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)

import copy
import math
import time
import statistics
import math
from decimal import Decimal
from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_DOWN

# a = get_int()
def get_int():
    return int(input())
# a = get_string()
def get_string():
    return input()
# a_list = get_int_list()
def get_int_list():
    return [int(x) for x in input().split()]
# a_list = get_string_list():
def get_string_list():
    return input().split()
# a, b = get_int_multi()
def get_int_multi():
    return map(int, input().split())
# a_list = get_string_char_list()
def get_string_char_list():
    return list(str(input()))
# print("{} {}".format(a, b))
# for num in range(0, a):
# a_list[idx]
# a_list = [0] * a
'''
while (idx < n) and ():

    idx += 1
'''



def main():
    start = time.time()

    n = get_int()
    #youso2 = []
    #youso5 = []
    youso = []

    ans = 0
    for i in range(0,n):
        s = input()
        wk = Decimal(s)
        wk = wk - wk.quantize(Decimal('0'), rounding=ROUND_DOWN)
        seisu = Decimal.is_zero(wk)

        if seisu:
            if '.' in s:
                s_i, s_d = s.split('.')
                s = s_i

            count2 = 0
            wk = int(s)
            for ii in range(0, 15):
                if wk % 2 == 0:
                    count2 += 1
                    wk = wk // 2
                else:
                    break

            count5 = 0
            wk = int(s)
            for ii in range(0, 6):
                if wk % 5 == 0:
                    count5 += 1
                    wk = wk // 5
                else:
                    break

            youso.append([count2, count5])
            #youso2.append(count2)
            #youso5.append(count5)

        else:
            s_i, s_d = s.split('.')

            count2 = 0
            wk = int(s_i + s_d)
            for ii in range(0, 35):
                if (wk * 2) % 10 == 0:
                    wk = wk * 2 / 10
                    count2 += 1
                else:
                    break

            #youso2.append(-len(s_d) + count2)

            count5 = 0
            wk = int(s_d)
            for ii in range(0,20):
                if (wk * 5) % 10 == 0:
                    wk = wk * 5 / 10
                    count5 += 1
                else:
                    break

            #youso5.append(-len(s_d) + count5)
            youso.append([-len(s_d) + count5, -len(s_d) + count2])

    #print(time.time() - start)
    #print(youso)

    youso.sort()
    #print(youso)

    ans = 0
    for i in range(0,n):
        y1 = youso[i]
        for ii in range(n-1, i, -1):
            y2 = youso[ii]
            if (y1[0] + y2[0] < 0):
                break

            if (y1[0] + y2[0] >= 0) and (y1[1] + y2[1] >= 0):
                ans += 1


    print(ans)
    #print(time.time() - start)

if __name__ == '__main__':
    main()