Duck In China With Man With Plastic Bag 1988 Emojis & Text

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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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➖➖🟨🟨 ➖➖🟨🔳🟧 🟨🟨🟨🟨 🟨🟨🟨🟨 ➖🟧🟧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀ ⠀⠀⡘⠀⠀⠠⠂⠁⠀⠀⠑⠄⠀⠀⠀⠔⠁⠀⠀⠉⠂⠀⠀⠘⡀⠀ ⠀⠀⠇⢀⣾⠖⠀⡨⠍⠓⠠⡸⠀⠀⠘⡠⠀⠊⠩⡀⠐⢾⣆⠀⡇⠀ ⠀⠠⠀⢸⡏⠀⡜⡄⠀⣹⣷⡈⡇⠀⡏⡀⠀⣿⣷⡈⡄⠈⣿⠀⠠⠀ ⢠⠁⠀⠘⣇⠀⢇⠹⣿⣿⡿⢃⣇⣀⣇⠻⣿⣿⡿⢁⠇⢀⡟⠀⠀⢡ ⢸⠀⠀⠀⠈⠒⢠⠗⠈⠉⠀⠈⠛⡟⠋⠀⠀⠉⠐⢦⠐⠊⠀⠀⠀⢸ ⠀⢣⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢠⠃ ⠀⠸⠈⠒⠠⡼⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡸⡤⠐⠊⢸⠀ ⠀⠀⠱⡀⠀⠈⠪⢟⡛⢿⡿⠛⠿⡿⠟⠻⢿⠟⢛⠯⠊⠀⠀⡰⠁⠀ ⠀⠀⠀⠈⠐⠄⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡀⠔⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡠⠔⠈⠉⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠹⣄⠈⠃⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣪⠥⠶⠊⢺⡄⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⡠⠃⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢄⡠⡄⠀⠀ ⠀⠀⠀⠀⢀⠞⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⡀⡸⠀⠃⡸⠆⠀ ⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⠉⠂⡐⠒⠈⠉⠀⠀⠀⠀⡠⠊⡹⢛⠇⠀⠐⣡⠃⠀ ⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⡰⠉⣐⣺⡤⠊⠀⠀⢚⡗⠀⠀ ⠀⠀⠀⡇⢆⠀⠀⠀⠀⡇⠄⠀⠀⠀⢀⡠⠒⠈⡠⢀⡀⠴⠁⠀⠀⣤⠋⠀⠀⠀ ⠀⠀⠀⠡⠀⢠⡀⠀⠀⠱⢈⡂⠀⠄⡤⠊⣈⠡⠒⢀⠺⠁⠀⢠⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠠⠡⢀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⡇⡖⠠⢤⡤⠤⠤⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⡠⠃⠀⡄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⡥⠒⠉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡷⣿⣧⣼⠙⠛⣷⣦⣄⣀⢰⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣟⣇⠃⡼⠇⢀⣀⣽⣍⢘⣿⠀⢇⣿⡿⠟⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡧⠈⠉⠉⠉⠉⢙⡫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀ ⠖⠒⠀⠄⠁⠀⠀⣀⣐⣲⠏⠀⢀⡠⠔⠒⠐⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⠭ ⡇⠀⠀⠀⠀⠀⣡⡋⠀⠀⢀⠔⠁⠀⠀⢀⡀⠀⠀⠈⢳⣶⡆⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠄⣆⣾⣿⣿⣦⡤⠁⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⣿⣅⣄⠀⠀⠀⠀⠀⠀ ⣂⠀⠀⢈⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠻⠶⢤⣄⣀⣀⣰ ⡿⢦⣴⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⣀⣀⠀⠀⣀⣠⣿⣿⣿⣿ ⠦⠐⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠽⡻⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⣿⣿⣿⣿⣿ ⠀⣠⣴⢶⣶⣶⡶⣶⣶⢶⢶⣶⢶⣶⣶⢶⢶⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⢀⠛⠛⠛⠛⠛⠚⠛⠛⠛⠓⠚⠓⠓⠓⠚⠚⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛ ⠀⠐⣲⢲⣄⣶⣶⣖⡆⡖⢲⣖⢰⣶⠲⢶⡴⠂⣶⣶⡆⣦⣰⢠⣦⣰⣲⣶⣶⢶ ⠀⠀⠙⠈⠀⠋⠋⠛⠁⠛⠋⠙⠊⠉⠊⠙⠘⠂⠋⠑⠁⠃⠘⠋⠉⠛⠀⠛⠀⠘ ⠠⣿⣿⣿⣿⣿⣟⣿⣻⣟⣿⣯⣯⣿⣯⣿⣿⣟⣿⣿⣿⣽⣿⣿⣽⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣳⠶⠚⠉⠉⠉⠉⠉⠉⠉⠙⠲⣶⡋⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢁⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣈⡽⠟⠓⠒⠲⢶⣖⠃⠀⠀⠀⠈⣓⣶⣖⣒⢲⠻⠿⣭⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤ ⠈⠙⢯⡛⠦⣄⠀⠀⢀⡾⠃⠀⢠⡞⠁⢀⣠⠿⢶⣶⣮⡉⠳⣄⠀⢠⡾⣉⣩⠿⢿⣶⣦⣀⠀⠙⢆⠀⠀⠻⣄⠀⠀⢀⡤⠖⣹⠟⠁ ⠀⠀⠀⠹⣄⠈⠳⢤⡾⠀⠀⢀⡟⠀⢠⠟⠁⠀⢺⡀⠈⣿⡆⠸⣆⡟⢘⡞⠁⠀⢸⡀⠈⣟⣦⠀⠘⣆⠀⠀⠹⣦⠴⠋⣀⡾⠁⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⡼⠀⠀⠀⣾⡇⠀⢸⠀⠀⠀⠀⠉⠒⠉⡗⠀⡏⡇⢸⡀⠀⠀⠀⠙⠓⠋⣹⠀⠀⣿⠀⠀⠀⢹⡄⠀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣴⠁⠀⠀⠀⠛⢧⠀⠈⢷⡀⠀⠀⠀⠀⣴⠃⣸⠃⢷⡀⢳⡀⠀⠀⠀⠀⣰⠏⠀⢠⠏⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠈⠳⣀⠀⠙⠓⠒⠒⠋⣁⡴⠃⠀⠈⠳⣄⡈⠓⠒⠒⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⢸⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣾⡄⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⠒⠛⠁⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⣾⠔⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠰⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠋⠁⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⣀⡀⠀⠀⠀⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠀⠀⠀⣀⡠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡗⠲⡶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⣶⠒⢯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⡠⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢶⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠏⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠀⠀⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡇⠀⢺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⣠⡀⠸⡻⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⢀⡾⠋⢈⣀⡀⢈⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠙⠳⣌⢹⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⢀⡴⠋⠉⣯⣻⢿⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣿⣶⠀⠀⢹⡿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡿⠁⠀⠀⣿⠇⠚⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢰⡇⠀⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡟⠉⠉⠀⠀⠀⠉⠉⠙⣷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⡚⠉⠉⠉⠀⢹⡀⠀⠀⠀⠀⠀⠀⣼⡆⠈⠉⠉⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⢠⠎⢩⣭⣍⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣶⣿⣿⡟⣾⣿⣿⠿⡄⠀⠀⡖⢙⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⡿⠿⣿⠋⡼⢿⣦⣄⢙⣾⣿⣿⣧⡈⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⣶⡾⢡⢞⣹⣶⣿⣿⣿⣿⣿⣿⣿⠧⢄⡈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⢟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠛⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡨⠃⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠟⡡⢬⠙⣿⣿⣿⣿⣿⡿⠿⠛⠋⠈⢻⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⢸⣁⠜⠈⠁⠀⠀⠉⠓⠀⣎⠍⠙⡆⠀⢙⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⢾⣿⣯⣹⡶⠀⠀⠈⠁⠊⠁⢀⣼⣿⣿⣿⣿⡆⠀ ⠀⠀⠰⣿⣿⣿⠛⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⢀⣿⣿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⠋⠉⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⠉⠉⢱⠀⠀ ⢠⠄⠒⢲⣿⣿⣿⣿⡇⣈⠄⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⠀⠀⢸⠀⠀ ⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣀⠀⠀⠠⠀⠀⠛⣿⣿⣿⣿⣿⠧⠤⠀⠼⠀⠀ ⠈⣄⣀⣀⣿⣿⣿⣿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⠀⠀⠀⢆⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⣬⣂⠤⠀⣀⣪⣾⣿⡏⠉⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠘⢿⣿⣿⣿⡿⠀⠀⠀⡿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⡱⠁⠀⠀⠀⣇⣀⣈⣉⣀⣸⠄⠀⠀⠀⠀⠀⠀
