Matching Parenthesis

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Shaun was given $N$ pairs of parenthesis ( ) by his teacher who gave him a difficult task.The task consists of two steps. First,Shaun should colour all $N$ pairs of parenthesis each with different color but opening and closing bracket of a particular pair should be of same colour. Then,Shaun should report to his teacher the number of ways he can arrange all $2*N$ brackets such that sequence form

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solution.cppC++17

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