⣀⣀⡀⠀⠀⠑⣄⣄⠀⠀ ⠀⠀⠀⠀⢠⠃⢬⠃⣠⠊⢡⠇⡠⣊⣴⠟⢰⡿⠛⠋⠉⠉⠛⠷⣦⡀⠸⣾⠀⠀ ⠀⡀⠀⠗⡿⢰⢈⣴⣥⡶⣾⣿⣛⠯⠁⠠⠋⠀⠀⠀⠀⠀⠀⠀⠘⢻⡀⡇⠠⠀ ⠀⢡⢯⡄⢧⢸⡾⡧⠔⣶⣿⣦⢔⣄⠀⠀⠀⢀⣔⡭⣶⣿⣟⠓⠶⣄⠅⢸⣔⠆ ⠀⠀⢻⡬⣆⠈⠀⢣⡀⠻⠿⠟⢀⡽⠀⠀⠀⠻⣇⠀⠿⣿⠟⠀⡠⡹⢠⢟⠎⠀ ⠀⠀⠀⠑⠌⡜⢄⠀⠑⠒⠀⠈⠁⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠝⢊⠁⡎⠂⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠈⢆⠀⠾⢧⡤⢀⣀⣀⡀⣀⣀⣤⡀⠀⠀⡰⡱⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢡⠱⡈⢆⠀⠀⠉⠒⠦⠤⠤⠴⡋⠁⠀⢀⠔⣵⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠱⡙⢮⡢⡀⠀⠀⠉⠓⠛⠉⠀⠀⡠⡪⣺⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡶⣒⡆⠱⠈⠻⣾⣆⡀⠀⠀⠀⠀⠀⣸⠞⡱⡿⢤⣀⠀⠀⠀⠀⠀ ⠀⣀⣀⣩⣿⠈⠀⢁⠀⡇⠀⡈⠻⣿⣿⣶⣶⣶⡾⠋⢠⠁⠁⠑⣿⣷⣦⣀⠀⠀ ⣿⣿⣿⣿⣿⠀⠀⠸⡀⣇⠀⠑⡄⡀⠉⠛⠿⠋⠀⡰⠸⢠⠀⠀⣿⣿⣿⣿⣮⣆ ⣿⣿⣿⣿⣿⣧⠀⠀⠱⡸⣄⠀⠈⠌⢢⠀⠀⣀⠜⣠⣣⠊⠀⣼⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⢀⡄⠀⠀⡇⢀⣾⡈⠈⠀⠀⠀⠀ ⠀⠀⠀⢰⢻⣴⣄⠀⠀⠀⢴⣿⣉⣡⣒⣥⣢⢄⣽⣦⠀⣹⡿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣿⡌⠀⠀⠀⠀⠉⢿⣽⣿⣟⣩⣿⣿⠇⢘⣿⠵⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢆⠛⠵⣦⠀⠀⠀⠊⠀⠀⠉⠉⠻⠟⠁⠰⠟⠛⣠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣤⣃⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡹⠤⡄⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢿⣿⣇⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠔⠁⠈⣠⠬⠰⡀⠀ ⠀⠀⠀⠀⢰⡻⠘⢿⠿⣷⣤⡀⠀⠀⠈⢣⠂⢄⢰⡀⢀⠀⡀⠀⣾⡿⣠⡀⡇⠀ ⠀⠀⠀⣀⣾⠳⡑⢼⡇⠀⠉⠛⢷⣦⣄⣀⠑⠬⣢⣻⣮⣷⢷⡠⠯⡿⠏⡱⠁⠀ ⠔⠒⢉⣾⡇⢧⠙⢎⠣⡀⠀⠀⠈⣿⣿⢟⣻⠖⢲⢋⣿⠟⠻⣓⠠⠔⠚⠁⠀⠀ ⡔⠊⡼⢹⣎⣇⡱⡘⡤⡇⠀⠀⠀⣸⣵⠋⠀⣠⢾⣡⢇⣾⠀⢸⠛⠤⣀⠀⠀⠀ ⠀⢰⣷⣾⣿⣆⠧⠇⡟⠃⠀⠀⢠⣿⢁⠔⡞⡡⡎⣹⣾⡏⠈⢺⣆⠀⠀⠉⠒⠢

⠀⠴⠶⠶⠿⠿⠿⠃⠀⠀⠸⠛⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀ ⠀⠨⢤⣀⡀⠀⠠⠀⠀⣀⣴⠦⠭⠙⠒⠂⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠙⠻⣿ ⠀⠁⣘⣗⡒⠛⠛⢋⣉⠥⠤⠤⣄⡒⠲⠶⠤⠤⠀⠀⠀⠭⠭⠭⠠⣐⣲⣤⡀⠘ ⠀⢄⠀⠀⡫⠭⠭⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡻⠀ ⠀⠀⢠⠊⠑⣀⣀⠠⠄⠀⠒⠂⠀⠈⠉⠉⠉⢿⣿⣿⣿⣿⣿⠿⢷⣶⣶⡖⠡⠄ ⠀⠀⡸⠀⢘⠌⠀⠀⠀⠀⢀⠶⢄⡀⠀⠀⠀⠈⠻⣿⣿⡿⢃⣴⡄⣿⡿⠉⢆⠀ ⠀⢐⠃⡠⠛⡗⡀⠀⠀⡰⠋⠀⠢⠑⡀⠀⠀⠀⠀⠈⠉⣴⡍⠈⡘⣿⣷⠤⢌⡄ ⢔⣁⢴⣅⢀⣜⡆⠀⢸⣷⢀⡠⠖⠉⠁⢢⠀⠀⠀⠀⠀⣿⠃⢊⣼⣿⣿⣄⠀⠈ ⠁⠀⠀⠙⡏⢄⣁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⣴⠟⠁⠈⠙⢿⣦⠀ ⣀⠀⠀⡠⠋⠄⢙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠘⣿⡆ ⢄⠉⠉⠀⠐⣐⡈⠁⠐⡲⠲⣶⣶⣦⣤⣄⠀⠀⠀⠀⣿⢫⠆⠀⠀⠀⠀⠀⢻⡇ ⠀⡆⠀⠀⠀⠀⠉⠉⠽⡺⠿⠿⠿⠿⢭⡿⠃⠀⠀⢠⠃⠀⣾⠀⠀⠀⠀⠀⢸⠁ ⢀⠃⠀⣴⡈⠐⡄⠸⣤⣤⡄⠀⠠⠀⠀⠀⠀⡀⣴⣅⠀⠀⢸⡀⠀⠀⠀⢀⠎⢀ ⠁⠀⠀⢄⣀⣴⠇⢰⠁⠁⠀⠀⠀⠀⣀⢄⠊⠀⣯⢣⡱⡄⠀⡇⠀⠀⡠⠂⣠⢊ ⠁⠢⡀⠀⠀⠀⠀⠈⠢⠤⠤⠄⠂⠉⠀⠈⠑⢁⢤⠑⠟⣴⣀⠤⣒⣉⡤⠖⠋⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠤⠐⠒⣉⠉⠀⢔⢏⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠩⡀⢟⣔⣉⣁⡐⣮⢊⠤⠖⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⠸⠏⡍⠘⢅⠀⠀⢙⠼⠯⠄⣂⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡀⡆⢀⠀⠀⡈⠝⡏⢹⣏⣱⢒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢅⣶⢾⡦⡊⠀⠐⠏⡎⠓⡅⢀⠃⠀⠀⠀⢀⠄⠒⢢⠀⠀⠀ ⠀⢠⡽⡉⢉⢦⣀⠈⠀⠁⠀⠾⡐⣠⠀⠀⠀⡎⠀⠀⠀⡁⠀⠀ ⠀⡦⠄⢸⡉⢝⣉⣐⣻⠤⠷⡴⣴⡏⣉⡓⠲⣧⣠⣀⣷⠁⠀⠀ ⠀⢿⣿⡞⣶⣶⣿⣿⣿⣿⣿⠃⠀⠀⠉⠑⠛⢡⠄⡨⠿⠀⠀⠀ ⠀⠀⠈⠿⣿⠇⠀⠻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡌⠑⠵⠀⠀ ⠀⠀⠀⠀⢹⣠⣤⠄⢸⣴⡖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢡⠀ ⠀⠀⠀⠀⠘⠛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⣄⠀⠈⠙⠻⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠲⠁⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣆⡄⣀⣤⢠⡄⢠⣰⣧⣀⠀⠀⠀⠀⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠿⣿⣷⢿⢿⣿⡿⠿⠿⢿⠋⠀⠀⠾⡄⠀⠀⢀ ⠀⠀⠀⠀⣀⣤⠠⢤⠂⡌⠀⠐⠀⠀⠀⠮⠀⠀⠀⠌⠀⠀⠀⠰⠈⡆⠀⢠ ⠀⠀⡄⠸⡄⠈⢆⡨⠀⢁⠀⠀⢀⠇⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⣡⣴⠁ ⣴⡉⠳⡀⠘⣆⢘⣧⣁⠈⠀⠐⠁⠀⣄⢀⣐⡀⠑⣄⠀⠀⠀⠀⢜⣸⠇⢀ ⣿⣿⣦⡙⣤⡛⣧⡈⠻⠠⠂⠐⠆⠉⢈⡉⠀⠉⠐⡼⠁⠀⠀⠀⠿⠃⣴⠎ ⠣⠎⠙⠛⠾⢷⠘⢧⡀⠠⠄⢸⠀⠀⠒⠒⠀⠒⠈⠀⠀⠀⢀⠆⠠⡸⠃⢼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⣤⡀⣠⠈⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⡦⠀⠀⠀⠀⢞⠁⢀⡀⠄⠜⠟⠙⡷⠋⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠊⠉⠉⠀⠀⠢⣹⡼⣧⣤⣼⣗⠒⠨⢥⣀⠦⡀⡆⠀⠀⠀⠀⠀⠀ ⠀⢰⡀⠠⡀⠀⠀⠀⠀⡰⠂⡸⠀⠸⠄⣠⣙⠇⠲⡟⢻⢿⡗⡰⢠⠀⠀⠀⠀⠀ ⠀⠆⠳⢄⠀⠢⡠⠄⢺⠉⡿⢿⣿⣴⣶⣄⠃⠀⠀⠁⣀⢘⡞⡧⢴⡆⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠉⡗⣒⠤⢭⣧⡠⢇⠁⠈⠛⠑⡒⠒⠟⢻⣟⠛⠂⠴⣿⣒⣠⠴⡄ ⢸⠀⠀⠀⢀⡴⠉⢀⠔⠁⠀⠹⣦⣌⠀⠐⠦⠤⠤⠠⠈⡹⠀⠀⠀⡈⠎⢀⣼⠁ ⠈⣇⠐⣤⣁⠀⠀⠘⢤⡀⠀⠀⠐⡙⠒⠀⢠⠤⢄⡤⠊⠀⠀⣸⠏⠀⡠⠿⠁⠀ ⠀⠈⠑⠪⢿⣿⣦⣄⣾⣿⣶⣄⠀⠈⠉⠉⢈⡯⣍⠀⠀⣀⣴⣿⣏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡯⡙⠻⡿⣷⠿⡤⠔⠋⢱⡈⣉⣿⡿⣿⣟⢼⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢻⠲⠥⣲⡈⣗⢝⠉⠉⠙⡃⢀⣸⣿⡇⣿⢾⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣬⣧⣯⢻⣗⣒⣾⣷⣍⣽⢿⠟⠛⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⢻⡉⠁⠀⠺⣿⡿⢿⣿⣿⣿⣿⡿⣯⢐⡯⠀⣱⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠐⠤⣢⠝⠀⠀⠀⣀⠤⠄⢒⣽⣃⣠⠖⣁⠀⠀⠀⠀

⣿⣾⡟⠀⠀⠀⣼⠀⡠⠉⠀⣀⠀⠀⠀⠀⠀⠀⠘⢞⣦⠀⠀⠀⠀⢡⠀⠀⠀⣀ ⢃⣸⠇⠀⠀⠀⡿⡔⠀⠀⢇⣣⠾⠷⢀⠤⠒⠨⣇⠈⢯⢆⠀⠀⠀⠀⢂⠀⢀⠀ ⡼⣿⠀⠀⠀⢠⠠⡇⡠⠤⠤⢉⣁⣠⡢⢈⣠⠤⠍⠀⠈⢮⠢⠀⠀⠀⠀⠈⠿⠥ ⠀⣸⢰⡿⠃⣼⠀⠃⠊⣉⣁⠒⠒⠊⠐⡷⠂⠀⠀⠀⠀⠈⢳⡑⣄⠀⠀⢂⠀⠀ ⠰⢻⡜⠀⡰⠀⣠⣾⡌⠀⠈⠓⠄⠀⠀⣤⣒⣀⠀⠀⠀⠀⠀⠑⢿⢦⡀⠘⠄⠀ ⣤⡘⠀⡰⣥⣄⠙⢿⣷⣄⣞⣿⠎⡀⠀⠓⠛⠉⠀⠀⠀⠀⠀⠀⢾⣦⣏⡲⠃⠀ ⣼⠁⡠⢿⣿⣿⣶⣤⣽⣇⠀⠀⢀⡧⣤⣤⠀⠤⡰⠚⠃⢀⡀⠀⢸⠉⠀⠳⣀⠀ ⣿⠊⠀⠀⠿⣿⣿⣿⣿⣿⣦⠀⠂⠻⢿⠃⠀⢀⣿⣿⡟⠛⠰⠆⡎⠄⠀⠀⠙⠀ ⠀⠀⠀⠐⣰⣿⣿⣿⣿⣿⣿⣶⡱⢶⣞⡳⢶⡻⡟⠀⣧⠀⠀⣰⠁⠈⠄⠀⠀⠀ ⠀⠲⠀⠀⠢⠈⢿⣿⢿⣿⣿⣿⣿⣮⣏⠾⠳⠟⠀⢀⠛⠀⣰⠃⠃⠀⠐⠀⠀⠀ ⠖⠌⠀⠲⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠇⣄⡀⠐⠒⢁⡸⡾⠁⡘⠀⠀⠀⠀⠀⠀ ⣁⠀⠀⣀⣴⡄⣀⣾⣿⣿⣿⣿⣿⣿⠟⠂⠉⠛⠛⠂⠁⢀⠔⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠁⠀⠐⠢⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⣑⠤⠄⠐⡲ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠉⠀⠀⠀⢀⣠⠄⡁⠀⠀⣠⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠒⠀⠆⡔⣽⣶⠄⠐⢹⣾⡇⠁⠠⢪⡂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠄⢈⠻⠟⠀⠀⠀⠉⠁⢠⢤⠄⠒⠁⠀ ⠀⠀⠀⠀⡀⠄⠒⠒⠐⠒⠨⢍⠀⠘⣄⡀⠀⠤⠶⢀⡤⠒⠛⠀⠀⠀⠀ ⠀⠀⡴⠁⠀⠀⠀⠔⠀⠀⠀⠀⠈⠢⡀⠀⢉⣰⠊⢰⡂⠀⠀⠀⠀⠀⠀ ⠀⠎⠃⠀⠀⡔⠁⠀⠀⣀⣀⡀⠀⠀⠑⣴⢋⠀⢠⠃⠀⢣⠀⠀⠀⠀⠀ ⢸⠀⡄⠀⢰⠀⠀⡠⠋⠁⠙⢿⣣⠠⠤⢙⣇⡀⠎⢸⠀⢸⠀⠀⠀⠀⠀ ⠘⡀⠡⠀⢸⠀⠰⠀⠀⠀⠀⠀⢧⠷⠤⠀⠈⢂⠀⡘⠀⢸⠀⠀⠀⠀⠀ ⠀⠐⢄⠱⡀⠆⡇⡀⠀⢀⠠⢊⠐⠑⢠⠀⠀⠀⠫⡇⠀⡈⠀⠀⠀⠀⠀ ⢦⠶⠬⠑⠊⠮⡧⠚⠩⡀⠈⠁⠀⠀⡐⠑⢄⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀ ⠀⠈⠒⠀⠐⠊⠀⠀⠀⠀⠑⠂⠐⠁⠇⠀⠀⠁⠢⠄⡌⠀⠀⠀⠀⠀⠀

⠀⡀⠀⠀⣧⠔⡢⠄⠠⣠⠹⣿⠋⠈⠿⣿⣾⣶⣾⡧⠶⠀⡀⢀⢀⠀⠀⠀⠀⠀ ⠧⠬⠃⠀⠻⣦⠒⠂⠀⠘⣮⡈⢁⣢⢘⣽⡟⠉⠈⠁⡠⡕⣆⣧⠿⠵⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⣄⡇⠀⠙⣦⡳⡭⠤⠤⣤⣖⡩⢶⡇⡟⠀⢜⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⢸⣿⣿⡇⢆⠤⠚⢳⠀⠀⢰⡣⢁⣀⣸⢱⣖⡁⠼⠤⠴⠚⠁⠀ ⠀⠀⠀⣀⠤⠚⠚⠁⠀⣹⣬⠤⡀⠀⠀⠀⠀⠀⠀⢈⣿⠃⠈⢳⡤⠤⠂⠐⠂⠠ ⠀⠀⠀⢀⠀⢀⣤⠶⣴⣿⠒⣭⣊⡄⠀⣠⣾⣛⡠⡘⢅⢠⡁⠀⠹⠚⠣⠁⠀⠀ ⠀⠈⠀⠀⠀⣼⡏⠀⣿⣟⡛⢯⣿⠇⣾⣿⣿⣤⣼⣿⠎⠈⡿⠿⠿⣇⠠⣤⣤⡄ ⠀⠀⠀⠀⠀⣿⣇⠀⠻⣽⣮⡵⣿⣖⣿⡟⢕⣋⣩⡿⠀⠀⠀⠀⠀⢹⠀⠀⠉⠁ ⠀⠀⠀⠀⢰⣿⣿⣶⣄⡠⠔⠋⠉⠉⠋⢝⠓⠒⠊⠀⠀⠀⠀⡆⡄⡼⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⢋⣀⣄⡈⠀⠂⠀⢄⠑⢄⠀⠀⠀⠀⠀⣇⢧⠛⡄⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣸⠉⠀⠉⠉⠉⠳⠤⡆⠈⡆⠀⠀⠀⢠⡏⡎⠀⡇⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠠⠔⠁⢜⡎⠀⠀⢠⡎⢰⠃⠀⢻⠀⠀⠀ ⠀⠀⠀⣿⡇⢻⠟⠛⠟⢿⣿⣦⠀⠀⠀⣀⣤⣮⣄⣠⣶⣿⣄⣼⠀⠀⢸⠀⠀⠀ ⠔⠂⠀⣿⡇⣼⠀⠀⠀⠀⣀⡟⠙⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠟⣀⡘⢆⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⣾⡉⠉⠳⠃⠈⡄⠘⢷⢄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠔⢁⡬⠛⠉⠑⠄⠀⠃⡀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠀⢀⠎⠀⠀⠀⣀⡸⡀⠀⢈⠀⠀⢰⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀ ⢀⢀⠜⡠⠀⠔⠉⠀⠀⢠⠊⠀⠄⢓⣀⡘⢀⠂⡌⠱⡀⠀⠀⠀⠀⠀⠢⡀⠀⠀ ⠘⠂⠴⠣⠸⠀⠀⢠⣴⡡⠄⡬⠊⡔⡡⠃⢸⡀⡏⠀⠈⠢⠀⠀⠀⠀⠀⠡⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠀⣀⣆⢀⣐⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢟⣮⣁⣾⠟⡩⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢟⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈ ⢿⣻⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢀⣠⠴⣺⢷⡋ ⠀⠉⠛⠳⣯⣓⣦⣀⡀⠀⠀⠑⣦⠀⠀⠀⡌⠀⠀⠀⠀⣀⣴⣾⣿⢚⠋⢏⠁⠀ ⢐⣩⣥⣶⠶⢿⣿⣿⣿⣷⣦⡤⣼⡇⠀⢸⣥⣤⣴⣾⣿⣿⠿⠶⠶⢶⣮⣭⡂⠀ ⠛⢉⡀⠀⠀⠀⠀⠀⠉⠻⠄⠫⠟⠀⠀⠈⠉⠉⠰⠋⠁⠀⠀⠀⠀⢀⣠⡿⠻⠟ ⠀⠘⢿⣶⣤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠄⣲⣾⣿⠟⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣷⣤⣈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣛⣋⣉⣛⣋⣉⣍⣉⣩⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢰ ⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣾ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠲ ⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀ ⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⢇⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣹⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠐⠒⠒⠂⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⡪⠓⠈⠀⠀⠀⠀⠀⢠⠤⠨⢕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠮⠚⢁⣀⠀⠀⠀⠀⢐⢄⣻⠀⠀⠀⠙⠚⢻⠇⠤⢄⠀⠀⠀⠀⠀ ⠀⠀⢀⠢⢁⠎⠉⠀⠉⠁⠢⢄⡀⠀⠹⡄⠀⠀⠀⠀⠈⠋⠹⣛⣒⠢⡀⠀⠀ ⠀⠀⠸⡄⡆⠀⠀⠀⠀⠀⠀⠀⣱⡄⠀⠈⠒⣢⣄⣀⡀⠀⢐⡀⣐⣴⣧⣧⡀ ⠀⠀⡖⢠⠀⠀⠀⠀⠀⠀⣦⣞⠁⠓⣾⡄⠀⣈⣒⣳⣟⣐⠀⠀⣀⣒⣿⣿⡇ ⠀⢰⢧⣿⣄⡀⠀⠀⠀⢀⡟⠉⡉⢢⠘⣷⡌⠧⣀⣘⡓⢲⣍⣿⣿⣿⣿⣟⠀ ⠀⠈⢫⢈⣧⡛⢦⣤⠴⠞⢧⣀⣀⠜⣡⣿⣄⡀⠈⣶⡗⣰⣿⣿⣿⣿⡿⣫⣶ ⠀⠀⠊⠤⣼⡷⠊⠀⠀⠊⢐⠤⢄⠰⣿⣝⣍⢡⣶⣿⣚⡿⣿⠿⣻⣯⣿⣿⣿ ⠀⣸⢴⡱⠋⠀⠀⢀⡠⠶⠅⠂⢁⡠⢝⠟⢹⣆⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⠊⠀⠀⣠⣴⣿⣷⣦⣬⠍⢒⠔⠁⠀⣈⠹⡟⠓⢲⡉⢻⣿⣿⣿⣿⣿⣿ ⡠⠁⢀⡠⠚⠻⠿⠛⢛⢟⡙⠋⢙⠬⠒⠉⢨⣀⠜⠀⢀⡇⢸⣿⣿⣿⣿⣿⣿ ⠧⠔⠁⠀⠀⠀⢀⡔⡥⢋⡱⠊⠙⡄⠀⡠⠺⠇⠀⠀⢸⡄⢺⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢠⠎⡔⠋⠡⡀⣀⠤⣹⠎⠀⣀⣔⢚⠉⢯⣉⣙⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠳⢶⢶⣖⡹⠴⠚⢉⣴⠞⠡⠂⡡⠂⠁⠘⡄⠫⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⡤⠄⠀⢰⣶⡆⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⠉⠉⠀⠐⠆⠀⠀⠀⠀⠲⠶⠶⠒⠚⠻⠷⣶⣤⣦⣤⣶⣶⣶⣶⣶⣆⣦⣀⣀⡆⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⠀⡤⡤⠀⣀⠈⠉⠉⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠘⠁⣠⠿⢛⣛⣓⣶⣛⡛⢿⣏⠀⠛⢁⡾⣭⣀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡇⠀⣼⠀⠀⠀⠀⠁⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⡀⣴⣋⣵⠾⠛⠛⠛⠛⠿⢭⣶⣝⣦⠖⢋⣥⣤⣽⣿⣭⣍⠓⠒⣶⠒⠀⠹⠦⠃⢠⡟⢀⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣿⠁⠀⠀⠀⡿⠁⣿⡥⠒⠀⠀⠀⠀⠀⠀⠱⠶⣿⡷⠚⠉⠁⠀⠀⠀⠉⠳⢽⣆⠻⣇⠀⣰⡄⠀⢸⠀⢿⡀⠘⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣇⠀⢠⣾⠃⠀⠀⢙⠦⣀⡀⢀⡤⠖⠋⠙⢳⠿⢾⡁⠀⠀⠀⠀⠀⠀⠀⢦⡙⣦⣻⢀⣍⠀⠀⢸⡇⠈⠛⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠈⠟⠀⠀⠀⠀⠉⠃⡼⠋⠀⠀⣠⠞⠛⠁⠀⠹⣗⡤⠤⣀⣀⡀⠤⠬⠷⠾⠁⠙⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⡴⠋⠀⣶⡖⠲⣄⡀⠉⠓⡒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠂⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⣴⣯⣿⡀⠀⣼⣅⣤⣰⣿⠀⠀⠀⣿⣦⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⢠⠞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠅ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⢠⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⣸⠇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢠⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⠀⠀⠀⠀⠀⠀⢠⡏⠀⣇⠀⠀⠀⠀⠀⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⣿⣿⣷⢀⣤⠏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣇⠀⠀⠀⠀⠀⠸⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⢠⣿⣷⣏⠈⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠁⠀⠈⠙⢿⣿⣿⠀⠙⣶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣤⣦⣀⣀⣀⣀⣤⣤⣶⡾⠧⠤⠤⠴⠾⠿⠿⢿⡟⠀⠘⡀⢸⣿⣿⣿⣿⣉⣉⣉⣉⣀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠹⣿⠀⠀⠈⠀⠀⠀⢀⣴⣇⣤⣴⠄⠀⠀⠀⢠⡇⠀ ⠀⢠⣾⠟⢛⢋⣉⣉⣡⣤⣤⣤⣤⡴⠶⠾⠶⢷⢷⣾⣿⡇⠀⣠⢇⠘⣿⣿⠏⠉⢹⠉⠉⢹⠉⠉⢹⡟⠋⠙⢻⠛⠲⣦⠀⢀⡇⠀⣀⣠⣤⠶⠞⠛⢉⣀⣴⠾⠇⠀⠀⠀⠘⠀⠀ ⠀⠀⣿⣷⣌⠛⢿⣯⢀⣤⢼⡿⢿⡿⢶⣤⠀⠀⠸⣿⣿⡇⠀⢿⠸⡄⠹⣿⠀⠀⣼⢀⣠⠾⠓⠒⠲⢧⣀⠀⢸⠀⠀⣿⣠⣿⠶⠛⢋⣉⣤⠴⠚⠛⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠙⢻⣿⣷⣦⡉⣿⢡⠈⢧⠀⢧⠀⢹⣦⣀⠀⣿⣿⠃⠀⠀⠀⠻⣄⠉⠳⠤⠿⠋⠁⣰⠀⡇⠸⠀⠉⣳⣾⠶⠚⢉⣡⣤⡶⠚⢏⠉⢀⡄⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⠹⣿⠛⠻⢶⡾⠖⠛⠶⠾⠷⠶⠿⠿⠿⣤⣤⣤⣀⣀⣈⠛⠲⠖⠀⠀⠴⠃⣀⣧⠴⠟⠋⣁⣤⠶⠿⠭⠴⠚⠁⠀⠀⠉⠉⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⡉⠉⠙⠛⠒⠒⠒⠒⠲⠶⠶⠤⠤⠤⣤⣭⣭⣉⣉⣩⣝⣛⣒⠛⠿⠦⠴⠾⢏⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣛⣛⣓⠤⢤⣀⠀⠀⣠⠞⠃⢀⡀⠀⠀⠀⠘⣯⠙⣟⠛⠛⠒⠒⠾⠿⠶⢦⣀⣈⣩⣭⠛⠛⠒⠲⠤⣤⢤⣄⣴⣿⠤⢤⣤⠤⠤⣤⣇⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠉⠉⠓⢶⣭⣳⡞⠁⠀⡴⠋⠀⢀⡀⠀⠀⠘⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠒⠲⠭⠿⢤⣿⠤⠤⠤⠧⠤⠤⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢘⡟⠀⠀⠈⠀⠠⠖⠋⠁⠀⠀⠀⠹⡆⢿⢀⣉⣉⣉⣙⡒⠒⠲⠦⣤⣀⠀⠀⠀⠀⢀⣀⣠⣤⣿⡤⠤⠤⠤⠴⠴⣿⡇⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⢻⡈⣧⠀⠀⠀⠀⠉⠉⠉⠓⠲⢌⣹⠶⣺⣍⡽⠷⠶⢶⠟⠒⠒⣶⣟⠁⠈⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⢻⣳⣖⣻⣶⣤⣀⣀⣀⣤⢴⣿⣯⣶⣶⣶⣤⣷⡘⣦⣀⣀⠀⠀⠀⠀⠀⢠⠞⡵⠚⠉⠀⠀⠀⠀⢸⡇⠀⠀⠙⠛⠁⠀⠹⡟⣇⠀⠀⠀ ⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⣠⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⣧⣾⣧⡤⠤⣤⣀⣀⢀⣸⣄⣀⣀⣤⠤⠤⠤⠾⠿⠿⠷⠦⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢃⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⠋⣰⠟⠞⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⢡⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⣦⡙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⣦⣙⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⢠⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣳ ⡿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠈⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⣿⣿⣿⣿⡇⢀⠖⠉⢸ ⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣼⡀⠀⣀ ⢤⡤⠀⠀⠀⣤⣾⣿⣿⣿⡿⡥⣤⣤⣶⡶⣶⣦⣤⣤⣬⣿⣤⣤⣤⣴⣿⣥⡤⠤⢤⣤⣤⣿⣷⣴⠦⢤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢀⣀⣉⣿⣿⣿⣿⣿⡾⣾⣿⣿⣿ ⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣀⠉⠉⠉⠉⢁⣛⣺⣿⣿⣷⣿⣿⣾⣿⢥⣶⠠⡎⢠⣾⣿⢶⣼⣇⢿⡧⠀⢰⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠉⠁⠘⠻⠃⣿⣿⣿ ⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢿⣿⡟⣻⠿⢶⣽⡞⣷⣤⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣇⣀⣘⣷⣿⣿⣿⣷⣦⡄⠘⠹⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣷⣿⣷⣾⣯⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠉⠻⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣷⣘⡛⠻⠶⣞⣫⣿⡿⢿⣿⣿⣦⣛⣉⣈⣁⣀⣈⣁⣙⣷⡀⣟⣹⣿⣿⣿⣧⣤⣀⣀⣾⣿⣿⣿⣿⣿⣿⣇⠀⠀⠠⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢽⣷⣦⡼⠟⣉⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⣹⡿⢻⣿⣿⣿⣦⡀⠀⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣀⣭⡶⠟⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣆⣠⡿⠃⠀⠛⣿⣿⣿⣿⣄⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠈⠀⠨⡝⠻⣿⣿⣿⣿⣿⡍⠀⠈⠀⠀⠈⠿⣿⣿⣿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣯⢩⣭⣶⣿⣾⣿⣿⡿⠋⠂⠀⠀⠀⠉⠲⣄⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⡟⢲⣤⡙⢿⡿⣿⣷⣤⣀⡀⠀⠀⠀⠙⣿⡟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⣻⠏⠀⣠⣦⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠀⠀⠀⠠⠴⣶⣦⣈⣛⣛⡋⠀⠀⠀⠀⠸⡟⣿⣄⠀⠀⠀⠈⠉⠙⠻⠶⣶⣤⠄⣥⢀ ⣿⣿⣿⣿⣿⣿⣧⣯⣽⡿⠟⠁⠀⠀⠀⠀⢀⡼⠁⢀⡞⠙⠙⣧⠀⠀⠀⡀⠀⠙⠛⠋⠀⢀⡴⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⢸⡗⠉⢻⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢫⣿⣿⣿⣿⣿⣿⣟⠑⠀⠀⠀⢀⣤⡤⢶⣿⡃⢠⡟⠀⠲⢤⣟⣷⡀⠀⠈⠢⠤⠀⠀⠒⠋⢀⣼⣿⣟⣾⣏⣿⣿⣿⣽⣿⣷⠀⠀⠘⣧⡀⠀⠀⠀⠉⠳⠦⣤⣤⡴⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⡀⢰⣴⣿⠿⠚⠉⢸⣡⡿⠁⠀⠀⢀⣾⣧⡻⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠂⢀⢼⡏⠳⢦⣄⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⠽⣮⣧⠋⠀⠀⢀⣠⣾⠟⠁⠀⢠⣾⠞⠈⠻⣿⣾⡷⣄⠃⡀⠀⠀⠀⠀⠀⠙⠻⡿⠿⠻⣿⣿⣿⣿⡇⠀⣠⣟⡇⠀⠀⣽⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠯⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠙⢻⣿⡟⠦⣤⣀⣀⠀⡀⠀⠾⢿⣋⣿⡿⡿⢿⣥⣶⡾⠏⢱⠃⠀⢀⡟⠀⠈⢻⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⣸⣿⢿⣟⣿⡿⠙⠋⣀⣶⣤⣼⣿⡿⠃⢠⠏⠀⢀⡼⠙⠛⠳⢦⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢿⡌⠛⠛⠛⠻⠿⠿⠛⠋⠡⠞⠋⠀⠀⠋⠀⠀⣾⠁⠀⠀⠀⠐⠁⠙⢷⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⣄⣰⣤⢀⡞⢹⢷⣤⠀⠀⠀ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢯⣧⡼⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣡⣿⣿⠈⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⠿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⡏⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢻⣇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⢻⣦⡀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣶⣄

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠁⢀⣀⣀⠀⠀⠀⣀⠀⢀⡀⢀⠀⠀⣀⠀⠀⠀⠀⠀⣼⣟⡀⠀⣿⠀⠀⠀⣀⢀⠀⠀⠀⣿⠀⠀⣠⡀⠀⠀⣀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠻⠀⣴⡿⠛⠛⣷⡄⠀⣿⡟⠛⠁⣾⡟⠛⢛⣷⠀⠀⠀⠈⢻⡟⠉⠐⣿⠀⠀⢻⠋⠛⣿⠀⠈⣿⢠⣴⡿⠋⢠⣾⠟⠛⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⣿⡏⠀⣿⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⣾⡇⠀⢠⣿⠀⠀⣴⡾⠟⢿⡇⠀⣿⡾⢿⡄⠀⢸⣿⠛⠛⠛⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣼⠀⠙⢷⣦⣴⠿⠁⠀⣿⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⣿⣧⠀⠈⣿⡆⠘⣿⣤⣴⣿⠇⠀⣿⠁⠈⢿⣦⠈⠻⣧⣤⣴⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢻⣶⣄⣀⣙⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⣿⣷⣼⣿⣿⣿⣿⣿⡿⠿⢦⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠚⣻⣿⣿⠛⠉⠀⠀⠀⠀⠘⣓⣤⣶⣿⣿⣿⡿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⢀⣼⣿⣿⠛⠉⠀⠀⠀⠀⠀⠙⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⢙⣿⡆⠀⠀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣷⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠛⠛⠋⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠐⣿⣿⣧⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠉⠀⠉⠹⣿⣷⠀⠀⠀⢠⣶⣿⡿⠟⠛⠻⣿⣿⣤⠀⠀⠀⠛⠛⠛⠿⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⠀⢸⣿⠀⠀⣶⣶⡄⢹⣿⡆⠀⠁⣰⣿⡏⠀⠀⣀⣀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢬⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢼⠀⢻⣿⣄⠀⠘⠛⠀⣼⣿⡇⠀⢠⣼⣿⣇⠀⠘⣿⠿⠀⠀⣿⣧⡇⢸⠀⠀⠀⠀⠀⠀⠘⢾⡻⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣿⣷⣦⣤⣾⣿⠟⠀⠀⠈⠇⢻⣿⣦⠀⠀⠀⣀⣴⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠛⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣌⣰⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⠿⠿⣶⣷⣶⣖⡒⠀⠀⣀⣈⣙⣛⢻⡛⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠉⠉⠉⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⠀⢀⣀⠀⠆⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⣱⠏⠁⢀⣯⣭⣙⠒⠦⣄⠀⠀⣀⣠⡤⠤⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣴⡿⠿⠿⣿⣷⣦⣨⡳⡄⢻⠀⠀⠀⢀⡀⣳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⣀⠀⠀⠀⠉⠀⠀⠀⣀⣽⣿⣿⣿⣿⣾⣷⣶⣾⣿⣿⣆⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⣀⣥⣄⣀⣀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠶⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⣼⡟⠉⠟⠛⠛⠛⠿⢿⣯⣹⣿⣿⣿⡿⠛⠙⠛⠛⠛⠛⠿⣄⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⣴⢋⠸⠏⠀⣀⣀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣤⣶⣶⣧⣀⣤⣴⣿⣷⢿⣷⣶⣄⠈⢳⡀⠀ ⠀⣼⢣⡞⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣾⣿⣛⣯⣭⣽⣷⣶⣶⣬⣼⣿⣿⣿⡇⠀⢳⠀ ⢰⣧⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⢘⡃⠀⢸⡇ ⠸⡟⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠁⠀⠙⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⠟⠀⠀⠀⠘⠃⠀⢸⡇ ⠀⢻⡄⠀⠀⠀⠀⠙⣿⣿⣿⣀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀ ⠀⠀⠙⢦⣀⠀⠀⠀⠻⠿⠋⢻⣦⣤⣤⣾⣌⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀ ⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣤⣤⡉⠉⠋⠉⠉⠀⣀⣀⣠⣤⣴⣾⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠛⠛⠛⠋⠉⠉⠉⠀⠈⣻⡆⢀⣠⡴⠶⠶⠶⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡋⣀⠐⠀⣣⣤⣽⡆⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⠀⠛⣦⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣟⠁⣠⡶⠟⠋⠁⣺⡇⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⡘⣆⡀⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⡿⠋⠀⠀⠀⣠⠟⠀⠀ ⠀⠀⢠⣿⣿⠿⠋⠉⠛⠿⣿⣿⣿⣿⡏⠉⠛⠋⠉⠉⣼⣿⡍⣰⡿⠁⠀⠀⢀⡠⠞⠁⠀⠀⠀ ⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣀⣀⣀⣠⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣉⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠴⠒⠶⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠉⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡇⣿⠀⠀⠀⢸⣿⣿⠇⠀⠀⠈⠙⣧⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣘⣿⣉⣀⡴⠶⢦⠀⠈⢷⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣿⣾⡟⠉⡄⠨⢭⣷⣶⣾⠃⠀⠘⣇⠀⠀⠘⢯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣄⣀⣀⣠⠴⠛⠁⠀⠀⠀⢿⠄⠀⠀⠈⢿⣯⠽⣦⣄⠀⠀⠀⠀⢀⣠⠴⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡟⢷⣶⣿⡷⠶⠒⢶⡋⠀⠀⠠⣼⣆⠀⠀⠀⠀⠙⢦⡈⠉⠙⠒⠒⠊⠉⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⣼⡿⠟⠉⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠙⠳⡀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠠⣄⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠈⠙⠶⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠅⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⠉⠀⢻⡀⠀⠀⠀⠀⡏⠀⠀⡼⠀⠀⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⢚⡿⠃⢀⡆⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢰⠀⠘⠳⣄⠀⠀⣰⠇⠀⠀⠇⠀⣸⡇⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⢀⣴⠋⣠⠟⠁⣠⡾⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⡞⣀⡤⠶⢻⡷⠚⣷⠀⠀⡾⠀⢀⣿⣄⡀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠈⠛⠺⠷⢤⣤⡟⣧⣀⣤⣿⠀⠀⠀⠀⠀⢀⣠⡶⠟⣀⣠⠄⠀⣀⣟⣴⠋⢠⠞⠋⢠⣴⡏⠀⢀⣿⠀⠀⣿⠀⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠰⠿⠷⢶⣯⣅⣠⠶⠞⠛⠉⠀⠀⣯⣀⣴⡏⢸⡁⠀⢸⡿⣇⠀⠛⣆⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠿⠶⠿⠃⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀⠀⢷⡀⠀⠳⡄⠈⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣄⣷⣀⢀⣹⣄⣸⣇

