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Copy & Paste dino Google Emojis & Symbols ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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