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A number **n **can be broken into three parts** n/2, n/3 and n/4 **(consider only **integer **part). Each number obtained in this process can be divided further recursively. Find the **maximum sum **that can be obtained by summing up the divided parts together.

**Note: **The maximum sum may be obtained without dividing n also.

**Example 1:**

Input:n = 12Output:13Explanation: Break n = 12 in three parts {12/2, 12/3, 12/4} = {6, 4, 3}, now current sum is = (6 + 4 + 3) = 13. Further breaking 6, 4 and 3 into parts will produce sum less than or equal to 6, 4 and 3 respectively.

â€‹**Example 2:**

**Input**:
n = 24
**Output:** 27
**Explanation**: Break n = 24 in three parts
{24/2, 24/3, 24/4} = {12, 8, 6}, now current
sum is = (12 + 8 + 6) = 26 . But recursively
breaking 12 would produce value 13.
So our maximum sum is 13 + 8 + 6 = 27.

**Your Task:**

You don't need to read input or print anything. Your task is to complete the function **maxSum() **which accepts an integer n and returns the maximum sum.

**Expected Time Complexity: **O(n)

**Expected Auxiliary Space: **O(n)

**Constraints:**

1 <= n <= 10^{6}

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Maximum Sum Problem

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