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.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) throws Exception {
		int n = sc.nextInt();

		int[] arr = input(n);
		long[][][] dp = new long[n][n][2];

		for(int slide = 0 ; slide< n ;slide++ ) {
			for(int row = 0 ; row < n - slide ; row++) {
				int col = row + slide ;
				if(row==col) {
					dp[row][col][0]=arr[row];
					dp[row][col][1]=0;
					continue;
				}
				
				if(dp[row+1][col][1]+arr[row] > dp[row][col-1][1]+arr[col]) {
					dp[row][col][0]=dp[row+1][col][1]+arr[row] ;
					dp[row][col][1]=dp[row+1][col][0] ;	
				}else {
					dp[row][col][0]=dp[row][col-1][1]+arr[col] ;
					dp[row][col][1]=dp[row][col-1][0] ;					
				}
			}
		}
		long ans  = dp[0][n-1][0]-dp[0][n-1][1];
		System.out.println(ans);
	}

	public static int[] input(int n) throws Exception {

		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		return arr;
	}

	public static int[][] input(int n, int m) throws Exception {

		int[][] arr = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {

				arr[i][j] = sc.nextInt();
			}
		}
		return arr;
	}

}
