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;

namespace AtCoder.DP
{
    class EDPC_N
    {
        static long[,] dp;
        static long[] acc;

        public static void Main()
        {
            var n = int.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
            dp = new long[n, n + 1];
            acc = new long[n + 1];

            for (int i = 0; i < n; i++)
                acc[i + 1] = acc[i] + a[i];

            Union(0, n);
            Console.WriteLine(dp[0, n]);
        }

        public static long Union(int left, int right)
        {
            if (right - left == 1 || dp[left, right] != 0)
                return dp[left, right];

            long min = long.MaxValue;
            for (int i = left + 1; i < right; i++)
            {
                var temp = Union(left, i) + Union(i, right);
                if (min > temp)
                    min = temp;
            }
            dp[left, right] = min + acc[right] - acc[left];
            return dp[left, right];
        }
    }
}