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.

All values in input are integers.
$2 \leq N \leq 400$
$1 \leq a_i \leq 10^9$

190

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)

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)