Is It Perfect
Bob has an initial array D of length n . Alice is a good friend of Bob. So Bob challenges Alice to finish the following task with this array D.
A Sequence G is called PERFECT if elements of G are distinct and one of the two following properties hold :
1. If product of elements of G is a perfect-square then number of elements of G should be even .
2. If product of elements of is not a perfect-square then number of elements of G should be odd .
Alice’s task is to find out the number of different ways to construct non-empty PERFECT sub-sequences of D. Alice is not an expert programmer. So now he wants your help. Can you find it?
A sub-sequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
Two ways are considered different if sets of indexes of elements chosen by these ways are different. You have to find the answer modulo 993344777.
First line contains one integer n (1 ≤ n ≤ 10^6) — the number of elements in the array.
Second line contains n integers - the elements of the array D where 1≤ D[i] ≤ 60 for 1 ≤ i ≤ n .
Print one integer — the number of different ways modulo 993344777.
2 2 8
3 3 2 7
For the first test case, you can make three sub-sequences :
1. you can choose only 2
2. you can choose only 8
3. you can choose both 2 and 8 because 2 * 8 = 16 is a perfect-square