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.

Examples

Input

4
10 20 30 40

Output

190

Input

5
10 10 10 10 10

Output

120

Input

3
1000000000 1000000000 1000000000

Output

5000000000

Input

6
7 6 8 6 1 1

Output

68

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