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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

public static class Program {
    public static void Main() {
        int n=int.Parse(Console.ReadLine());
        long[]a=Console.ReadLine().Split().Select(long.Parse).ToArray();
        long[,]sum=new long[n+1,n+1];
        for(int i=0;i<n;i++){
            sum[i,i+1]=a[i];
            for(int j=i+2;j<=n;j++){
                sum[i,j]=sum[i,j-1]+a[j-1];
            }
        }
        long[,]dp=new long[n+1,n+1];
        for(int i=0;i<n;i++){
            dp[i,i+1]=0;
            for(int j=i+2;j<=n;j++){
                dp[i,j]=long.MaxValue;
            }
        }
        for(int len=2;len<=n;len++){
            for(int l=0;l+len<=n;l++){
                int r=l+len;
                for(int i=l+1;i<=r-1;i++){
                    Chmin(ref dp[l,r], dp[l,i]+dp[i,r]);
                }
                dp[l,r]+=sum[l,r];
            }
        }
        Console.WriteLine(dp[0,n]);
    }
    public static void Chmin(ref long x, long y){
        x=Math.Min(x,y);
    }
}