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.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";
    static int lenbuf = 0, ptrbuf = 0;
    private static byte[] inbuf = new byte[1024];

    static void solve() {
        int n = ni();
        int[] a = na(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]);
                }
            }
        }
        out.print(dp[0][n-1]);
    }

    public static void main(String[] args) throws Exception {
        long S = System.currentTimeMillis();
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);

        solve();
        out.flush();
        long G = System.currentTimeMillis();
        tr(G - S + "ms");
    }

    private static boolean eof() {
        if (lenbuf == -1) {
            return true;
        }
        int lptr = ptrbuf;
        while (lptr < lenbuf) {
            if (!isSpaceChar(inbuf[lptr++])) {
                return false;
            }
        }

        try {
            is.mark(1000);
            while (true) {
                int b = is.read();
                if (b == -1) {
                    is.reset();
                    return true;
                } else if (!isSpaceChar(b)) {
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    //	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
    private static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) {
            ;
        }
        return b;
    }

    private static double nd() {
        return Double.parseDouble(ns());
    }

    private static char nc() {
        return (char) skip();
    }

    private static String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }

    private static int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
            ;
        }
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) {
            ;
        }
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static void tr(Object... o) {
        if (INPUT.length() != 0) {
            System.out.println(Arrays.deepToString(o));
        }
    }
}
