# Number of ways to insert two pairs of parentheses into a string of N characters

Given a string str of length N, the task is to find the number of ways to insert only 2 pairs of parentheses into the given string such that the resultant string is still valid.

Examples:

Input: str = “ab”
Output: 6
((a))b, ((a)b), ((ab)), (a)(b), (a(b)), a((b))
which are a total of 6 ways.

Input: str = “aab”
Output: 20

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: it can be observed that for the lengths of the string 1, 2, 3, …, N a series will be formed as 1, 6, 20, 50, 105, 196, 336, 540, … whose Nth term is (N + 1)2 * ((N + 1)2 – 1) / 12.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the number of ways ` `// to insert the bracket pairs ` `int` `cntWays(string str, ``int` `n) ` `{ ` `    ``int` `x = n + 1; ` `    ``int` `ways = x * x * (x * x - 1) / 12; ` `    ``return` `ways; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``string str = ``"ab"``; ` `    ``int` `n = str.length(); ` ` `  `    ``cout << cntWays(str, n); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the number of ways ` `// to insert the bracket pairs ` `static` `int` `cntWays(String str, ``int` `n) ` `{ ` `    ``int` `x = n + ``1``; ` `    ``int` `ways = x * x * (x * x - ``1``) / ``12``; ` `    ``return` `ways; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args)  ` `{ ` `    ``String str = ``"ab"``; ` `    ``int` `n = str.length(); ` ` `  `    ``System.out.println(cntWays(str, n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to return the number of ways  ` `# to insert the bracket pairs  ` `def` `cntWays(string, n) : ` ` `  `    ``x ``=` `n ``+` `1``;  ` `    ``ways ``=` `x ``*` `x ``*` `(x ``*` `x ``-` `1``) ``/``/` `12``;  ` `    ``return` `ways;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``string ``=` `"ab"``;  ` `    ``n ``=` `len``(string);  ` ` `  `    ``print``(cntWays(string, n));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Function to return the number of ways ` `// to insert the bracket pairs ` `static` `int` `cntWays(String str, ``int` `n) ` `{ ` `    ``int` `x = n + 1; ` `    ``int` `ways = x * x * (x * x - 1) / 12; ` `    ``return` `ways; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args)  ` `{ ` `    ``String str = ``"ab"``; ` `    ``int` `n = str.Length; ` ` `  `    ``Console.WriteLine(cntWays(str, n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```6
```

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Improved By : AnkitRai01, Rajput-Ji