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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

//using System.Numerics;
using CS=System.Runtime.CompilerServices;
//using System.Diagnostics;
using static System.Math;
using ll=System.Int64;
using static Contest_A.Lib_IO;
using static Contest_A.Lib_Minifunc;


namespace Contest_A {

public static class Entry
{

	public static void Main() {
		checked{
			long n;
			Lib_IO.rm(out n);
			string[] sa;
			rl(n,out sa);
			long ans = 0;

			CumulativeSum2D cs = new CumulativeSum2D(20,20);
			for (int i = 0; i < n; i++)
			{
				var ss = sa[i].Split(".");
				ll v = ll.Parse(ss[0])*1000000000;
				if(ss.Length==2) {
					var sss = ss[1] + new string('0',9-ss[1].Length);
					v += ll.Parse(sss);
				}
				int c2=0;
				int c5=0;
				while(v%2==0){
					c2++;
					v/=2;
				}
				while(v%5==0){
					c5++;
					v/=5;
				}
				ans += cs.Sum(max(18-c2,0),max(18-c5,0),20,20);
				cs.Add(min(c2,19),min(c5,19),1);
			}




			Lib_IO.wm(ans);
		}
	}


public class CumulativeSum2D {
	private long[][] _data, _lazyadd;
	private int _lazyix, _lazyiy;
	public readonly long LengthX, LengthY;

	public CumulativeSum2D(long sizeX, long sizeY){
		_data = new long[sizeX+1][];
		_lazyadd = new long[sizeX][];
		for(int i=0;i<sizeX;i++) {
			_data[i] = new long[sizeY+1];
			_lazyadd[i] = new long[sizeY];
		}
		_data[sizeX] = new long[sizeY+1];
		_lazyix = _lazyadd.Length;
		_lazyiy = _lazyadd[0].Length;
		LengthX = sizeX;
		LengthY = sizeY;
	}
	public CumulativeSum2D(long[][] val) : this(val.Length, val[0].Length){
		for(int i=0;i<val.Length;i++) for(int j=0;j<val[i].Length;j++) 
			_data[i+1][j+1] = val[i][j]+_data[i][j+1]+_data[i+1][j]-_data[i][j];
	}
	public void Add(long kx, long ky, long val){
		for(int i=(int)kx+1;i<_data.Length;i++) for(int j=(int)ky+1;j<_data[i].Length;j++) 
			_data[i][j] += val;
	}
	public void AddLazy(long kx, long ky, long val) {
		if(kx<_lazyix) _lazyix = (int)kx;
		if(ky<_lazyiy) _lazyiy = (int)ky;
		_lazyadd[kx][ky] += val;
	}
	private void build(){
		if(_lazyadd.Length<=_lazyix && _lazyadd[0].Length<=_lazyiy) return;
		long[] lz1d = new long[_lazyadd[0].Length];
		for(int i=_lazyix+1;i<_data.Length;i++) {
			long lzsum = 0;
			for(int j=_lazyiy+1;j<_data[i].Length;j++) {
				lzsum += _lazyadd[i-1][j-1];
				lz1d[j-1] += lzsum;
				_data[i][j] += lz1d[j-1];
				_lazyadd[i-1][j-1] = 0;
			}
		}
		_lazyix = _lazyadd.Length;
		_lazyiy = _lazyadd[0].Length;
	}
	public long Sum(long kx, long ky) {
		build();
		return _data[kx+1][ky+1];
	}
	// 閉開区間[x1:x2),[y1:y2)で囲まれた長方形エリアの累積和を計算
	public long Sum(long x1, long y1, long x2, long y2) {
		build();
		return (_data[x2][y2]-_data[x1][y2]-_data[x2][y1]+_data[x1][y1]);
	}

