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.

4
10 20 30 40

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)

5
10 10 10 10 10

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)

3
1000000000 1000000000 1000000000

5000000000

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

6
7 6 8 6 1 1

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)