Given a positive integer total_value, partition it into the sum of at least two positive integers. Find the maximum possible product of these integers. Return the maximum product as an integer.
Example 1
Input: total_value=5
Output: 6
Explanation: 5 = 2 + 3, 2*3 = 6
Example 2
Input: total_value=8
Output: 18
Explanation: 8 = 3 + 3 + 2, 3*3*2 = 18
Example 3
Input: total_value=12
Output: 81
Explanation: 12 = 3 + 3 + 3 + 3, 3*3*3*3 = 81
Constraints
Case 1
Input: total_value=6
Expected: 9
Case 2
Input: total_value=9
Expected: 27
Case 3
Input: total_value=15
Expected: 243