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.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;


public class Main{
	public static class FastReader {
		BufferedReader br;
		StringTokenizer root;
		
 
		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
 
		String next() {
			while (root == null || !root.hasMoreTokens()) {
				try {
					root = new StringTokenizer(br.readLine());
				} catch (Exception addd) {
					addd.printStackTrace();
				}
			}
			return root.nextToken();
		}
 
		int nextInt() {
			return Integer.parseInt(next());
		}
 
		double nextDouble() {
			return Double.parseDouble(next());
		}
 
		long nextLong() {
			return Long.parseLong(next());
		}
 
		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception addd) {
				addd.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	
	public static FastReader sc = new FastReader();
 
	static int mod = (int) (1e9+7);
	static List<Integer>[] edges ;
	static long[][] dp ;
	static int[] a;
	public static void main(String[] args) {

		int n = sc.nextInt();
	    a = new int[n+1];
	    long total = 0;
	    for(int i=1;i<=n;++i) {
	    	a[i] = sc.nextInt();
	    	total+=a[i];
	    }
	    
	    dp = new long[n+1][n+1];
	    for(int i=0;i<dp.length;++i) Arrays.fill(dp[i], -1);
	  
	   // out.println(f(1,n));
	    long x = f(1,n);
	    long y = total - x;
	    long ans = x - y;
	    out.println(ans);
	    

		
	out.close();
}
	private static long f(int i, int j) {
		if(i+1 == j) return Math.max(a[i], a[j]);
		if(i > j) return 0;
		if(dp[i][j] != -1) return dp[i][j];
		/*
		 * case 
		 * 1,2
		 * 1,n
		 * n,1
		 * n-1,n
		 * 
		 */
		long o1 = a[i] + f(i+2,j);
		long o2 = a[i] + f(i+1,j-1);
		long o3 = a[j] + f(i+1,j-1);
		long o4 = a[j] + f(i,j-2);
		return dp[i][j] = Math.max(Math.min(o1, o2),Math.min(o3, o4));
	}
	
	
}

