**Time limit:**1.00 s**Memory limit:**512 MB

On each move, you may choose any subarray and split it into two subarrays. The cost of such a move is the sum of values in the chosen subarray.

What is the minimum total cost if you act optimally?

**Input**

The first input line has an integer $n$: the array size. The array elements are numbered $1,2,\dots,n$.

The second line has $n$ integers $x_1,x_2,\dots,x_n$: the contents of the array.

**Output**

Print one integer: the minimum total cost.

**Constraints**

- $1 \le n \le 5000$

- $1 \le x_i \le 10^9$

**Example**

Input:

`5`

2 7 3 2 5

Output:

`43`