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.util.*;


public class Main{
    static HashSet<Integer> set;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        // Start writing your solution here. -------------------------------------
        long MOD = 1000000007;
        //int t = sc.nextInt();
        int t = 1;

        while(t -- > 0)
        {
            int n = sc.nextInt();
            long [] a = new long[n + 1];
            long [] presum = new long[n + 1];
            long [][]dp = new long[n + 1][n + 1];
            for(int i = 1; i <= n; i++) {
                a[i] = sc.nextInt();
                presum[i] = presum[i - 1] + a[i];
            }
            for(int i = 1; i <= n; i++) dp[i][i] = a[i];
            for(int k = 1; k <= n; k ++){
                for(int i = 1; i + k <= n; i++) {
                    dp[i][i + k] = Math.max(a[i] + presum[i + k] - presum[i] - dp[i + 1][i + k],
                            a[i + k] + presum[i + k - 1] - presum[i - 1] - dp[i][i + k - 1]);
                }
            }
            out.println(2 * dp[1][n] - presum[n]);
            //for(int ii = 0; ii <= n; ii++) System.out.println(Arrays.toString(dp[ii]));
        }
        out.close();

        /*
        int n      = sc.nextInt();        // read input as integer
        long k     = sc.nextLong();       // read input as long
        double d   = sc.nextDouble();     // read input as double
        String str = sc.next();           // read input as String
        String s   = sc.nextLine();       // read whole line as String

        int result = 3*n;
        out.println(result);                    // print via PrintWriter
        */
        // Stop writing your solution here. -------------------------------------
        out.close();
    }
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                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());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}