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
# n=int(input())
n=int(input())
a=list(map(int,input().split(" ")))
mat=[[(0,0) for i in range(n)] for j in range(n)]
for l in range(1,n+1):
	for i in range(n-l+1):
		j=i+l-1
		# print(i,j)
		# if(i<=j):
		if(i==j):
			x=a[i]
			y=-a[i]
			mat[i][j]=(x,y)
		else:
			# print(i+1)
			x=max(a[i]+mat[i+1][j][1],a[j]+mat[i][j-1][1])
			y=min(-a[i]+mat[i+1][j][0],-a[j]+mat[i][j-1][0])
			mat[i][j]=(x,y)
print(mat[0][n-1][0])
# print(mat)