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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

class Main
{
    static long prefix[];
    static long dp[][];
    public static void main(String[] args) throws IOException {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        String str[]=br.readLine().split(" ");
        prefix=new long[str.length+1];
        long arr[]=new long[str.length];
        for(int i=0;i<str.length;i++)
            arr[i]=Long.parseLong(str[i]);
        preprocess(arr);
        dp=new long[arr.length+1][arr.length+1];
        for(int i=0;i<dp.length;i++)
            for(int j=0;j<dp[0].length;j++)
                dp[i][j]=-1;
//        System.out.println(Arrays.toString(prefix));
        System.out.println(calculate(arr,0,arr.length-1));

    }

    private static void preprocess(long arr[]) {
        for(int i=0;i<arr.length;i++)
        {
            prefix[i+1]=prefix[i]+arr[i];
        }

    }

    private static long calculate(long[] arr, int i, int j) {
        if(i==j)
            return 0;
        if(dp[i][j]!=-1)
            return dp[i][j];
        long min=Long.MAX_VALUE;
        long sum=prefix[j+1]-prefix[i];
        for(int k=i;k<j;k++)
        {
            long c1=calculate(arr,i,k);
            long c2=calculate(arr,k+1,j);
            min=Math.min(min,sum+c1+c2);
        }
        return dp[i][j]=min;
    }
}