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: Accepted)

import sys;input=sys.stdin.readline


N, = map(int, input().split())
M = 51
C2 = [0]*M
C5 = [0]*M
C = [[0]*(M+1) for _ in range(M+1)]
CC = []
for _ in range(N):
    c2, c5 = 9, 9
    s = input().strip()
    if "." in s:
        a, b = s.split(".")
        b.rstrip("0")
        if len(b) != 0:
            c2 -= len(b)
            c5 -= len(b)
        x = int(a + b)
    else:
        x = int(s)
#    print(x, c2, c5)
    while x % 2 == 0:
        x//=2
        c2 += 1
    while x % 5 == 0:
        x//=5
        c5 += 1
    C[c2][c5] += 1
    CC.append((c2, c5))
R = [[0]*(M+1) for _ in range(M+1)]
for i in range(1, M+1):
    for j in range(1, M+1):
        R[i][j] = R[i-1][j] + R[i][j-1] - R[i-1][j-1] + C[i-1][j-1]
r = 0
for a, b in CC:
    if a >= 9 and b >= 9:
        r -= 1
    a, b = max(18-a, 0), max(18-b, 0)
    r += R[M][M] - R[a][M] - R[M][b] + R[a][b]
print(r//2)