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
#L

N=int(input())
a=list(map(int,input().split()))

S=[0]*(N+1)
for i in range(N):
    S[i+1]=S[i]+a[i]

dp=[[0]*(N+1) for _ in range(N+1)]#[l,r)の範囲が残っているときに取れる最大値

for i in range(1,N+1):#r-lの値
    for j in range(N):#lの値
        r=j+i
        if r>N:
            break
        l=j
        x=a[l]+(S[r]-S[l+1]) - dp[l+1][r]
        y=a[r-1]+(S[r-1]-S[l]) - dp[l][r-1]
        dp[l][r]=max(x,y)

print(2*dp[0][N] - S[-1] )