Score : 100 points

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.

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Print the minimum possible total cost incurred.

4
10 20 30 40

Taro should do as follows (slimes being combined are shown in bold):

5
10 10 10 10 10

Taro should do, for example, as follows:

3
1000000000 1000000000 1000000000

5000000000

The answer may not fit into a 32-bit integer type.

6
7 6 8 6 1 1

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)