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 f(a,i,j,dp):
    if dp[i][j]==-1:
        if i>j:
            return 0

        dp[i][j]=max(a[i]+min(f(a,i+2,j,dp),f(a,i+1,j-1,dp)),
                                a[j]+min(f(a,i+1,j-1,dp),f(a,i,j-2,dp)))
    return dp[i][j]
        
n=int(input())
dp=[[-1 for i in range(n)] for j in range(n)]
a=list(map(int,input().split()))
for i in range(n):
    dp[i][i]=a[i]

for i in range(n-1):
    dp[i][i+1]=max(a[i],a[i+1])

s1=f(a,0,n-1,dp)

print(s1-sum(a)+s1)
