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.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {

    private static final int MOD = (int)1e9 + 7; //998244353;

    public Main(FastScanner in, PrintWriter out) {
        int N = in.nextInt();
        Pair<Long, Long>[] A = new Pair[N];
        Map<Pair<Long, Long>, Integer> set = new HashMap<>();
        for (int i = 0; i < N; i++) {
            long a = in.nextLong(), b = in.nextLong();
            long gcd = gcd(a, b);
            if (gcd != 0) {
                a /= gcd;
                b /= gcd;
            }
            // make sure b >= 0
            if (a != 0 && b == 0)
                A[i] = new Pair(1L, 0L);
            else if (a == 0 && b != 0)
                A[i] = new Pair(0L, 1L);
            else if (b < 0)
                A[i] = new Pair(-a, -b);
            else
                A[i] = new Pair(a, b);
            set.merge(A[i], 1, Integer::sum);
        }

        int[] pow2 = new int[N + 1];
        pow2[0] = 1;
        for (int i = 1; i <= N; i++)
            pow2[i] = pow2[i - 1] * 2 % MOD;

        Pair<Long, Long> p0 = new Pair<>(0L, 0L);
        int count0 = set.getOrDefault(p0, 0);
        set.remove(p0);

        long ans = 1;
        for (Pair<Long, Long> p : A) {
            Pair<Long, Long> other; // bad pairs to p
            // make sure other.b >= 0
            if (p.a < 0L)
                other = new Pair<>(p.b, -p.a);
            else if (p.a == 0L)
                other = new Pair<>(1L, 0L);
            else
                other = new Pair<>(-p.b, p.a);
            int x0 = set.getOrDefault(p, 0);
            int x1 = set.getOrDefault(other, 0);
            ans *= (pow2[x0] + pow2[x1] - 1); // - 1 to remove the extra empty set
            ans %= MOD;
            // out.printf("%s %s, %d, %d%n", p, other, x0, x1);

            set.remove(p);
            set.remove(other);
        }

        // - 1 to remove empty et
        ans = (ans + count0 - 1 + MOD) % MOD;

        out.println(ans);

    }

    private int pow(int x, int p) {
        long res = 1, a = x;
        while (p > 0) {
            if (p % 2 == 1)
                res = res * a % MOD;

            a = a * a % MOD;
            p /= 2;
        }
        return (int)res;
    }

    private long gcd(long a, long b) {
        while (true) {
            if (b == 0) return a;
            long tmp = a;
            a = b;
            b = tmp % b;
        }
    }

    public static void main(String[] args) {
        PrintWriter out = new PrintWriter(System.out);
        // Scanner in = new Scanner(
                // new BufferedReader(new InputStreamReader(System.in)));
        FastScanner in = new FastScanner(System.in);

        Main sol = new Main(in, out);

        out.close();
    }
}

// Pair
class Pair<T extends Comparable<? super T>, U extends Comparable<? super U>> implements Comparable<Pair<T, U>> {
    T a;
    U b;
    Pair() { }
    Pair(T a, U b) {
        this.a = a;
        this.b = b;
    }

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

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

    @Override
    public boolean equals(Object obj) {
        if(this == obj) return true;
        if(obj == null) return false;
        if(this.getClass() != obj.getClass()) return false;
        Pair that = (Pair) obj;
        if(this.a.getClass() != that.a.getClass()) return false;
        if(this.b.getClass() != that.b.getClass()) return false;
        if(!this.a.equals(that.a)) return false;
        if(!this.b.equals(that.b)) return false;
        return true;
    }

    @Override
    public int compareTo(Pair<T, U> that) {
        int c = (this.a).compareTo(that.a);
        if(c == 0) c = (this.b).compareTo(that.b);
        return c;
    }
}


class FastScanner{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

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

    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++];
    }

    boolean isSpaceChar(int c)
    {
        return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
    }

    boolean isEndline(int c)
    {
        return c=='\n'||c=='\r'||c==-1;
    }

    int nextInt()
    {
        return Integer.parseInt(next());
    }

    long nextLong()
    {
        return Long.parseLong(next());
    }

    double nextDouble()
    {
        return Double.parseDouble(next());
    }

    String next(){
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isSpaceChar(c));
        return res.toString();
    }

    String nextLine(){
        int c = read();
        while (isEndline(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = read();
        }while(!isEndline(c));
        return res.toString();
    }
}