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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

/* src: (35 lines)

N = inputInt()
B[:N] = 0, 0
for i in range(N):
    w = string()
    flag = False
    for c in inputWord():
        if c == '.':
            flag = True
        else:
            assert '0'<=c<='9'
            w.push_back(c)
            if flag:
                --B[i][0]
                --B[i][1]
    a = atoll(w.c_str())
    while a % 2 == 0:
        a /= 2
        ++B[i][0]
    while a % 5 == 0:
        a /= 5
        ++B[i][1]
B.sort()
sum = 0
n = N - 1
bit = BIT!(int)(200)
for b2, b5 in B:
    assert -50<=b2<=50
    assert -50<=b5<=50
    while 0 <= n and 0 <= b2 + B[n][0]:
        ++bit[B[n][1] + 100]
        --n
    sum += bit.sum_back(100 - b5)
    sum -= 0 <= b2 and 0 <= b5
assert sum % 2 == 0
print(sum / 2)

*/

//#define NDEBUG

#include <cassert>
#include <vector>
#include <deque>
#include <string>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <cstdlib>
#include <cstdio>
#include <cstring>

using namespace std;

const char*inputCLineOrWord(int mode){static char buf[2097152];static int bufLen=sizeof(buf);static int bufPos=sizeof(buf);static bool canReadFlag=true;static bool crFlag=false;static bool enterFlag=false;if(canReadFlag&&(enterFlag?bufLen<=bufPos:(int)sizeof(buf)<=bufPos+bufPos)){if(0<bufLen-bufPos){memmove(buf,buf+bufPos,bufLen-bufPos);bufLen-=bufPos;}else{bufLen=0;}char*result=fgets(buf+bufLen,sizeof(buf)-bufLen,stdin);canReadFlag=(result!=NULL);if(result!=NULL){int n=strlen(result);enterFlag=(n!=(int)sizeof(buf)-1-bufLen||(1<=bufLen+n&&buf[bufLen+n-1]=='\n'));bufLen+=n;}bufPos=0;}if(mode==0){int pos=bufPos;while(true){char c=buf[pos];if(c==32){buf[pos++]='\0';break;}else if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;while(true){char c=buf[bufPos];if(c==32||c==10||c==13){++bufPos;}else{break;}}return ret;}else if(mode==1){int pos=bufPos;while(true){char c=buf[pos];if(c==10){if(crFlag){crFlag=false;if(bufPos==pos){pos=++bufPos;continue;}}buf[pos++]='\0';break;}else if(c==13){crFlag=true;buf[pos++]='\0';break;}else if(c==0){break;}++pos;}const char*ret=buf+bufPos;bufPos=pos;if(crFlag){while(true){char c=buf[bufPos];if(c==13){++bufPos;crFlag=false;break;}else{break;}}}return ret;}else if(mode==2){return bufLen<=bufPos?NULL:buf+bufPos;}assert(false);return NULL;}const char*inputCWord(){return inputCLineOrWord(0);}int inputInt(){return atoi(inputCWord());}std::string inputWord(){return inputCWord();}template<class T> class BIT{private:std::vector<T> data;public:inline BIT(int n=0):data(n){assert(0<=n);}inline int size(){return(int)data.size();}inline void resize(int n){data.resize(n);}inline void clear(){data.clear();}inline void add(int i,T o=1){assert(0<=i);assert(i<(int)data.size());if(o==0){return;}data[i]+=o;while(i){i&=i-1;data[i]+=o;}}inline T sum_back(int i)const{if(i){T ret=0;while(i<(int)data.size()){ret+=data[i];i+=i&-i;}return ret;}else{return data[0];}}inline T sum(int i)const{assert(0<=i);assert(i<=(int)data.size());return data[0]-sum_back(i);}inline T sum(int l,int r)const{assert(0<=l);assert(l<=(int)data.size());assert(0<=r);assert(r<=(int)data.size());return sum_back(l)-sum_back(r);}inline T get(int i)const{assert(0<=i);assert(i<(int)data.size());T ret=data[i];int j=1;int i2=~i;while(i2&j){int ij=i+j;if((int)data.size()<=ij){break;}ret-=data[ij];j+=j;}return ret;}class ref{private:BIT*bit;int i;public:inline ref(BIT*bit,int i):bit(bit),i(i){}inline void operator=(const T&o){bit->add(i,o-bit->get(i));}inline void operator+=(const T&o){bit->add(i,o);}inline void operator-=(const T&o){bit->add(i,-o);}inline void operator*=(const T&o){bit->add(i,bit->get(i)*(o-1));}inline void operator /=(const T&o){T v=bit->get(i);bit->add(i,v / o-v);}inline void operator++(){bit->add(i,1);}inline void operator++(int){bit->add(i,1);}inline void operator--(){bit->add(i,-1);}inline void operator--(int){bit->add(i,-1);}inline operator T()const{return bit->get(i);}};inline ref operator[](int i){assert(0<=i);assert(i<(int)data.size());return ref(this,i);}inline T operator[](int i)const{assert(0<=i);assert(i<(int)data.size());return get(i);}};void print_unit(bool val){printf("%s",val?"true":"false");}void print_unit(char val){printf("%c",val);}void print_unit(int val){printf("%d",val);}void print_unit(unsigned int val){printf("%u",val);}void print_unit(size_t val){printf("%zd",val);}void print_unit(const void*val){printf("%p",val);}void print_unit(long long val){printf("%lld",val);}void print_unit(__int128 val){char buf[128];int idx=128;buf[--idx]='\0';bool sign=false;if(val<0){sign=true;val=-val;}while(val){buf[--idx]='0'+(val % 10);val /=10;}if(sign){buf[--idx]='-';}printf("%s",buf+idx);}void print_unit(double val){printf("%g",val);}void print_unit(const char*val){printf("%s",val);}void print_unit(const std::string&val){printf("%s",val.c_str());}template<class T>void print_unit(const std::vector<T>&val){printf("vec(%d) {",(int)val.size());for(int i=0;i<(int)val.size();++i){fputc(' ',stdout);print_unit(val[i]);}printf(" }");}
#define _print0()
#define _print1(e)print_unit(e)
#define _print2(e1,e2)_print1(e1),fputc(' ',stdout),_print1(e2)
#define _print3(e1,e2,e3)_print2(e1,e2),fputc(' ',stdout),_print1(e3)
#define _print4(e1,e2,e3,e4)_print2(e1,e2),fputc(' ',stdout),_print2(e3,e4)
#define _print5(e1,e2,e3,e4,e5)_print3(e1,e2,e3),fputc(' ',stdout),_print2(e4,e5)
#define _print6(e1,e2,e3,e4,e5,e6)_print3(e1,e2,e3),fputc(' ',stdout),_print3(e4,e5,e6)
#define _print7(e1,e2,e3,e4,e5,e6,e7)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print3(e5,e6,e7)
#define _print8(e1,e2,e3,e4,e5,e6,e7,e8)_print4(e1,e2,e3,e4),fputc(' ',stdout),_print4(e5,e6,e7,e8)
#define _print9(e1,e2,e3,e4,e5,e6,e7,e8,e9)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print4(e6,e7,e8,e9)
#define _print10(e1,e2,e3,e4,e5,e6,e7,e8,e9,e10)_print5(e1,e2,e3,e4,e5),fputc(' ',stdout),_print5(e6,e7,e8,e9,e10)
#define _GET_PRINT_MACRO_NAME(_1,_2,_3,_4,_5,_6,_7,_8,_9,_10,NAME,...)NAME
#define print(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__),fputc('\n',stdout)
#define print0(...)_GET_PRINT_MACRO_NAME(__VA_ARGS__,_print10,_print9,_print8,_print7,_print6,_print5,_print4,_print3,_print2,_print1,_print0)(__VA_ARGS__)

