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class Solution {
public:
    int dp[502][502];
    int maxCoins(vector<int>& nums) {
        int n = nums.size();
        memset(dp, 0, sizeof dp);
        nums.insert(nums.begin(), 1);
        nums.insert(nums.end(), 1);
        for(int len=1; len<=n; len++){
            for(int start=1; start<=n-len+1; start++){
                int end = start+len-1;
                int ans = INT_MIN;
                for(int mid=start; mid<=end; mid++){
                    ans = max(ans, dp[start][mid-1]+dp[mid+1][end]+nums[mid]*nums[start-1]*nums[end+1]);
                }
                dp[start][end] = ans;
            }
        }
        return dp[1][n];
    }
};