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)


# dp[0]=l[0]
# dp[1]=l[0]+l[1]
# mp = l[0]+l[1]
def fun(arr):
    l = [int(j) for j in arr.split()]
    if len(l)==1:
        return 0
    if len(l)==0:
        return 0
    min_pair = 1
    
    ans = l[0]+l[1]
    # l = []
    for i in range(1,len(l)):
        if l[i]+l[i-1]<ans:
            min_pair = i
            ans = l[i]+l[i-1]
    mx = 10**11
    for i in range(1,len(l)):
        if l[i]+l[i-1]==ans:
            s = ""
            for j in range(i-1):
                s = s+str(l[j])+" "
            s = s+str(l[i]+l[i-1])+" "
            for j in range(i+1,len(l)):
                s = s+str(l[j])+" "
            
            x = fun(s)
            # print(s, "dekh",x)
            mx = min(l[i]+l[i-1]+x, mx)
            i1 = i
    # print(mx)
    # ans1.append(mx)
    return mx
        
n = int(input())
l = [int(j) for j in input().split()]
s=""
for i in l:
    s = s+str(i)+" "
# ans1=[]
print(fun(s))
# print("f", sum(ans1))