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 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {

    public static void main(String[] args) throws Exception {

        new Main().go();
    }

    PrintWriter out;
    Reader in;
    BufferedReader br;

    Main() throws IOException {

        try {

            //br = new BufferedReader( new FileReader("input.txt") );
            //in = new Reader("input.txt");
            in = new Reader("input.txt");
            out = new PrintWriter( new BufferedWriter(new FileWriter("output.txt")) );
        }
        catch (Exception e) {

            //br = new BufferedReader( new InputStreamReader( System.in ) );
            in = new Reader();
            out = new PrintWriter( new BufferedWriter(new OutputStreamWriter(System.out)) );
        }
    }

    void go() throws Exception {

        //int t = in.nextInt();
        int t = 1;
        while (t > 0) {
            solve();
            t--;
        }

        out.flush();
        out.close();
    }


    int inf = 2000000000;
    int mod = 1000000007;
    double eps = 0.000000001;

    int n;
    int m;

    ArrayList<Integer>[] g;
    int[] a;
    void solve() throws IOException {
        int n = in.nextInt();
        long[] st = new long[n + 1];
        long cur = 1;
        for (int i = 0; i <= n; i++) {
            st[i] = (cur - 1 + mod) % mod;
            cur = (cur * 2) % mod;
        }
        HashMap<Long, Integer> first = new HashMap<>();
        HashMap<Long, Integer> second = new HashMap<>();
        int same = 0;
        int sameNeg = 0;
        int zeros = 0;
        for (int i = 0; i < n; i++) {
            long a = in.nextLong();
            long b = in.nextLong();

            if (a == 0 && b == 0) {
                zeros++;
                continue;
            }

            if (a == 0) {
                first.put(0L, first.getOrDefault(0, 0) + 1);
                continue;
            }

            if (b == 0) {
                second.put(0L, second.getOrDefault(0, 0) + 1);
                continue;
            }

            if (Math.abs(a) > Math.abs(b)) {
                long d = a / b;
                first.put(d, first.getOrDefault(d, 0) + 1);
            } else if (Math.abs(a) < Math.abs(b)) {
                long d = b / a;
                second.put(d, second.getOrDefault(d, 0) + 1);
            } else {
                long d = a / b;
                if (d > 0) {
                    same++;
                }
                else {
                    sameNeg++;
                }
            }
        }


        ArrayList<Pair<Integer, Integer>> list = new ArrayList<>();
        for (long k : first.keySet()) {
            int x = second.getOrDefault(-k, 0);
            list.add(new Pair(first.get(k), x));
            second.remove(-k);
        }

        for (long k : second.keySet()) {
            list.add(new Pair(0, second.get(k)));
        }

        long ans = (st[same] + st[sameNeg]) % mod;
        for (Pair<Integer, Integer> p : list) {
            int x = p.a;
            int y = p.b;
            long s1 = (ans * st[x]) % mod;
            long s2 = (ans * st[y]) % mod;
            ans = (ans + st[x]) % mod;
            ans = (ans + st[y]) % mod;
            ans = (ans + s1) % mod;
            ans = (ans + s2) % mod;
        }
        ans = (zeros + ans) % mod;

        out.println(ans);
    }

    static class Pair<A extends Comparable<A>, B extends Comparable<B>> implements Comparable<Pair<A, B>> {

        public final A a;
        public final B b;

        Pair(A a, B b) {
            this.a = a;
            this.b = b;
        }

        public int compareTo(Pair<A, B> p) {
            if (!a.equals(p.a))
                return a.compareTo(p.a);
            else
                return b.compareTo(p.b);
        }
    }

    class Item {

        int a;
        int b;
        int c;

        Item(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }

    }


    class Reader {

        BufferedReader  br;
        StringTokenizer tok;

        Reader(String file) throws IOException {
            br = new BufferedReader( new FileReader(file) );
        }

        Reader() throws IOException {
            br = new BufferedReader( new InputStreamReader(System.in) );
        }

        String next() throws IOException {

            while (tok == null || !tok.hasMoreElements())
                tok = new StringTokenizer(br.readLine());
            return tok.nextToken();
        }

        int nextInt() throws NumberFormatException, IOException {
            return Integer.valueOf(next());
        }

        long nextLong() throws NumberFormatException, IOException {
            return Long.valueOf(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.valueOf(next());
        }


        String nextLine() throws IOException {
            return br.readLine();
        }

    }

    static class InputReader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public InputReader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public InputReader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }

}