Problem:
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).

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

Solution in PyPy3 (7.3.0) (judge verdict: Wrong Answer)

n = int(input())
a = [round(float(input()) * 10**9) for _ in range(n)]
cs = [[0] * 20 for _ in range(20)]

dc = []
for i in a:
    x = 0
    for _ in range(19):
        if i % 2 == 0:
            i //= 2
            x += 1
    y = 0
    for _ in range(19):
        if i % 5 == 0:
            i //= 5
            y += 1

    cs[18-x][18-y] += 1
    dc.append((x, y))
for i in range(20):
    for j in range(19):
        cs[i][j+1] += cs[i][j]
for i in range(20):
    for j in range(19):
        cs[j+1][i] += cs[j][i]


ans = 0
for x, y in dc:
    ans += cs[x][y]
for i in a:
    if i % 10**9 == 0:
        ans -= 1
ans //= 2

print(ans)