Given a positive integern, break it into the sum ofat leasttwo positive integers and maximize the product of those integers. Return the maximum product you can get.

For example, givenn= 2, return 1 (2 = 1 + 1); givenn= 10, return 36 (10 = 3 + 3 + 4).

Note: You may assume thatnis not less than 2 and not larger than 58.

class Solution {
    public int integerBreak(int n) {
        int[] dp = new int[n + 1];

        dp[0] = dp[1] = 1;
        for (int i = 2; i <= n; i++){
            dp[i] = 1;
            for (int j = 1; j < i; j++){
                dp[i] = Math.max(dp[i], Math.max(dp[j], j) * (i - j));
            }
        }

        return dp[n];
    }
}