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

Initially, they are given a sequence $a=(a_1,a_2,\dots ,a_N)$. Until $a$ becomes empty, the two players perform the following operation alternately, starting from Taro:

• Remove the element at the beginning or the end of $a$. The player earns $x$ points, where $x$ is the removed element.

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

Assuming that the two players play optimally, find the resulting value of $X-Y$.

Constraints

• All values in input are integers.
• $1\le N\le 3000$
• $1\le a_i\le {10}^9$

Input Specification

The first line will contain the integer $N$.

The next line will contain $N$ integers, $a_1,a_2,\dots ,a_N$.

Output Specification

Print the resulting value of $X-Y$, 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, $X=30+80=110$ and $Y=90+10=100$.

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, $X=10+10=20$ and $Y=100$.

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, $X=5+1+9=15$, and $Y=4+7+2=13$.