## Educational DP Contest AtCoder L - Deque

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Points: 10
Time limit: 1.0s
Memory limit: 1G

Problem types

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 .