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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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⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆。˚˙✧˖°📷 ༘ ⋆。˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧。⋆🌻⋆。‧˚⛷🧚‍♀️🛖
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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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