⣿⡏⠀⣠⢤⡵⣪⡿⠉⣰⣿⣿⡏⠀⢰⣿⣿⣿⠇⠸⣿⣿⡆⠻⣿⣿⠈⠶⠀⣠ ⣿⢠⣾⣿⠟⣰⣿⢁⠀⣾⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣷⠀⢻⣧⠴⣷⡇⠈ ⡇⣿⣿⡟⢀⣿⡇⠀⣀⣿⣿⡿⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⠀⠸⣿⣿⣿⣿⠀ ⢸⣿⣿⡇⢸⣿⡇⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⡆⠀⣿⣿⣿⣸⡇ ⣾⣿⣿⣇⠸⣿⣇⠀⠀⣿⣿⣿⡀⠀⣸⣿⡿⠿⠤⠤⣿⣿⣿⠧⢤⢿⣿⢣⣿⡇ ⣿⣿⣿⣿⣤⣿⣿⣶⣶⣾⡿⠟⠛⠉⠀⠈⠛⠛⣛⣯⣿⣽⣽⣩⣟⣴⣧⣾⣿⠃ ⣿⣿⣿⡇⣿⣿⣌⣮⣾⣶⣶⣢⡀⠀⠀⠀⠀⣼⠟⠛⡿⢻⣿⣿⠟⠁⣿⣿⡿⠀ ⣿⣿⣿⣷⣿⣿⢿⡛⠉⢸⣉⣿⣷⠀⠀⠀⢰⡏⠀⠀⢗⡻⢿⣿⡯⢽⠟⢹⠇⠀ ⣿⣿⣿⣿⣿⡯⣿⣷⣀⣈⣫⣭⠽⠆⠀⠀⠘⠒⠀⠴⠒⠺⢟⣱⡌⢡⡎⣸⠀⢀ ⣿⣿⣿⣿⣿⣷⡸⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢰⠼⢤⠃⢠⣾ ⡻⣿⣿⣿⣿⣿⡷⢣⠀⠀⠀⠀⠀⠀⠙⠛⡉⢀⠀⠀⠀⠀⠀⠀⣼⠖⠋⣰⣿⣯ ⣿⣎⢿⣿⣿⣿⢿⡟⣆⠀⠀⠀⠀⣴⣗⣗⣮⡷⡿⠂⠀⠀⢀⡼⠣⣰⣾⢿⣾⣿ ⣿⣿⣧⢻⣿⣿⣿⣿⣎⢳⣄⡀⠀⠈⠪⣉⠡⠼⠁⠀⢀⣴⣿⣿⣾⡟⣵⣿⣿⣿ ⢹⣿⣿⣧⣻⣿⣿⣿⢿⣦⠊⢻⣶⣤⣀⡀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣸⣿⣿⣿⡿ ⢆⢻⣿⣿⣯⣿⣿⣿⣿⣿⣷⡦⣿⣿⣿⡟⢿⣿⣿⠏⣾⣿⣿⣿⣇⣿⣿⣿⡿⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡚⣡⡴⠆⢻⣿⣿⣷⣤⡀⠠⣿⡃⢀⣴⣿⢿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠰⠒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⣇⠈⠤⠤⠀⠀⠀⠀⠉⠀⢻⣅⠀⠀⠀⠉⣿⣿⠿⣿⣶⠾⢿⣿⣿⣽⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢿⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣀⠀⣈⣀⣀⣬⣿⣆⣸⣿⣯⣥⣤⣤⣤⣤⣴⣶⣶⣶⣶⡶⠿⣿⣅⠀⠀⣠⡶⠂⠀⠀⠀⠐⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⢉⣽⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⡿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣋⠉⠀⠀⠀⠀⠀⠈⠀⢙⣻⡃⠀⢠⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠈⠻⣿⡝⣦⡀⠀⠀⣀⣴⣾⡿⠋⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠻⣿⣟⡻⢶⣤⣀⠀⠀⠀⠀⡀⢉⣿⠙⠉⠽⠀⣤⣄⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣷⣤⣾⡿⠿⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣌⡙⡳⣦⣄⣴⣿⣿⣿⣤⣀⡶⠀⢸⣿⣿⣭⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⣶⡟⣻⡟⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⣦⡁⡛⣿⣍⠀⠀⠀⠈⠙⠂⠀⢀⣀⣀⣤ ⠶⠶⢶⣶⡿⠿⠿⠟⠛⠉⠉⠉⠉⠀⠀⣼⠏⣼⡟⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠻⣦⡉⣼⢷⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢋⡿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⢷⣄⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣼⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⢿⣆⠘⠿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⠀⢀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⣸⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠙⢧⡸⠀⢠⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⢿⡄⠀⠀⠀⠀⠀ ⢶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⠀⣤⡟⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠾⣿⣦⠗⠀⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠸⣷⠀⠀⠀⠀⠀ ⠀⠙⠂⠀⠀⠁⢈⡟⢉⡉⣿⡟⠃⢰⡿⠃⠀⣸⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣴⡟⠻⣧⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠍⠋⣠⡏⠁⠀⠈⠃⠀⢀⣏⣀⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣤⣾⣯⣤⣤⣬⣿⣦⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠁⡞⠀⠀⠀⠂⣼⠋⠉⠘⣿⠀⠀⠀⠀⠁⠀⢠⠁⠀⣴⣿⣿⡟⣿⣿⣿⡏⠉⠉⣿⠋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡶⠋⠁⣸⡏⠀⠀⠀⠀⠀⢠⣿⣠⣤⣶⣾⣧⣄⠀⠀⠈⠐⠃⠀⣼⡿⢹⣿⣿⡟⠉⠉⡇⠀⡰⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠌⠻⣦⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⣀⡿⠁⠀⡄⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⢿⣄⣀⠀⠀⠳⣶⡟⠀⠀⢿⡆⠂⢉⡿⠃⡰⠁⠀⠀⣸⠟⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⣍⠻⣦⣀⠈⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢹⡀⡀⠀⢻⡿⡀⣿⠿⢣⣼⠀⣩⢟⣳⣤⢤⣈⣳⣤⣀⣈⣉⣉⣩⠤⠊⠀⠀⢀⡴⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡓⢾⣿⣷⡆⣀⣀⠓⠚ ⠀⠀⠀⠀⠀⠀⢸⡟⠠⣤⠀⠈⠁⠹⠄⠘⣷⠃⠘⠶⠴⢧⣾⣿⢿⠋⠀⠀⠈⠉⠙⠋⠉⠉⠀⣄⣠⣤⣴⣞⢋⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣿⡇⠀⢨⠻⡏⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⢰⣸⡇⢰⡞⣷⡄⠀⠀⠐⠶⣿⣦⣤⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠉⣩⡷⠀⢀⣴⣿⡀⢠⠀⠀⠠⠀⠀⠀⠀⣸⠛⣿⠀⢸⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣷⡀⢻⡌⠻⢶⣄⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠿⠷⠷⠛⠉⢀⣿⠃⠀⠀⣠⡆⠀⣠⠆⢰⡏⠀⢹⡇⢸⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢯⠷⣌⡻⣤⣀⣼⣿⣿⣿⡷⠶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣠⠏⢀⣴⣿⢀⡿⠁⠀⠀⢿⣼⠆⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢲⡄⠈⢧⡈⠛⠻⢦⣄⣻⣏⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠐⣋⣴⠟⢡⣿⡾⠁⠀⢰⡄⠈⢿⣦⢿⠀⠀⠀⠀ ⠀⠀⠀⠢⣄⠀⣇⠀⠀⠳⡄⠀⠀⠀⠉⢿⣎⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣤⣤⣶⠞⠋⠁⣰⡟⢹⡅⠀⠀⢸⣇⠀⠀⠈⢛⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⣹⣧⡀⠀⠙⢦⡀⠀⠀⠈⠻⣮⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣤⣾⣿⡿⢿⡿⣿⣼⡆⠀⠈⠉⠀⣼⢻⡄⠀⠀⢻⡄⠀⠀⠈⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣮⣻⢦⣄⡀⠙⢦⡀⠀⠀⢸⣿⣿⡿⠈⢻⣿⣦⣀⠀⠀⠀⠀⠀⣀⣠⣶⣾⠟⠋⣉⡾⠟⠁⠀⢸⣷⣿⣿⣷⡀⠀⠀⠀⣿⠀⢿⣤⠀⠈⢷⡄⠀⠀⠀⠐⢄⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠙⠛⠻⠿⠷⠦⢷⠀⠀⢸⣿⢿⡇⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⢁⣴⠟⠁⠀⠚⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⣿⣇⢸⡝⢷⡀⠈⢿⣷⣦⡀⠀⠈⠿ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⠈⢿⣆⠀⠀⠀⠈⠙⠿⣿⣿⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏⠙⠷⣤⡀⢿⣿⠈⢿⡈⠻⣤⡈⠻⣯⡻⣦⣄⠀ ⠀⠦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠞⠋⠉⠀⠈⢻⣆⠈⣿⢷⣤⣀⠀⠀⢀⣼⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠈⠻⢾⣿⡀⠸⣧⡀⠈⠙⢦⣌⠻⣽⡛⠓ ⠈⠀⠈⠳⢄⣰⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⣈⢙⢛⣛⣿⠟⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⢀⣀⠀⠟⣧⡀⢻⣷⠀⠀⠺⣿⣟⣶⡛⠥ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⣀⣀⣄⣀⡀⠀⣀⠀⠈⠛⠷⣿⣿⣟⡛⢛⡛⢶⣦⣄⠀⠙⢦⡀⠀⠀⠀⠀⢀⣀⣀⢀⣿⡇⢀⢀⣴⣿⣿⠇⠀⠈⣻⣮⣿⣧⡀⠀⢻⣿⡿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⠛⠛⠿⠿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⡉⠉⠙⠋⠻⠦⡌⢻⣿⣦⣀⣙⡶⠖⢛⣋⣩⣤⣤⣭⡿⠃⢠⣾⣿⣧⣿⠀⠀⠀⠀⢈⡿⢿⣷⡀⠈⢿⣎⡉⢛
⠀⠀⣠⠞⠋⠀⢀⣤⡾⠋⠉⠁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⣆⠈⠻⣿⢷⣶⣬⡹⣆⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀ ⣤⠞⠁⠀⠀⣰⠟⠉⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠘⣦⠙⢷⣍⢻⡄⠀⠀⠀⠹⣦⡀⠀⠀⡈ ⣽⠖⠲⢶⡾⣋⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢠⠟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢷⡀⠻⣾⣷⡀⠀⠀⠀⠘⣿⣿⣿⠇ ⢁⣀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢹⣿⣧⠀⠀⠀⠀⠈⢯⣿⠀ ⠿⠛⠉⠀⣀⣀⣤⡴⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⡾⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢸⣿⡄⠀⠀⠀⠀⠀⢻⠀ ⣤⣶⣶⣟⣯⡿⠃⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢤⢸⠀ ⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⢿⣇⠀⠀⠀⠘⣿⠀ ⣴⢿⣿⠋⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠂⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⡀⠀⠀⢹⡄⠀⠀⠀⢸⠀ ⣯⡿⠁⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡆⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⢸⣷⠀⠀⠀⢸⠀ ⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⡸⠀⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⡇⠀⠀⠀⢉⡇⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢠⡇⡆⠀⠀⠀⢰⠃⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣻⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⠃⠀⠀⣼⠀⣷⣀⠀⣀⣜⣀⣀⣸⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⠘⣇⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡾⣿⢸⡇⠀⢠⡟⠛⢻⢋⠉⢸⡇⠀⠀⠘⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⢹⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡀⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡟⠀⣿⠈⡇⠀⣸⠀⠀⠘⣾⠀⡼⠀⠀⠀⠀⢧⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢺⠦⢼⣄⣆⢸⠀⠸⠀⠀⠀⠀⠈⡇⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣠⢯⠀⠀⣿⡀⠇⢀⡇⠀⠀⠀⣹⣆⡃⠀⣀⡀⠀⢸⡀⢸⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡇⣇⢀⡏⠀⠘⡇⠉⢻⠢⢤⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣴⠋⢸⠀⠀⡇⡇⢨⣿⣷⣶⣾⣿⣿⣿⣿⣷⣦⣍⡓⠦⣇⢸⠀⢧⠀⠀⠀⠀⠀⠀⠀⣸⠁⣿⢸⠇⠀⠀⠁⠀⢿⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⡾⠁⠀⠘⡇⢲⡿⣷⡐⠛⣿⣻⢿⣿⣿⣟⡛⠿⠿⣿⣦⡀⢹⣸⠀⢸⡆⠀⠀⠀⠀⣿⢠⣿⣶⣿⣟⣀⡀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢿⠀⠀⢠⡞⠀⠀⠁⢠⣧⢸⡇⠈⠋⠀⠻⠧⠤⠤⠤⠼⠿⠄⠀⠀⠀⠀⠀⡇⠀⠀⢧⠀⠀⠀⡼⢿⣼⣿⣿⣿⣿⣿⣿⣿⣶⡃⢸⠀⣸⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠇⡟⠀⢀⠏⠀⠀⠀⠀⢸⠿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡄⠀⣰⠇⠸⠿⣍⣛⣛⢭⣄⠁⠈⢻⣿⣾⣀⡇⠀⢠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⢰⡇⢀⡞⢀⠀⠀⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠉⣹⣿⢸⠃⢀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⢰⢸⠃⡾⠁⠸⡇⠀⠀⠀⢸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡿⡏⢀⣾⣻⠀⠀⠀⠀⠀⡐ ⠀⠀⠀⣾⢹⢸⡼⣸⣇⠀⠀⣇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠏⢠⡞⢸⣿⡆⠀⠀⠀⢸⠁ ⠀⠀⢸⠇⢸⡎⣿⠇⣻⡄⠀⢸⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢠⡞⠀⠋⠀⣸⢸⡇⠀⠀⠀⢠⢠ ⠀⢰⡏⠀⡏⠇⡏⠀⣿⢷⠀⠘⡆⠀⠀⢸⣿⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣾⣧⠀⠀⠀⡏⢸⡇⠀⠀⠀⣿⣄ ⠀⣾⠁⣸⢿⢠⠇⠀⣿⡸⡆⠀⣷⠀⠀⢸⣿⠁⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⢠⣧⣸⡆⠀⠀⠀⢸⣷⠀⠀⠠⣿⠉ ⢀⠇⢀⣿⢸⣷⡇⠀⢹⣿⣿⡀⠸⡄⠀⢸⣿⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⣾⠀⣾⠀⢹⣿⠀⠀⠀⡎⠛⠀⠀⢀⣰⣦ ⠀⠀⢸⠹⡄⠹⣷⡄⠀⢿⣾⣇⠀⢇⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢋⣸⣷⡇⣼⠻⣆⠀⣹⡄⠀⢰⠃⠀⠀⠀⣤⣽⡷ ⠀⠀⠸⠀⠹⣄⠹⣿⣄⠸⡈⢻⡄⠸⡀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠯⣿⡾⠈⢿⣿⣸⠋⠀⠹⡄⠈⡇⠀⡞⠀⠀⣀⠀⣀⡈⠃ ⠀⠀⠀⠀⠀⠙⢦⡘⠛⢿⡇⠀⠻⡄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⣀⠀⠀⠀⠀⣀⣤⡖⢋⠁⠀⠀⠀⠀⠉⠓⠸⡿⠋⠀⠀⠀⡇⠀⣷⢰⠻⣶⠚⠉⠀⣿⣷⣾ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠙⣠⣴⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡶⠒⠊⢻⠀⠹⣜⢧⡀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⡟⠀⣿⠅⠀⢻⠖⠒⠶⣮⣭⣱ ⠀⠀⠀⠀⠀⣠⡤⣤⣤⣴⠿⣿⣦⡀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⣧⠀⠈⠳⣍⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢠⣧⣀⡏⠀⠀⠸⡗⠂⠉⠉⠉⠉ ⢀⣀⣀⣠⣾⣋⣀⠀⠀⠈⠑⢤⡙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠈⠳⣤⡀⠈⠓⠀⠀⠀⠀⠀⠀⠘⠆⠀⠏⠈⠻⣦⣄⠀⠀⣿⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠙⢦⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣙⡟⠒⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢿⣷⣀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠀⠀⠉⠳⣄⠀⠀⠦⢭⣓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠔⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠈⠳⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠐⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⢳⠸⣦⣀⠀⠀⠀⠀⢘⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⢀⡔⢹⠀⡄⠀⠀⠀⢸⠀⢻⠈⠛⠲⣄⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠰⠁⠀⢀⣤⠔⠋⠀⠸⣄⠑⠀⠀⠀⣸⣀⡿⠀⠀⠀⠘⣦⠈⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠘⠦⣀⢀⣆⣿⡿⠁⠀⣀⣀⣀⣺⣷⡜⢿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⣼⢠⠀⣠⣇⡜⠀⣠⣤⣤⠄⠀⠀⠀⠀⠉⠉⢙⣄⠀⠀⠉⣿⡿⠀⣿⣷⣆⠛⣿⠂⠀⠀⠀ ⠀⠀⠀⢹⣿⢠⢿⠻⡇⠀⠀⠿⠟⠁⠀⢀⣴⠚⠉⠉⠉⠉⠉⢲⣄⣈⣀⣀⣠⡾⢿⡆⣿⠀⠀⠀⠀ ⠀⠀⣰⠋⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣯⡀⠀⠀⠀ ⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡏⠱⡄⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⡠⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⡀⠀ ⣼⠀⠀⠀⠀⢀⣜⣁⣀⣀⣠⠤⠖⠊⠁⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧⠀ ⢻⠀⠀⠀⠀⡜⠀⣼⡏⠁⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀ ⠈⣇⠀⠀⢸⠁⠀⢻⣇⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇ ⠀⠈⢆⣠⡧⠀⠠⠤⠜⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠳⣄⡼⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⠔⠢⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠾⢍⣈⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⢿⡄⠀⣰⣿⠆⠀⢨⣿⣵⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⢈⡽⠛⠿⣿⣯⣽⣦⠀⢀⣠⠀⠀⠀⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⡿⢷⡟⣾⢀⣠⣾⣿⣧⡤⠴⠶⠒⠒⠲⠶⠦⢤⣄⡈⢳⣴⠚⢿⣄⠀⠀⠀⢬⣭⣿⣿⡛⢁⣀⣤⣾⡟⠀⠀⠀ ⢀⠈⢧⠀⠀⠀⠀⢀⡾⠃⠀⢀⣼⠋⣰⣿⣧⣏⣾⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⡈⠻⣦⡀⠀⢰⠇⠉⠉⠉⠉⠁⢰⣿⢣⣇⡰⠃ ⠈⢦⡸⣷⣤⣤⡶⢿⣷⠟⠉⣿⣡⣾⣿⡿⢻⣿⣿⡅⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣿⣦⠏⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀ ⠀⠀⠁⢸⣛⣿⣶⡾⢋⣠⣴⢿⣿⡼⠋⠀⠀⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠰⣤⣤⣤⣴⣾⠛⠁⠀⠀⠀⠀ ⠀⠀⠠⠈⠀⢉⣿⣿⣿⣿⣿⣸⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡞⢿⣿⣿⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠟⣹⠏⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣿⠈⣿⡛⠿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⡿⠁⢠⣿⠀⢰⡟⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡿⢸⣿⣷⡀⠘⣿⣧⠀⠀ ⠀⠀⠢⢄⠀⠀⣼⣿⠆⣿⠁⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣿⡇⠀⠈⣿⠀⠀ ⠀⠀⠀⢀⣀⣾⣿⡟⢸⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣿⢸⣿⣿⡇⠀⠀⠛⠀⠀ ⠀⠀⠀⠛⠛⢉⣿⣷⣾⣇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠰⠋⠀⣿⠈⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣿⣆⠸⣷⣭⣳⣶⡶⠗⠀ ⠀⠀⠀⣿⠙⣌⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠘⣆⠈⡇⠈⠙⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡟⢻⣿⡄⠉⢉⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠲⡇⠀⢀⠔⠾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢀⣼⠏⢹⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣀⠹⡄⢾⡇⠀⢹⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⡿⡅⠋⢀⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣄⠉⠙⢦⡉⠒⠚⡇⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⠋⣠⡿⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⠦⢄⣙⣦⣄⣷⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⢀⣿⠋⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡇⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⣀⠀⠀⠀⢀⣀⣀⠤⠔⠚⠉⠀⠀⠀⣠⣞⣛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠁⠀⠀⣀⠀⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⣶ ⡿⠀⢀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⣰⠃⠀⠀⠀⠀⣏⠈⢯⡀⢩⣿⣶⣦⣄⡀⠀⠀⢀⣠⣄⡀⠹⣧⠀⠀⠹⣧⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣷⣶⡏⠀⠀⠀⠀⠀⠀⠀⢰⡿⠐⢿⠇⠀⠀⠀⠀⠀⠹⣦⣼⣯⡉⠉⠛⠛⠉⢁⡴⠋⢉⣀⣀⣉⡛⣿⣦⠀⠀⠹⣷⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⡀⠀⢀ ⢈⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠂⠀⢀⡴⢋⣠⠞⠉⠁⠀⠈⠉⠛⢻⠆⠀⠀⠘⢿⡤⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠟⢿⡿⣻⠧ ⣿⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⡐⠃⣿⢀⡤⠒⠋⠉⠉⠛⠲⠤⣄⣀⣤⣴⡿⣠⠞⠁⣀⣤⡶⠿⠟⠲⠞⠀⠀⠀⠀⠀⠈⢿⣦⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⠛⠋⠉ ⠁⠀⠀⣿⠃⢀⣴⡶⣿⡿⠁⢰⣿⠀⠀⢿⠀⡤⠞⠉⠉⠙⠓⠲⢤⣤⣤⣬⣵⠞⠋⢠⣾⣫⣵⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠙⣆⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⠀⡿⣱⠞⠋⠀⢀⡿⡏⠀⠀⢸⡆⠀⠀⣠⣤⣴⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡈⣷⣄⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⢩⣋⣿⢀⡾⠋⠀⠀⠀⣼⠁⠀⠀⠀⣀⣿⡀⠸⠋⠀⠀⠐⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣿⡿⢶⣄⠀⠀⠀⠀⢷⠀⠀⠀⠀ ⠀⠛⠉⢻⡾⠁⠀⠀⠀⣸⠋⠀⢠⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⠹⡄⠀⠀⠀⠀⢸⣟⣫⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣘⣿⣷⣄⠀⠀⢸⡟⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⠀⣰⣏⡀⠀⠀⠙⢿⣿⣿⣿⣷⣠⠀⠀⣤⣶⣿⣷⡄⢹⡄⠀⠀⠀⠀⠿⣵⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣍⠈⣿⠈⠓⢦⣨⡿⠀⠀⠀ ⢿⣿⣼⠃⠀⠀⠀⣴⠛⣻⣿⣷⣦⡀⠈⠻⣿⣿⣿⣿⡷⢠⢾⣟⣿⣿⠟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⣄⣰⠛⠁⠀⠀⠀ ⢀⣾⡏⠀⠀⢐⣼⣿⣿⣿⣿⣿⣿⣷⣄⡀⠈⣻⣿⣿⣷⠀⠀⠈⠉⠁⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣠⢤⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⠿⠃⠈⠻⣿⣆⠀⠀⠀⠀ ⣘⣿⠁⠀⣠⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⡯⠶⢾⣿⣿⣿⡿⠉⠉⠙⠻⣽⡚⠉⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⢻⣆⣠⠄⠀ ⣿⣿⣠⠾⠋⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⡼⠙⢷⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣲⣶⣶⣶⣖⣛⣷⡤⢤⣀⡀⢸⢿⡇⠀⠀⠀⠀⠀⠀⠹⣿⠢⠀ ⣿⣿⡅⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠙⡇⠀⠀⠉⠛⣿⡉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠂⠀⠀⠀⠉⠙⠒⢯⡿⠀⠻⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠁⠀⠀⠃⠀⠀⠀⠀⣤⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠿⢤⣀⣀⣠⣼⣿⣲⣶⠭⠶⣾⣿⣿⡿⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣸⠇⡇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠃⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡚⠙⢿⣻⣗⣾⡟⠒⣺⣋⡵⢾⡟⠁⠀⠀⡞⣿⠀⠀⠀⠀⢀⣴⡟⢰⠇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⣀⡀⠀⠀⠀⠀⣶⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣷⡘⠿⣭⣉⣭⣥⣾⡿⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⣰⡿⠁⡼⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢋⠓⠀⠀⠀⠀⠀⠉⠀⠀⠻⠿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠙⠒⠲⠶⠃⠀⠀⠀⠀⣸⠃⢸⠀⠀⣀⣼⡿⠁⢰⠇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⣀⣄⠀⠙⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⢸⣿⠙⣧⠀⠀⠀⠀⠲⠤⢤⣤⠞⠃⠀⡿⣠⡾⣻⠟⠁⠀⡾⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠛⠁⠋⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⡇⠘⢷⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⢞⣭⠾⠋⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⣠⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⡀⢦⠉⠛⠿⢿⣿⣿⣭⡭⠽⠟⠋⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡀⠀⠀⠀⠀⠸⣦⣼⣾⣿⣿⠄⢠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠁⠷⠈⢳⣄⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢦⡑⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡌⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠠⠙⣯⡁⠀⠀⠀⠀ ⠉⠳⢦⣀⡀⠀⣠⠞⠀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠁⠈⢻⡆⠖⠀⠀ ⠀⠀⠀⠈⢹⡟⠁⢀⠟⢉⣿⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀ ⠀⠀⠀⢀⠏⠀⢀⣟⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⡄⠀ ⠀⠀⢠⡞⠀⢠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀ ⠀⠀⢸⠁⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⡇ ⠀⠀⢸⠄⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠶⢦⣤⣤⣀⣤⣴⠶⠾⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆⠀⠀⠀⠀⡇ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠿⠷⠒⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠄⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⡆⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠸⣷⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⡘⣿⣰⡏⠀⠀⠀⠀ ⠀⠈⡄⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠛⠋⠉⠛⠀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠉⠛⠶⠤⠤⣄⣀⠀⠤⢄⡀⠀⠈⣿⠟⠀⠀⡿⠂⠀ ⠀⣰⠃⠀⢀⡠⠴⠛⠉⣀⣀⣤⣤⣤⣶⣶⣿⣿⣯⠉⠉⢉⣹⠏⠈⠙⢃⠙⠻⠈⣱⣿⣿⣻⣿⣿⢶⣶⣤⣤⣄⣀⠉⠙⠀⠀⠤⣀⠀⠀⠀⢸⡇⠀⠀ ⢰⡏⣄⢠⠎⠀⣠⣶⡿⢿⣿⣿⣭⣿⣿⣿⣿⣻⣿⠀⢀⣼⠁⠐⠀⠀⠘⠋⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢈⠏⡓⢶⣄⠀⠀⠨⣅⠐⣄⢸⠁⠀⠀ ⢸⡄⡿⠁⠀⢸⢡⣏⠀⠀⠀⠀⠁⠀⠘⢉⣽⡟⠁⠀⠛⠋⢡⣆⠀⠐⢴⡰⣶⣿⣿⠉⠛⢿⠿⠿⠿⠋⠀⣠⠞⠀⠀⠠⢻⡇⠀⠀⠘⡆⠸⡏⠀⠀⠀ ⠀⢳⢧⠀⠀⠸⣾⣿⣆⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠛⠁⠐⠀⠈⣹⣮⠙⣿⡄⠘⠏⠉⠉⠉⠋⡉⠁⠀⠀⠀⠀⠀⢿⡄⠀⠀⢹⡀⡟⠀⠀⠀ ⠀⠈⢸⡆⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠘⠙⠷⠈⠛⢧⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢸⠃⠇⠀⠀⠀ ⠀⠀⠀⢹⣦⡄⠀⠬⣽⣶⣶⡶⠤⠈⠉⠀⠀⠀⠀⠈⠳⣆⠀⢀⣴⡦⠞⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀⣠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠒⠀⠀⣭⣶⠿⣿⣦⡅⠀⠀⠀⠀⠀⠀⠙⣶⡾⠋⠀⠀⠀⠀⠀⠀⠂⠈⣅⠀⠀⠀⡀⠀⠀⠠⢴⣟⣰⡿⠋⠁⠀⢀⡼⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣫⣿⣿⣶⣦⣄⡀⠀⠀⠘⢷⠀⠀⠀⠀⠈⣄⠀⢸⣇⣿⣶⣦⣾⣿⣿⢷⣶⣤⣀⠀⠀⠀⠶⠾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣾⣫⣾⣿⣿⣿⣿⣿⣿⣷⣿⣦⣀⠀⠀⠘⠂⢰⣶⣿⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠿⠗⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣫⡟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠛⠿⢧⣙⢿⡿⢿⡷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢟⣿⣿⠿⠃⠉⠄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢠⡔⠹⣇⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠳⠫⣷⠀⠀⠀⢹⣿⣿⣿⠿⠟⠛⠉⠉⠋⠉⠉⠛⢛⣿⠛⠁⠀⠀⠀⠀⠀⣟⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⢾⡷⣀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠛⠛⠛⠛⠷⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠃⠀⣀⣀⣀⣀⡀⠀⠀⢀⣭⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠁⠀⣼⡏⢉⣿⣿⣿⡆⠀⣾⢡⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠸⣷⣄⣻⣿⡿⠁⠀⠙⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⢀⣴⡾⠿⠿⢿⡿⢷⣤⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠺⠇⠘⠃⠀⠉⠙⠛⢷⣄⠀ ⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠂ ⠀⠀⠀⠀⠀⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢉⣹⡿⠷⢶⢶⡶⠶⠛⠛⠁⠀ ⠀⠀⢠⣶⠟⠋⠙⠛⠀⠀⠀⠀⠀⠀⠈⢿⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⡄⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣄⠀⠀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣧⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣧⣀⡿⠉⠛⢷⣶⠶⠤⢦⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠃⠀⠀⢸⡇⠀⠀⢸⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡶⠀⠘⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣤⡶⣶⡶⣤⡀⠀⠀⠀ ⠀⢀⣠⣿⡯⠞⠁⠀⠈⠪⡹⣆⠀⠀ ⡰⢫⣿⣿⡄⠀⠀⣀⣀⣤⣵⣽⣀⠀ ⡇⣼⣿⣿⡇⢠⣾⣿⢖⠉⠉⠉⢳⡇ ⢱⣿⣿⣿⡇⢸⣿⣿⠘⠀⠀⠀⠸⣿ ⠀⣿⣿⣿⡇⢸⣿⣿⡀⠀⠀⠀⣰⡟ ⠀⣿⣿⣿⣧⢀⠻⢿⣿⣿⣿⣿⣯⠀ ⢀⣿⣿⣿⣿⣆⠀⠈⢲⣻⡿⠚⣿⡇ ⠈⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⡿⠁ ⠀⢿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⡇⠀ ⠐⠈⠛⠻⠿⠛⠃⠀⠉⠉⠉⠉⠀⠘

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