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⠀⢀⠀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡿⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠠⠤⠤⠠⠤⠀⠀⠀⠀⠀⠠⠤⠄⠀⠒⠒⠒⠀⠀⢀⣲⣿⣶⣶⣶⣦⣄⡀ ⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⡴⠶⠾⠛⠋⣉⣁⢀⠀⣀⡀⠤⠄⠀⠀⠀⠤⠤⠴⠶⠶⠶⠦⠤⠠⠖⠲⠶⠾⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣠⠿⣦⣀⠀⠀⠀⠀⠀⠀⢠⠶⠃⠀⠀⠀⠀⠀⣐⣾⣋⣥⣤⠴⠶⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿ ⠀⠀⠴⠁⠀⡟⢯⣉⡛⠛⠳⠶⠶⢤⣾⣶⣦⣤⡴⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⢻ ⢦⠀⠀⠀⠀⠙⠾⣯⠉⠛⠒⠒⠛⠛⠉⠉⠁⠀⠀⢀⣀⣀⣐⣲⣤⣤⡤⠶⠖⠒⣛⣛⣋⣭⣭⣭⣥⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣄⣀⣈⠉⠉⠙⢻⣶⣦⣄⡀⠀⢀⠏ ⠀⠀⠀⠀⡗⠒⢲⠾⣷⡦⣄⣀⣀⣀⣠⡴⠶⠞⠋⠉⠉⢁⣀⣀⡤⠶⠶⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣦⠌⠀ ⠀⠀⢠⠀⡇⠀⠃⠀⠘⢧⣀⡀⠀⠀⢀⣀⣠⠴⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠀⠀ ⠀⠀⠈⢷⡇⠀⠀⠀⢀⣿⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⠾⠋⠹⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠤⠔⠒⠒⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣞⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⢹⡦⣤⣤⡤⠖⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⡃⠀⠉⠐⠒⠒ ⠀⡀⠀⠀⠀⣾⡇⠀⠀⢀⡟⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⠀⠀⢹⣿⣿⣿⡟⠻⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⢼⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠏⠀⣠⣿⣿⣿⠃⢸⣿⣿⣿⠃⠀⠈⠳⡀⠀⠀ ⠀⠀⠀⠀⣼⡟⠀⠀⠀⣷⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠂⠤⣀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠛⠁⣠⠴⠛⠉⠋⠁⡆⢸⣿⣿⣇⠀⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⢈⡟⠀⠀⢠⡾⠋⠙⢇⠻⡄⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠙⢧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀⠀⢠⠇⣾⣿⣿⣿⣷⠲⢦⣄⣸⡇⠀ ⠀⢀⡴⠋⠀⠀⣴⠏⠀⠀⠀⠸⣴⡇⠀⠀⠀⠀⢠⣾⣏⠀⠀⠀⠀⠀⠀⢈⣷⣶⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⣷⡷⠀⢀⣴⠋⣸⣿⣿⣿⣿⡟⠀⠀⠈⠙⠳⣤ ⡴⠋⠁⠀⠀⣾⣷⣆⠀⠀⢀⣼⠟⣸⣄⠀⠀⠀⣾⣿⣿⣧⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠇⡴⠋⢀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⣠⠖⠛⠉⠉⠙⢿⣿⣧⡶⣻⠏⠊⢻⠃⠀⠀⠀⠹⣿⣿⣿⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠇⠀⢀⣴⣿⡿⠟⠻⢿⢿⣿⣿⣿⣦⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠈⢿⡿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣼⠛⠦⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⣶⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⠁⢀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀ ⢦⣀⡀⠀⠀⠀⢀⡴⠋⢸⠀⢸⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀ ⡀⠈⠛⠛⠛⠋⠁⠀⠀⠸⡄⠘⣆⠀⠙⠓⠶⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀ ⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⢦⡀⠀⠀⠀⠀⠀⣠⠞⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠸⡆⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀ ⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠿⠤⠤⠤⡖⣚⣥⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢹⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀ ⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡉⠻⠿⠿⠿⠿⠿⠿⠿⠿⠥⠤⠶⢞⣿⡟⠁⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠈⣧⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣰⠃⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⢹⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀ ⠀⢠⠎⠀⠀⠀⢀⣴⣟⠁⠀⠈⠑⣄⠀⠀⠻⣄⣀⣀⣀⣀⣀⣀⠀⢀⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣥⡄⠀⠀⠀⠀⠀⠘⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡏⠀⠀⢀ ⡴⠋⠀⠀⠀⠀⡿⠻⠽⠃⠀⠀⢀⡞⡆⠀⠀⢹⠟⢿⣿⠿⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣿⢸⣽⠛⢦⡄⠀⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣿ ⠁⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣠⡞⣹⠃⠀⢠⠃⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⢻⡌⢿⣧⠀⢹⣦⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢠⢟⠈ ⡆⠀⠀⠀⠀⠀⠀⠙⠶⢶⣺⡥⠞⠁⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠋⡙⣦⠀⠀⢀⣠⠿⣿⣄⠹⣷⡄⠹⡅⠀⠀⢈⠇⠀⠀⠀⠀⣀⡴⠛⠁⠀⢀⡴⠧⣠⠞ ⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⣀⡤⠗⠛⠁⠀⠀⠀⠀⠉⢳⡴⠋⠁⠀⠀⠉⠳⡾⣿⣦⣹⡄⠀⠸⠀⣀⣤⠴⠚⠉⠀⣀⣠⣴⡿⠖⠛⠁⠀ ⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠛⠛⠛⠉⠉⠀⣀⠀⠀⠀⠀⢀⠀⢀⣠⠎⠀⣠⡶⠛⢷⡀⠀⠙⡄⠙⣿⣧⣤⡼⠛⣉⣀⣀⣤⣶⣿⡟⣛⠁⠀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⣾⣿⣷⣄⣀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠳⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠛⠻⠶⣦⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⢠⣶⣶⣄⣉⡉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⠀⠈⢻⣆ ⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣻⣻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣀⠈⠙⠛⠛⠛⠛⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠻⠃⣽⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃ ⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⢻⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣀⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡶⠲⣄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠞⠁⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⠶⠟⠋⠀⠀⠉⠛⢷⣤⡀⠀⠀⢠⣶⣦⡈⠉⠉⠉⠛⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⢀⣀⣀⣀⣀⣀⠀⠀⣠⡿⢷⣤⣀⣼⡇⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠏⢀⣴⠟⠉⠉⠉⠛⠉⣶⡟⠛⠷⣦⣄⠉⠙⠳⣄⠀⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⣰⡟⠁⠀⠀⠀⠀⠀⣠⡿⠷⣦⣄⣀⠙⠃⠀⠀⠉⠓⠀⠹⣷⣶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣻⠟⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠈⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠃⣰⡆⢠⠀⡀⠀⣿⠃⠀⠀⠀⠀⠀⢿⣇⠀⢀⣀⣀⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣴⣿⡀⣿⣀⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠛⠷⠶⠶⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠘⠛⠛⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠋⠉⠉⠉⠉⠉⠉⠓⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢿⣿⡿⠃⠀⠀⠚⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠈⠋⠁⠠⠤⣤⡤⠤⠤⠖⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢷⡀⠠⣷⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢷⣠⠟⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠻⣄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣹⡏⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⠤⠤⠚⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡷⠎⡁⢿⡆⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠄⢠⣼⠃⣸⠇⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀ ⢾⡭⢵⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀ ⠿⣵⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀ ⠀⠉⠉⠉⠒⠒⠲⠤⠤⠤⠤⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⠤⠀⠀⠠⠄⠂⠁⠀⠀⢀⡠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣀⣤⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⣤⣤⠤⠴⠛⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⡄⢾⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣈⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢊⡭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣌⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⣫⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⡏⠀⠀⠀⠈⠛⢾⣛⢲⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢞⡴⠁⠁⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⣆⠀⠀⠀⠀⠀⠀⠉⠉⢹⡿⢦⠴⠖⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢏⡜⠀⣴⠒⠈⠉⠉⠉⠉⠒⠤⣄⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠉⣹⣷⠿⠤⢤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠈⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠂⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⡇⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⡀⠀⠀⠈⠙⠒⢲⣦⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣡⣾⣷⣾⣷⡀⠀ ⠀⠀⠀⢸⠀⠁⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣠⡾⠟⢿⣀⣀⣦⠀⠀⠀⠹⣯⣛⢿⣝⢻⡄⢐⠀⠉⠁⠀⠉⣍⢙⣿⣿⣿⣿⡄ ⠀⠀⠀⢸⢡⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠠⠀⠀⠈⣿⣿⡄⠀⢀⣤⣤⣭⣭⣝⣿⣀⣈⣀⡀⠀⠀⣀⣄⣽⣿⣿⣿⣿⠃ ⠀⠀⢠⣞⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠉⠑⠢⡀⠈⢿⣧⣀⠸⣯⡀⠀⠀⣽⠿⠧⣬⣉⠙⣿⣟⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⢸⣤⣿⢿⣿⡷⣤⡀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠰⠄⠀⢿⡄⠈⣿⡟⠁⠈⠙⣓⠒⠷⣦⠀⠠⢹⣷⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⢻⡭⠈⣼⣧⡙⠻⣶⣄⣤⣴⠾⠿⢻⣆⡀⠀⠀⣠⠟⢁⣼⣿⣧⡀⠀⠀⠈⢹⣷⣾⠃⠸⢿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣶⣶ ⠀⠀⠀⣠⠇⠘⠛⢿⣷⣄⡩⠋⠉⠀⢀⡤⠤⢉⠙⠉⠛⠃⢠⣾⣿⢿⡿⠿⠗⠀⣀⣼⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿ ⠀⠀⢠⡇⠘⠶⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠿⠒⢂⡠⠻⣿⢿⣬⣿⣦⡀⣾⣿⣿⣿⣧⣼⣿⢺⣿⣟⣛⣭⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢸⢡⡞⢠⡿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣞⣁⠤⠒⠁⠀⠀⣉⢿⡿⠛⣯⣥⠈⠉⢋⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣶⡟⠈⣧⠋⠀⠀⠀⠀⠀⢀⣴⡾⠋⠉⠁⣀⣀⡤⠔⠒⠉⣠⠞⠀⠀⢿⣿⣷⣾⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢿⣿⠞⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⣭⡤⠤⠔⠒⣠⠞⠁⠀⠀⠀⢀⣹⣿⠟⠃⠐⠲⣧⠀⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣠⠋⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠺⡑⠤⢄⡠⠔⠊⢝⡄⠈⢙⡆⠀⠀⢹⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡴⠁⠀⠀⣠⠖⠋⠀⠉⠻⠿⠉⠉⢉⡽⢋⣤⠂⠀⠀⣀⡷⠚⠉⠀⠀⠀⢸⣇⡴⠋⠀⠀⠀⣸⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠋⠉⣂⡴⠋⠉⣇⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⢰⣿⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣼⣁⡤⠞⠁⠀⠀⠀⢻⣆⠀⣠⠞⠁⠘⠃⠀⢀⣠⣄⣠⣿⣦⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢠⠞⠋⠉⢰⡀⠀⠀⣀⣤⠴⢻⡯⠆⠀⠀⣀⣼⣟⠋⣉⣈⣳⣄⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣯⡀⠀⠀⣀⣽⣶⠋⣉⣴⡾⠿⠃⢀⣴⡾⠟⢉⡥⠚⢁⡠⠔⠋⠻⡏⠑⣆⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⣛⣻⠿⡏⣇⣤⠾⠟⠋⠁⢀⣰⣾⡿⠋⠀⡔⠋⣠⠔⠉⠀⠀⠀⠀⢻⠀⠈⢷⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠄⠒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⠀⠀⢠⣾⣿⠀⠀⠠⢤⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⢘⣿⣋⣠⠴⣄⠀⢳⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⡉⠄⠘⠷⢶⡟⠀⠀⣧⠀⠈⢻⣓⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⢿⣳⣦⣔⣊⣁⠤⠀⠀⣹⠀⠀⠀⠙⣎⠻⠦⢄⣀⠠⠔⠊⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⣸⡶⠟⠋⠁⠀⠈⢣⠀⠀⠙⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⣀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢢⠀⠀⠀⢈⡇⠀⠀⠀⠀⠙⠢⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣀⣤⠶⢻⡀⠀⠀⠀⠸⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠴⡾⠀⡀⠀⢀⡴⠟⠁⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⢷⡀⠀⢀⡇⠀⠸⠀⣸⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀ ⢠⡞⢡⠞⢁⣴⠁⢀⡎⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⢆⡠⠤⣻⠖⢺⠀⠰⠆⠀⣿⣀⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀ ⠈⠉⠛⠲⠞⠹⠤⣼⠇⠀⠀⠀⣠⡴⢛⡡⠴⠀⣠⣯⠞⢠⠞⢁⡴⡟⠀⣰⣇⠀⣷⠀⠉⠉⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠊⠉⠀⠀⠀⠘⠒⠺⠁⣧⣠⣿⠹⡤⠭⠆⠀⠀⠀⠀⠀⠀⠉⠒⢤⡄⠀⣄⠀⢠⡀⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣈⣆⣀⢳⣀⣧

⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⢿⠉⠉⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠸⠀⠀⣀⣀⣤⠤⠄⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣷⣦ ⠀⠀⢀⠷⣄⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢠⣾⣛⣉⡭⠤⠶⠒⠚⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿ ⠀⠀⠂⠠⡟⣯⣍⣛⠒⣒⣲⣶⡶⠶⠶⠚⠋⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠⠤⠤⠠⠀⠀⠠⠤⠤⠴⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠈⢻ ⠁⠀⠀⣀⣈⣻⣄⡈⠉⠉⠁⠀⣀⣠⡤⠴⠶⠒⠒⣒⣚⣭⠭⠤⠶⠖⠒⠒⠒⠂⠀⠀⠉⠉⠉⠛⠓⠒⠒⠲⠶⠦⢤⣤⣿⣿⣶⣄⠀⠋ ⠀⠀⡀⡇⠀⠃⠙⣍⡁⠀⠉⠉⣁⡠⠤⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠇⠀ ⠀⠀⠻⠇⠀⠀⣠⡇⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠀⠀⣴⡞⠁⠙⣄⠀⠀⢀⣀⠤⠤⠒⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠻⠄⢀⣀ ⠀⠀⠀⠀⣿⠀⠀⢠⠏⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⠙⣿⣿⣿⠷⣄⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⣾⡴⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠏⢀⣴⣿⡷⠀⣿⣿⡟⠀⠈⢣⠀⠀ ⠀⠀⠀⣾⠁⠀⣠⠿⣿⢦⠀⠀⠀⠀⠀⢀⣴⠟⠉⠐⢦⡈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢀⣴⠋⠁⠁⢀⢦⣿⣿⣦⣀⡀⠀⡇⠀ ⠀⢀⡔⠁⢀⡴⠃⠀⠘⣦⡇⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢳⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢀⠞⣼⣿⣿⣿⠁⠉⠓⠿⣄ ⠴⠋⢀⣀⣾⣦⡀⠀⣠⡟⣧⡀⠀⠀⣿⣿⣧⠀⢀⣠⠶⠋⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠔⢁⣼⣿⣿⣿⣿⣄⠀⠀⠀⠈ ⠔⠉⠉⠀⠙⠿⣷⡾⠛⠉⠋⠀⠀⠀⠙⠿⠿⠚⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⣴⣿⠟⠉⠛⠻⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡉⡷⢄⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣴⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀ ⠳⢤⣀⣀⡠⠔⠁⣇⠘⡄⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀ ⣆⠀⠀⠀⠀⠀⠀⠘⣆⠱⡄⠀⠈⠉⠉⠉⡻⢷⣶⣶⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀ ⠈⢣⠀⠀⠀⠀⠀⠀⠈⠑⠻⠦⠤⠤⢔⣫⣤⣶⣿⣿⣿⣿⣿⣿⠿⢿⣷⠀⠀⠀⠀⠀⠀⣸⠏⠀⢡⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀ ⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⣉⢛⣛⣛⣛⣛⣛⣓⣒⣚⡿⠟⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢀⠁⠀⠀⢀⡴⠒⠒⠢⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⡴⠃⠀⠀⢐⠿⠿⠂⠀⠀⣿⠀⠀⢹⠿⣿⠿⠛⠒⠒⠉⠁⠀⠀⠀⠀⠀⢀⡠⠞⡟⣿⡟⢤⡀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣼ ⠀⠀⠀⠀⠀⢧⡀⠀⡠⢾⡝⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡚⠉⠀⠀⣹⡘⢷⡀⢻⡦⠀⠀⢿⠀⠀⠀⠀⠀⡰⠋⠀⢀⡾⢀ ⠧⣀⠀⠀⠀⠀⠉⠛⠚⠉⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠱⣄⡠⠖⠙⠛⢮⣻⣦⢱⡀⠀⡌⠀⢀⣠⠴⠋⠀⣀⣴⣯⠗⠋ ⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⣀⠊⢀⡤⠶⣆⠀⠻⡙⢻⣧⣠⠶⢋⣁⣀⣤⣶⣿⠋⠁⠀⠀⣀

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⣿⣿⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠁⠀⠀⣀⠀⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⣶ ⡿⠀⢀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⣰⠃⠀⠀⠀⠀⣏⠈⢯⡀⢩⣿⣶⣦⣄⡀⠀⠀⢀⣠⣄⡀⠹⣧⠀⠀⠹⣧⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣷⣶⡏⠀⠀⠀⠀⠀⠀⠀⢰⡿⠐⢿⠇⠀⠀⠀⠀⠀⠹⣦⣼⣯⡉⠉⠛⠛⠉⢁⡴⠋⢉⣀⣀⣉⡛⣿⣦⠀⠀⠹⣷⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡀⠀⢀ ⢈⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠂⠀⢀⡴⢋⣠⠞⠉⠁⠀⠈⠉⠛⢻⠆⠀⠀⠘⢿⡤⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠟⢿⡿⣻⠧ ⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⡐⠃⣿⢀⡤⠒⠋⠉⠉⠛⠲⠤⣄⣀⣤⣴⡿⣠⠞⠁⣀⣤⡶⠿⠟⠲⠞⠀⠀⠀⠀⠀⠈⢿⣦⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⠛⠋⠉ ⠁⠀⠀⣿⠃⢀⣴⡶⣿⡿⠁⢰⣿⠀⠀⢿⠀⡤⠞⠉⠉⠙⠓⠲⢤⣤⣤⣬⣵⠞⠋⢠⣾⣫⣵⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠙⣆⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⠀⡿⣱⠞⠋⠀⢀⡿⡏⠀⠀⢸⡆⠀⠀⣠⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡈⣷⣄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⢩⣋⣿⢀⡾⠋⠀⠀⠀⣼⠁⠀⠀⠀⣀⣿⡀⠸⠋⠀⠀⠐⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⡿⢶⣄⠀⠀⠀⠀⢷⠀⠀⠀⠀ ⠀⠛⠉⢻⡾⠁⠀⠀⠀⣸⠋⠀⢠⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⠹⡄⠀⠀⠀⠀⢸⣟⣫⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣘⣿⣷⣄⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⣰⣏⡀⠀⠀⠙⢿⣿⣿⣿⣷⣠⠀⠀⣤⣶⣿⣷⡄⢹⡄⠀⠀⠀⠀⠿⣵⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣍⠈⣿⠈⠓⢦⣨⡿⠀⠀⠀ ⢿⣿⣼⠃⠀⠀⠀⣴⠛⣻⣿⣷⣦⡀⠈⠻⣿⣿⣿⣿⡷⢠⢾⣟⣿⣿⠟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣄⣰⠛⠁⠀⠀⠀ ⢀⣾⡏⠀⠀⢐⣼⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⣻⣿⣿⣷⠀⠀⠈⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣠⢤⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⠿⠃⠈⠻⣿⣆⠀⠀⠀⠀ ⣘⣿⠁⠀⣠⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⡯⠶⢾⣿⣿⣿⡿⠉⠉⠙⠻⣽⡚⠉⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⢻⣆⣠⠄⠀ ⣿⣿⣠⠾⠋⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⡼⠙⢷⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣲⣶⣶⣶⣖⣛⣷⡤⢤⣀⡀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠹⣿⠢⠀ ⣿⣿⡅⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⡇⠀⠀⠉⠛⣿⡉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠂⠀⠀⠀⠉⠙⠒⢯⡿⠀⠻⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠁⠀⠀⠃⠀⠀⠀⠀⣤⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠿⢤⣀⣀⣠⣼⣿⣲⣶⠭⠶⣾⣿⣿⡿⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣸⠇⡇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠃⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡚⠙⢿⣻⣗⣾⡟⠒⣺⣋⡵⢾⡟⠁⠀⠀⡞⣿⠀⠀⠀⠀⢀⣴⡟⢰⠇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⣀⡀⠀⠀⠀⠀⣶⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣷⡘⠿⣭⣉⣭⣥⣾⡿⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⣰⡿⠁⡼⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢋⠓⠀⠀⠀⠀⠀⠉⠀⠀⠻⠿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠒⠲⠶⠃⠀⠀⠀⠀⣸⠃⢸⠀⠀⣀⣼⡿⠁⢰⠇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⣀⣄⠀⠙⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⢸⣿⠙⣧⠀⠀⠀⠀⠲⠤⢤⣤⠞⠃⠀⡿⣠⡾⣻⠟⠁⠀⡾⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠛⠁⠋⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⡇⠘⢷⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⢞⣭⠾⠋⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡀⢦⠉⠛⠿⢿⣿⣿⣭⡭⠽⠟⠋⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡀⠀⠀⠀⠀⠸⣦⣼⣾⣿⣿⠄⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠁⠷⠈⢳⣄⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⢰⡏⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠖⡿⠉⣯⢱⠇⢰⡆⠀⠀⢠⡆⠉⣉⠉⢉⡛⢷⣤⣄⣀⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣁⣴⣿⢿⡟⠛⠛⠛⠛⠛⠛⠻⠷⠦⣭⣴⡻⡄⠀⣰⠇⠉⡻⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡿⢋⣰⢿⢁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣽⣶⣺⠁⠹⣦⣀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⢀⡞⢁⣷⠏⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠲⠈⠉⣿⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠈⠀⢸⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡳⣄⣹⡄⠀⠀⠀⠀⣸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡄⣿⡃⠀⠀⠀⣠⡿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⢛⣓⠶⣦⣤⡞⠁⣷⡄⠀⢸⣦⠀⣀⣤⣴⡞⡛⠀⠀⠀⢷⡈⢙⡿⠛⠋⠉⠳⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⣀⠀⠀⢸⡿⠛⣿⠶⣿⣤⡀⠉⠁⠀⠀⠻⢻⣽⣷⠟⠛⠳⣦⠀⠀⠘⣷⣾⣀⡀⠀⠀⠀⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢸⣷⣄⣿⣀⣐⣻⠁⠀⠀⠀⠀⠀⠘⣃⢙⠀⠀⠀⣇⣦⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⢻⡀⠀ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠈⠛⠿⢿⣯⣠⣶⠀⠀⢿⣆⠀⣾⣿⣟⡋⠉⠉⠉⠀⠀⠀⠀⢠⡾⠈⣿⡄⠀⠈⣧⠀ ⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠛⡁⣿⠀⠀⠈⢿⣷⠌⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⡇⠀⠘⣾⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⠛⠷⠤⣧⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⣻⡦⢾⡇⠸⡀⢹⠀ ⠀⠀⠀⠀⠀⣷⣀⣀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢧⢸⡇ ⠀⠀⠀⠀⠀⢸⣇⠀⡤⠀⢤⡄⠁⠀⠀⢀⣤⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣀⢤⣆⠀⢀⣾⣿⠀⠀⠈⣎⡇ ⠀⠀⠀⠀⠀⠀⠹⣷⣄⣰⡣⠀⣤⠀⠐⠟⠣⣊⣹⡛⠉⠙⠳⠶⠀⠀⠀⠀⠀⢀⡠⠞⢡⣿⣿⠻⡿⠟⠁⡀⢇⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⡠⠾⠁⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠐⣺⡿⠃⣿⠀⢱⠈⠀⠀⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠰⠞⠉⣁⣴⠞⠋⠀⠀⢿⡀⢸⠀⡇⢸⡀⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠛⠋⠉⠉⠀⠀⠀⠀⠀⢸⡇⢸⡀⢇⠈⣇⠀⢰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡇⢸⠀⠸⡄⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⣿⡇⡼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢡⠈⡆⠀⢱⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⣿⡟⣢⠟⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠸⡀⢱⠀⡾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣀⣧⠀⠀⣿⡞⠋⢉⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠀⢧⠀⢰⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡟⠉⢩⡾⠟⠋⠀⠀⠈⢳⣄⠚⠿⠦⢤⣀⣀⣀⡀⠀⠀⠀⠀⢹⣄⡀⠀⠈⠀⢸⡄⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⠿⠛⠉⠘⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⢉⣣⣤⡴⣶⣿⠏⠙⠿⠝⠶⣤⣀⠀⠈⠉⠙⠲⢤⣼⠁⠀⠀ ⣀⣤⣶⣟⣻⣿⣁⣶⠘⡇⠀⠀⠈⢉⣘⣿⣦⣤⣶⣺⣟⠛⣁⣀⣀⡉⠀⠀⠀⢰⡄⠰⣶⣝⣛⠶⣦⣤⣀⢀⡀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢿⣿⣷⡍⠉⠀⣼⣿⣿⠟⢋⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣷⣾⣿⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾ ⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣛⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀ ⣆⣛⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣏⣤⡶ ⠻⣿⣼⣮⣝⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⢋⣩⣿⣿⣯⠀ ⠀⠉⠙⠻⠻⢷⣮⣙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣭⡿⠿⠛⡿⠛⠉⠀⠀ ⠀⢀⣀⣤⡤⠤⠭⠿⢿⣶⣯⣿⣷⣦⣄⣀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠟⠿⠭⠤⠤⢤⣙⣦⠀⠀⠀ ⠈⢉⣡⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣿⡇⠀⠀⢸⣿⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣬⣍⠁⠀⠀ ⣶⣿⠿⠛⠋⠉⠁⠀⠀⠈⠉⠉⠙⠻⢿⣿⡏⠙⣿⢷⣿⡿⠁⠀⠀⠈⠻⡶⠿⠟⡋⣹⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣷⣦⣴ ⠉⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠂⠉⠻⠇ ⠀⠀⠘⢿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡒⠂⠠⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠴⠒⠒⠊⠉⣁⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⠶⠶⢶⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣅⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛ ⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀ ⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀ ⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⠛ ⠀⠀⠘⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡟⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣧⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢟⡁⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠐⠒⠒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣱⡤⠤⠒⠒⢈⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠊⠁⠀⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣖⠒⢤⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡒⠒⠒⠀⢳⠀⢠⢚⣿⣷⣶⡄⠀⠀⠋⣿⣿⣿⡇⠀⠁⢀⡠⢚⠗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠁⠈⢼⣿⣿⣿⠀⠀⠀⠀⠹⢿⣿⠇⠀⠀⠀⠈⠉⠓⢲⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠬⠟⠃⠀⡀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⡶⠒⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⢀⣈⡙⠒⠒⠒⠲⣧⠀⠀⠀⠀⠀⢀⣀⣄⠀⢀⡀⢲⡤⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠓⠦⣀⢸⡤⠓⠢⢄⣀⠀⠉⠉⣁⡴⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢩⡏⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠎⠇⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⣴⠛⠋⠀⠀⡴⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠎⢸⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⣴⣶⣤⣀⠀⠀⠀⠀⠀⢿⣿⣁⡤⠀⠀⢸⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⢸⠀⠀⠀⠀⡞⠀⠀⠀⢀⡴⠋⠉⠀⠹⢿⣿⡝⣄⠀⠀⠀⠘⡟⣟⠀⠀⣠⠇⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠈⡆⠀⠀⠠⡇⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⢿⠺⣍⠁⠀⠉⠙⠚⣖⠊⠁⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡄⠀⠸⡀⠀⠀⡇⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠿⠓⠦⠤⠀⠀⠈⢣⡀⠀⢸⠁⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣄⠀⠹⣄⠀⠹⡀⢰⠁⠀⠀⠀⠀⠀⠀⢀⠴⠁⢨⠳⢄⡀⠀⠀⠀⠀⠀⠻⣐⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠈⢢⡀⢣⢸⠀⢤⣀⣀⣀⠤⠒⢁⣠⠔⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣦⠴⢶⡩⠤⠛⠲⠭⣮⣿⣠⠖⠻⢍⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⠋⡷⣄⠀⠀⠀⠀⠘⠀⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠢⢄⡀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠉⠒⢤⣀⣀⣀⣠⡤⠚⡇⠀⡇⠈⠑⢤⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⢰⠃⠀⡇⠀⠀⠀⠈⠑⠂⢤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢠⣾⠏⠀⢸⣿⠀⠀⠀⠀⠸⣿⡁⠈⠙⢿⣦⡀⢹⣿⠻⣦⡀⠁⠉⠹⣿⣧⡀⠉⡄⠉⠁⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠏⠀⢀⣴⣠⣴⠟⡡⠎⠁⠸⢿⣦⡀⠀⠀⠰⠈⢿⣆⠀⠀⠙⢿⣾⣿⣦⠈⠛⢷⣄⡀⠹⣿⣿⣄⠀⠂⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⢠⣿⡿⠛⣡⠞⠁⠀⠀⠀⠀⠉⠻⢷⣤⣀⠄⠀⢻⣧⡀⠀⠀⠈⠛⠿⣷⡀⠀⠉⠻⣦⣽⣧⠙⢷⣄⠀⠀⡀⣿⣧⡀⠀ ⠀⢀⣴⣿⠃⣠⡾⠋⣠⠞⠁⠀⠀⡀⠀⠀⠀⡆⠀⠀⠈⠙⠿⣶⣄⣻⢿⣆⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠙⠻⠷⠌⠻⣷⣄⡄⢹⣿⣷⣤ ⣠⣾⣿⣯⡾⠋⠀⠚⠁⠀⠀⠀⠀⢡⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣧⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⣿⣿⡉⢻ ⢟⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⡆⠈⣧⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠙⠻⣷⠀ ⣿⣋⣥⠤⡶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⠀⠀⢐⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⣉⣀⣀⣤⣤⣀⡀⠹⠀ ⡏⠁⠀⠀⢀⠀⠀⠉⠛⢷⣶⣄⡀⠀⠀⠀⠉⠊⠁⡄⠀⠀⣇⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄ ⠁⠀⠀⣄⣺⣥⣤⣤⣤⣴⣬⣿⣿⣿⣶⣤⣀⠀⠀⠰⠀⠀⢸⡀⠈⢷⣄⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡿⠀ ⣠⣾⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣷⣶⣤⣀⣀⣾⣧⠀⢸⡿⣷⣶⣶⣾⣿⣿⠟⣡⠖⠋⠑⢦⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀ ⠻⣿⣿⠉⠀⠀⠀⠀⠀⢠⠖⠋⠉⠳⡌⠻⣿⣿⣟⠻⠛⠋⢁⠉⠻⢛⡀⠀⢉⣡⠾⣿⠃⠀⢳⡀⠀⠀⣠⠇⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀ ⠀⣿⣿⡄⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡇⠀⠈⣿⡍⠀⠀⠀⠀⠉⠒⠿⠀⠀⠉⠀⣠⣿⡀⠀⠀⠉⠒⠋⠀⠀⠀⣀⣠⣴⠿⠟⠃⠀⠀⠀ ⡇⠙⣿⣿⣦⡀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠈⠛⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠒⠒⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢰ ⣿⡄⠀⠙⠻⢿⣶⣤⣤⣤⣤⣤⠤⠀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⡉⠉⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏ ⠷⣦⣌⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀ ⣰⡿⣿⡝⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⡇ ⡟⠀⠸⣷⡞⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣷ ⠀⠀⠀⠙⣷⡀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣄⣀⣀⣀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡄⠀⠀⢹ ⠀⠀⠀⠀⠘⣷⣿⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠈⣷⠀⠀⠈ ⠀⠀⠀⠀⠀⢸⡇⣸⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⢹⣧⡀⠀ ⢀⣀⣤⡴⠶⣾⠿⣿⠀⠀⠀⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣿⣿⠀⠀⠀⠀⢿⡿⢿ ⠟⣫⠟⢡⡾⠃⢸⣿⠀⠀⠀⠀⢿⡟⣿⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⢻⡏⠀⠀⠀⠀⠸⣇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠚⠉⠉⢉⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⠚⠉⠀⠠⢄⠀⠀⠀⠀⢊⠽⠧⣈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠾⡁⠀⣶⡇⣀⠔⠋⠁⠒⠒⠤⡟⡧⠚⠁⣠⣤⡖⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡴⠋⢀⣄⣱⢤⡍⣴⣯⠔⠒⠶⢶⡦⣄⣿⣧⣴⠛⠋⠁⣠⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢆⠀⣿⡿⠻⡀⠁⠻⣄⠀⠀⠀⠀⠈⢳⡿⠻⢇⠤⠐⠉⣀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⢡⠀⠀⠈⠑⠢⠤⢤⣶⡯⢤⣤⠤⢴⣚⠉⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⠐⠇⠀⢰⠀⠀⠀⢀⡠⠒⠉⣿⢀⣰⣿⣤⡼⣷⢌⡑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⠀⣠⣶⣨⣧⢄⠔⠉⠀⠀⠠⡿⢹⡈⠯⢧⠃⠘⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⠀⠀⠀⠀⠀ ⠀⠀⠈⡷⣿⣿⣹⣿⡤⠔⠀⠀⠀⢰⠃⠀⡇⠀⠀⡇⡀⢰⠁⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢣⡀⠀⠀⠀ ⠀⠀⠈⣧⣼⣏⠉⠉⢉⣲⡀⠀⠐⠃⠀⠞⠀⠀⠀⣿⠏⡼⠲⣤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀ ⠀⠀⢀⡟⠋⠈⢑⠶⢿⠞⣿⠿⠷⢒⣢⡤⠤⣴⣂⠀⣸⢅⣼⡿⠷⢦⣤⣄⣀⣇⠀⠀⠀⡀⣠⣸⠏⠀⠀⠀ ⠀⠀⢸⡛⠢⠤⢬⣇⠬⢽⣉⣤⣤⣤⣤⣿⠿⠿⠟⣿⠿⣶⣶⠤⣄⣀⡀⠉⠙⡿⣇⣸⣤⣴⣿⡇⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣶⣼⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠒⠋⠽⠶⣇⡀⠉⠁⢘⣿⡷⠀⠀⠀⠀ ⠀⠀⠙⠛⠿⣿⣧⣼⣿⡿⠿⠿⢿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⡟⢛⣏⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠈⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⠀⢡⠈⠈⠳⠘⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⢹⣇⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠈⠂⠀⠀⠀⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣶⣾⡗⠀⠀⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠉⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⡠⠤⠤⠤⠾⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⡖⢻⢩⡍⣩⠉⠉⣩⠉⢓⠒⡒⢧⣄⣀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣣⣴⠿⣟⠛⠉⠉⠙⠛⠛⠳⠶⢾⣧⣀⡼⢈⡹⣆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⣰⢊⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣇⣈⠳⢦⠀⠉⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⠁⣼⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣆⣸⡆⠀⠀⠀⣸⡆⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⣤⣀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⣀⡀⠘⢷⡸⣇⣀⣀⣤⡟⠁⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠀⣿⣯⣽⣷⣋⠀⠿⠀⠘⣷⣴⣶⣿⣽⣀⠀⠈⣧⣸⠋⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⢿⣄⣧⣈⣽⠃⠀⠀⠀⠀⢏⣹⠀⠀⢩⣄⠀⠈⠉⠓⢦⡀⠀⠘⡄⠀ ⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠙⠛⣿⣴⡖⠀⢺⣆⠸⣿⣯⠉⠉⠁⠀⠀⠀⢰⠃⢿⡄⠀⢳⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⣶⡀⠀⠀⠁⢠⣇⣀⠀⠙⠃⠀⠀⢀⡀⠀⠀⠀⠀⠸⡆⣠⡇⠄⢹⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠈⠁⣼⠃⠸⣘⡆ ⠀⠀⠀⠀⢹⡀⠀⢀⠦⠀⠀⢀⣤⢤⣀⣠⣄⣀⠀⠀⠀⠻⠃⠀⣀⣤⣦⣀⣼⡿⠀⠀⢳⡇ ⠀⠀⠀⠀⠀⠻⣷⠚⢀⠖⠀⠈⠙⣷⡷⠀⠀⠉⠁⠀⠀⠀⣠⢎⣥⡿⢿⠙⠉⠀⠀⡆⠈⡇ ⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⣀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠔⢋⣡⠴⠋⠀⢸⠀⡇⠄⢀⠰⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠀⠀⠀⠀⢸⡇⡇⢸⠘⡄⢰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡃⠀⢠⣄⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⡿⠈⡀⠑⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠇⠀⢰⡿⢗⡆⣸⠀⠀⠀⠀⠀⠀⠀⡜⠀⡋⡆⠣⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣤⣴⠀⠸⣟⠉⣩⡟⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⢰⠀⡜⠀⠀ ⠀⠀⠀⢀⣠⣤⡶⠟⣿⣤⡘⠋⠁⠀⠀⠈⠲⠌⢉⣱⣶⠶⢦⣤⣀⠀⠈⠒⠤⣄⡀⡿⠀⠀ ⣀⣤⣶⣻⣟⣥⡰⡆⠀⠙⢛⣳⣤⣤⣤⣶⠞⢉⣉⡉⠁⠀⠠⡄⢬⣟⣶⢤⣤⣀⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⣋⡉⠁⠀⠀⠀⠀⠒⠀⠈⠉⠙⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣋⣥⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠷⢦⣝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣿⡍⠀⠀⠀⠀⠀⠛⢿⣬⠛⠶⢤⣶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣡⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠲⣄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠟⢻⣿⣇⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⡴⠉⠀⣀⢀⣒⡷⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠆⠈⢳⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢩⣭⣥⣤⣍⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡏⡼⠁⠀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⣽⡿⠾⠓⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠖⠛⠂⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠂⠀⠰⠆⢠⣿⣇⣸⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡆⠀⠀⡀⠀⠀⠀⠀⢤⣽⣿⣦⣤⣤⣤⣄⠀⠀⠠⢸⣦⣄⠀⢠⣴⡾⣿⣭⣽⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⣸⡀⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣴⣿⠟⠃⢿⣦⣤⣀⣷⠀⠀⠀⠀⠘⠿⣦⣍⣻⣶⣌⣻⡆⢠⡄⡀⠄⠀⠀⠀⠰⢶⣄⣽⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⡟⢹⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣟⣁⣀⠀⠀⠀⠘⣿⣿⡄⠀⠀⢀⣤⣄⣀⣉⣉⣙⢻⣏⣀⣀⡀⠀⠀⠀⠀⢠⢤⣄⣠⣾⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⣠⡇⢸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡯⠖⠒⠤⢤⡀⠀⢻⡏⣷⡀⠀⢸⣿⠁⠀⠀⠀⢹⣿⣟⣋⡙⠛⠛⢷⣶⡶⠶⠾⣿⣿⣿⣿⣿⣿⡏⠁⠀ ⠀⠀⠀⢰⡟⠳⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠀⡄⠀⠀⢱⠀⡀⠹⣿⣷⣦⠌⠻⣷⣤⣀⡀⠛⠋⠉⠉⠙⠳⣦⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡁⠀⠀ ⠀⠀⠀⠀⣷⣶⣿⠛⣿⣿⠛⣷⣄⠀⡀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠓⠀⠀⢩⣷⠇⠀⣷⣟⠁⠀⠀⠀⠉⣭⣉⠙⠻⣧⠀⠂⣃⣹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠈⢧⡽⠀⣠⣿⣦⡸⠛⢿⣶⣄⣴⣰⣶⣿⣿⢻⠿⣇⠀⠀⠀⠀⣠⡾⠋⢀⣾⣿⡿⣄⠀⠀⠀⠀⠈⢹⣿⣦⣿⠃⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣶⣶⣾ ⠀⠀⠀⠀⠀⢈⡇⠰⠿⢿⣿⣷⡀⠈⢛⡟⠛⠉⠀⠀⢀⣀⡉⠛⠻⠿⠿⠯⠕⠀⣠⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⢀⣿⡿⢃⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿ ⠀⠀⠀⠀⣶⠋⢤⡐⡀⠀⣹⣿⣿⠖⠋⠀⠀⠀⠀⠴⠋⠀⠉⠓⢤⣄⣀⣀⠀⢰⢫⣻⣿⠈⢿⣌⠉⠀⢠⣴⣿⣿⣿⣿⠛⢻⣿⡟⣿⣿⣿⣿⡿⠿⣻⣿⣵⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⠀⢁⡍⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠉⢀⣠⠖⠉⢻⣏⢿⣷⣾⣿⣷⡄⠻⣿⣿⣿⣻⣿⣾⣾⣿⠃⣿⣿⢭⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡇⣰⡟⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⣠⡤⠖⠉⠀⠀⠀⠀⣩⠟⣾⠟⢹⣇⣶⠆⠀⠈⠉⣩⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣴⠿⠇⢹⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠖⠋⠉⠁⠀⠀⣀⣠⠤⠖⠉⢠⡾⠁⠀⢸⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣇⣿⣄⣼⠋⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦⣴⡤⠤⠖⠒⠛⠋⣁⡠⠄⢀⡶⠋⠀⠀⠀⠀⠙⠻⣿⣿⣿⣟⣋⣀⣠⡍⠛⠿⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠛⣿⡟⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣒⠛⠋⠉⢀⡴⠋⠀⠀⠀⠀⠀⣀⣠⠤⠿⣾⡉⠁⠀⠈⠹⣿⡄⠀⠀⢲⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⠟⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠞⢻⡀⠲⠤⣀⣤⠖⠛⠹⡝⡆⠀⠀⢙⡆⠀⠀⠀⢹⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣴⠃⠀⠀⠀⢀⣤⠞⠉⠉⠉⠻⣾⣿⡉⠉⠉⠛⣩⠟⠁⣠⠆⠈⠀⠀⠈⣷⡴⠚⠉⠀⠀⠀⠀⢡⡇⢀⡴⠋⠀⠀⠀⠀⢸⡿⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⠃⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⣠⠟⢷⡀⠀⣠⠶⢻⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⢠⣿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠫⣀⡾⠁⠀⣀⡵⠟⠁⠀⠘⡼⡄⠀⠀⠀⠀⣠⠾⢿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣰⣿⣀⣤⠾⠋⠀⠀⠀⠀⠀⠻⣵⠀⢀⣠⠞⠉⠀⠈⠁⢠⠀⣀⣠⣤⣤⣤⣯⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢀⣴⡿⠛⠉⢠⡂⠀⠀⠀⠀⠀⣀⣤⠷⣿⣫⠥⠀⠀⠀⠀⣠⡿⠞⠛⠉⠉⠹⣦⡀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⡾⠡⠀⠀⠀⠀⠻⣆⣠⡴⠶⠛⢉⣠⢶⣿⡁⠀⢀⣀⣴⣿⠿⠖⢒⡴⠞⠉⠉⣉⡿⢦⡶⠶⢤⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢶⣿⣦⣂⣤⣤⡴⠾⠟⣿⣄⣤⣾⠿⠛⠋⠁⢀⣴⢿⡿⠋⠁⣠⠞⠋⢀⣠⠔⠋⠁⠀⠈⢿⡀⠈⠻⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⣹⡟⢿⡇⣯⣤⡶⠿⠟⠉⠀⠀⣀⣠⣾⣿⡿⠋⠀⢠⠞⣁⣀⡴⠛⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠉⠢⠁⣌⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⣀⣀⠀⢀⡠⢄⠀ ⠀⠀⠀⢣⠀⣼⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠑⠊⢀⠏⠀ ⠀⢀⡀⢠⣿⠃⠀⠀⠀⠤⠤⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡤⠊⠀⠀ ⢋⢀⢃⣿⠷⠒⢉⣿⣿⣿⢷⠶⣦⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⠀⠘⣿⡀⠀⠀ ⠀⠁⡸⡿⡄⠀⠈⣿⣿⠧⣀⣠⡟⢰⢶⠶⠶⣶⣤⣤⣀⡀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⢸⡇⠳⡀⠀⠘⢿⣷⢋⠜⠁⠸⡙⣄⣠⠿⣿⣿⣿⣿⠏⢲⠀⠀⢸⣇⠔⡄ ⢸⠑⠁⣥⠐⡍⠂⠤⠔⠛⠁⠀⠀⠀⠳⣿⣿⣿⡿⠟⣛⠏⡠⠋⠀⢠⠀⠁⡰⠃ ⠈⠢⠎⢿⡄⠈⠔⠁⠀⠀⠘⠒⠒⠜⠀⠈⠛⠻⠦⡞⠒⢋⠀⠲⠀⢠⣦⠔⠁⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⠄⠀⠃⠀⡰⡻⠁⣀⠁⠀ ⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⠙⢄⠊⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠟⠋⠈⢆⠀⢠⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⠲⣄⣠⡶⠛⢶⠀⣰⠃⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⢿⡛⠛⠶⠦⢴⣷⣾⣆⡀⠀⣼⡟⠀⠀⢸⣷⠃⠀⠀⢳⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠉⠛⠻⠿⣦⣤⣀⢸⡇⠀⠀⠀⠸⠋⢸⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⣼⡷⠀⠀⣀⠀⠘⣧⠀⠀⠀⠀⣀⣤⡶⢦⣄⣸⡏⠙⠻⣷⣤⡀⠀⠀⢀⣼⠟⠋⠉⠹⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠉⠀⠀⢿⠟⠀⢰⡇⠀⠀⠀⣴⡟⠁⣤⡀⠘⣿⡇⠀⠀⠀⠉⠻⢷⣴⡟⠁⠀⠀⠀⢠⣟⡠⠚⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠻⣧⡀⠉⠀⣠⡿⠁⠀⣠⣶⠶⢿⡛⠙⢿⣄⠀⠀⣠⣿⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤⣤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⣾⠋⠀⣤⡀⠈⣧⠀⠹⣷⣴⠟⠁⠀⣰⣃⣠⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⠛⠁⣠⡿⠀⠀⠸⣿⡀⠀⠈⠉⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠞⠋⠀⠀⠀⠀⢻⡇⠀⢠⣞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢀⣾⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠠⣉⣶⣶⡖⠃⠀⠀⢠⣿⢳⡒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠙⠷⣤⣤⠇⠀⠀⠀⠀⠀⢀⡾⠟⠙⠢⠀⠀⠀⢠⣾⣯⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠴⠒⠚⠋⣩⣿⣶⣤⣖⣿⣿⣿⣿⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠈⢻⣄⠀⠀⢀⣠⣴⣶⣶⣿⣓⡒⠦⣄ ⣀⣰⡞⢋⣽⣿⣩⠿⠻⣧⣽⣿⣿⣿⣿⣷⣄⠉⠛⠛⠷⠶⢶⣶⣶⣶⣶⣶⣿⡿⠛⠉⠀⠀⠀⢀⣼⣿⣇⡞⢹⠟⣿⠶⢤⣀⠀⠀⠶⠠ ⠀⠉⢡⣿⣥⠟⠻⣄⣠⡼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⣿⣿⡿⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣠⠟⣳⣯⣄⡼⠉⢻⣦⠀⠀ ⠀⠀⠘⢿⣿⣦⣠⠟⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⣶⣯⣠⡿⠛⣶⣏⡼⠇⠀ ⠀⠀⠀⠀⠙⣿⣿⣴⣛⡽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣠⡟⠛⣾⣯⣾⡛⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠛⠿⠷⠿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡆⠙⢿⣿⣿⣿⣇⠀⠀⣠⠞⠋⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣟⠁⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⢸⣇⢀⣤⡿⠋⠀⠙⠷⠤⢿⣶⡚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⣶⣤⣴⣿⣿⣿⣿⣿⣷⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠄⠿⠙⠈ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠲⠒⠒⠒⠒⠖⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⢀⠀⢳⡏⣏⢧⠠ ⠀⠀⠀⠀⠇⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀⠀⠀⠀⡄⡷⠙ ⠀⠀⠀⠀⠀⣄⠲⠓⠉⠉⠉⠈⠀⠀⠄⣦⢒⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣈⢀⠀⠀⠀⠀⠀⠀⠁⣏⠀⠀⠁⠚⠴⠦⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠤⠤⠤⠤⣠⣀⢀⠀⠋⡤⠀⠀⠀⠀⠀⠀⡀⣀⢤⠲⠙⠉⠋⠒⡗⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡖⢠ ⠍⠚⠙⠈⠀⡆⠒⠉⠉⠒⠒⡴⠀⠀⠀⠀⠀⠀⠋⢰⠀⠀⠀⠀⠀⡆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣰⠀⠀⠀ ⡿⣘⣀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⠀⠀⠉⠋⠘⠀⠀⠀⠀⠀⠀⠏⣯⠀⠀⠀⠀ ⠀⠀⡀⣇⠳⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⣡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠺⠒⠴⡤⣀⠀⡀⢦⠓⠉⠋⠗⣻⡟⣿⠀⠀⠀⠀ ⠀⠀⠀⡀⢸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠃⣽⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⣦⣿⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⠸⠀⠀⢹⠀⠁⡟⠁⡷⡿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡋⠛⣿⣿⣿⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡆⢾⠙⠀⠀⠀⠀⠀⠀⠀⢯⠀⡆⠙⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⢸⠀⠀⡇⣤⣤⣷⣻⣰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣄⠲⠒⠖ ⠀⠀⠀⠇⣸⡇⠀⠀⠀⣇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⢀⡏⠀⠀⠀⠀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⡇⠈⢸⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀ ⡇⢸⠘⠜⣧⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠁⣽⢺⠀⠀⠀⠀⠀⠀⠀ ⡄⢿⣷⢻⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⡿⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢳⣿⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣿⢟⢚⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢾⡳⣳⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠤⠲⠓⠛⠙⠉⠉⠉⠋⠛⠛⠾⣿⣼⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⣿⠋⣿⡀⡸⢥⠭⠯⠊⠙⠉⠙⠉⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⡇⡿⣾⠐⣿⣟⣁⣿⣇⠞⣹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠈⣶⣹⢇⡊⣺⣿⢟⢺⡿⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠹⡆⣏⣤⢿⢿⣿⢰⣿⢳⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⢦⠒⡖⠒⢲⡶⢴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⣿⡷⣞⣿⡽⣿⣯⡽⣾⣟⡾⣽⡿⣟⣾⣟⣽⣻⣷⣟⢷⣻⢿⣯⣟⣽⣻⢾⣿⣟⢯⣷⣟⢯⣽⢿⣾⡿⣯⣷⣟⣯⢿⣷⢯⣷⢯⣿⡷⣽⣾⣻⣷⣾⣟⣳⣿⣯⣟⢷⣻⣽⡿⣟⣯⢾⣿⣯⣷⣟⣷⣟⡽⣻⣾⣽⢿⣽⣻⢿⣷⡽⣿⣟⡾⣻⣽⢿⣻⣾⣽⣻⢿⣯⣿⠒⡿⣿⡹⢿⣟⣿⣿⣧⢻⠉⡇⣿⢿⡻⣿⣯⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢾⣻⣾⣽⢾⣿⢯⣾⣟⣯⢿⣷⣯⣞⡿⣟⣯⡿⣟⣷⡿⣯⣟⡾⣻⢿⣯⡿⣟⢷⣻⣿⣯⣟⣯⡷⢿⣯⢾⣽⣿⡾⣽⡿⣳⣾⣽⢿⣻⣿⡿⣿⣿⣶⣿⣿⣻⣽⢾⣻⣿⢯⣿⣞⡿⣯⣟⢾⣿⣯⣳⣿⡷⣟⢾⣿⣯⣞⡿⣟⡾⣻⣷⡽⢿⣷⣟⣯⡽⢿⣷⣯⣞⡿⣟⣯⣾⡟⣻⣼⣉⣤⣿⣿⣿⣿⣿⢙⡄⣤⣶⣶⣴⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣳⣿⣟⣽⢿⣽⣾⣟⣯⡾⣽⣻⣽⢿⣽⢿⣯⡿⣯⡿⣳⢿⣯⣽⡾⢿⣯⡾⣻⣽⡿⢾⣻⣷⣽⡿⣳⣿⣟⢾⣽⣿⡿⣿⣿⣾⣿⣶⣤⣄⡀⠂⠐⠀⣦⣿⣽⣿⣻⢷⣻⢿⣷⣯⣟⡷⣟⢾⣽⣿⡷⣯⢿⣯⢷⣾⣟⣻⢿⣷⣟⣻⣷⡿⣯⣞⢿⣯⣟⣽⣻⣽⢿⣽⣻⣿⣳⣿⣞⣿⣿⣌⣿⢻⣿⣿⣿⢻⡿⡿⣿⡿⢿⠙⡌⣿⣿⣿⣿⣿⣿⣿⡟⣿ ⣽⣾⡿⣞⡿⣟⡾⣽⣻⣷⣟⣽⡿⣯⣟⡽⣾⣟⢯⣷⡽⣿⢯⣻⣽⣾⣟⢾⣿⣟⣯⡷⣟⣽⣾⡿⣞⣿⡽⢿⣿⣿⣷⣴⣢⣄⢀⠒⠂⢀⡂⠄⠀⡀⠀⠠⡀⣶⣿⣿⣻⣽⡿⣯⣞⡿⣯⢷⣽⣻⣿⣿⣷⣿⣿⣻⣷⣻⢾⣻⣾⡿⣟⣯⡿⣳⣽⣾⣟⢯⣷⢯⣾⡿⣯⣟⡽⣿⡽⣾⣻⣽⣿⢾⣿⣬⣷⣾⣄⣠⣄⣤⣤⣤⣿⣼⡶⣿⣿⡘⣟⣿⣿⣿⣿ ⣾⣟⣾⣟⣻⢾⣽⣾⣟⣻⣽⡾⢿⣽⢾⣻⣿⣯⣟⣷⡿⣯⣟⢯⣷⣯⢿⣷⣟⡷⣯⣷⣟⡾⣽⣾⣟⢾⣻⣿⣿⢀⠠⠀⠡⠀⢂⠀⢀⠀⠈⠐⠠⠀⠀⠄⠀⡀⣆⡿⣯⣷⢿⣻⣿⢿⣿⣿⣾⣿⣶⣛⣥⠲⣿⣾⣻⢿⣷⣯⣟⢷⣻⣷⡿⣯⣟⣽⣻⣷⣽⢿⣷⣯⣟⢾⣻⣾⡿⣯⢷⣿⢯⣷⣯⣿⣷⣿⢻⠟⣷⣿⣿⣿⣿⣰⠉⡀⣅⣹⣿⣿⣿⢿⡿ ⣽⣾⣟⢾⣻⣿⣳⣾⣽⡿⣟⣯⢷⣻⣿⣳⢿⣷⡿⣯⡷⢾⣻⣾⣽⢾⣻⣿⣳⣿⣞⣿⢯⣾⣟⣯⢿⣯⣳⣿⣿⢌⠈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣷⣯⣶⣞⣟⣧⢟⣣⢶⣛⢦⡛⣬⡹⣿⣷⣯⡾⣻⣷⡾⣽⣻⣾⡿⣟⢯⣻⣽⣾⡿⣟⣽⣻⢿⣯⣷⣟⢾⣽⣿⡽⣾⣻⣷⡾⣽⣿⣿⣿⡁⣟⣻⣟⣈⡿⣿⣿⡐⣤⣷⣿⣹⣆⣿ ⣾⣽⢿⣽⣾⡿⣯⣷⣟⢯⣻⣽⣿⡷⣞⣿⡽⣾⡿⣟⣾⣟⣻⣽⣾⣟⣾⡽⣿⡷⣯⣟⢾⣿⣯⣟⢯⣷⣯⣳⣿⢻⠀⠄⠀⠀⠂⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠀⠀⠀⣆⣿⢭⣳⢮⡝⣱⡼⡛⣥⠞⣏⠄⣿⣿⣯⣟⣯⣻⣷⣯⡿⣞⢿⣽⣻⢿⣯⣷⣟⡾⣻⢿⣯⣟⣯⢾⣽⣾⡿⣟⣯⣟⣾⣟⣳⣿⣿⣿⠻⣛⣉⣥⣿⣤⣷⣿⠛⠛⡛⣏⣶⠅⣿ ⣿⣟⣯⡷⣯⢾⣽⣿⡾⣻⢿⣯⣳⣾⣽⢿⣻⣷⣻⢾⣿⣟⢯⣷⣯⢿⣷⣯⣟⣾⣟⢯⣽⢿⣾⡽⣿⣯⣞⣿⣯⣻⠄⠂⡈⠁⠀⠄⠀⢀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⡀⣷⢫⣵⡞⡭⡜⠳⣡⠷⢎⣈⣿⣿⢷⣻⢿⣷⣯⢷⣻⣽⢿⣾⣟⡷⣟⣽⢿⣯⢾⣻⣽⢿⣿⣷⣾⣷⢿⣽⣻⢾⣿⣯⣳⣿⣿⣿⣿⣿⣿⣼⣄⣷⠘⣇⣾⣴⣿⣠⠉⡻⣧ ⢾⣻⣿⣯⣳⣿⣞⢿⣯⣽⡿⣟⣷⣯⣻⢾⣽⣾⡿⣟⢷⣻⣿⣳⣿⡷⣽⣻⢿⣷⣯⣟⣯⡷⣟⣽⡾⣻⣽⢿⣾⣿⢸⢀⠂⠁⠀⠠⡁⠀⠐⠀⠐⡀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⣄⣻⢮⣚⡝⢣⣱⡼⢳⢂⣿⣿⣻⣽⡾⣻⣽⣿⡷⣟⢷⣽⣾⣻⣽⡿⣞⢿⣷⢯⣿⣿⣌⠠⠀⠀⣧⣿⡷⣟⢿⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⡖⣶⢿⡉⠟⣿⣿⡘ ⣾⣻⢾⣽⣿⡷⣯⢷⣻⣷⡽⣻⣿⢯⣻⣿⣳⣽⣿⡽⣾⡿⣞⣿⡽⣾⡿⣟⡷⣽⢾⣻⣾⣽⢾⣻⣿⢷⣯⢿⣯⣷⣿⡙⠂⠀⠠⡁⠄⡂⠄⠃⠀⠠⠁⠀⠁⠀⢀⠀⠂⠀⠀⠀⠀⡄⣧⢟⣫⣕⡮⡟⢃⢠⣿⣟⡿⣳⣿⣟⣯⡾⣽⣻⣿⡷⣯⢿⣷⢯⣷⣞⣿⢯⣿⣾⢀⠈⠀⠂⢁⣿⣯⣿⢑⡤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢿⡿⣿⣿ ⣿⣯⣟⣯⣟⣻⣷⣽⣻⣽⣻⣷⡽⢿⣽⡿⣳⣽⢾⣻⣿⣯⣟⢷⣻⣽⣿⡽⣿⡾⣽⣾⣟⣻⣷⣽⡿⣯⣟⢯⣷⣯⣿⡞⠈⡀⠰⢂⡀⠘⢈⠡⡈⠄⠂⠁⠈⠡⠋⠉⠀⠀⠀⠀⠀⠈⠀⣏⣿⡻⢿⣝⠩⢦⡇⣿⡽⣾⣟⡽⣻⣷⣻⢾⣽⣻⣿⡷⣽⣻⣷⣯⢿⣯⣷⣽⠂⠀⡔⠦⡶⣿⣿⣼⠂⡌⠧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⢷⣽⣻⢷⣻⣾⣟⡷⣯⣟⣯⡿⣯⡷⣟⣯⣟⣯⢷⣻⣷⡽⣾⡿⣯⣟⡾⢿⣽⣻⣿⢷⣽⣾⡿⣟⢯⣻⣾⣻⣷⣟⢿⠀⢈⡐⠜⢂⠍⡈⠱⠚⢩⠴⢫⡱⢸⢦⡘⣰⢽⠊⠱⠛⠟⣿⣿⣷⣷⣾⣿⠿⣉⡵⣿⣟⣯⢿⣷⣟⣯⡾⣽⣾⣟⡽⣿⡷⣟⣾⣟⡷⣟⣾⣿⠹⠀⠀⢀⠠⠄⢂⡄⠀⠠⢏⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣾⡽⣿⡽⣾⣟⣾⣟⡽⣻⢷⣽⣻⣷⣞⡿⣟⣯⣳⣿⡷⣯⢷⣻⢿⣯⢷⣻⣷⡽⣿⡷⣯⢾⣻⢾⣻⣿⣞⣻⣿⣿⢡⠌⠏⠋⢥⠳⣌⡹⠶⣊⡵⢎⡱⡜⢎⡑⢦⡘⠟⣿⣿⣿⣾⣰⠲⠃⣄⣧⣿⢿⡻⣽⣿⢿⣯⣽⡿⣳⣿⣟⣯⣽⡿⣳⣿⡷⣟⣻⣾⡿⣟⣯⣿⠻⠀⠀⠀⠀⠁⠉⠉⡋⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡿⣟⣯⣟⡷⣯⢾⣿⢯⣾⣟⣯⡿⣞⣻⣷⢾⣻⣽⣿⡽⣻⣽⣿⣞⡿⣟⣷⣟⣯⡾⣻⣽⢿⣽⣾⣟⢾⣻⣽⢿⣿⣾⣣⡜⣙⠷⣩⠶⣎⡙⢮⣍⡲⢍⡢⠜⢏⡡⢜⠣⣤⣷⣾⢲⡄⣠⢀⠀⠀⠀⣄⣶⣿⡿⣗⣿⢿⣽⣻⣿⣞⡿⣽⡿⣟⣾⡿⣯⡽⢾⣽⢿⣾⣟⢯⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⢾⣿⢯⣻⣽⢾⣿⢯⣷⣟⣯⣞⡽⣾⣟⣻⣽⢿⣷⢯⣻⣷⡽⢿⣯⢷⣻⣿⡷⣯⣟⢷⣻⣽⡾⣽⢿⣷⣞⡿⣿⣷⡔⢫⡴⡛⢥⡳⢮⣙⠶⢎⣙⠦⢋⢤⡜⠓⢢⡔⢠⣀⠀⠀⠀⠁⠀⠠⠀⡀⢣⠈⠀⣄⣦⣻⡽⣶⣿⣟⡷⣯⢷⣻⣽⡿⣟⢷⣽⣻⣾⣻⢷⣽⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣽⢾⣻⢾⣽⣿⢯⣷⣯⡿⣳⣽⣾⣟⣻⢷⣻⣽⣻⣾⡽⣿⡽⣻⣽⣾⣟⡽⣾⣟⡾⣻⢿⣳⣿⣯⣞⣻⣿⣿⣾⣙⡴⢛⣥⠞⣣⠧⢎⣑⡽⢎⡘⢲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢿⠫⠀⠀⠃⠋⠻⠈⠀⡀⣦⣿⣯⣿⣿⣞⣿⡽⣾⣟⡾⣻⣽⡿⣞⣽⣿⣞⡿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣿⣯⣟⣯⡷⣟⣷⢯⣻⣾⣟⣯⢷⣻⣾⡿⣟⢯⣷⣟⢯⣾⡿⣟⣯⢷⣻⣷⢿⣯⢷⣻⣷⢯⣾⣟⣿⣾⣹⢦⡛⣌⠳⢭⡝⢪⢶⡤⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢰⠀⠀⡀⣿⣿⣨⢀⠈⠀⠀⣤⣳⣾⣿⢿⣳⣿⢷⣽⣻⣽⡾⣽⣻⢿⣯⣽⡿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣟⡽⢿⣾⣟⣯⣳⣿⢯⣻⣽⣻⣽⣿⢯⣷⣟⡽⣿⣯⣞⢿⣽⢾⣻⣾⣽⣻⣿⡷⣟⣾⣟⣻⣷⣟⣿⣿⢭⡹⢶⠴⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣇⢤⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⡽⣾⡿⣟⡾⣽⣾⣟⡽⢿⣷⢯⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢯⣿⡷⣟⣳⣽⣾⡿⣟⢯⣷⢯⣷⡽⣿⣯⣟⡾⢿⣯⣟⢷⣻⣽⣾⣟⣻⢷⣻⣾⡿⣟⢷⣻⣾⣿⣹⣙⣀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢃⡀⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⣧⣻⣿⣳⢿⣯⣟⣷⣞⡿⣳⣿⣞⡿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⡷⣯⣳⣾⣟⣯⢷⣻⣽⣾⣟⣻⣽⡿⣳⢿⣯⣟⣯⡽⣾⡿⣟⣯⢿⣳⣿⢯⣷⣟⡽⣾⡿⣟⣷⣯⣽⣿⢿⠷⡛⢉⠬⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢣⡈⠐⠀⠀⠀⡀⠑⠋⠛⡟⠿⣾⣟⢿⣷⣯⡾⣽⡾⣽⣾⣻⣾⡿⣟⣽⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⡾⣽⣻⣾⣽⣻⣽⣾⡿⣟⣯⣳⢿⣯⣟⣯⡿⣳⢿⣯⣞⣿⢯⣷⢯⣻⣽⢾⣽⣾⣟⡷⣯⢷⣻⣽⢾⣻⣾⡽⣾⣻⣷⣿⢯⠾⠻⡛⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⡉⠿⠷⡯⣿⣯⣷⣽⣻⣷⣟⣯⡿⣳⣽⣾⣟⣾⣟⣯⢷⣽⣻⢷⣻⣽⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣽⣻⢿⣷⣟⡾⣟⣯⢷⣻⣽⣾⡿⣟⢯⣷⡽⣿⡽⣾⣟⢾⣽⣾⣟⡽⣻⣿⣯⣟⣯⣳⣾⣽⡿⣯⣟⣯⣟⣯⣟⣷⣯⡿⣯⣟⣯⣿⣽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⣽⣿⣻⢿⣳⣾⣽⡿⣟⣯⡾⣽⡿⣯⣟⣯⢷⣽⣻⣽⣾⡿⣟⣯⡿⣞⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⢿⣳⣾⡿⣟⣯⣟⣷⡾⣟⣯⢷⣻⣽⣾⡿⣟⡾⣽⢿⣾⣟⣯⢷⣻⢾⣻⢿⣯⣳⣽⣿⣞⣻⢷⣾⣟⡾⣽⡾⣻⢿⣷⢯⣻⣽⢾⣿⣻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⣿⣻⢿⣳⣿⣟⣯⣞⡿⣯⣞⣽⡿⢷⣻⣽⣾⡿⣟⡷⣽⢾⣻⣽⡿⣞⢿⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⢿⣳⣿⣟⢷⣻⣽⡾⣻⣽⣻⣽⣾⡿⣟⣯⣳⢿⣯⣟⢯⣾⣟⣳⣿⢯⣽⣻⢾⣽⣾⣟⡽⣾⣟⣻⣷⢿⣯⣟⣷⣞⡿⣯⣞⡿⣟⣯⣳⣿⢻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣿⣞⡿⣯⣞⡽⣾⣟⢷⣻⣽⣾⡽⣿⡾⣟⣯⢷⣻⣾⡽⣿⣞⣻⢷⣽⣻⢷⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⡿⣯⣟⡷⣯⡿⣳⣽⢿⣾⣟⡷⣯⢷⣻⣽⣾⡿⣟⢯⣷⣟⣯⣻⢷⣻⣷⡽⣾⣟⣯⢷⣻⣷⣽⡿⣯⡽⢿⣻⣽⣿⣞⢿⣯⢷⣻⣽⣾⣟⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣆⡿⣿⣯⢷⣻⣽⣾⣟⣻⣷⡾⣟⣯⣻⢷⣽⣻⣽⣾⡿⣟⣯⡷⣟⣽⣻⣷⡽⣾⡿⣟⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡾⣽⡾⣻⣽⡿⣯⣞⡿⣟⣯⣳⣽⣾⡿⣟⣯⢷⣻⣽⣾⡿⣟⡾⣽⣻⣾⡽⣿⣞⣻⣽⣻⣾⡿⣟⢯⣷⡽⢿⣯⡿⣟⢷⣯⣻⢷⣻⣽⢿⣯⣿⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⣿⢿⣯⣻⢷⣻⣽⢾⣻⣿⣯⣞⢿⣯⣳⣽⡿⣞⣽⢾⣻⣽⣻⣽⡿⣳⣿⡷⣯⣳⢿⣳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦ ⢿⣯⣟⣷⢯⣷⢯⣻⣷⣟⡷⣯⣳⣾⣟⢷⣯⣳⣿⡷⣟⣯⣳⢿⣯⣟⢯⣷⣯⡷⣟⣯⣟⢯⣷⢯⣻⣽⣾⡿⣞⢿⣯⡽⣿⣞⡽⣾⡿⣟⢯⣷⣟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣏⣿⣯⣟⡷⣯⡷⣟⣾⣟⢯⣻⣽⢿⣷⣯⣟⡷⣯⣟⣷⣯⣟⡷⣯⡽⣿⡷⣯⣟⣯⡿⣯⣟⡽⣻⣿⣷⣯⣿⣷⣻⣾⣽⣿⣿⣷⣿⣾⢓⠀⠠⠀⠀ ⣻⣽⡾⣻⣽⣾⣟⡾⣽⣻⣽⣻⣽⣾⣟⣻⣽⣾⡿⣯⡽⣿⣯⡽⢾⣻⣿⣯⣞⣽⣻⢷⣻⣽⣾⣟⡽⣻⣾⢿⣯⢷⣻⣽⡿⣯⣟⣯⢷⣻⣽⣿⡷⣟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠉⠉⠛⠛⡿⣷⣟⡷⣯⣟⣯⢷⣯⣳⢿⣯⡷⣞⣻⢿⣯⣳⣽⡾⣻⢿⣳⣿⢯⣽⣻⣷⣞⡿⣟⢯⣻⢷⣻⢾⣽⣻⣾⡽⣿⡽⣾⣻⢷⣻⣽⣿⣏⠠⠐⠃⠿⣶ ⣻⣷⣟⢷⣯⣽⢾⣿⣞⡿⣟⢯⣻⣾⢿⣯⡽⣿⢯⣻⣽⡿⢷⣯⣽⣻⢾⣻⣽⣾⡽⣾⡿⣟⣯⢷⣻⢿⣷⢯⣷⣯⣟⡷⣟⢯⣻⣽⣿⡷⣯⡷⣽⡾⣿⢿⡄⠤⠑⠀⠉⡉⠏⠛⠿⠿⣯⣷⣟⣽⣿⣯⣽⣻⣽⢾⣻⣿⣯⣟⣯⡾⣟⣷⣯⣟⢯⣷⣯⣟⣯⢿⣳⣿⢯⣷⡽⣻⣽⣾⣟⢯⣷⡽⣿⡷⣯⣟⢷⣯⣳⢿⣳⣿⣟⣯⣞⡿⣯⢻⣩⠐⣆⠀⠀ ⣾⣽⣻⣽⢾⣻⣽⢿⣽⣻⢾⣻⢿⣯⣟⢯⣷⡽⢿⣯⡽⣻⣽⢾⣻⢾⣽⢿⣷⣯⣟⣯⢷⣻⣽⣾⣟⡽⣻⣽⣾⣟⡷⣯⣟⢯⣽⡿⣳⣾⣟⣽⡾⣽⣾⣟⢿⠿⡿⣷⣾⣽⣻⣽⣾⡿⣟⣯⡷⣟⢯⣾⣟⡽⣾⣟⣻⢷⣻⢿⣯⣟⣯⣻⢷⣻⣽⣿⣞⡿⢯⣻⣷⢯⣷⣯⣟⡷⣟⣽⣻⣷⣯⡿⣞⣻⢾⣽⣻⣽⣾⡿⣯⡽⢿⣻⣽⢾⣿⢻⣿⡱⠀⠀⠀ ⣿⣞⡿⣟⣯⢷⣻⣽⡿⢷⣯⢷⣻⢷⣻⣽⣾⡿⣟⢯⣷⢯⣻⣽⣾⣟⣯⡷⣻⢷⣽⣻⣾⡿⣟⣷⢯⣾⡿⣯⣞⣽⣾⣟⢯⣻⣷⡽⣿⣞⣽⡾⣽⣻⣽⢿⣷⢯⣻⣽⣿⣞⡿⣟⣯⢷⣻⣷⣯⣞⢿⣯⢷⣻⣷⣽⡿⣯⣟⡷⣟⢯⣷⡽⣾⡿⣟⢯⣷⣟⢯⣽⣻⣿⣳⣽⡿⣯⣟⡷⣟⣯⣟⡷⣟⣯⣟⣯⡷⣟⣷⢯⣾⣟⡽⢾⣻⣷⣟⣿⣛⠻⠛⠛⠈ ⢿⣯⢷⣻⣽⣾⣟⡽⣻⣽⣻⣽⣻⣾⡽⣾⣟⢾⣻⣿⣯⣞⡽⣾⣟⣳⣽⣿⡷⣽⡾⢿⣯⢾⣻⣽⢿⣯⢿⣳⣽⣾⣟⣳⢿⣯⣳⣽⡿⣯⣟⣽⣻⢷⣽⣻⣾⣟⡽⣻⢷⣯⢷⣻⣽⣾⣟⣯⢷⣯⢿⣷⣯⡷⣽⡾⢿⣯⡽⣾⡿⣟⣾⡽⣿⢯⣽⣻⣷⢯⣾⡿⣟⡷⣯⣞⢿⣯⡽⣿⡾⣽⡾⣽⣻⢷⣻⣽⣾⡿⣯⢷⣯⢿⣳⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣽⣾⡿⣟⣯⢷⣽⡿⣳⢾⣽⢿⣯⣟⣯⢾⣽⣻⢾⣻⣽⣾⣟⣽⣻⣷⡽⣾⡿⣯⣞⢿⣯⢷⣽⣻⢷⣻⣽⣻⣽⣿⣯⡾⣟⣻⣷⡽⢿⣽⡾⣻⣷⡽⢿⣯⢿⣳⣽⣻⣾⣻⢷⣻⣽⣻⣽⣾⣟⡽⣻⣽⣿⡷⣯⢷⣻⣾⣟⣳⢿⣯⣟⢯⣿⡷⣟⣯⢷⣯⢷⣻⣽⢾⣿⢯⣽⣻⢾⣽⣻⣽⣾⡽⣾⡿⣟⣷⢯⣷⣯⣟⡷⣯⡿⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⢾⣻⣽⣻⢾⣽⣿⡽⣻⣽⣿⣞⡿⣳⢿⣯⣟⣯⡷⣟⢾⣽⣿⣞⡿⣟⣯⡽⣿⢯⣻⣽⢿⣽⣻⣷⡽⣾⡿⣟⢯⣷⡽⢿⣷⣯⡽⣾⡿⣟⡷⣯⣻⣷⡿⣯⣞⡿⣯⣟⢯⣷⣟⣯⡾⣽⡿⣞⣿⢯⣾⣟⡽⣻⣽⣻⣾⡿⣟⣯⣽⡿⢯⣾⣟⡷⣯⡷⣯⣳⣽⣿⡷⣟⣯⢷⣻⣽⡿⣟⣯⡷⣟⣽⣻⣷⢾⣽⣻⣽⣿⣞⡿⣯⣟⡷⣞⣿⣿⣿⣝⣹⢦⡜⣳ ⣽⢿⣷⢯⣷⣞⡿⣞⡿⣟⢯⣷⣟⣯⡽⢿⣽⣻⣷⢯⣷⣟⡷⣟⣻⢷⣻⣽⡾⢿⣯⡿⣞⡿⣟⣯⡷⣯⢷⣻⣷⣽⡾⣻⣽⢾⣻⣾⣽⡾⣻⢷⣻⣾⡽⢿⣽⣻⢷⣻⣽⣾⡿⣟⣯⣟⢷⣯⢷⣻⣽⢿⣯⡿⣳⢿⣷⢯⣻⣽⡾⢿⣯⣟⣯⣳⣿⣳⣽⣻⣾⡽⣾⡿⣟⣯⡿⣞⡿⢯⣽⣻⣽⡿⣞⣻⣷⣞⡿⣟⢯⣷⢯⣷⡽⣾⣟⣳⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣽⣻⣽⣿⣯⣞⢿⣯⣟⣯⡷⢿⣯⣟⡷⣟⣯⣟⣯⡿⣯⣞⡽⣾⡿⣟⣯⢷⣻⢷⣯⢷⣻⣽⣾⣟⣯⣳⣿⡷⣯⢷⣻⣽⢿⣾⣟⣯⣻⣷⢯⣷⣯⣞⡿⣟⣯⡾⣟⣷⢯⣻⣷⡽⣻⣽⣾⡿⣟⢯⣷⡽⣿⡷⣯⣞⡽⣾⣟⣻⢷⣻⣽⣾⡿⣯⣟⢯⣾⣟⣯⢷⣽⣻⢷⣯⢷⣽⡿⢯⣽⡿⣞⣻⣷⣞⢿⣯⣟⣯⣟⣯⡽⣾⣟⣯⣿⣿⣿⣿⡻⣛⣿ ⣽⡿⣟⢯⣷⡽⢿⣽⣻⢷⣻⣾⣽⡿⣟⡷⣯⡿⣳⢾⣻⢷⣻⣽⣾⣟⢾⣻⣿⣯⣞⣻⣷⣽⡿⣳⣾⣟⣳⣿⡷⣯⣟⣯⡾⣽⡿⣟⣳⢾⣽⣻⣾⣽⢾⣽⣻⢿⣯⣟⣯⣳⣽⡾⣻⣽⡿⣞⣿⢯⣻⣷⣽⡿⣳⣽⣻⣽⣾⣟⢾⣻⣾⡽⣾⣟⢾⣻⢿⣳⣽⣻⣽⣾⡿⣟⣳⣾⣽⡿⢯⣽⡿⢯⣽⣻⣽⣿⢯⣻⢷⣻⢷⣽⡿⣯⣟⢯⣿⣿⣿⣿⣿⣿⣿ ⣽⡿⢷⣯⣽⡿⣞⡿⣟⣯⡾⣟⣽⡿⣞⣻⢿⣳⣿⣟⣯⣻⢷⣻⣾⢿⣯⣳⢿⣯⣟⣯⣽⡿⣳⣿⣞⣽⣾⡿⣯⣟⡽⣾⣟⣻⢷⣯⣳⣿⣟⢯⣾⣟⣯⣻⢷⣻⢿⣯⣟⣯⣟⣯⢷⣻⢾⣿⢯⣷⡽⣿⡽⣻⣽⣻⢷⣻⣾⢿⣯⢷⣽⣻⣾⢿⣯⢷⣻⣽⣻⢷⣻⣾⢿⣯⣳⣿⣟⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣻⣷⡽⣾⡿⢯⣻⢷⣻⣿⣿⣿⣿⣿⣿⣿ ⣾⡿⣳⢿⣷⢯⣷⣟⢯⣷⣟⣯⡽⢿⣯⣽⡿⣯⡽⢿⣯⡽⣿⢯⣽⢿⣯⣽⡿⣟⢯⣷⡽⣻⣾⡽⣾⣟⣯⣳⢿⣯⡽⣿⢯⣽⣻⣿⣯⣞⡽⢿⣽⣻⣽⡾⣻⢾⣻⢷⣾⣟⡿⣟⣷⢯⣽⢿⣯⣽⡿⢯⣽⡿⣯⡽⣿⢯⣽⢿⣯⣽⡿⢯⣽⢿⣯⣽⡿⣯⡽⣿⢯⣽⢿⣯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⣯⡽⣿⢯⣽⡿⣯⡽⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣯⡷⣯⣟⣯⡷⣟⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⣻⣽⡿⣟⣯⣟⣯⣟⣯⡽⢿⣯⡽⢿⣯⡽⢾⣻⣽⣻⢿⣯⡿⣻⣿⢿⣿⣿⣻⣿⣿⣤⣿⣻⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣷⣿⣿⣿⣿⣿ ⢿⣯⣟⣯⣟⡿⣾⣾⣷⣶⣷⣶⣶⣷⣶⣾⣶⣾⣶⣾⣷⣶⣾⣷⣶⣷⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣖⣶⢶⡶⢶⣶⠶⢶⡶⣴⢀⠀⡀⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣿⡿⣽⡿⣿⣿ ⣻⢷⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣯⣿ ⣻⣿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿ ⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠙⠋⠛⠈⠀⠉⠛⠙⠀⠀⠀⠀⠀⠁⣿⣼⢠⠃⠛⠀⠃⠙⠀⠃⠙⠀⠀⠀⠋⠘⠀⠃⠈⠃⠛⠈⠀⠛⠀⠀⠃⠙⠀⠋⠘⠀⠀⠀⠀⠋⠙⠋⠙⠀⠀⠉⠛⠙⠈⠀⠁⡿⣸⢠⠀⠀⠀⠋⠛⠈⠀⠛⠀⠛⠈⠀⠛⠈⠀⠀⠀⠛⠈⠋⠘⠃⠙⠀⠀⠛⠘⠀⠛⠈⠀⠀⠀⠁⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿ ⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢼⡅⣿⠣⣏⣾⠀⣠⣀⣧⣿⠀⠀⠀⠀⡟⣾⣿⠈⡇⣿⠀⡇⣿⠀⡷⣺⠀⠀⠀⣿⢼⠀⣿⢼⡀⣧⢻⠄⣿⢰⠁⣿⣿⠋⣿⣿⠈⠀⠀⠀⣿⣼⡀⣿⢺⡇⣿⣀⣄⣿⠠⡟⣾⣿⠈⠀⠀⠀⡀⣷⣸⠆⣿⢈⣿⢸⠀⣿⢸⠀⠀⠀⣿⢘⣿⢸⡇⣿⠀⠇⣿⢻⡟⣿⢿⠀⠀⠀⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣹⡀⣷⢻⣿⠘⠀⠿⠻⡿⣴⠀⠀⠀⡇⣾⢀⣇⢿⡄⣷⠻⣞⣿⠛⣿⢼⠀⠀⠀⣆⣿⠛⣿⣸⠓⡟⢿⡐⣿⠠⡷⢸⣆⣿⢰⣦⢻⠀⠀⠀⣷⣸⠀⣷⢸⡀⣷⠿⠟⣴⢧⣾⠀⣦⢻⠀⠀⠀⠓⡿⣿⠆⣿⠀⣶⢿⡛⣿⢸⠀⠀⠀⣿⠘⣷⢸⡆⣿⠂⣿⢐⣧⣿⡀⣿⢸⠀⠀⠄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣽⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⡀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡷⣸⠀⣆⣰⠀⣿⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣆⣰⠀⢾⠀⠀⢀⠀⣿⢰⠀⠀⠀⣿⠰⣷⣰⠆⢻⠀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣯ ⣿⣯⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⣿ ⢿⣻⣾⣿⠻⠙⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠀⠈⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠁⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠈⠁⠀⠀⠀⠈⠁⠀⠀⠁⠉⠙⠯⡟⣳⣿ ⣃⣄⣖⣭⣥⣾⣿⣿⣯⣻⣽⣾⣽⣾⣻⣷⣟⣯⣽⣿⣯⣷⣟⣯⣳⣽⣾⣻⣽⣾⣽⣾⣻⣽⣿⣯⣽⣿⣯⣳⣽⣿⣯⣽⣿⣯⣽⣿⣯⣽⣾⣽⣾⣽⣾⣻⣽⣿⣯⣽⣾⣻⣽⣾⣽⣾⣽⣾⣻⣷⣯⣞⣻⣷⣽⣾⠿⠳⡝⠉⠤⠘⠢⡑⠌⠠⠜⠃⠡⠔⠊⠡⠔⠊⢡⠆⡈⠑⠢⠌⠑⠢⠌⠑⠢⠌⠑⠢⠌⣑⣦⣮⣷⣿⣟⣻⣽⣿⣯⣽⣻⣷⡾⣻⣿ ⠤⡑⠤⠐⡩⠆⢂⡄⣢⣄⣦⣶⣶⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣷⣶⣾⣷⣾⣷⣷⣶⣾⣷⣶⣾⣷⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣷⣶⣿⣶⣿⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣿⣷⢾⣿⣷⣾⡿⣷⣾⣿⣶⣿⣷⠾⢿⠛⡘⢆⡀⠰⡐⠢⢄⡐⠢⢄⠰⢆⡄⠐⢢⡄⠐⢢⡄⠐⢢⡄⠐⢢⡄⠒⢂⡐⢒⡠⣔⣦⣶⣾⣷⣿⣟⣻⣽⢾⣿ ⡐⠢⣉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣠ ⡐⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠙⠙⠋⠈⠁⠛⠈⠀⠙⠙⠙⠀⠀⠀⠀⠉⠋⠙⠈⠁⠛⠀⠋⠙⠀⠃⠛⠈⠁⠛⠀⠋⠘⠀⠀⠀⠁⠉⠛⠉⠀⠋⠙⠁⠛⠀⠃⠘⠁⠙⠀⠁⠙⠁⠛⠈⠀⠋⠙⠀⠋⠘⠀⠁⠛⠘⠀⠀⠀⠀⠋⠙⠉⠈⠁⠛⠀⠋⠘⠀⠛⠀⠋⠈⠀⠛⠈⠋⠘⠀⠃⠛⠀⠃⠛⠀⠁⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢺⡆⣿⠓⣏⣿⠀⣇⣿⠆⣿⡻⣉⢀⠀⠀⠁⡿⣚⣟⣿⠆⣿⠘⣀⣿⢸⡀⣇⢿⡀⣿⠘⣿⣸⠀⠀⠀⡟⣞⡛⣿⢺⣧⢻⡀⣆⢿⡿⣽⡇⣿⠀⡇⣿⡃⣿⠰⠃⣿⣿⠋⣾⣿⠈⡀⣧⢿⠀⠀⠀⠇⢻⣳⣟⢿⡇⣿⠰⣄⣷⠟⣿⢈⣿⢸⠀⣿⢘⣿⢸⠀⡟⣿⢹⣟⣿⠸⠀⣅⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢼⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⣷⢽⡀⣷⢻⣟⠈⠃⡟⣿⠘⠳⡟⣿⠠⠀⠀⡄⣧⢻⡟⣶⡁⣿⠰⠛⣿⢻⠓⡟⢿⡘⣿⠐⣿⢸⠀⠀⠀⣆⣿⠛⣿⢰⣏⢾⠀⠟⣼⣧⣻⡄⣷⠿⡿⣿⠆⣿⠠⡟⣼⡆⣿⢰⣧⣸⠓⡟⣿⠘⠀⠀⡀⣷⠻⡟⣰⠇⣿⠰⠃⡾⣥⣿⢈⣶⢿⠞⣿⠰⣷⣸⠇⣾⣀⣷⣼⡄⣿⠂⠛⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⠀⡄⣼⠀⡀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⣿⠰⠀⣶⢠⠀⣆⣼⠀⡿⠀⣷⢸⠀⠀⠀⠀⠀⡀⠀⠀⡗⢼⠀⣀⠀⡇⣾⠀⡀⢀⠀⢀⠂⣿⠀⡀⠀⠀⣀⠀⠀⢀⠀⣄⣼⠀⠀⠀⠀⠀⠀⢀⠀⡆⣿⠠⡀⢀⠀⣿⠰⠀⣀⠀⡀⠀⡗⠸⠀⢀⠀⡀⢀⠀⢀⠀⣀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⡽⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⡷⣛⢷⠻⠈⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣯⡝⣻⢯⣽⣟⢯⡽⡻⢯⡽⢟⢯⡹⢿⢫⣽⡻⢯⡹⢿⢫⣽⡻⢯⡽⡟⢯⣝⠿⣏⠽⡻⢯⡽⢟⢯⡹⢿⢫⣽⠟⢯⡹⢿⢫⣽⠿⢯⡽⠿⢯⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣹⠾⣋⡱⢞⣍⡳⢎⣋⡱⢮⠝⣣⡜⠫⢱⢮⡝⢣⡜⢫⡱⠼⢛⣣⢜⢫⠱⢮⠝⣣⠜⢫⡱⢞⡍⠳⠈⠙⠡⠌⠉⠁⠌⠉⠡⠌⠉⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠘⣿⠿⢻⡜⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣟⠀⠀⠀⠈⢀⣿⡿⠃⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠈⠉⠁⠀⠀⠛⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡐⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣀⠀⠀⣠⣴⣿⣷⣲⣶⣿⣯⣜⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠟⠋⠝⢟⠻⣟⠿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣏⡀⠀⠀⢸⡸⠾⣅⢈⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⡏⣿⣿⠀⠀⠀⠀⠀⠀⢳⡝⣾⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣇⣗⣷⡀⠀⠀⠀⠐⠴⠁⡹⢼⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠍⡽⡽⣿⠹⣿⠇⡀⡀⠀⡀⠀⠤⠱⡘⣾⣿⡏⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣄⡁⠀⠊⢧⣿⠀⣧⠁⠀⠓⠠⢀⠐⡜⣿⣿⡇⣿⣿⡇ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣲⢤⣄⣿⢈⣾⣷⡀⢠⣣⢠⠀⢨⣨⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⢿⣤⣭⡇⠈⣿⣠⡟⢃⠟⠠⠛⡆⡵⡔⠽⣿⣿⣿⣿⡇ ⠀⠀⠀⣰⣿⣿⡗⣻⣿⣿⣟⣾⣿⣉⢂⣹⣃⣧⣦⣶⠐⠒⠒⠒⠒⠢⢾⣿⣿⣻⠇ ⠀⠀⣰⣿⣿⣿⣿⣿⣯⣿⡇⠋⠈⠂⠘⠘⠋⠁⠉⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⠀ ⠀⢰⣿⣿⣿⣿⣿⡿⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇ ⢀⣿⣿⣿⣻⣿⣿⣯⣴⢂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⣇⠀⠀⣄⠚⡀⢀⢀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣣⠠⠟⠀⠘⢸⠇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⠿⣄⠀⡟⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠃ ⢸⣿⣿⣿⣷⡹⠙⢿⢿⠿⠳⢀⣠⠐⠀⠀⣹⠃⠀⠀⠀⢀⣾⣧⣬⣭⣿⣿⣿⣿⡄ ⣸⣿⣿⣧⡙⢿⣷⣴⢤⡤⣄⠀⠈⠙⠓⢰⡏⠀⠀⠀⢀⣾⣯⣽⣿⣿⣿⣿⣿⣿⠁ ⣿⢿⣿⣿⣿⣷⣷⣍⣁⣉⣁⣀⡀⠀⢀⡾⠀⠀⠀⠄⡾⠿⠿⣿⣿⣿⣿⣿⣿⡿⠀ ⠈⠉⠍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠟⠀⠀⠀⠀⠀⣷⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⡇⢀⠶⡀⢰⡀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⠀⡇⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡇⢰⣇⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢶⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⠛⡿⣿⣶⣿⣿⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠺⠤⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡥⠴⣾⣿⣿⣿⡿⢟⣹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⣭⣅⣀⣻⣿⣻⣿⣿⣦⡹⠿⠛⠙⠟⠻⠀⢀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣬⣙⠙⠛⠛⠛⠛⠛⠛⠻⣛⣠⣀⡠⠴⠜⠛⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠉⡀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠁⠢⠤⠄⠒⠉⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⢀⣠⣦⣶⢿⣛⢯⠯⣝⠮⣝⡹⣏⢿⡻⢿⣳⣤⣀⣀⣰⣴⣾⢿⡿⣿⢷⣄⠀⠐⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣁⣶⣷⢿⣫⣓⣮⢓⡮⢇⡻⣬⢛⡼⣣⡝⡶⣹⢣⣓⢮⢻⠿⣿⣹⢮⣗⣻⡼⢯⣿⣷⡄⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢠⣶⣿⡿⢛⣽⣿⣿⣿⣿⣿⣿⣷⡭⢏⡶⢣⡝⡞⣥⢻⣬⡓⣏⠾⣹⢻⣿⡼⣧⣿⣿⣿⣿⣿⠄⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣜⣧⣿⡿⣾⣷⣶⣿⣼⡭⢧⣫⠽⣿⣿⣿⣿⣿⣿⣿⡀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣿⡿⠏⠀⢺⣿⣿⣿⣟⠻⣿⢿⣿⣿⣿⣿⡾⢏⣾⣿⣿⣿⣿⣿⣿⣿⣷⣧⡻⣜⣿⣿⣿⣾⣿⡟⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⡇⠀⠀⣸⣿⣿⣿⣿⣦⡹⣸⣿⣿⣿⠏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡼⣿⣿⠿⠋⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢰⣿⣾⡇⠀⠀⠘⢯⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⡟⢻⡟⣽⣿⣿⣿⣿⣿⡵⣻⣆⠀⢀⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣞⣷⡀⠀⠀⠀⠹⠿⣿⣿⣿⣿⡿⢹⠁⠀⠸⣿⣿⣿⣿⣷⣌⠀⣿⣿⣿⣿⣿⣿⢞⡵⡏⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣷⢮⣝⣿⡷⣶⣤⣤⣤⣼⡟⢋⠅⢢⠙⣧⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⠮⣝⣷⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣿⣟⢾⡹⣏⠷⣎⢷⡹⣖⠏⢄⠊⡄⠃⡜⠻⣆⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⡟⣾⡗⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⣀⣤⣾⣿⣯⠷⣭⢻⡜⣧⠟⢡⠘⡠⢃⠌⡒⣀⠣⢈⡙⣷⣦⣝⣻⡿⠿⣿⣿⣿⣛⢧⣛⣾⡏⠀⡰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⠒⠒⠒⠔⠉⣀⣴⣶⣿⡻⣝⣾⣿⣿⣍⠩⡉⠔⣈⠢⠑⡄⢣⠘⡰⢀⠆⡡⠐⢯⣻⡜⣯⣛⢿⡻⣝⣶⣯⣷⡿⠟⠀⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⣠⣤⣀⣾⡷⣦⣤⣶⣿⣿⣿⣖⣿⣿⣿⣿⣿⣿⣷⣬⠒⡀⠆⡑⡈⠆⡱⢀⠣⡘⠤⢉⠌⢷⡝⣶⡹⣎⢷⣹⣛⣿⠟⠁⣀⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⣱⣦⣾⡿⣹⢻⣧⡽⣽⠟⠿⣿⣿⣿⣿⣿⣿⡿⠞⠋⠉⠀⠉⠻⢦⣕⣠⢁⠒⠤⢁⠆⢡⠘⡠⠊⠤⣙⠳⠽⣎⣷⡷⠛⠁⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⣶⣿⢻⣱⡭⢇⡯⢽⢿⣧⣌⠂⣽⣿⣿⠟⠛⠁⢀⣡⠖⠃⠒⠄⡀⠀⠀⠉⠛⠓⠾⠦⢮⣤⣧⣴⣭⣴⠴⠾⠚⠋⠉⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⠏⢸⣿⣼⣧⣛⢿⣿⡘⡉⢄⣿⡋⡐⢿⠁⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⢀⣀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⢊⣵⣄⣀⣴⣾⣿⣿⣿⣏⠢⢈⣿⣶⢾⠟⢡⠐⣺⠆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⢫⣴⠟⡉⢌⡶⠛⠛⠛⢋⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⡿⣿⠟⠉⠈⠻⢦⣘⣴⠏⢀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⢹⣿⣿⣿⣿⠟⣀⠔⠒⠂⠤⠤⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠢⣙⠛⠛⣁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠠⠶⠚⣩⡶⡳⠒⣫⣴⣶⣿⣷⣾⣿⣿⣷⣶⣶⣦⣌⣀⡂⠤⠀⠐⠦⠴⢖⡄ ⠀⠁⠀⠰⠣⠉⣴⣿⣿⣿⠿⢿⣿⡿⣿⣿⢿⣿⡿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠠⠛ ⠀⠀⠀⣗⢀⢰⣿⡟⡡⠄⠤⠈⠀⠀⠈⠁⠀⠁⠀⠒⠊⢽⣿⣿⡄⠀⠀⠀⠈⡀ ⠀⠀⠀⡇⢸⣿⡟⠉⡠⣤⣦⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠹⣿⣷⠂⠈⠁⠈⡇ ⡀⠶⠶⡿⠓⠙⠁⠈⠫⠟⠃⠃⠀⠀⠀⠀⠀⠀⠻⠿⠃⠃⠀⠙⠉⠣⡀⠀⣤⠇ ⣟⣉⡿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣀⣟⣂ ⠿⠿⡇⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡇⠀⠀ ⠀⢸⣻⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⢯⣉⣉ ⠀⣼⣿⠧⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠚⣧⢸⠉⠉ ⠀⣶⢹⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⡇⢸⠀⠀ ⠀⣿⡞⠀⠀⠀⢈⠈⢳⠄⠠⢀⡀⠀⠀⠀⠀⠀⠠⣴⣿⠃⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⢹⡇⠀⠀⠀⠰⡅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⡃⠀⠀⠀ ⣤⣿⢑⣭⣉⡃⠙⣵⡇⠒⠶⠒⠂⢤⡤⠤⠤⠤⣤⣴⣇⣀⣀⣀⣀⡔⠁⠀⠀⠀ ⠻⣼⡘⣿⣻⠿⢿⣻⣿⣿⣿⣷⣶⡆⠀⣶⣶⢤⣤⣽⢻⣤⣀⣀⡝⣰⠀⢠⡇⠀ ⠓⠳⣿⡺⠿⠭⠽⡏⠇⠂⠀⠀⠀⠁⣀⡙⠫⠭⣛⡿⠸⡛⠛⠻⢰⠟⠘⣾⡿⢿