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.*;
import java.io.*;

public class Main {

	public static void main(String[] args) {
		Main ans = new Main();
		System.out.println(ans.solve());
	}

	private long solve() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		long [] array = new long[N+1];
		long sum=0;
		for(int i=1;i<=N;i++){
			array[i] = sc.nextLong();
			sum += array[i];
		}

		long [][]dp = new long[3002][3002];

		long X = solve(array, 1, N, 1, dp);
		long Y = sum-X;
		return X-Y;
	}


	private long solve(long[]array, int left, int right, int turn, long[][] dp) {

		if(left>right) return 0;
		if (dp[left][right] != 0) return dp[left][right];

		long answer =0;
		if (turn==1) {
			long leftVal = array[left] + solve(array, left+1, right, 0, dp);
			long rightVal = array[right] + solve(array, left, right-1, 0, dp);
			answer = Math.max(leftVal, rightVal);
		} else {
			long leftVal = solve(array, left+1, right, 1, dp);
			long rightVal = solve(array, left, right-1, 1, dp);
			answer = Math.min(leftVal, rightVal);
		}

		dp[left][right] = answer;

		return answer;
	}

}