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.Scanner;

public class Main {
    static long[][] aa;
    static long maxx(int ind1,int ind2,int[] arr,int flag){
        if(ind1>=arr.length || ind2<0 || ind1>ind2){
            return 0;
        }
        if(ind1==ind2){
            return arr[ind1];
        }
        if(aa[ind1][ind2]!=-1){
            return aa[ind1][ind2];
        }
        //if(flag==0){
            return aa[ind1][ind2]=Math.max( -maxx(ind1+1,ind2,arr,1)+(long)arr[ind1],-maxx(ind1,ind2-1,arr,1)+(long)arr[ind2]  );
      //  }
//        else{
//            return aa[ind1][ind2][flag]=Math.min(maxx(ind1+1,ind2,arr,0),maxx(ind1,ind2-1,arr,0));
//        }


    }

    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        int n= scanner.nextInt();
        int[] a=new int[n];
        long sum=0;
        for(int j=0;j<n;j++){
            a[j]= scanner.nextInt();
            sum=(long)((long)sum+(long)a[j]);
        }
        aa=new long[n][n];
        for(int j=0;j<n;j++){
            for(int i=0;i<n;i++){
               // for(int k=0;k<2;k++){
                    aa[j][i]=-1;
                //}
            }
        }
        //System.out.println(-(long)sum+(long)2*(long)maxx(0,n-1,a,0));
       System.out.println(maxx(0,n-1,a,0));
    }

}
