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
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	static int count;
	static long[][] dp;
	static long[] numberArray;

	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);

		count = scan.nextInt();
		scan.nextLine();

		numberArray = Arrays.stream(scan.nextLine().split(" "))
				.mapToLong(Long::parseLong)
				.toArray();

		dp = new long[count + 1][count + 1];

		long result = dpMethod(new int[] { 0, 0 });

		println(result);
	}

	public static long dpMethod(int[] situation) {

		if (dp[situation[0]][situation[1]] != 0) {
			return dp[situation[0]][situation[1]];
		}

		if (situation[0] + situation[1] == count) {
			return 0;
		}

		long value = Math.max(
				numberArray[situation[0]] - dpMethod(
						new int[] { situation[0] + 1, situation[1] }),
				numberArray[count - 1 - situation[1]] - dpMethod(
						new int[] { situation[0], situation[1] + 1 }));

		dp[situation[0]][situation[1]] = value;

		return value;
	}

	public static void println(Object target) {
		System.out.println(target);
	}
}
