Square Subsets

题意翻译

Petya又迟到了...老师给了他额外的任务。对于一些数组a，Petya需要找到从中间选择非空子集，使它们的乘积等于某个整数的平方的方法的数量。 如果这些方法所选择的元素的索引不同，则认为这两种是不同的方法。 因为结果可能很大，结果需要$mod \; 10^9+7$ 感谢@KriaeTh 提供的翻译

题目描述

Petya was late for the lesson too. The teacher gave him an additional task. For some array $ a $ Petya should find the number of different ways to select non-empty subset of elements from it in such a way that their product is equal to a square of some integer. Two ways are considered different if sets of indexes of elements chosen by these ways are different. Since the answer can be very large, you should find the answer modulo $ 10^{9}+7 $ .

输入输出格式

输入格式

First line contains one integer $ n $ ( $ 1<=n<=10^{5} $ ) — the number of elements in the array. Second line contains $ n $ integers $ a_{i} $ ( $ 1<=a_{i}<=70 $ ) — the elements of the array.

输出格式

Print one integer — the number of different ways to choose some elements so that their product is a square of a certain integer modulo $ 10^{9}+7 $ .

输入输出样例

输入样例 #1

4
1 1 1 1

输出样例 #1

15

输入样例 #2

4
2 2 2 2

输出样例 #2

7

输入样例 #3

5
1 2 4 5 8

输出样例 #3

7

说明

In first sample product of elements chosen by any way is $ 1 $ and $ 1=1^{2} $ . So the answer is $ 2^{4}-1=15 $ . In second sample there are six different ways to choose elements so that their product is $ 4 $ , and only one way so that their product is $ 16 $ . So the answer is $ 6+1=7 $ .

题意翻译

Petya又迟到了...老师给了他额外的任务。对于一些数组a，Petya需要找到从中间选择非空子集，使它们的乘积等于某个整数的平方的方法的数量。 如果这些方法所选择的元素的索引不同，则认为这两种是不同的方法。 因为结果可能很大，结果需要$mod \; 10^9+7$ 感谢@KriaeTh 提供的翻译