题目描述
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
输入格式
见题面
输出格式
见题面