class Solution {
    public int integerBreak(int n) {
        int[] dp = new int[n+1];
        dp[2] = 1;
        for (int i = 3; i <= n; i++) {
            for (int j = 1; j < i; j++){
                dp[i] = Math.max(dp[i], Math.max(j*(i-j), j*dp[i-j]));
            }
        }
        return dp[n];
    }
}

class Solution {
    public int numTrees(int n) {
        int[] dp = new int[n+1];
        dp[0] = 1;
        dp[1] = 1;

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

        return dp[n];
    }
}