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())
*A, = map(int, input().split())
dp = [[-1]*(N+1-i) for i in range(N+1)]
for i in range(N+1):
    dp[0][i] = 0
t = (N & 1)
for l in range(1, N+1):
    S = dp[l-1]; T = dp[l]
    t ^= 1
    if t:
        T[:] = (min(S[i+1] - A[i], S[i] - A[i+l-1]) for i in range(N-l+1))
    else:
        T[:] = (max(S[i+1] + A[i], S[i] + A[i+l-1]) for i in range(N-l+1))
print(dp[N][0])