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 
{   
	
	static long MOD=(long) (1e9+7);
	public static void main(String[] args) throws IOException 
	{ 
	
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		StringTokenizer s=new StringTokenizer(br.readLine());
		
		int n=Integer.parseInt(s.nextToken());
		 s=new StringTokenizer(br.readLine());
		int arr[]=new int[n];
		
		for(int i=0;i<n;i++) {
			arr[i]=Integer.parseInt(s.nextToken());
		}
		long[][] dp = new long[n][n];
       

		for(int L = n-1; L >= 0; --L) {
			for(int R = L; R < n; ++R) {
				if(R==L) dp[L][R] = arr[L];
				else dp[L][R] = Math.max(arr[L] - dp[L+1][R], arr[R] - dp[L][R-1]);
			}
		}
		
		

        pw.println(dp[0][n-1]);
		
		pw.close();
		
	}
	
	
	
	
	
}