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;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Program
{
	static void Main()
	{
		int n = int.Parse(Console.ReadLine());
		long[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);
    long[,] length = new long[n,n];
    long[,] cost = new long[n,n];
    for(int i = 0; i < n; i++)
    {
      for(int j = 0; j < n; j++)
      {
        cost[i,j] = long.MaxValue;
      }
    }
    for(int i = 0; i < n; i++)
    {
      length[i,i] = nums[i];
      cost[i,i] = 0;
    }

    for(int l = 2; l <= n; l++)//区間の長さ
    {
      for(int i = 0; i < n+1-l; i++)//左端
      {
        for(int j = 1; j < l; j++)//左側の区間の長さ
        {
          length[i,i+l-1] = length[i,i+j-1] + length[i+j,i+l-1];
          cost[i,i+l-1] = Math.Min(cost[i,i+l-1], cost[i,i+j-1] + cost[i+j,i+l-1] + length[i,i+l-1]);
          //Console.WriteLine(i+" "+(i+l-1)+" "+cost[i,i+l-1]);
        }
      }
    }
    
		Console.WriteLine(cost[0,n-1]);
	}
}