Taro and Jiro will play the following game against each other.

Initially, they are given a sequence . Until becomes empty, the two players perform the following operation alternately, starting from Taro:

- Remove the element at the beginning or the end of . The player earns points, where is the removed element.

Let and be Taro's and Jiro's total score at the end of the game, respectively. Taro tries to maximize , while Jiro tries to minimize .

Assuming that the two players play optimally, find the resulting value of .

#### Constraints

- All values in input are integers.

#### Input Specification

The first line will contain the integer .

The next line will contain integers, .

#### Output Specification

Print the resulting value of , assuming that the two players play optimally.

#### Sample Input 1

```
4
10 80 90 30
```

#### Sample Output 1

`10`

#### Explanation For Sample 1

The game proceeds as follows when the two players play optimally (the element being removed is written bold):

- Taro: (10, 80, 90,
**30**) → (10, 80, 90) - Jiro: (10, 80,
**90**) → (10, 80) - Taro: (10,
**80**) → (10) - Jiro: (
**10**) → ()

Here, and .

#### Sample Input 2

```
3
10 100 10
```

#### Sample Output 2

`-80`

#### Explanation For Sample 2

The game proceeds, for example, as follows when the two players play optimally:

- Taro: (
**10**, 100, 10) → (100, 10) - Jiro: (
**100**, 10) → (10) - Taro: (
**10**) → ()

Here, and .

#### Sample Input 3

```
1
10
```

#### Sample Output 3

`10`

#### Sample Input 4

```
10
1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1
```

#### Sample Output 4

`4999999995`

#### Explanation For Sample 4

The answer may not fit into a 32-bit integer type.

#### Sample Input 5

```
6
4 2 9 7 1 5
```

#### Sample Output 5

`2`

#### Explanation For Sample 5

The game proceeds, for example, as follows when the two players play optimally:

- Taro: (4, 2, 9, 7, 1,
**5**) → (4, 2, 9, 7, 1) - Jiro: (
**4**, 2, 9, 7, 1) → (2, 9, 7, 1) - Taro: (2, 9, 7,
**1**) → (2, 9, 7) - Jiro: (2, 9,
**7**) → (2, 9) - Taro: (2,
**9**) → (2) - Jiro: (
**2**) → ()

Here, , and .

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