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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from itertools import accumulate
import sys
input = sys.stdin.readline
from itertools import chain

dp = []
dp2 = []
aac = []

def fdp(l, r):
    global dp, dp2
    if dp2[l][r]:
        return dp[l][r]
    else:
        dp2[l][r] = 1
        if l == r:
            return 0
        result_tmp = float('inf')
        for kugiri in range(l, r):
            result_tmp = min(result_tmp, fdp(l, kugiri) + fdp(kugiri+1, r))
        result = result_tmp + (aac[r+1] - aac[l])
        dp[l][r] = result
        return result
def main():
    global dp, dp2, aac
    n = int(input())
    a = tuple(map(int, input().split()))
    aac = list(accumulate(a))
    aac = tuple(chain([0], aac))
    dp = [[0] * n for _ in range(n)]
    dp2 = [[0] * n for _ in range(n)]
    fdp(0, n - 1)
    print(dp[0][-1])
if __name__ == '__main__':
    main()