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: Wrong Answer)

n = int(input())

int_cnt = 0
int_25 = [[0 for _ in range(10)] for _ in range(10)]
float_25 = [[0 for _ in range(10)] for _ in range(10)]
float_2 = [[0 for _ in range(10)] for _ in range(10)]
float_5 = [[0 for _ in range(10)] for _ in range(10)]

for _ in range(n):
    a = float(input())
    if a % 1 == 0:
        int_cnt += 1
        t = 0
        while a % 2 == 0:
            a //= 2
            t += 1
        t = min(t, 9)
        f = 0
        while a % 5 == 0:
            a //= 5
            f += 1
        f = min(f, 9)
        int_25[t][f] += 1
    else:
        a *= 10 ** 9
        a = int(a)
        cnt = 9
        while a % 10 == 0:
            a //= 10
            cnt -= 1
        t = 0
        while a % 2 == 0:
            a //= 2
            t += 1
        f = 0
        while a % 5 == 0:
            a //= 5
            f += 1
        tt = min(t - cnt, 9)
        ff = min(f - cnt, 9)
        tt = max(tt, 0)
        tf = max(ff, 0)
        float_25[max(0, cnt - t)][max(0, cnt - f)] += 1
        float_2[tt][max(0, cnt - f)] += 1
        float_5[max(0, cnt - t)][ff] += 1


ans = int_cnt * (int_cnt - 1) // 2
for i in range(10):
    for j in range(10):
        for k in range(i + 1):
            for l in range(j + 1):
                ans += int_25[i][j] * float_25[k][l]

for i in range(10):
    for j in range(10):
        for k in range(10):
            for l in range(10):
                if (i - j > 0) and (k - l > 0):
                    ans += float_2[i][l] * float_5[j][k]
    
print(ans)