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
def coun(a,i,j):
    if dp[i][j]!=-1:
        return dp[i][j]

    if i==j:
        return a[i]
    elif abs(i-j)==1:

        return max(a[i],a[j])
    dp[i][j]= max(min(coun(a,i+2,j),coun(a,i+1,j-1))+a[i],min(coun(a,i+1,j-1),coun(a,i,j-2))+a[j])

    return dp[i][j]

n= int(input())
a =[int(X ) for  X in input().split()]
dp = [[-1 for i in range(n)]for j in range(n)]
print(2*coun(a,0,n-1)-sum(a))