Problem:
Score: 500 points

Problem Statement

We have caught N sardines. The deliciousness and fragrantness of the i-th sardine is A_i and B_i, respectively.

We will choose one or more of these sardines and put them into a cooler. However, two sardines on bad terms cannot be chosen at the same time.

The i-th and j-th sardines (i \neq j) are on bad terms if and only if A_i \cdot A_j + B_i \cdot B_j = 0.

In how many ways can we choose the set of sardines to put into the cooler? Since the count can be enormous, print it modulo 1000000007.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

-10^{18} \leq A_i, B_i \leq 10^{18}

Input

Input is given from Standard Input in the following format:

N
A_1 B_1
:
A_N B_N

Output

Print the count modulo 1000000007.

Sample Input 1

3
1 2
-1 1
2 -1

Sample Output 1

5

There are five ways to choose the set of sardines, as follows:

The 1-st

The 1-st and 2-nd

The 2-nd

The 2-nd and 3-rd

The 3-rd

Sample Input 2

10
3 2
3 2
-1 1
2 -1
-3 -9
-8 12
7 7
8 1
8 2
8 4

Sample Output 2

479

Solution in Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.io.*;
        import java.math.*;
        import java.util.*;
        import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 26).start();
    }

    long modPow(long a, long p, long m) {
        if (a == 1) return 1;
        long ans = 1;
        while (p > 0) {
            if (p % 2 == 1) ans = (ans * a) % m;
            a = (a * a) % m;
            p >>= 1;
        }
        return ans;
    }

    long modInv(long a, long m) {
        return modPow(a, m - 2, m);
    }

    long gcd(long a,long b){
        if(b==0)return a;
        return gcd(b,a%b);
    }

    long mod=1000000007;
    long modAdd(long a,long b){
        a%=mod;
        b%=mod;
        return (a+b)%mod;
    }

    long modSub(long a,long b){
        a%=mod;
        b%=mod;
        return ((a-b)%mod+mod)%mod;
    }

    long modMul(long a,long b){
        a%=mod;
        b%=mod;
        return (a*b)%mod;
    }



    PrintWriter out;
    InputReader sc;

    public void run() {
        sc = new InputReader(System.in);
        // Scanner sc=new Scanner(System.in);
        //  Random sc=new Random();
        out = new PrintWriter(System.out);


        int n=sc.nextInt();
        long a[][]=new long[n][2];
        int zero=0;
        HashMap<Node,Integer> hm=new HashMap<>();
        for (int i = 0; i <n ; i++) {
            for (int j = 0; j <2 ; j++) {
                a[i][j]=sc.nextLong();
            }
            if((a[i][0]==0 || a[i][1]==0) && !(a[i][0]==0 && a[i][1]==0))zero++;
            else if(a[i][0]==0 && a[i][1]==0);
            else{
                long gcd=gcd(Math.abs(a[i][0]),Math.abs(a[i][1]));
                a[i][0]/=gcd;
                a[i][1]/=gcd;
                Node temp=new Node(a[i][0],a[i][1]);
                hm.put(temp,hm.getOrDefault(temp,0)+1);
            }
        }
        long ans=1;
        HashSet<Node> hs=new HashSet<>();
        ArrayList<Pair> l=new ArrayList<>();
        for(Node pair1:hm.keySet()){
            if(hs.contains(pair1))continue;
            Node oposite=new Node(pair1.denominator,pair1.numerator,-1l*pair1.sign);
            if(hm.containsKey(oposite)){
                l.add(new Pair(hm.get(pair1),hm.get(oposite)));
                hs.add(pair1);
                hs.add(oposite);
            }
            else {
                l.add(new Pair(hm.get(pair1),-1));
                hs.add(pair1);
            }
        }
        for(Pair x:l){
            if(x.b!=-1)ans=modMul(ans,modAdd(modPow(2,x.a,mod),modSub(modPow(2,x.b,mod),1)));
            else ans=modMul(ans,modPow(2,x.a,mod));
        }
        if(zero==0){
            out.println(modSub(ans,1));
        }
        else{
            out.println(modAdd(modMul(ans,zero),modSub(ans,1)));
        }


        out.println(-1/(1));



        out.close();
    }

    class Pair{
        long a,b;

        public Pair(long a, long b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public String toString() {
            return "Pair{" +
                    "a=" + a +
                    ", b=" + b +
                    '}';
        }
    }

    class Node{
        @Override
        public String toString() {
            return "Node{" +
                    "numerator=" + numerator +
                    ", denominator=" + denominator +
                    ", sign=" + sign +
                    '}';
        }

        long numerator,denominator,sign;

        public Node(long numerator, long denominator) {
            this.numerator = Math.abs(numerator);
            this.denominator = Math.abs(denominator);
            sign=(numerator>=1?1:-1)*(denominator>=1?1:-1);
        }

        public Node(long numerator, long denominator,long s) {
            this.numerator = Math.abs(numerator);
            this.denominator = Math.abs(denominator);
            sign=s;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Node)) return false;

            Node node = (Node) o;

            if (numerator != node.numerator) return false;
            if (denominator != node.denominator) return false;
            return sign == node.sign;
        }

        @Override
        public int hashCode() {
            int result = (int) (numerator ^ (numerator >>> 32));
            result = 31 * result + (int) (denominator ^ (denominator >>> 32));
            result = 31 * result + (int) (sign ^ (sign >>> 32));
            return result;
        }
    }

}