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.*;
public class Main {
	static long dp[][][]=new long[3002][3002][2];
	public static void main(String args[]){
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		long arr[]=new long[n];
		long sum=0;
		for(int i=0;i<n;i++){
			arr[i]=sc.nextLong();
			sum+=arr[i];
		}
		long ans=helper(0,n-1,0,arr);
		System.out.println(2*ans-sum);
	}
	public static long helper(int i,int j,int turn,long[] arr){
		if(i>j){
			return 0;
		}
		if(dp[i][j][turn]!=0){
			return dp[i][j][turn];
		}
		if(turn==0){
			return dp[i][j][turn]=Math.max(arr[i]+helper(i+1,j,1,arr),arr[j]+helper(i,j-1,1,arr));
		}
		else{
			return dp[i][j][turn]=Math.min(helper(i+1,j,0,arr),helper(i,j-1,0,arr));
		}
	}
}
