## Educational DP Contest AtCoder N - Slimes

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Points: 12
Time limit: 1.0s
Memory limit: 1G

Problem type

There are slimes lining up in a row. Initially, the -th slime from the left has a size of .

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 , where and are the sizes of the slimes before combining them. Here, a cost of 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.

#### Input Specification

The first line will contain the integer .

The next line will contain integers, .

#### Output Specification

Print the minimum possible total cost incurred.

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

#### Sample Input 1

4
10 20 30 40

#### Sample Output 1

190

#### Explanation For Sample 1

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

#### Explanation For Sample 2

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

#### Sample Input 4

6
7 6 8 6 1 1

#### Sample Output 4

68

#### Explanation For Sample 4

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)