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 $i < j$).