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.*;
import java.util.*;





public class Main {

    static MyScanner in = new MyScanner();
    static   PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
    int N;
    static int max = 200001;
    static int [] dr = {1,-1,0,0};
    static int [] dc={0,0,-1,1};
    static class Edge{
        int u,w;
        Edge(int u, int w){
            this.u =u;this.w = w;
        }
    }
    public static void main(String args[]) throws IOException {
        int N = in.nextInt();
        long [] arr = new long[N+1];
        for(int i=1;i<=N;i++){
            arr[i] = in.nextInt();
        }
        long [][] dp = new long[N+1][N+1];
        for(int L=N;L>0;L--){
            for(int R = L;R<=N;R++){
                if(L==R){
                    dp[L][R] = arr[L];
                }else{
                    long leftChoice = arr[L]-dp[L+1][R];
                    long rightChoice = arr[R]-dp[L][R-1];
                    dp[L][R] = Math.max(leftChoice,rightChoice);
                }
            }
        }
        out.println(dp[1][N]);
        out.flush();
        }
       static boolean isEven(long a){
            return (a&1)==0;
        }
       static  void swap (int a, int b){

        int temmp = b;
        b=a;
        a = temmp;
        }
        static boolean same(int [] arr,int [] temp){
            Arrays.sort(arr);
           Arrays.sort(temp);
            for(int i=0;i<arr.length;i++){
                if(temp[i]!=arr[i])
                return false;
            }
            return true;
        }

 
  


    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;
        }
  
     }
    }