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.LinkedList;
import java.util.StringTokenizer;

public class Main {

	
	public static void main(String[] args) {
		FastScanner scanner=new FastScanner();
		int n=scanner.nextInt();
		int a[]=scanner.readArray(n);
		
		long dp[][]=new long[n][n];
		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]);

	}
	static class FastScanner{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		long nextLong() {
			return Long.parseLong(next());
		}
		int [] readArray(int n) {
			int a[]=new int[n];
			for(int i=0;i<n;i++) a[i]=nextInt();
			return a;
		}
		
		
	}

}
