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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⢀⠼⡹⢟⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⢾⡒⠒⠂⢀⠴⢁⢔⡵⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣑⣄⠀⠉⢀⡴⠏⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠈⠳⠄⠈⠀⣠⠎⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⢈⠆⠀⠀⣠⠞⠁⣸⣋⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣞⣹⢤⠀⠈⠁⠀⣠⠴⠁⠀⡴⠁⠀⠀⠂⢻⣽⡓⢢⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠜⠀⠀⢀⡞⠁⠈⠁⡜⠐⠋⠀⠀⠀⠚⠿⠃⠀⠈⢲⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠞⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀ ⠀⠀⠀⠀⠀⠀⣠⣞⣠⣾⣿⠁⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳ ⠀⠀⠀⠀⢀⣜⠟⢱⣿⣿⠇⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠁⠀⠸⣿⣿⣀⡐⠊⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣴⣿⣟⣦⠀⢀⣄⣤⡀⠀⠀⢀⢠⢀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⢀⠐⣀⣴⣿⡏⠉⠫⣃⡱⢄⠁⠿⠗⠯⠿⠏⠸⠫⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⣔⡥⠚⠁⢸⠁⠀⠐⠑⠁⡸⢾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⣀⡤⠕⠁⠀⠀⠀⢀⠄⠀⠀⠀⢀⠢⠇⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠠⣤⠞⠋⠀⠀⠀⠀⠀⠀⢸⠈⣆⠀⠀⠀⡄⢠⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠈⠉⠀⠀⠀⠀⠀⠀⠠⠴⢾⣠⡿⠒⠀⣀⣿⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣝⡡⠋⠁⠉⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢉⣴⣼⣿⣿⣿⣧⡀⠀⠀⡀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣠⣴⡿⠿⠛⠣⣽⢛⠇⣳⡀⠈⠹⠿⢽⡟⢳⣴⡟⢳⣼⡟⢷⢸⣷⡟⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⣠⣾⣿⣿⣷⠆⠀⠀⠈⢋⣜⡁⣬⣳⡄⠀⠸⠷⠞⠙⠷⠞⠹⠇⠸⠸⠏⠷⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣴⠟⠉⠀⢸⠋⠁⠀⠀⠤⠉⠞⠀⠐⢛⡼⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣵⠟⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣱⠏⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⢀⣴⣎⠴⠋⠀⠀⠀⠀⠀⠀⠀⡇⢄⠀⠀⠀⠀⠀⠀⠀⡴⢠⡟⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢆⠀⠀⠀⠀⢀⠚⠁⡄⠀⠀⠛⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⢠⢶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣥⠂⢀⠀⠈⠀⣴⡃⠀⡞⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⠀⢰⣿⡷⠤⡇⠀⠀⢸⣷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣁⡜⢸⣿⣃⣀⣀⡇⢀⣷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠟⢉⡴⠃⠀⠀⠀⠈⣱⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠥⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⢀⣴⡄ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⠀⠀⠀⣰⣿⡇⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣴⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⣫⣿⡿⠀⠀⣴⣿⡟⠁⢹⣿⠀⠀⠀⢠⣄⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⢰⣿⠀⠀⢀⣴⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⠟⢁⣴⣿⡿⠃⠀⣼⣿⡟⠀⠀⠀⣿⡇⠀⢠⣯⣿⣇⠀⠀⢠⣿⣿⠃⠀⠀⠀⣾⡏⣠⣾⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⢏⣴⣿⣿⠟⠁⠀⣼⣿⡟⠀⠀⠀⢠⣿⡇⠀⣾⣿⣿⣿⠀⠀⣾⣿⡏⠀⠀⠀⢰⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⣄⠀⣰⣿⡿⠀⠀⠀⠀⣾⣿⠀⣸⣿⣿⢻⣿⡀⢰⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⠿⠿⠛⠿⣿⢀⣿⣿⠁⠀⠀⠀⣸⣿⡏⢠⣿⣿⡇⢸⣿⡇⣾⣿⡏⠀⠀⠀⢰⣿⠟⠉⠙⢿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⠇⠈⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀⣰⣿⡿⠀⣾⣿⣿⠁⢸⣿⣷⣿⣿⠃⠀⠀⠀⣾⡿⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀ ⠀⢠⣿⣿⡟⠀⠀⠀⣠⣾⣿⡿⣿⣿⠀⠀⠀⣰⣿⣿⠁⣼⣿⣿⠃⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀ ⠀⣾⣿⡿⠀⣀⣴⣾⣿⣿⠟⢰⣿⡇⠀⠀⣰⣿⣿⠃⣰⣿⣿⡏⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀ ⠘⣿⣿⣷⣿⣿⣿⡿⠟⠁⠀⠘⣿⡇⢠⣾⣿⣿⠇⢰⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⠃⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⢏⣿⡆⠀⠀ ⠀⠘⠿⠿⡿⠛⠋⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠃⠀⠙⢿⡿⠁⠀⠀⠀⠈⠻⣿⡟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠙⠓⢚⠓⠋⠉⠉⠛⠒⠲⠶⠲⣒⠒⡶⢶⣦⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠉⠉⠂⠀⠀⠀⠀⠀⠒⠲⢿⣿⣿⣿⣿⡿⠋⠁⣰⠳⠌⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⢀⣴⣃⣸⣇⠀⢸⣿⣟⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠉⠉⠰⣿⣿⣿⡆⠸⣿⣿⣿⣭⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⣸⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠴⠟⠉⣿⠇⠀⣸⣿⣿⣿⣿⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⠀⢽⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣄⠀⠀⢛⣠⡾⢋⣿⣿⣿⣿⡇⠈⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⢀⠈⠀⠀⠀⢀⣤⡄⠀⠀⠀⠈⠙⠃⣤⡀⠀⠀⠀⠀⠀⠈⠙⣷⡤⠿⣿⣶⣿⣿⣿⣿⠿⠿⠀⠸⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠠⠞⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⡇⠀⠀⠀⠀⠀⠀⠘⣧⠈⠛⠛⠿⢿⣿⣯⠀⠀⠀⠸⡟⣿⡄ ⠀⠀⠀⠀⠀⠀⣿⠛⣃⡴⣀⣤⣶⣴⣿⡟⠛⠛⠻⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠉⠙⠀⠀⠀⠀⠀⢹⣇ ⠀⠀⠀⠀⠀⢀⣿⣟⣿⣿⣿⣷⣿⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⣀⠤⠦⠤⠀⣀⠘⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣟⠀⢰⡞⠧⠈⠁⠚⣲⣿⣷⣦⡼⣆⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⢁⠀⠉⢲⣤⣶⣾⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣶⣯⣽⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣦⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⢀⡄⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡷⠀⠀⢀⣴⡆ ⠀⠀⠀⢀⣷⣿⢟⣿⠇⢠⣾⠃⢸⡆⠀⣠⡀⠀⢀⣷⠀⠀⢸⡇⢀⣴⣿⠏⠀ ⠀⠀⠀⣼⣟⣵⣿⠏⢀⣿⠃⠀⢸⡇⢰⣿⣧⠀⣼⡏⠀⠀⣾⣴⡿⠋⠁⠀⠀ ⠀⠀⢸⣿⣿⣿⣷⣀⣾⠇⠀⠀⣾⢁⣿⡿⣿⢰⣿⠃⠀⢰⣿⠿⣷⣄⠀⠀⠀ ⠀⢠⣿⠋⠉⠁⣼⣿⡟⠀⠀⣼⡏⣼⣿⠁⣿⣾⡿⠀⠀⣾⠃⠀⠉⣿⠀⠀⠀ ⢀⣿⡏⢀⣠⣾⠟⣿⠃⠀⣼⡿⢱⣿⠇⠀⣿⣿⡇⠀⢰⡟⠀⠀⠀⠘⣇⠀⠀ ⠸⣿⣶⣿⠟⠃⠀⢿⣠⣾⡿⢡⣿⡟⠀⠀⣿⣿⠁⠀⢸⠁⠀⠀⠀⠀⣿⡆⠀ ⠀⠉⠉⠀⠀⠀⠀⠘⠟⠛⠁⠀⠙⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀

⢠⡀⣀⣤⢀⣄⣠⠀⠀⣄⠀⣀⣄⣀⣀⣠⠀⠀⣀⣀⣠⣠⡀⠀⢀⣄⢠⡄⣄⣠⣤⡄ ⠸⣿⡇⡧⠼⡄⠳⡀⠀⢸⣦⣇⡇⢸⢸⣿⠀⠀⢹⠈⣿⣿⠄⠀⢸⣿⣏⣷⣿⣿⣿⡃ ⠀⠟⠇⠧⠀⠼⠤⠇⠀⠈⠿⠋⠇⠸⠈⢿⠀⠀⠸⠾⣿⠿⠄⠀⠸⠿⠻⠏⠟⠻⠟⠷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠺⢂⡶⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⣿⡒⠘⢧⣴⣿⠷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣡⣴⣿⠿⣾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠒⣹⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⢀⡴⠚⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠉⠉⠒⢶⠞⠁⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠘⢦⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠁⢀⡠⠔⠚⠉⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠤⠒⠉⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄⠉⠒⠲⣤⣤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠑⠢⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠒⠶⢾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⣶⣆⡿⡀⣿⠀⠀⢠⠟⢻⠟⠻⡟⠁⠀⢻⠏⢿⣷⢺⠃⠀⢸⣿⣠⢿⣸⣆⡷⣿⠇ ⠀⢸⣿⡁⣿⣿⡄⠀⢸⣶⣼⡋⢸⡇⠀⠀⠸⣇⣾⣿⢺⠁⠀⢸⣷⣾⣸⣿⣿⡇⣽⡄ ⠀⠙⠁⠙⠁⠙⠀⠀⠈⠛⠙⠓⠈⠁⠀⠀⠀⠋⠙⠋⠘⠀⠀⠈⢛⠀⠋⠉⠁⠁⠙⠋

⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜ ⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛ ⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬛⬛⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬛ ⬛⬜⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜⬛⬜⬜⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛ ⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛ ⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⣴⣿⣦⡀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⠆⠀⣰⣿⣿⣿⣿⣦⣠⣾⣿⡿⢿⣿⡇⠀⠀⣀⣤⣦⡄ ⠀⠀⠈⠻⠿⠿⣿⣿⡇⠀⢰⣿⣿⠃⠈⠻⣿⣿⡿⠋⠀⢸⣿⣷⣾⣿⣿⣿⣿⡇ ⢸⣿⣷⣦⠀⠀⠀⠉⠋⠀⠘⠛⠋⠀⠀⠀⠈⠉⠀⠀⠀⠘⢿⠿⠛⠉⣿⣿⡟⠀ ⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀ ⠰⠿⠇⠀⣿⠿⠿⢿⣦⠀⠀⣠⣾⠿⠿⣷⡄⠀⠀⣿⡆⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⣸⣿⠇⢠⣿⠃⠀⠀⢹⣿⠀⠀⣿⣧⢀⣤⡀⣼⣿⠀⠀⣀⠀ ⠀⠀⠀⠀⣿⠿⠿⠟⠋⠀⠈⣿⣦⡀⢀⣼⡿⠀⠀⢸⣿⣾⠿⣷⣿⡇⠀⠘⠿⠃ ⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠋⠀⠀⠀⠈⠿⠃⠀⠘⠿⠁⣴⣶⣤⡀ ⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠙⠻⠿⠃ ⠀⠀⢀⣿⣿⡟⣀⣀⡀⠀⠀⢀⣤⣄⠀⠀⢀⣀⣠⣿⣿⠇⠀⢰⣦⣀⣤⣄⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⣿⣿⣠⣶⣿⣿⣿⣇⣰⣿⣿⣿⣿⠏⠀⠀⣨⣿⣿⣿⣿⡀⠀ ⠀⠈⠛⠛⠛⠉⢹⣿⣿⣿⡿⠋⠙⣿⣿⣿⡿⠃⠉⠉⠀⠀⠐⣿⣿⠿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⢰⣷⡆⠀⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠠⢂⠎⠘⠀⠀⠾⠃⠙⣄⠠⠀⠀⢀⠀⢠⡀⢼⢵⡂⠀⠀ ⠀⢀⠒⠁⠀⠀⠀⠀⠀⠑⡯⠛⠁⠀⢠⢄⣦⡟⡗⣀⠍⣲⠀⠀ ⢠⠁⢀⠀⠀⠀⠀⠀⠀⠀⢃⣠⠄⡿⣼⣼⠓⡡⠊⣠⣴⡅⠀⠀ ⢸⠀⠈⠄⠀⠀⠀⠀⠀⠀⡄⠘⡹⠳⠃⡠⠊⣠⣞⢳⠀⠈⢇⠀ ⠈⡄⠀⠈⡆⠀⠰⠀⢂⠀⣇⠀⠁⡠⢊⠔⠈⠋⠀⠀⠀⠀⠀⡇ ⠀⠘⢄⡀⢲⠀⡇⠉⠘⡄⢳⡪⢋⠔⠁⠀⠈⠀⠄⢀⠐⠀⠀⡅ ⠀⠀⠀⠀⠉⡇⠇⠀⠀⢉⢦⢑⣷⠃⠀⢀⠔⠬⠤⢼⠰⠤⠐⠁ ⠀⠀⠀⠀⠀⠣⣐⡄⠀⠈⠈⠀⠀⠀⠀⠉⠁⠀⠀⣆⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂⢀⣀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⣿⣿⣿⡉⠉⠉⠙⠻⠦⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⢸⣿⠿⠿⠛⠀⠀⣀⡀⠀⢙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡦⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡰⠀⢰⡏⠂⠻⠃⠀⠀⠀⢀⣰⣿⣿⠒⠛⣿⣇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡿⢁⣼⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠉⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⢙⣦⣄⠈⠀⠀⠀⠀⠀⠀⡤⠖⠉⣄⢸⣆⡴⠂⠻⣷⢟⣩⣤⡄⠀⠀⠀⠀⠀ ⠀⢠⠖⠁⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⣛⠏⢻⢶⣾⠀⠈⠀⠀⠀⠀⠃⠀⣧⡀⢿⣿⣿⣧⣀⡀⠰⠟⢉⣉⣀⡀⠁⠀⠀⠀ ⠰⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⢶⣄⣿⣷⣼⡇⢹⡆⠉⣁⡴⠞⠋⢁⣸⠃⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣶⢿⣆⠀⣿⠀⢹⡞⣧⠙⠗⠀⣡⠞⠋⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣠⣦⠄⢻⣾⣿⣦⣿⣧⣸⠇⠛⠀⣠⠞⠁⠀⢀⣤⣾⣳⣶⡆⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⢩⣦⣦⣬⣧⠀⣿⡏⠙⠋⠀⣠⠞⠁⠀⢀⣴⣿⡁⠛⠷⠛⢲⣦⡀⠀⠀⠀ ⢸⡀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠞⠋⣸⡆⠻⠿⠋⠀⠀⣠⠞⠁⠀⣠⡶⣛⢛⡻⣿⠀⠀⠀⠈⠹⡁⠀⠂⠀ ⠸⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣼⠏⠀⠀⠀⠀⣠⠞⠁⠀⣤⢿⣭⣿⠞⠋⠉⠛⠀⠀⠀⠀⠀⠹⣆⠀⢣ ⠀⢷⡀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢠⡶⠀⠀⢸⡀⠀⠀⣏⠀⠀⠀⠉⠀⠀⠀⣠⠞⠁⢀⡴⠋⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈ ⠀⠘⢧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡜⠀⠀⠀⠨⣧⠀⠀⢻⠳⣤⣀⠀⠀⣠⠞⠁⣀⡶⠋⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠈⢧⡀⠀⠀⠀⢰⣷⠀⠀⠀⡗⠋⠉⠙⠓⠿⡄⠀⢸⡷⢤⣌⣩⡟⠁⢠⡾⠁⠀⠀⠀⠀⠐⡇⠀⠀⡀⠀⣀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀ ⠀⠐⢄⠀⠙⠦⣄⣀⠈⣿⠀⠀⠀⣇⣀⣀⣀⣀⣀⣷⡀⠈⢿⣦⡼⠋⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃⠀⢹⡄⠀⢸⠇⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠁⠀⠀⠀⠈⠉⠛⢷⠀⠀⡏⠀⠀⠀⠀⠀⠉⠛⢦⡀⠙⠦⣴⣏⣹⣗⠂⠀⠀⠀⠀⠀⢰⠏⡰⠃⠀⠀⠘⡇⠀⡼⠀⠀⢀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡆⠀⣇⠀⠀⠀⠀⠀⠀⢠⠞⢛⣦⣤⣤⣿⠍⠉⠀⠀⠀⠀⣀⡴⠋⣰⠛⠓⠒⠒⢲⡇⢠⡗⠒⠚⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄⠀⠀⠀⠀⠀⢯⣤⠞⠁⠀⠁⠈⠀⠀⠀⠀⠐⣿⣯⠴⠚⠁⠀⠀⠀⠀⣼⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢷⣄⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⡁⠀⠀⠀⠀⠀⠀⢰⡇⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡈⠉⠉⢉⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⣤⣆⡄⡄⠀⣄⢴⠀⣤⠀⠀⢴⣄⠀⣴⣴⣦⣶⠀ ⠀⠻⠣⠘⠸⠀⠻⠻⠀⠹⠀⠘⣺⡣⠀⠿⠛⠛⠟⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠡⢨⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡤⣫⣈⡶⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠓⡲⡟⠉⠀⠁⠀⠀⠀⠀ ⠀⠀⢰⠂⠤⠤⠊⠁⣀⠔⠋⠀⢡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠀⠓⠐⠈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠄⠀⠀⠀⠀⢀⠄⠀⠁⡜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡀⠀⠀⠊⢀⡀⢤⡴⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣤⠔⠊⠀⠀⢻⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢆⡬⠽⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣜⣈⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣤⡶⣲⠀⢰⠒⡒⡞⠀⢒⢲⣶⡂⢰⢆⢦⣦⢲⠀ ⠀⠟⠒⠹⠀⠘⠟⠄⠇⠀⠸⠸⠻⠀⠘⠏⠞⠛⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣦⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡟⠉⠈⠉⢉⣉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠛⠹⢯⣍⣉⣽⢹⣿⡷⣶⣶⣶⡶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠂⠙⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠲⠶⣿⣿⣿⣿⡿⢿⣿⠿⠉⠀⠀⡾⠷⢌⢛⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠻⣿⡟⠀⣠⡷⠈⢿⡆⠀⠘⣿⣿⡛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡿⢠⡼⠛⣲⣶⢾⣿⡄⠀⣿⣿⣿⣬⡿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⣴⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠉⣿⣿⣿⣿⣿⠀⠿⢿⣿⣿⣿⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣤⡀⣴⡿⠋⢨⣿⠟⠀⠀⣼⣿⣿⣿⣿⣷⡙⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