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 solve(l, r, A, dp):
    if r - l < 2:
        return max(A[l:r + 1])

    x1 = dp[l + 2][r] if dp[l + 2][r] != -1 else solve(l + 2, r, A, dp)
    x2 = dp[l + 1][r - 1] if dp[l + 1][r - 1] != -1 else solve(l + 1, r - 1, A, dp)
    x3 = dp[l][r - 2] if dp[l][r - 2] != -1 else solve(l, r - 2, A, dp)

    dp[l][r] = max(min(x1, x2) + A[l], min(x2, x3) + A[r])

    return dp[l][r]


N = int(input())
A = [int(i) for i in input().split()]
dp = [[-1] * N for i in range(N)]
print(2*solve(0, N-1, A, dp)-sum(A))
