⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⣀⣤⣄⡀⣿⢀⣠⣤⣀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠘⠋⠉⠉⢻⣿⠟⠉⠉⠙⠃⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡶⠿⣿⠿⢶⣶⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀ ⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀ ⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠾⠾⠶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠋⣉⣁⣤⣤⣶⣶⣶⣤⣤⣈⡉⠛⠻⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠋⠁⢤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡤⠉⠙⠻⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⠀⠀⢀⣀⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⠀⠀⢸ ⢸⡇⠀⢸⡟⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠀⠀⢸ ⠸⡇⠀⠘⣧⠀⣿⣿⣶⣦⣤⣄⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣤⣤⣶⣶⣿⡿⠀⣿⠀⠀⢸ ⠀⣿⠀⠀⣿⠀⠻⠿⠛⠋⠉⠁⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠈⠉⠛⠛⠿⡇⢠⡟⠀⠀⡟ ⠀⢻⡄⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⣿⣟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⡇ ⠀⢸⡇⠀⠸⣧⠀⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠀⣿⠀⠀⢸⠀ ⠀⠀⣿⠀⠀⣿⡀⢹⣿⣿⣿⠿⠗⠒⠒⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⠒⠒⠾⢿⣿⣿⣿⠇⢠⡏⠀⠀⡿⠀ ⠀⠀⢹⡇⠀⢸⣇⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⣼⠃⠀⢸⠇⠀ ⠀⠀⠀⣿⠀⠀⣿⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⡟⠀⠀⡿⠀⠀ ⠀⠀⠀⢹⡆⠀⢸⣧⠀⣿⣷⣶⣤⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⣠⣤⣶⣾⡿⠁⣼⠃⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢿⡆⠸⠿⠟⠛⠉⠁⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠈⠉⠛⠻⢿⠃⣰⡏⠀⢀⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣆⠀⠘⣷⠀⢳⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⡞⢁⣿⠁⠀⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠹⣧⠀⢿⣿⣿⠷⠆⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠆⠲⠾⣿⣿⡟⢀⣾⠃⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠹⣧⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⢀⣾⠃⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠘⣷⡀⠳⣦⣄⣀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣠⣴⠞⢠⡿⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠙⣧⡀⠻⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠏⢀⡾⠃⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠘⢿⣄⠀⠀⠀⠀⠀⠉⠛⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⣰⡟⠁⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠹⣧⡀⠀⠀⠀⣀⣤⣶⣿⣶⣤⣀⠀⠀⠀⢀⣾⠋⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠈⠻⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⣴⠟⠁⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠙⢷⣄⠘⠻⣿⣿⣿⠟⠁⣠⡾⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠙⢷⣄⠈⠛⠁⣠⡾⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠙⠳⣴⠞⠉⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡳⣴⠞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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