# Find the permutation of first N natural numbers such that sum of i % P<sub>i</sub> is maximum possible

Given a number N. The task is to find the permutation P of first N natural numbers such that sum of i % Pi is maximum possible. The task is to find the maximum possible sum not it’s permutation.

Examples:

Input: N = 5
Output: 10
Possible permutation is 2 3 4 5 1.
Modulus values will be {1, 2, 3, 4, 0}.
1 + 2 + 3 + 4 + 0 = 10

Input: N = 8
Output: 28

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

Approach: Maximum possible sum is (N * (N – 1)) / 2 and it is formed by the permutation 2, 3, 4, 5, ….. N, 1.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the permutation of ` `// the first N natural numbers such that ` `// the sum of (i % Pi) is maximum possible ` `// and return the maximum sum ` `int` `Max_Sum(``int` `n) ` `{ ` `    ``return` `(n * (n - 1)) / 2; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 8; ` ` `  `    ``// Function call ` `    ``cout << Max_Sum(n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to find the permutation of ` `// the first N natural numbers such that ` `// the sum of (i % Pi) is maximum possible ` `// and return the maximum sum ` `static` `int` `Max_Sum(``int` `n) ` `{ ` `    ``return` `(n * (n - ``1``)) / ``2``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `n = ``8``; ` ` `  `    ``// Function call ` `    ``System.out.println(Max_Sum(n)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

 `# Python3 implementation of the approach ` ` `  `# Function to find the permutation of ` `# the first N natural numbers such that ` `# the sum of (i % Pi) is maximum possible ` `# and return the maximum sum ` `def` `Max_Sum(n) : ` `     `  `    ``return` `(n ``*` `(n ``-` `1``)) ``/``/` `2``; ` ` `  `# Driver code ` `if` `__name__ ``=``=` `"__main__"` `: ` `     `  `    ``n ``=` `8``; ` ` `  `    ``# Function call ` `    ``print``(Max_Sum(n)); ` `     `  `# This code is contributed by AnkitRai01 `

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to find the permutation of ` `// the first N natural numbers such that ` `// the sum of (i % Pi) is maximum possible ` `// and return the maximum sum ` `static` `int` `Max_Sum(``int` `n) ` `{ ` `    ``return` `(n * (n - 1)) / 2; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args) ` `{ ` `    ``int` `n = 8; ` ` `  `    ``// Function call ` `    ``Console.WriteLine(Max_Sum(n)); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:
```28
```

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