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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.TreeSet;
import java.util.TreeMap;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ABullet solver = new ABullet();
        solver.solve(1, in, out);
        out.close();
    }

    static class ABullet {
        int mod;

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

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            int n = sc.nextInt();
            mod = (int) 1e9 + 7;
            TreeMap<pair, Integer> map = new TreeMap<>();
            for (int i = 0; i < n; i++) {
                long a = sc.nextLong(), b = sc.nextLong();
                pair temp = makePair(a, b);
                map.put(temp, map.getOrDefault(temp, 0) + 1);
            }
            long ans = 1;
            TreeSet<pair> visited = new TreeSet<>();
            visited.add(new pair(0, 0));
            for (Map.Entry<pair, Integer> entry : map.entrySet()) {
                pair p = entry.getKey();
                int c = entry.getValue();
                if (visited.contains(p))
                    continue;
                pair incomp = new pair(-p.b, p.a), incomp2 = new pair(p.b, -p.a);
                visited.add(incomp);
                visited.add(incomp2);
                int c2 = map.getOrDefault(incomp, 0);
                c2 += map.getOrDefault(incomp2, 0);
                ans *= (fastPowMod(2, c) % mod + fastPowMod(2, c2) % mod - 1 + mod) % mod;
            }
            pw.println((ans - 1 + mod) % mod);
        }

        private pair makePair(long a, long b) {
            if (a == 0 && b == 0)
                return new pair(0, 0);
            if (a == 0)
                return new pair(0, 1);
            if (b == 0)
                return new pair(1, 0);
            int bool = a < 0 ? 1 : 0;
            bool ^= b < 0 ? 1 : 0;
            a = Math.abs(a);
            b = Math.abs(b);
            long gcd = gcd(a, b);
            return new pair((bool == 1 ? -1 : 1) * a / gcd, b / gcd);
        }

        public long fastPowMod(long a, long b) {
            if (b == 0)
                return 1;
            long temp = fastPowMod(a, b / 2) % mod;
            if (b % 2 == 1)
                return a % mod * temp % mod * temp % mod;
            else
                return temp % mod * temp % mod;
        }

        public class pair implements Comparable<pair> {
            long a;
            long b;

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

            public int compareTo(pair pair) {
                return a == pair.a ? Long.compare(b, pair.b) : Long.compare(a, pair.a);
            }

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

        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

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

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

    }
}