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.*;
import java.io.*;
import java.lang.*;
public class Main{
public static long help(int[] arr,long[][] dp,int i, int j){
	if(i>j||j<=0||i>arr.length-1){return 0;}
	if(dp[i][j]!=0){return dp[i][j];}
	long x=arr[i]+Math.min(help(arr,dp,i+2,j),help(arr,dp,i+1,j-1));
	long y=arr[j]+Math.min(help(arr,dp,i+1,j-1),help(arr,dp,i,j-2));
	return dp[i][j]=Math.max(x,y);
}
public static void main(String[] args) throws FileNotFoundException, IOException{
       Scanner s=new Scanner(System.in);
       BufferedWriter out=new BufferedWriter(new OutputStreamWriter(System.out));
       int n=s.nextInt();
       long[][] dp=new long[n+1][n+1];
       int[] arr=new int[n+1];
       long sum=0;
       for(int i=1;i<=n;i++){arr[i]=s.nextInt();sum+=arr[i];}       
         out.write((2*help(arr,dp,1,n)-sum)+"\n");       
        out.flush();
  }
}
