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 deque(a):
    n = len(a)
    cur = [(x, 0) for x in a]
    nxt = [(0, 0)] * n
    for l in range(2, n + 1):
        for i in range(n - l + 1):
            j = i + l - 1
            x, y = cur[i]
            z, t = cur[i + 1]
            if a[i] + t - z > a[j] + y - x:
                nxt[i] = (a[i] + t, z)
            else:
                nxt[i] = (a[j] + y, x)
        cur, nxt = nxt, cur
    return cur[0][0] - cur[0][1]


def main():
    input()  # n
    a = [int(x) for x in input().split()]
    return deque(a)


print(main())
