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 Python (3.8.2) (judge verdict: Accepted)

n = int(input())
As = [int(round(float(input())*10**9)) for _ in  range(n)]

fives = [0] * n
twos = [0] * n
cnts = [[0] * 20 for i in range(20)]
for i, a in enumerate(As):
    tmp = a
    five = 0
    two = 0
    while tmp % 5 == 0:
        five += 1
        tmp //= 5
    while tmp % 2 == 0:
        two += 1
        tmp //= 2
    cnts[min(two,18)][min(five,18)] += 1

# fiveの和とtwoの和が共に18以上ならOK
# 条件を満たすcnts        
ans = 0
for i1 in range(19):
    for j1 in range(19):
        for i2 in range(19):
            for j2 in range(19):
                if i1+i2 >= 18 and j1+j2>=18:
                    ans += cnts[i1][j1]*cnts[i2][j2]

# 自分自身を除外
for i in range(19):
    for j in range(19):
        if i*2 >= 18 and j*2 >= 18:
            ans -= cnts[i][j]

# ダブルカウント
ans //= 2
print(ans)