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).

Examples

Input

5
7.5
2.4
17.000000001
17
16.000000000


Output

3


Input

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001


Output

8
#include<bits/stdc++.h>
using namespace std;
int cnt[65][65],cnt2,cnt5;
long long ans,tmp;
int main(){
	double x;int n;
	cin>>n;
	for(int i=1;i<=n;++i){
		cin>>x;
		tmp=llround(x*1e9);
		//cout<<tmp<<endl;
		cnt2=cnt5=0;
		while(tmp%2==0) ++cnt2,tmp/=2;
		while(tmp%5==0) ++cnt5,tmp/=5;
		for(int j=0;j<=64;++j)
			for(int k=0;k<=64;++k)
				if(cnt2+j>=18 && cnt5+k>=18)ans+=cnt[j][k];
		cnt[cnt2][cnt5]++;
	}
	cout<<ans;
	return 0;
} 