}












}



#region BaseModule


public static class Lib_Minifunc{
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
	[CS.MethodImpl(256)] public static void swap1<T>(ref T a,ref T b) { T t = a; a = b; b = t; }
	[CS.MethodImpl(256)] public static void swap2<T>(ref T a,ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換
	[CS.MethodImpl(256)] public static bool chmin<T>(ref T a,T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	[CS.MethodImpl(256)] public static bool chmax<T>(ref T a,T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	[CS.MethodImpl(256)] public static bool inside(long i,long n) => (0<=i&&i<n);
	[CS.MethodImpl(256)] public static bool inside(long x,long y,long w,long h) => (inside(x,w)&&inside(y,h));
	[CS.MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmin(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable { T m = a[0]; for (int i=1;i<a.Length;i++) chmax(ref m, a[i]); return m; }
	[CS.MethodImpl(256)] public static long mod(long a,long m=MOD1) { var v = a%m; return (v<0?(m<0?v-m:v+m):v); }
	[CS.MethodImpl(256)] public static long ceil(long a,long b) => (a%b==0||(a<0&&0<b)||(0<a&&b<0)?a/b:a/b+1);	// 整数商の切り上げ
	[CS.MethodImpl(256)] public static long round(double a) => Convert.ToInt64(a);	// 四捨五入
	public static string YES(bool a) => a?"YES":"NO";
	public static string yes(bool a) => a?"Yes":"No";
	[CS.MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[CS.MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[CS.MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	public static T[] initc<T>(long l1) where T : new() { var m = new T[l1]; for (int i=0;i<m.Length;i++) m[i] = new T(); return m; }	// new制約は遅い
	public static int[] range(long s, long c) => Enumerable.Range((int)s,(int)c).ToArray();
	[CS.MethodImpl(256)] public static T[] inita<T>(long l1,T v=default(T)) => Enumerable.Repeat(v,(int)l1).ToArray();
	public static T[][] inita<T>(long l1,long l2,T v=default(T)) { var m = new T[l1][]; for (int i=0;i<m.Length;i++) m[i] = inita(l2,v); return m; }
	public static T[][][] inita<T>(long l1,long l2,long l3,T v=default(T)) { var m = new T[l1][][]; for (int i=0;i<m.Length;i++) m[i] = inita(l2,l3,v); return m; }
	public static void shift(this IList<int> l,int o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	public static void shift(this IList<long> l,long o) { for (int i = 0;i<l.Count;i++) l[i]+=o; }
	[CS.MethodImpl(256)] public static bool initd<T,U>(this IDictionary<T,U> d, T k, U v=default(U)) { if(d.ContainsKey(k)) { return false; } else { d[k] = v; return true; } }
	public static void sort<T>(this T[] a,int o=1, Comparison<T> f=null) where T : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.CompareTo(y));break;
			case -1: Array.Sort(a,(x,y)=>y.CompareTo(x));break;
			default: break;
		}
	}
	public static void sort<T,U>(this P<T,U>[] a,int o, Comparison<P<T,U>> f=null) where T : IComparable where U : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			default: break;
		}
	}
	public static void sort<T,U,V>(this P<T,U,V>[] a,int o, Comparison<P<T,U,V>> f=null) where T : IComparable where U : IComparable where V : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			default: break;
		}
	}
	public static void sort<T,U,V,W>(this P<T,U,V,W>[] a,int o, Comparison<P<T,U,V,W>> f=null) where T : IComparable where U : IComparable where V : IComparable where W : IComparable {
		switch(o){
			case  0: Array.Sort(a,f);break;
			case  1: Array.Sort(a,(x,y)=>x.A.CompareTo(y.A));break;
			case -1: Array.Sort(a,(x,y)=>y.A.CompareTo(x.A));break;
			case  2: Array.Sort(a,(x,y)=>x.B.CompareTo(y.B));break;
			case -2: Array.Sort(a,(x,y)=>y.B.CompareTo(x.B));break;
			case  3: Array.Sort(a,(x,y)=>x.C.CompareTo(y.C));break;
			case -3: Array.Sort(a,(x,y)=>y.C.CompareTo(x.C));break;
			case  4: Array.Sort(a,(x,y)=>x.D.CompareTo(y.D));break;
			case -4: Array.Sort(a,(x,y)=>y.D.CompareTo(x.D));break;
			default: break;
		}
	}
}


public struct P<T,U>
{
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V>
{
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W>
{
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO
{
	class Prt : System.IO.StreamWriter
	{
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[CS.MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[CS.MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[CS.MethodImpl(256)] static T cv<T>(string s) =>
		eq<T,int>()	? ct<T,int>(int.Parse(s))
	  : eq<T,long>()   ? ct<T,long>(long.Parse(s))
	  : eq<T,double>() ? ct<T,double>(double.Parse(s,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = new T[z.Length];
		for(int i=0;i<a.Length;i++) a[i] = cv<T>(z[i]);
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[CS.MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length-1;i++) Console.Write(wfm(a[i].GetType())+" ",a[i]);
			Console.WriteLine(wfm(a[a.Length-1].GetType()),a[a.Length-1]);
		});
	}
	public static void wa<T>(IList<T> a) { wxa(new IList<T>[]{a}, " "); }
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			if(a.Count==0){
				Console.WriteLine();
			}else{
				foreach(T x in a) Console.WriteLine(f,x);
			}
		});
	}
	static void wxa<T>(IList<IList<T>> a, string s) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + s;
			foreach(var b in a) {
				if(b.Count==0){
					Console.WriteLine();
				}else{
					for(int i=0;i<b.Count-1;i++) Console.Write(g,b[i]);
					Console.WriteLine(f,b[b.Count-1]);
				}
			}
		});
	}
	public static void wx<T>(IList<IList<T>> a) { wxa(a, " "); }
	public static void wg<T>(IList<IList<T>> a) { wxa(a, ""); }
}

#endregion



}