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>

typedef unsigned long long ull;

ull slime_combine(ull *a, size_t N) {
    ull sz[N][N], cost[N][N], tmp;
    size_t i, j, k, l;
    for (i = 0 ; i<N ; i++) {
        sz[i][i] = a[i];
        cost[i][i] = 0;
    }
    for (l = 1 ; l<N ; l++)
        for (i = 0, j = l ; j<N ; i++, j++) {
            cost[i][j] = cost[i+1][j] + a[i] + sz[i+1][j];
            sz[i][j] = a[i] + sz[i+1][j];
            for (k = i+1 ; k<j ; k++) {
                tmp = cost[i][k] + cost[k+1][j] + sz[i][k] + sz[k+1][j];
                if (tmp<cost[i][j]) cost[i][j] = tmp;
            }
        }
    return cost[0][N-1];
}

int main() {
    unsigned N;
    scanf("%u", &N);
    ull a[N];
    for (unsigned i = 0 ; i<N ; i++) scanf("%llu", a+i);
    printf("%llu", slime_combine(a, N));
    return 0;
}