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.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {
	static final long MOD = 1000000007L;
	
	class Node {
		long a, b;
		
		public Node(long a, long b) {
			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;
			Node node = (Node) o;
			return a == node.a &&
					b == node.b;
		}
		
		@Override
		public int hashCode() {
			return Objects.hash(a, b);
		}
	}
	
	Main() {
		FastScanner scanner = new FastScanner();
		int N = scanner.nextInt();
		
		HashMap<Node, Integer> P = new HashMap<>();
		HashMap<Node, Integer> M = new HashMap<>();
		int aZero = 0, bZero = 0;
		
		for (int i = 0; i < N; i++) {
			long a = scanner.nextLong();
			long b = scanner.nextLong();
			
			if ( a == 0 && b == 0) {
				continue;
			} else if ( a == 0 ) {
				aZero++;
				continue;
			} else if ( b == 0 ) {
				bZero++;
				continue;
			}
			
			if ( (a > 0 && b > 0) || (a < 0 && b < 0) ) {
				a = Math.abs(a);
				b = Math.abs(b);
				long gcd = gcd(a, b);
				Node n = new Node(a/gcd, b/gcd);
				P.put( n, P.getOrDefault(n, 0)+1);
			} else {
				a = Math.abs(a);
				b = Math.abs(b);
				long gcd = gcd(a, b);
				Node n = new Node(b/gcd, a/gcd);
				M.put( n, M.getOrDefault(n, 0)+1);
			}
		}
		
		long Ans = 1L;
		for ( Node key : P.keySet() ) {
			if ( M.containsKey(key) ) {
				long c = ( modPow(P.get(key)) + modPow(M.get(key)) ) % MOD - 1;
				if (c < 0) c += MOD;
				Ans = Ans*c%MOD;
				M.remove(key);
			} else {
				Ans = Ans*modPow(P.get(key))%MOD;
			}
		}
		
		for ( Node key : M.keySet() ) {
			Ans = Ans*modPow(M.get(key))%MOD;
		}
		
		long c = ( modPow(aZero) + modPow(bZero) ) % MOD - 1;
		if (c < 0) c += MOD;
		Ans = Ans*c%MOD;
		
		//全てを選ばないことは禁止されている
		Ans -= 1;
		if (Ans < 0) Ans += MOD;
		
		System.out.println(Ans);

	}
	
	long gcd(long a, long b) {
		if ( a % b == 0) return b;
		return gcd(b,a%b);
	}
	
	public static void main(String[] args) {
		new Main();
	}
	
	long modPow(long n) {
		long res = 1;
		long a = 2L;
		while (n > 0) {
			if ( (n & 1) == 1) res = res * a % MOD;
			a = a * a % MOD;
			n >>= 1;
		}
		return res;
	}
}


class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	
	private int readByte() {
		if (hasNextByte()) return buffer[ptr++];
		else return -1;
	}
	
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		return hasNextByte();
	}
	
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}