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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
input=sys.stdin.readline
sys.setrecursionlimit(100000000)
MOD = 10**9+7
INF = 10 ** 10
from functools  import lru_cache

MAXN = 405
a = [0] * MAXN
dp = [[-1] * MAXN for _ in range(MAXN)]
def dfs(l,r):
    if dp[l][r] != -1:
        return dp[l][r]
    if r - l == 1:
        dp[l][r] = 0
        return 0
    else:
        ans = INF
        for i in range(l + 1,r):
            ans = min(ans,dfs(l,i) + dfs(i,r)) 
        if l == 0:
            ans += a[r - 1]
        else:
            ans += a[r - 1] - a[l - 1]
        dp[l][r] = ans
        return ans

def main():
    n = int(input())
    b = list(map(int,input().split()))
    a[:n] = b

    for i in range(1,n):
        a[i] += a[i - 1]
    
    ans = dfs(0,n)
    print(ans)
if __name__=='__main__':
    main()