Score : $300$ points

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.

Constraints

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

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 $i < j$).

5
7.5
2.4
17.000000001
17
16.000000000

3

There are 3 pairs with integer product:

• $7.5 \cdot 2.4 = 18$
• $7.5 \cdot 16 = 120$
• $17 \cdot 16 = 272$

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

8