[USACO 2012 Ope G]Balanced Cow Subsets
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 32 M，其他语言64 M
64bit IO Format: %lld

题目描述

Farmer John's owns N cows (2 <= N <= 20), where cow i produces M(i) units of milk each day (1 <= M(i) <= 100,000,000). FJ wants to streamline the process of milking his cows every day, so he installs a brand new milking machine in his barn. Unfortunately, the machine turns out to be far too sensitive: it only works properly if the cows on the left side of the barn have the exact same total milk output as the cows on the right side of the barn! 
 Let us call a subset of cows "balanced" if it can be partitioned into two groups having equal milk output. Since only a balanced subset of cows can make the milking machine work, FJ wonders how many subsets of his N cows are balanced. Please help him compute this quantity.

输入描述:

* Line 1: The integer N.

* Lines 2..1+N: Line i+1 contains M(i).

输出描述:

* Line 1: The number of balanced subsets of cows.
示例1

输入

复制 
4
1
2
3
4

输出

复制 
3

说明

INPUT DETAILS:
There are 4 cows, with milk outputs 1, 2, 3, and 4.

OUTPUT DETAILS:
There are three balanced subsets: the subset {1,2,3}, which can be
partitioned into {1,2} and {3}, the subset {1,3,4}, which can be
partitioned into {1,3} and {4}, and the subset {1,2,3,4} which can be
partitioned into {1,4} and {2,3}.