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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int N = Integer.parseInt(br.readLine());
		int[] A = new int[N];
		
		String[] S = br.readLine().split(" ");
		for(int i = 0; i < N ; i++) {
			A[i] = Integer.parseInt(S[i]);
		}
		
		long[][] taro = new long[N][N];
		long[][] jiro = new long[N][N];
		
		for(int i = 0; i < N; i++) {
			taro[i][i] = A[i];
			jiro[i][i] = -A[i];
		}
		
		
		for(int i = 0; i < N; i++) {
			int diagnol = i+1;
			int start = 0;
			int end = start + diagnol;
			while(end < N) {
				
				taro[start][end] = Math.max(A[start] + jiro[start+1][end],
										   A[end] + jiro[start][end-1]);
				
				jiro[start][end] = Math.min(-A[start] + taro[start+1][end],
						   -A[end] + taro[start][end-1]);
				start++;
				end = start + diagnol;
			}
		}
		
		System.out.println(taro[0][N-1]);
	}
}
