Description
Given an integer n, break it into at least two positive integers and maximize the product of those integers.
Examples
Input:
n = 10Output:
36Explanation:
10 = 3 + 3 + 4, product = 36
Input:
n = 4Output:
4Explanation:
4 = 2 + 2, product = 2 × 2 = 4. One could also break it as 4 = 1 + 3 with product = 3, or 4 = 1 + 1 + 2 with product = 2, but 2 + 2 gives the maximum product of 4.
Input:
n = 7Output:
12Explanation:
7 = 3 + 4, product = 3 × 4 = 12. Alternative breakdowns like 7 = 2 + 2 + 3 give product = 12, and 7 = 3 + 2 + 2 also gives product = 12. Other options like 7 = 1 + 6 (product = 6) or 7 = 2 + 5 (product = 10) yield smaller products.
Constraints
- •
2 ≤ n ≤ 58