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 {
    static long mod = (int)Math.pow(10,9)+7;
	public static void main(String[] args) throws IOException {
		FastScanner sc = new FastScanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int zero = 0;
		HashMap<Pair<Long,Long>,Pair<Long,Long>> map = new HashMap<Pair<Long,Long>,Pair<Long,Long>>();
		for(int i = 0; i < n; i++){
		    long x = sc.nextLong();
		    long y = sc.nextLong();
		    if(x == 0 && y == 0){
		        zero++;
		        continue;
		    }
		    long g = gcd(Math.abs(x),Math.abs(y));
		    x /= g;
		    y /= g;
		    if(y < 0){
		        x = -x; 
		        y = -y;
		    }
		    if(y == 0 && x < 0){
		        x = -x; 
		        y = -y;
		    }
		    boolean rot90 = (x <= 0);
		    if(rot90){
		        long tmp = x;
		        x = y; 
		        y = -tmp;
		    }
            Pair<Long,Long> p = new Pair(x,y);
            Pair<Long,Long> cnt = map.getOrDefault(p,new Pair(0L,0L));
            if(rot90){
                cnt.first++;
            }else{
                cnt.second++;
            }
		    map.put(p,cnt);
		}
		long ans = 1;
		for(Map.Entry<Pair<Long,Long>,Pair<Long,Long>> e : map.entrySet()){
		    Pair<Long,Long> k = e.getKey();
		    Pair<Long,Long> v = e.getValue();
		    //System.out.println(k.first + " "+k.second + " " + v.first + " " + v.second);
		    long s = v.first;
		    long t = v.second;
		    long now = 1;
		    now += rep2(2,s)-1;
		    now %= mod;
		    now += rep2(2,t)-1;
		    now %= mod;
		    ans *= now;
		    ans %= mod;
		}
		ans--;
		ans += zero;
		pw.println(ans);
		pw.close();
	}
	
	private static long gcd(long a, long b){
        while (b > 0)
        {
            long temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
    
    private static long rep2(long b, long n){
        if(n == 0) return 1;
        if(n == 1) return b;
        long bn = rep2(b,n/2)%mod;
        if(n % 2 == 0){
            return (long)(bn%mod*bn%mod)%mod;
        }else{
            return (long)(bn%mod*bn%mod)%mod*b%mod;
        }
    }
    
}

class Pair<F, S> {
    public F first;
    public S second;

    public Pair (F first, S second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals (Object obj) {
        if (! (obj instanceof Pair))
            return false;
        Pair pair = (Pair) obj;
        return (first.equals (pair.first) && second.equals (pair.second));
    }

    @Override
    public int hashCode () {
        return first.hashCode () ^ second.hashCode ();
    }
}
class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

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

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

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

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

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

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

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