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
import sys
input=sys.stdin.readline
def chmax(a,b):
    if a>=b:
        return a
    return b
def chmin(a,b):
    if a<=b:
        return a
    return b
def main():
    N=int(input())
    a=list(map(int,input().split()))
    dp=[[0]*(N+2) for _ in range(N+2)]
    for len in range(1,N+1):
        for i in range(N+1-len):
            j=i+len
            if (N-len)%2==0:
                dp[i][j]=chmax(dp[i+1][j]+a[i],dp[i][j-1]+a[j-1])
            else:
                dp[i][j]=chmin(dp[i+1][j]-a[i],dp[i][j-1]-a[j-1])
    print(dp[0][N])
main()