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++14 (GCC 5.4.1) (judge verdict: Accepted)

/*  -*- coding: utf-8 -*-
 *
 * n.cc: N - Slimes
 */

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<iostream>
#include<string>
#include<vector>
#include<map>
#include<set>
#include<stack>
#include<list>
#include<queue>
#include<deque>
#include<algorithm>
#include<numeric>
#include<utility>
#include<complex>
#include<functional>

using namespace std;

/* constant */

const int MAX_N = 400;
const long long LINF = 1LL << 62;

/* typedef */

typedef long long ll;

/* global variables */

ll dp[MAX_N][MAX_N + 1], szs[MAX_N + 1];

/* subroutines */

inline void setmin(ll &a, ll b) { if (a > b) a = b; }

/* main */

int main() {
  int n;
  scanf("%d", &n);

  szs[0] = 0;
  for (int i = 0; i < n; i++) {
    int ai;
    scanf("%d", &ai);
    szs[i + 1] = szs[i] + ai;
  }

  for (int l = 2; l <= n; l++)
    for (int i = 0, j = l; j <= n; i++, j++) {
      ll mind = LINF;
      ll szij = szs[j] - szs[i];
      for (int k = i + 1; k < j; k++)
	setmin(mind, dp[i][k] + dp[k][j] + szij);
      dp[i][j] = mind;
    }

  printf("%lld\n", dp[0][n]);
  return 0;
}