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

What is the maximum possible score for the first player when both players play optimally?

**Input**

The first input line contains an integer $n$: the size of the list.

The next line has $n$ integers $x_1,x_2,\ldots,x_n$: the contents of the list.

**Output**

Print the maximum possible score for the first player.

**Constraints**

- $1 \le n \le 5000$

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

**Example**

Input:

`4`

4 5 1 3

Output:

`8`