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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedList;
import java.util.StringTokenizer;

public class Main{
	
	public static void main(String[] args) throws IOException {
		
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st;
		
		int N = Integer.parseInt(br.readLine());
		
		int[] a = new int[N];
		st = new StringTokenizer(br.readLine());
		for(int i=0; i<N; i++) {
			a[i] = Integer.parseInt(st.nextToken());
		}
		
		long[][] dp = new long[N+1][N+1];
		
		for(int i=N-1; i>=0; i--) {
			for(int j=i; j<N; j++) {
				if(i==j) {
					dp[i][j] = a[i];
				}else {
					dp[i][j] = Math.max(a[i] - dp[i+1][j], a[j] - dp[i][j-1]);
				}
			}
		}
		System.out.println(dp[0][N-1]);
		
	}
}
