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 \le N \le 400~
• ~1 \le a_i \le 10^9~

Input Specification

The first line will contain the integer ~N~.

The next line will contain ~N~ integers, ~a_1, a_2, \dots, a_N~.

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)