#include<cstdio>
#define int long long
const int N=200005;
int n,v[20][20],a;
inline void rd()
{
	int x=9,r=0;char c;
	for(;(c=getchar())<'0'||c>'9';);
	for(r=c^48;(c=getchar())>='0'&&c<='9';r=r*10+(c^48));
	if(c=='.')for(;(c=getchar())>='0'&&c<='9';r=r*10+(c^48),--x);
	int y=x,z=x;for(;!(r&1)&&y<18;r>>=1,++y);for(;!(r%5)&&z<18;r/=5,++z);
	for(int i=18-y;i<=18;++i)for(int j=18-z;j<=18;++j)a+=v[i][j];++v[y][z];
}
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;++i)rd();
	return printf("%lld",a),0;
}
### Prompt

Create a solution in Cpp for the following problem:

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

### Response

```cpp
#include<cstdio>
#define int long long
const int N=200005;
int n,v[20][20],a;
inline void rd()
{
	int x=9,r=0;char c;
	for(;(c=getchar())<'0'||c>'9';);
	for(r=c^48;(c=getchar())>='0'&&c<='9';r=r*10+(c^48));
	if(c=='.')for(;(c=getchar())>='0'&&c<='9';r=r*10+(c^48),--x);
	int y=x,z=x;for(;!(r&1)&&y<18;r>>=1,++y);for(;!(r%5)&&z<18;r/=5,++z);
	for(int i=18-y;i<=18;++i)for(int j=18-z;j<=18;++j)a+=v[i][j];++v[y][z];
}
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;++i)rd();
	return printf("%lld",a),0;
}
```