Problem:
Score : 100 points

Problem Statement

There are N slimes lining up in a row.
Initially, the i-th slime from the left has a size of a_i.

Taro is trying to combine all the slimes into a larger slime.
He will perform the following operation repeatedly until there is only one slime:

Choose two adjacent slimes, and combine them into a new slime. The new slime has a size of x + y, where x and y are the sizes of the slimes before combining them. Here, a cost of x + y is incurred. The positional relationship of the slimes does not change while combining slimes.

Find the minimum possible total cost incurred.

Constraints

All values in input are integers.

2 \leq N \leq 400

1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

Print the minimum possible total cost incurred.

Sample Input 1

4
10 20 30 40

Sample Output 1

190

Taro should do as follows (slimes being combined are shown in bold):

(10, 20, 30, 40) → (30, 30, 40)

(30, 30, 40) → (60, 40)

(60, 40) → (100)

Sample Input 2

5
10 10 10 10 10

Sample Output 2

120

Taro should do, for example, as follows:

(10, 10, 10, 10, 10) → (20, 10, 10, 10)

(20, 10, 10, 10) → (20, 20, 10)

(20, 20, 10) → (20, 30)

(20, 30) → (50)

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 4

6
7 6 8 6 1 1

Sample Output 4

68

Taro should do, for example, as follows:

(7, 6, 8, 6, 1, 1) → (7, 6, 8, 6, 2)

(7, 6, 8, 6, 2) → (7, 6, 8, 8)

(7, 6, 8, 8) → (13, 8, 8)

(13, 8, 8) → (13, 16)

(13, 16) → (29)

Solution in Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
public class Main {
    
    public static long sum(int[] arr, int i, int j) {
        int sum = 0;
        for(int k = i; k <= j; k++){
            sum += arr[k];
            
        }
        return sum;
    }

    static long solve(int[] arr, int i, int j,long[][] dp){
        if(i>= j)
            return 0;
        if(dp[i][j] != -1)
            return dp[i][j];

        long ans = Long.MAX_VALUE;
        
        for(int k = i; k < j; k++){
          ans =  Math.min(ans, solve(arr,i,k,dp) + solve(arr, k+1, j,dp) + sum(arr,i,k) + sum(arr,k+1,j));
        }

        return  dp[i][j] = ans;
        
    }
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer token;
        int n = Integer.parseInt(br.readLine().trim());
        int[] arr = new int[n];
        token = new StringTokenizer(br.readLine().trim()," ");
        for(int i = 0; i < arr.length; i++){
            arr[i] = Integer.parseInt(token.nextToken());
        }
        
        long[][] dp = new long[arr.length][arr.length];
       for(int i = 0; i < dp.length; i++)
           Arrays.fill(dp[i],-1);

       System.out.println(solve(arr, 0, arr.length-1,dp));
    }
}