// generated code (by mmlang) :

int N;
vector<tuple<int, int> > B;
string w;
bool flag;
long long a;
int sum;
int n;
BIT<int> bit;

int main() {
    N = inputInt();
    B.resize(max((int)B.size(), (int)N)); for(int $1=0, $e=(0<=N ? N : (int)B.size()+N); $1<$e; ++$1) {
        const auto & $c1 = 0;
        const auto & $c2 = 0;
        B[$1] = tuple<int, int>($c1, $c2);
    }
    for(int i=0, $e=N; i<$e; ++i) {
        w = string();
        flag = false;
        for(const char & c : inputWord()) {
            if(c == '.') {
                flag = true;
            }
            else {
                assert(('0' <= c && c <= '9'));
                w.push_back(c);
                if(flag) {
                    --get<0>(B[i]);
                    --get<1>(B[i]);
                }
            }
        }
        a = atoll(w.c_str());
        while(a % 2 == 0) {
            a /= 2;
            ++get<0>(B[i]);
        }
        while(a % 5 == 0) {
            a /= 5;
            ++get<1>(B[i]);
        }
    }
    sort(B.begin(), B.end());
    sum = 0;
    n = N - 1;
    bit = BIT<int>(200);
    for(const tuple<int, int> & $fr : B) { const int & b2 = get<0>($fr); const int & b5 = get<1>($fr);
        assert((-50 <= b2 && b2 <= 50));
        assert((-50 <= b5 && b5 <= 50));
        while(0 <= n && 0 <= b2 + get<0>(B[n])) {
            ++bit[get<1>(B[n]) + 100];
            --n;
        }
        sum += bit.sum_back(100 - b5);
        sum -= 0 <= b2 && 0 <= b5;
    }
    assert(sum % 2 == 0);
    print(sum / 2);
    return 0;
}