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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>

typedef int32_t i32;
typedef int64_t i64;

#define MIN(a,b) ((a)<(b)?(a):(b))
#define ALLOC(size,type) ((type*)calloc((size),sizeof(type)))

#define POS(i, j) ((i) * (n + 1) + (j))

void run (void) {
  i32 n;
  scanf ("%" SCNi32, &n);
  i64 *a = ALLOC (n + 1, i64);
  for (i32 i = 0; i < n; ++i) {
    scanf ("%" SCNi64, a + i);
  }
  for (i32 i = n - 1; i >= 0; --i) {
    a[i] += a[i + 1];
  }
  i64 *dp = ALLOC ((n + 1) * (n + 1), i64);
  for (i32 len = 2; len <= n; ++len) {
    for (i32 l = 0; l <= n - len; ++l) {
      i32 r = l + len;
      i64 min = dp[POS(l, l + 1)] + dp[POS(l + 1, r)];
      for (i32 i = l + 2; i < r; ++i) {
        i64 x = dp[POS(l, i)] + dp[POS(i, r)];
        min = MIN (min, x);
      }
      dp[POS(l, r)] = min + a[l] - a[r];
    }
  }
  printf ("%" PRIi64 "\n", dp[POS(0, n)]);
}

int main (void) {
  run();
  return 0;
}