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.Arrays;
import java.util.Scanner;

public class Main {
    static final Scanner sc  = new Scanner(System.in);
    static final int     MOD = (int) 1E9 + 7;
    
    public static void main(String[] args) {
        int N = nint();
        int[] a = nints(N, 1, 0);
        long[][] dp = new long[N+1][N+1];
        
        
        for (int l = 1; l <= N; l++) {
            // l == r
            dp[l][l] = isFirst(N, l, l) ? a[l] : -a[l];
        }
        
        for (int i = 1; i < N; i++) {
            for (int j = 1; j + i <= N; j++) {
                int l = j;
                int r = j + i;
                
                if (isFirst(N, l, r)) {
                    dp[l][r] = max(
                            dp[l][r-1] + a[r],
                            dp[l+1][r] + a[l]);
                    
                } else {
                    dp[l][r] = min(
                            dp[l][r-1] - a[r],
                            dp[l+1][r] - a[l]);
                }
            }
        }

        System.out.println(dp[1][N]);
    }
    
    private static boolean isFirst(int N, int l, int r) {
        if (r < l) throw new RuntimeException();
        int d = r - l + 1;
        
        return (N - d) % 2 == 0;
    }
    
    private static int nint() {
        return sc.nextInt();
    }

    private static int[] nints(int n) {
        return nints(n, 0, 0);
    }

    private static int[] nints(int n, int padL, int padR) {
        int[] a = new int[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nint();
        return a;
    }

    private static long nlong() {
        return sc.nextLong();
    }

    private static long[] nlongs(int n) {
        return nlongs(n, 0, 0);
    }

    private static long[] nlongs(int n, int padL, int padR) {
        long[] a = new long[padL + n + padR];
        for (int i = 0; i < n; i++)
            a[padL + i] = nlong();
        return a;
    }

    private static double ndouble() {
        return sc.nextDouble();
    }

    private static double[] ndoubles(int n) {
        return ndoubles(n, 0, 0);
    }

    private static double[] ndoubles(int n, int padL, int padR) {
        double[] d = new double[n + padL + padR];
        for (int i = 0; i < n; i++) {
            d[padL + i] = ndouble();
        }
        return d;
    }

    private static String nstr() {
        return sc.next();
    }

    private static char[] nchars() {
        return sc.next().toCharArray();
    }

    private static char[] nchars(int padL, int padR) {
        char[] temp = sc.next().toCharArray();
        char[] ret = new char[temp.length + padL + padR];
        System.arraycopy(temp, 0, ret, padL, temp.length);
        return ret;
    }

    private static char[][] nchars2(int h, int w) {
        return nchars2(h, w, 0, 0);
    }

    private static char[][] nchars2(int h, int w, int padLU, int padRD) {
        char[][] a2 = new char[h + padLU + padRD][w + padLU + padRD];
        for (int i = 0; i < h; i++)
            System.arraycopy(nchars(), 0, a2[padLU + i], padLU, w);
        return a2;
    }

    private static long min(long... ls) {
        return Arrays.stream(ls).min().getAsLong();
    }

    private static int min(int... is) {
        return Arrays.stream(is).min().getAsInt();
    }

    private static long max(long... ls) {
        return Arrays.stream(ls).max().getAsLong();
    }

    private static int max(int... is) {
        return Arrays.stream(is).max().getAsInt();
    }

    private static long abs(long a, long b) {
        return Math.abs(a - b);
    }
}
