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Integer Break

Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.

Given an integer n, break it into the sum of k positive integers, where k >= 2, and maximize the product of those integers.

Return the maximum product you can get.

Example 1

Input: n = 2

Output: 1

Explanation: 2 = 1 + 1, 1 × 1 = 1.

Example 2

Input: n = 10

Output: 36

Explanation: 10 = 3 + 3 + 4, 3 × 3 × 4 = 36.

Constraints

  • 2 <= n <= 58

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