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 collections

N=int(input())
A=[]
PRECISION_DIGITS=9
cnt={} #collections.defaultdict(int)


for n in range(N):
	tmpA = float(input())
	tmpA = round(tmpA*10**PRECISION_DIGITS)
	#print(tmpA)

	five = 0
	two = 0
	while (tmpA % 2) == 0:
		two += 1
		tmpA //= 2
	while (tmpA % 5) == 0:
		five += 1
		tmpA //= 5

	# (10**9) -> (two,five)=(9,9)
	two -= PRECISION_DIGITS
	five -= PRECISION_DIGITS

	cnt.setdefault((two,five),0)
	cnt[(two,five)]+=1

# print(cnt)
ans = 0
for t1, cnt1 in cnt.items():
	for t2, cnt2 in cnt.items():
		# 2**a(a>=0) and 5**b(b>=0) => integer
		if 0 <= t1[0]+t2[0] and 0 <= t1[1]+t2[1]:
			if t1 < t2:
				ans += int(cnt1*cnt2)
			elif t1 == t2:
				# same entry
				# Total number of combinations choose 2 items
				# nC2 = n*(n-1)/2
				ans += int((cnt1*(cnt2-1))/2)


print(ans)