Problem Statement

You are given $N real values A_1, A_2, \ldots, A_N$.
Compute the number of pairs of indices (i, j)
such that i < j and the product $A_i \cdot A_j$ is integer.

Input

Input is given from Standard Input in the following format.
N
A_1
A_2
$\vdots$
A_N

Output

Print the number of pairs with integer product $A_i \cdot A_j ($and i < j).

Constraints

• $2 \leq N \leq 200$\,000
• 0 < A_i < 10^4
• A_i is given with at most 9 digits after the decimal.

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

• 7.$5 \cdot 2.4 = 18$
• 7.$5 \cdot 16 = 120$
• $17 \cdot 16 = 272$

Sample Input 2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Sample Output 2

8

见题面 Input 部分

见题面 Output 部分