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