Deque

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

Initially, they are given a sequence a = (a_1, a_2, \ldots, 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 \leq N \leq 3000
• 1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_N

Output

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

Examples

Input

4 10 80 90 30

Output

10

Input

3 10 100 10

Output

-80

Input

1 10

Output

10

Input

10 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1

Output

4999999995

Input

6 4 2 9 7 1 5

Output

2

inputFormat

input are integers.

• 1 \leq N \leq 3000
• 1 \leq a_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_N

outputFormat

Output

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

Examples

Input

4 10 80 90 30

Output

10

Input

3 10 100 10

Output

-80

Input

1 10

Output

10

Input

10 1000000000 1 1000000000 1 1000000000 1 1000000000 1 1000000000 1

Output

4999999995

Input

6 4 2 9 7 1 5

Output

2

样例

4
10 80 90 30

10