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)

import sys

import numpy as np
from numba import njit, i8


def input():
    return sys.stdin.readline().strip()


def convert(S):
    i, *d = S.split(".")
    i = int(i) * 1_000_000_000
    if d:
        return i + int(d[0].ljust(9, "0"))
    else:
        return i


def div_cnt(n, d):
    res = 0
    while n % d == 0:
        res += 1
        n //= d
    return res


@njit(i8(i8[:, :]), cache=True)
def solve(table):
    ans = 0
    for i in range(19):
        for j in range(19):
            cur = table[i][j]
            if cur == 0:
                continue
            for k in range(18 - i, 19):
                for l in range(18 - j, 19):
                    if k == i and j == l:
                        ans += cur * (cur - 1)
                    else:
                        ans += cur * table[k][l]
    return ans


N = int(input())
A = list(convert(input()) for _ in range(N))
divs = [(div_cnt(a, 2), div_cnt(a, 5)) for a in A]

table = np.zeros((19, 19), np.int64)
for t, f in divs:
    table[min(t, 18)][min(f, 18)] += 1
print(solve(table) // 2)