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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠉⣀⣀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⠋⢁⣠⣴⣾⠟⠿⣷⣦⣀⠈⠛⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⠟⠋⢀⣿⣶⣿⠟⢋⡄⠀⠀⢨⡙⢻⣿⣶⣟⡈⠙⠻⣷⣤⡀⠀⠀ ⣴⡿⠟⠉⣀⣤⣾⡿⢿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⡿⢿⣷⣤⣀⠉⠻⢷⣦ ⣿⡇⢰⣾⠿⠋⠁⢶⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⡦⠈⠛⢿⣷⠀⢸⣿ ⣿⡇⢸⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⠀⢸⣿ ⣿⡇⢸⣿⠀⣿⣶⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⣀⣤⣶⣿⢸⣿⠀⢸⣿ ⣿⣇⣸⣿⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣄⣸⣿ ⣿⡏⢹⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⠉⢹⣿ ⣿⡇⢸⣿⠀⣿⠿⠛⠉⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠛⠿⡇⢸⣿⠀⢸⣿ ⣿⡇⢸⣿⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⠀⠀⣾⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⠀⢸⣿ ⣿⡇⠸⢿⣦⣄⡀⠾⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⡿⠗⢀⣠⣾⡿⠀⢸⣿ ⠻⣷⣦⣀⠉⠛⢿⣷⣾⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣷⣾⠿⠛⠁⣠⣴⡾⠟ ⠀⠀⠉⠛⢿⣦⣄⡈⣿⠿⣿⣦⣌⠃⠀⠀⢘⣡⣼⣿⠿⣯⢁⣠⣴⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⡀⠙⠻⢿⣦⣶⡿⠟⠉⢀⣤⣿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⣀⠉⠁⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⠿⠿⠿⢷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡟⠛⠛⠛⠻⠿⠿⢿⣶⣶⣦⣤⣤⣀⣀⡀⣀⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀ ⠀⠻⣿⣦⡀⠀⠉⠓⠶⢦⣄⣀⠉⠉⠛⠛⠻⠿⠟⠋⠁⠀⠀⠀⣤⡀⠀⠀⢠⠀⠀⠀⣠⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⢻⣿ ⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⡀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢷⡀⠸⡇⠀⣰⠇⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⡶⠶⠶⠒⠂⠀⠀⣠⣾⠟ ⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⣠⣴⣿⣯⣭⣽⣷⣆⠀⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⡀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀ ⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡗⢻⣿⣧⣽⣿⣿⣿⣧⠀⠀⣀⣀⠀⢠⣿⣧⣼⣿⣿⣿⣿⠗⠰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠸⠃⠈⠻⣿⣿⣿⣿⣿⡿⠃⠾⣥⡬⠗⠸⣿⣿⣿⣿⣿⡿⠛⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣄⣰⣄⠀⠀⠉⠉⠉⠁⠀⢀⣀⣠⣄⣀⡀⠀⠉⠉⠉⠀⠀⢀⣠⣾⣥⣤⣤⣤⣶⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⠛⢿⣷⣦⣤⣴⣶⣶⣦⣤⣤⣤⣤⣬⣥⡴⠶⠾⠿⠿⠿⠿⠛⢛⣿⣿⣿⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠈⠉⠀⠈⠁⣾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⣀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠋⣿⠛⠃⠀⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡀⠈⢹⡿⠶⣶⣼⡇⠀⢀⣀⣀⣤⣴⣾⠟⠋⣡⣿⡟⠀⢻⣶⠶⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡈⢿⣦⣸⠇⢀⡿⠿⠿⡿⠿⠿⣿⠛⠋⠁⠀⣴⠟⣿⣧⡀⠈⢁⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣦⣈⣽⣀⣾⠃⠀⢸⡇⠀⢸⡇⠀⢀⣠⡾⠋⢰⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⡟⠛⠃⠀⠀⣾⠀⠀⢸⡇⠐⠿⠋⠀⠀⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⡴⠋⠀⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠋⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡴⠶⠦⠤⣤⣄⣀⡀⢀⣠⡴⠖⠚⠋⠛⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠙⢦⡀⠉⠒⠤⣍⡉⠉⠁⠀⠐⢤⠐⠀⡰⠀⠀⠈⠙⠉⢉⣉⣉⣉⠍⠉⣩⠇ ⠀⠀⠻⣄⠀⠀⠀⢻⢤⣞⣿⣿⡆⢀⡀⢠⣟⣿⣷⠄⡾⠉⠀⠀⠀⣠⡾⠃⠀ ⠀⠀⠀⠙⠳⣤⣀⣈⣀⠙⠿⠟⠃⢓⡊⠙⠻⠛⠋⣠⣃⣀⣀⣤⠞⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⡝⠓⠒⢺⠷⠒⠒⠒⠛⠛⢉⣩⠿⣿⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡟⢲⢤⣸⡄⠀⢀⣠⠴⣺⡏⣏⣤⡾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢞⣺⣠⠋⠹⠉⡏⢁⡴⣹⣧⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⡟⢁⠄⡇⢠⠈⠉⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⡇⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠀⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡀⠹⠛⠉⠀⣠⣴⣿⣷⣦⣀⠀⠉⠻⠏⢠⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠛⠉⢹⣿⣿⡇⠉⠓⠀⠀⠀⠈⠛⢿⣷⣤⣀⠀⠀ ⣴⡿⠟⠋⠀⣀⣤⠶⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠶⣄⡀⠈⠙⠻⣷⣦ ⣿⡇⠀⣴⣾⣿⣤⡀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡆⠀⢸⣿ ⣿⡇⠀⣿⢿⣿⣿⣿⣶⣄⠀⠀⢀⣤⣿⣿⣤⡀⠀⢀⣠⣾⣿⣿⣿⣿⡇⠀⢸⣿ ⣿⡇⠀⣿⠀⠈⠉⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠛⠉⠀⠘⡇⠀⢸⣿ ⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟ ⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶ ⣿⡇⠀⣿⠀⢀⣀⣤⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣤⣀⠀⢸⡇⠀⢸⣿ ⣿⡇⠀⣿⣾⣿⣿⣿⠿⠋⠀⠀⠈⠛⣿⣿⠋⠁⠀⠈⠙⢿⣿⣿⣿⣿⡇⠀⢸⣿ ⣿⡇⠀⠻⢿⣿⠛⠁⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠇⠀⢸⣿ ⠻⣿⣦⣄⡀⠉⠛⠶⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠶⠋⠁⢀⣠⣶⡿⠟ ⠀⠀⠉⠛⢿⣶⣤⡀⠀⠀⠀⣤⣀⣸⣿⣿⡇⣀⡤⠀⠀⠀⢀⣤⣾⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠁⣰⣦⣀⠀⠙⠻⣿⡿⠟⠉⠀⣀⣴⣆⠘⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣄⠀⢀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⢿⣿⣶⣶⣦⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢠ ⠹⡆⠀⠀⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⣠⣶⣷⣶⣄⠀⠀⠀⠀⠀⠀⠁⣠⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⢾⡿⠟⠋⠁⡠⠚ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⢨⣿⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⢠⠞⠀⠀ ⠀⢀⡼⢤⡀⠀⠀⠀⠀⠛⠃⢹⣄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⣾⢿⡟⠀⠀⠀⠀⠀⠀⢀⠊⢣⠀⠀ ⠀⡞⢁⡮⠿⢿⣦⣀⠀⠈⠧⠼⡿⣆⠀⠀⠀⠀⠀⠀⠐⠒⠊⠉⠉⠑⠒⠤⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⠇⠀⠀⢀⣀⣤⠞⠁⠀⠀⢣⠀ ⣼⢡⡿⠁⠀⠀⠻⣿⣷⣤⣤⡴⠋⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣴⠿⠁⢦⣤⣶⣿⡿⠛⠋⠁⠀⠀⠀⠀⠈⡆ ⡏⣾⡇⣸⣄⢀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⡀⠀⠸⢿⣿⣿⣷⣧⣀⠀⠀⠀⠀⠀⣀⣼ ⣧⠟⠀⣿⣿⣿⡟⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⢿⣿⣿⣿⣏⣽⣿⣾⣟⠀⠀⠉⠹ ⠃⢀⣴⡿⣿⣿⣇⡀⣠⣏⢀⣀⡀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣻⠛⠻⡄⠀⠀⠀ ⣤⣿⣭⣿⣿⣿⣿⣿⣷⡿⠏⠁⠈⠉⠉⠛⠛⠿⠛⠛⠛⠛⠛⢛⢛⣻⣻⣶⣿⢷⣶⣶⣠⣄⣤⣄⣤⣠⡤⠾⢿⣿⣿⠿⣿⠟⠛⢶⡀⠀ ⡿⡟⠀⣾⣿⣏⣼⠟⣿⡁⠀⠀⢀⣠⡀⠀⠀⠀⠠⣄⣴⡶⡾⢿⠟⡟⠓⠚⠛⠛⠛⠿⣿⣦⡀⠙⠛⠳⢄⡀⠀⠹⣿⣙⡋⠉⠉⠻⣷⣀ ⠓⣧⣤⣶⣿⣿⣿⣾⢡⢀⣤⣤⣼⣽⣿⣶⣤⣤⣤⣮⣼⣥⡄⡼⣤⣭⡆⠀⠀⠀⠀⠀⠹⣿⠏⠉⣒⣀⡀⠙⢄⠀⣹⣿⣿⣄⣰⣀⠁⢉ ⣾⣿⣿⣿⣿⣿⢛⡏⣼⣸⣶⣿⣿⣿⣏⣿⣿⣿⣹⣇⣇⣸⣠⣇⣼⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⠄⠳⡘⣿⣿⣿⣿⣿⣶⣾ ⠘⢿⣿⡿⠛⡿⠈⠉⠉⢉⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣶⠋⠀⠀⠀⢻⡿⠿⣿⣿⣿⠏⡉ ⠐⡆⠉⠓⢶⣅⣀⠀⡼⠿⠛⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠛⠛⠛⠉⠉⠈⢹⡇⠀⠀⣀⡤⢠⣴⡶⠿⠋⠀⣴⠂ ⠀⢷⡀⠀⠀⢹⡟⠓⠤⠤⠴⠿⠤⠤⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⢸⣦⣤⣀⣀⣀⣀⡀⠠⠤⢾⣇⡴⠿⠿⠟⠛⠉⠀⠀⣀⣰⡇⠀ ⠀⢸⡏⠓⢦⣀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡒⢂⣀⠀⠀⠒⠚⠚⣖⠛⢛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡴⠾⢻⣼⠀⠀ ⠀⠀⡇⠀⠀⠀⠉⠑⠒⠦⠤⣄⣉⠛⢲⠦⠤⠀⠀⢧⣘⣏⣹⣿⣍⣿⣯⣭⣇⡸⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠛⠉⠁⠀⠀⢸⠇⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠒⠚⠋⠉⠉⠉⢁⣿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⡀⠰⣬⢿⡆⠀⠀⠀⠀⠀⠀⢀⣀⣾⡟⣷⡞⣿⣿⣦⣿⣿⣷⣀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠘⢷⣿⣇⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⣉⠉⢉⡉⢉⣉⣉⣉⣩⡀⠀⠀⠀⢀⣀⣤⣶⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠐⠚⠓⠚⠛⠓⠚⠛⢃⠀⠀⠘⣯⣽⡛⠓⢀⠀⠀⠀⣠⡶⠶⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠈⠀⠀⠈⠉⠉⠉⠙⠁⠀⢀⣛⠟⠀⠼⠗⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⠿⠿⠿⠿⢿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⠟⣋⣭⣴⣶⡆⠀⠀⢰⣶⣦⣬⣙⠻⢿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠋⠰⣾⠟⠋⠉⠀⠀⣀⣀⠀⠀⠉⠙⠻⢿⡦⠙⠻⣷⣄⠀⠀⠀ ⠀⠀⣴⣿⢋⡀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⢀⡙⢿⣧⡀⠀ ⠀⣼⡿⢡⣾⠟⠀⠀⢾⣷⣄⠀⠀⠀⣿⣿⠀⠀⠀⣠⣾⣷⠄⠀⠹⣿⡌⢿⣷⠀ ⢰⣿⢃⣿⡟⠀⠀⠀⠀⠙⢿⣷⣤⣶⣿⣿⣶⣤⣾⣿⠟⠁⠀⠀⠀⠹⣿⡌⣿⣇ ⣾⡟⠸⠿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠿⠇⢸⣿ ⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿ ⢿⣧⢰⣶⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣶⡖⢸⣿ ⠸⣿⡌⣿⣇⠀⠀⠀⠀⣠⣾⣿⠟⠿⣿⣿⠿⠛⢿⣷⣄⠀⠀⠀⠀⢰⣿⢃⣿⡏ ⠀⢻⣷⡘⣿⣦⠀⠀⢾⣿⠟⠁⠀⠀⣿⣿⠀⠀⠀⠙⢿⣷⠆⠀⣰⣿⠃⣼⡿⠀ ⠀⠀⢻⣷⣌⠋⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠈⢣⣾⡿⠁⠀ ⠀⠀⠀⠙⢿⣷⣄⠰⣷⣦⣄⣀⠀⠀⠉⠉⠀⠀⢀⣀⣴⣾⠶⣀⣴⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣷⣦⣍⡛⠻⠿⠇⠀⠀⢸⠿⠿⢛⣉⣤⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣷⣶⣶⣶⣶⣶⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
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