⢐⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⠀⠀⠀⠀⣿⠀⣀⣾⠟⣿⣿⣿⣿⣿⣧⠈⠻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢯⣯⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠼⣿⣄⠀⢰⣶⡾⣛⣡⣾⣿⣿⣿⣿⣿⣿⡆⠀⢻⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣶⣶⣀⠀⢀⣀⣀⣀⣀⣉⣰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠸⠃⠀⢘⢻⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⡴⠃⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠈⠛⠙⠛⠿⣿⣿⣿⡏⠀⠀⠀⠀⢸⡎⢿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⢁⣠⡀⢀⣠⣄⣠⣾⣿⡿⠿⠿⠿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠠⠟⠉⠿⠀⠀⠀⠀⠀⠀⠈⢿⡆ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣥⣶⣛⣩⣵⣿⣛⣿⣿⡿⣿⠁⠀⠀⠀⠘⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣭⣼⣿⣿⣿⣿⡿⠟⠋⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠐⠂⠀⠀⠀⢀⡀⠀⠀⠀⠈⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣠⡴⢊⣙⡛⣋⠀⣤⣬⡀⠉⢳⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⢹⠶⠈⠁⡈⠉⣿⣿⣿⣷⣦⣬⣷⡀⠀⠀⠀⠙⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠛⠹⣤⣀⣲⣶⣷⣾⣿⣿⣿⣿⣿⡅⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⣴⠾⠿⢟⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢰⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡿⣯⣟⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣳⡿⣿⣩⣖⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡷⣟⢯⡷⣿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣶⣻⣽⢾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣡⣾⣳⣷⣏⣥⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣞⣹⡾⣏⣷⢿⡿⣾⣿⣯⣽⣽⣛⡶⡦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡞⣫⣷⣻⢷⣫⢿⣽⣯⡿⣷⣯⣿⣿⣿⣿⣿⣷⣍⠻⣄⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⢾⣻⣼⣯⣷⣿⢿⣋⢧⠓⡽⣞⣿⣻⡿⣿⣾⣻⢿⣿⡌⢷⠀⠀⠀⠀ ⣴⢞⡿⣮⣿⣿⣿⣻⢯⢯⣷⡽⣎⡽⡸⣝⡾⣽⣻⢷⣻⣽⣟⣯⣿⡞⢣⡄⠀⠀ ⣷⢿⣿⣿⣿⣟⣾⢳⣯⣿⣾⢿⡜⡴⣛⡼⣹⢷⣻⣟⣯⣷⢯⣿⡽⣿⣧⠹⣄⠀ ⣿⣞⣿⣿⣿⣽⣚⣿⣾⣿⣟⡳⣜⡱⢣⡟⣭⢿⣽⡾⣟⣾⣿⣳⣿⢯⣿⣷⡈⢦ ⠋⢯⣙⣿⣻⣾⣿⣻⢯⠷⣍⡳⣌⢳⢫⣞⣽⣻⢾⣽⣿⣻⣾⢿⡽⣟⣾⡽⣷⠈ ⠀⠀⠈⠉⣿⣽⡗⣯⣋⢟⡬⢳⡜⣧⣻⢮⣷⢿⣟⣿⣾⢿⣽⣟⡿⣽⣳⡿⣿⡆ ⠀⠀⠀⠀⣿⢾⡝⣶⡙⣮⠝⣧⢻⡼⢯⣟⣯⡿⣯⢿⣞⡿⣽⣞⡿⣽⣳⣿⢿⣷ ⠀⠀⠀⢀⣿⠻⡝⢦⠻⣔⠻⣌⠳⣝⡻⣞⢷⡻⣽⣛⠾⣽⢳⡾⣽⡿⣽⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⡆⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⢀⣼⣿⣿⠇⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠛⢁⣾⣿⣿⠀⠀⢀⣾⣿⣿⠋⠀⠸⣿⣿⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⢠⣿⡇⠀⠀⢀⣴⣾⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠀⣰⣿⣿⣿⠃⠀⢀⣾⣿⡿⠁⠀⠀⠀⢹⣿⠀⠀⠀⣼⣽⣿⣷⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⣸⣿⠇⣠⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⣠⣾⣿⣿⡿⠁⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣥⣾⣿⣿⣿⠋⠀⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⣿⣿⠇⠀⠀⠀⠀⢀⣿⣿⡇⠀⣼⣿⣿⡏⢹⣿⣧⠀⣸⣿⣿⡏⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⢰⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⣿⠀⣸⣿⣿⣿⠃⢸⣿⣿⢀⣿⣿⣿⠁⠀⠀⠀⠀⣼⣿⡿⠉⠀⠘⢯⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⠃⠉⠀⠀⠀⠀⢠⣿⣿⣾⣿⡿⠀⠀⠀⠀⠀⣸⣿⣿⠇⢀⣿⣿⣿⡟⠀⢸⣿⣿⣸⣿⣿⡿⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣰⣿⣿⡏⠀⣾⣿⣿⡿⠁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠁⠀⠀⢀⣠⣿⣿⣿⡿⢻⣿⣿⠀⠀⠀⠀⣰⣿⣿⡿⠀⣼⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀ ⣼⣿⣿⡿⠁⢀⣠⣶⣿⣿⣿⣿⠟⠀⣿⣿⡇⠀⠀⠀⣼⣿⣿⡿⠁⣰⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀ ⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⠟⠁⠀⠀⢻⣿⡇⠀⣠⣾⣿⣿⣿⠁⢠⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣷⠀⠀⠀ ⢘⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣧⣶⣿⣿⣿⡿⠁⠀⢿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀ ⠀⠀⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠟⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⠇⠀⠀⠀⠀⠀⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢭⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⠀⢀⢠⣀⠀⣀⠀⣀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⢀⢀⡀⠀⠀⠀⢀⡀⣠⡀⣄⢀⣀⣠⡀ ⣿⣷⣿⢹⡏⢸⡏⢹⡏⠀⠀⠈⣧⠀⡏⢹⠉⡟⠉⣏⡇⠀⠀⢹⡏⢹⣿⣽⡏⠀⠀⢸⣿⣧⡟⡇⣿⣾⣏⣿⡇ ⠈⣿⣿⢻⡏⠉⢳⡀⠹⣆⠀⠀⢾⣿⣿⢸⠀⡇⠀⣿⣿⠀⠀⢸⣇⣸⣿⣿⡍⠁⠀⣿⣿⣿⣷⡿⣿⢻⣿⣿⣆ ⠀⠋⠽⠸⠷⠀⠾⠓⠾⠛⠀⠀⠸⠟⠏⠸⠀⠇⠀⠿⠿⠀⠀⠘⠛⠺⢿⢙⡷⠀⠀⠻⠿⠇⠻⠇⠟⠘⠿⠸⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣴⡀⣀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⣠⡟⠉⢳⡀⠀⢠⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣰⢿⣍⠉⠈⢿⣾⣻⡿⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⣀⣤⣾⣿⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⡤⠖⣾⣯⡿⠛⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠉⠁⣠⡴⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⢀⣴⠟⠉⠀⠀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠈⠙⠲⣶⠾⠋⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠻⣆⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠘⠀⠀⠀⣀⡤⠖⠚⢻⣷⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣲⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠉⠙⠒⠶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣰⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠀⠀⣩⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⠗⠒⠒⠺⢯⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⣄⡶⢸⣷⠐⡗⡇⠀⠀⠀⣿⠒⢿⡖⠒⣾⡞⠂⠀⠐⣶⠖⢺⣿⡆⣿⠓⠀⠀⣾⢿⠀⣸⣧⢰⣇⢸⢸⣿⡇ ⠀⠹⣿⣾⠈⣶⣷⡇⠀⠀⢸⣇⣀⢸⡧⠄⣾⡇⠀⠀⠀⢼⠀⣸⣿⣧⢸⠦⠀⠀⣿⣿⣱⡏⢸⣾⣿⣾⠈⣿⠀ ⠀⢸⣿⢳⣠⠟⣿⡿⠀⠀⠸⣯⣹⣿⡇⠀⣿⡇⠀⠀⠀⢸⣧⢾⣿⡯⣸⡀⠀⠀⢹⣿⡟⣷⣼⡿⡏⢿⠈⣿⣧ ⠀⠉⠁⠀⠉⠀⠈⠁⠀⠀⠀⠈⠉⠈⠉⠁⠈⠀⠀⠀⠀⠈⠙⠈⠉⠁⠈⠉⠀⠀⠀⣉⠀⠈⠁⠀⠁⠈⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠟⠉⠡⠍⠉⠉⠉⢙⣹⣤⣶⣶⠶⣲⡢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣡⢖⣷⡀⣿⣵⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠞⠀⢰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡽⢻⡇⢉⣿⣿⡷⡄⠀⠀ ⠀⠀⠀⢀⣾⡀⠀⠺⠁⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠳⣄⢨⣔⣫⣿⣿⣷⠘⣄⠀ ⠀⠀⠀⢸⣿⠇⠐⠀⢀⣤⣿⣶⣶⡶⠖⠛⠆⠀⠀⠀⠘⡆⠛⠻⢿⣏⠀⠀⠾⡆ ⠀⠀⠀⢸⣵⣮⣾⣿⠿⠃⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⣴⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⣿⣿⡇⠀⡠⣠⡄⣀⠒⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠁⠸⣉⣤⣼⣿⡿⠚⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠉⠛⠿⠿⢿⡞⠻⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀

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⠀⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣟ ⠞⢿⡟⠿⡿⢁⡼⡿⢫⣿⣿⡟⣧⢳⣻⣿⣿⣿⣿⣿⣿⣿⡻⡞⣿⣿⣿⣯⢿⣿ ⠀⠘⣿⠞⠁⡜⠞⠁⠈⠋⠻⣿⡌⢁⣿⣿⣿⣿⣯⡉⢿⡏⢀⣽⣿⣿⣿⣏⣼⢟ ⠀⠀⢉⠷⢦⢴⣏⠁⠀⠀⠀⠘⠃⠉⡽⣿⢃⣿⣿⠀⠸⠷⠊⡝⣫⠃⠛⠈⠀⠈ ⠁⣤⡐⠃⢠⠦⢻⡆⠀⠀⠀⠀⠀⠀⠀⠙⠀⠹⠁⠂⠀⠀⠈⠀⠃⠀⠀⠀⠀⡈ ⠂⢸⣻⣔⢐⠁⠹⢅⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀ ⠀⠀⣧⠻⡶⣤⠀⠀⠈⢿⠀⠀⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡁⠐⠀ ⠀⠀⠲⡄⢱⢍⢳⡁⠐⣄⠠⢀⠕⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⠐⠁⠀⠀ ⠀⠀⠀⠹⣼⠈⢧⣻⣄⣇⠀⠠⡜⢡⡄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣥⡋⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣹⣿⣿⣿⡇⣟⠍⠻⡄⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀ ⣀⢄⡀⢀⠀⠀⠻⣿⣿⣿⣿⡁⠐⠈⠻⠤⡖⢋⣵⠟⡉⣹⣿⠈⣿⡿⠛⡆⢀⡴ ⣶⣷⣿⣄⠰⣀⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠈⡁⠀⠄⢁⣏⡼⠋⠀⠈⢙⣟⡀ ⣿⣿⣿⣿⣻⣷⣇⣈⡀⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣾⣿⣢⢄⠀⠀⣿⣶⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡝⣿⢟⣾⣷⡄⠀⠀⠀⣀⢴⣿⣿⣟⣷⣕⣀⠈⠻⢧

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