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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

public class Main {
    static In in = new In();
    static Out out = new Out();
    static final long mod = 1000000007;
    static final long inf = 0x1fffffffffffffffL;
    static final int iinf = 0x3fffffff;
    static final int[] da = {-1, 0, 1, 0, -1, 1, 1, -1, -1};

    void solve() {
        int n = in.nextInt();
        Map<LongPair, IntPair> map = new HashMap<>();
        long[] pow = new long[n + 1];
        pow[0] = 1;
        for (int i = 1; i <= n; i++) {
            pow[i] = pow[i - 1] * 2 % mod;
        }
        long zz = 0;
        for (int i = 0; i < n; i++) {
            long a = in.nextLong();
            long b = in.nextLong();
            if (a == 0 && b == 0) {
                zz++;
            } else {
                long gcd = gcd(Math.abs(a), Math.abs(b));
                a /= gcd;
                b /= gcd;
                if (a == 0 || a <= 0 == b <= 0) {
                    map.merge(new LongPair(Math.abs(a), Math.abs(b)), new IntPair(1, 0), (aa, bb) -> new IntPair(aa.first + bb.first, aa.second + bb.second));
                } else {
                    map.merge(new LongPair(Math.abs(b), Math.abs(a)), new IntPair(0, 1), (aa, bb) -> new IntPair(aa.first + bb.first, aa.second + bb.second));
                }
            }
        }
        long ans = 1;
        for (Map.Entry<LongPair, IntPair> entry : map.entrySet()) {
            ans = ans * (pow[entry.getValue().first] + pow[entry.getValue().second] - 1) % mod;
        }
        ans = (ans + zz - 1 + mod) % mod;
        out.println(ans);
    }

    long gcd(long a, long b) {
        return 0 < b ? gcd(b, a % b) : a;
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }
}

class IntPair {
    int first;
    int second;

    IntPair(int first, int second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof IntPair)) {
            return false;
        }
        IntPair that = (IntPair)o;
        return first == that.first && second == that.second;
    }

    @Override
    public int hashCode() {
        return Objects.hash(first, second);
    }

    @Override
    public String toString() {
        return String.format("[%s, %s]", first, second);
    }
}

class LongPair {
    long first;
    long second;

    LongPair(long first, long second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (!(o instanceof LongPair)) {
            return false;
        }
        LongPair that = (LongPair)o;
        return first == that.first && second == that.second;
    }

    @Override
    public int hashCode() {
        return Objects.hash(first, second);
    }

    @Override
    public String toString() {
        return String.format("[%s, %s]", first, second);
    }
}

class In {
    private BufferedReader reader = new BufferedReader(new InputStreamReader(System.in), 0x10000);
    private StringTokenizer tokenizer;

    String next() {
        try {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (IOException ignored) {
        }
        return tokenizer.nextToken();
    }

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

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

    char[][] nextCharArray(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

    int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        return a;
    }

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

    long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nextLong();
        }
        return a;
    }

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}

class Out {
    private PrintWriter out = new PrintWriter(System.out);
    boolean autoFlush = false;

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(int[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (int i : a) {
            joiner.add(Integer.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void println(long[] a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (long i : a) {
            joiner.add(Long.toString(i));
        }
        out.println(joiner);
        if (autoFlush) {
            out.flush();
        }
    }

    void flush() {
        out.flush();
    }
}