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 Ruby (2.7.1) (judge verdict: Accepted)

n = gets.chomp.to_i
a = Array.new(n,0)

a = a.map do
    s = gets.split(".")
    res = s[0].to_i*1000000000
    if s.size >1
        res += s[1].to_i*(10**(10-s[1].size))
    end
    res
end
cnt = Array.new(22).map{Array.new(22,0)}
dp = Array.new(22).map{Array.new(22,0)}
p = a.map do |e|
    c2 = c5 = 0
    while e%2==0
        e /= 2
        c2 += 1
    end
    
    while e%5==0
        e /= 5
        c5 += 1
    end
    cnt[[20,c2].min][[20,c5].min] += 1
    [c2,c5]
end

for i in 0..20
    for j in 0..20
        dp[i+1][j+1] = dp[i][j+1]+dp[i+1][j]-dp[i][j]+cnt[i][j];
    end
    # pp dp[i+1]
end
ans = 0
p.each do |e|
    c2,c5 = e
    t2 = [0,18-c2].max
    t5 = [0,18-c5].max
    ans += n-dp[t2][21]-dp[21][t5]+dp[t2][t5]
    ans -= 1 if c2 >= 9 && c5 >= 9
    # pp ans
end

puts ans/2