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: Accepted)

import java.io.BufferedInputStream;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Random;

public class Main {

    private static final long MOD = 1_000_000_007;

    public static void main(String[] args) throws Exception {
        try (BufferedInputStream in = new BufferedInputStream(System.in);
             PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out))) {

            _Scanner sc = new _Scanner(in);
            
            // 21:56-
            
            Map<X, Integer> map = new LinkedHashMap<>();
            List<X> list = new ArrayList<>();
            int n = sc.nextInt();
            long ans = 0L;
            for (int i = 0; i < n; i++) {
                long a = sc.nextLong();
                long b = sc.nextLong();
                if (a == 0 && b == 0) {
                    ans++;
                    continue;
                }
                long gcd = gcd(a, b);
                X x = new X((long) Math.signum(Math.signum(a) * Math.signum(b)), Math.abs(a / gcd), Math.abs(b / gcd));
                if (x.a == 0) x.sig = 1;
                if (x.b == 0) x.sig = -1;
                list.add(x);
                map.merge(x, 1, Integer::sum);
            }

            long[] pows = new long[n + 1];
            pows[0] = 1;
            for (int i = 1; i < pows.length; i++) pows[i] = (pows[i - 1] * 2) % MOD;

            long total = 1;
            for (X x : list) {
                int a = map.getOrDefault(x, 0);
                int b = map.getOrDefault(new X(-x.sig, x.b, x.a), 0);
                map.put(x, 0);
                map.put(new X(-x.sig, x.b, x.a), 0);

                total = (total * ((pows[a] + pows[b] - 1) % MOD)) % MOD;
            }

            total = (MOD + total - 1) % MOD;
            total = (total + ans) % MOD;

            out.println(total);
        }
    }

    private static long gcd(long a, long b) {
        while (b != 0) {
            long t = a % b;
            a = b;
            b = t;
        }
        return a;
    }

    private static class X {
    	long sig, a, b;

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

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            X x = (X) o;
            return sig == x.sig &&
                    a == x.a &&
                    b == x.b;
        }

        @Override
        public int hashCode() {
            return Objects.hash(sig, a, b);
        }

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

    

    private static void reverse(int[] vs) {
        for (int i = 0; i < vs.length / 2; i++) {
            swap(vs, i, vs.length - 1 - i);
        }
    }

    static class _Scanner {
        InputStream is;
        _Scanner(InputStream is) {
            this.is = is;
        }
        byte[] bb = new byte[1 << 15];
        int k, l;
        byte getc() {
            try {
                if (k >= l) {
                    k = 0;
                    l = is.read(bb);
                    if (l < 0) return -1;
                }
                return bb[k++];
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        byte skip() {
            byte b;
            while ((b = getc()) <= 32)
                ;
            return b;
        }

        int nextInt() {
            int n = 0;
            int sig = 1;
            for (byte b = skip(); b > 32; b = getc()) {
                if (b == '-') {
                    sig = -1;
                } else {
                    n = n * 10 + b - '0';
                }
            }
            return sig * n;
        }

        long nextLong() {
            long n = 0;
            long sig = 1;
            for (byte b = skip(); b > 32; b = getc()) {
                if (b == '-') {
                    sig = -1;
                } else {
                    n = n * 10 + b - '0';
                }
            }
            return sig * n;
        }

        public String next() {
            StringBuilder sb = new StringBuilder();
            for (int b = skip(); b > 32; b = getc()) {
                sb.append(((char) b));
            }
            return sb.toString();
        }
    }

    private static void shuffle(int[] ar) {
        Random rnd = new Random();
        for (int i = 0; i < ar.length; i++) {
            int j = i + rnd.nextInt(ar.length - i);
            swap(ar, i, j);
        }
    }

    private static void shuffle(Object[] ar) {
        Random rnd = new Random();
        for (int i = 0; i < ar.length; i++) {
            int j = i + rnd.nextInt(ar.length - i);
            swap(ar, i, j);
        }
    }

    private static void swap(int[] ar, int i, int j) {
        int t = ar[i];
        ar[i] = ar[j];
        ar[j] = t;
    }

    private static void swap(Object[] ar, int i, int j) {
        Object t = ar[i];
        ar[i] = ar[j];
        ar[j] = t;
    }


}