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 C# (Mono-csc 3.5.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	struct Pair{
		long A, B;
		
		public Pair(long a, long b){
			A = a; B = b;
		}
	}
	public void Solve(){
		
		
		var di = new Dictionary<Q, int>();
		int[] zeros = new int[3];
		for(int i=0;i<N;i++){
			if(A[i] == 0 || B[i] == 0){
				if(A[i] == 0 && B[i] == 0) zeros[0]++;
				if(A[i] == 0 && B[i] != 0) zeros[1]++;
				if(A[i] != 0 && B[i] == 0) zeros[2]++;
				continue;
			}
			var r = (Q)A[i] / (Q)B[i];
			if(di.ContainsKey(r) == false) di.Add(r, 0);
			di[r]+=1;
		}
		
		mlong tot = 1;
		mlong[] P2 = new mlong[N + 2];
		P2[0] = 1;
		for(int i=1;i<N+2;i++) P2[i] = 2 * P2[i - 1];
		
		var hs = new HashSet<Q>();
		foreach(var r in di.Keys){
			Q nr = 1 / r * -1;
			if(hs.Contains(r)) continue;
			if(!di.ContainsKey(nr)){
				tot *= P2[di[r]];
				hs.Add(r);
			} else {
				var c1 = P2[di[r]];
				var c2 = P2[di[nr]];
				tot *= (c1 + c2 - 1);
				hs.Add(r);
				hs.Add(nr);
			}
		}
		
		if(zeros[1] > 0 && zeros[2] > 0){
			var c1 = P2[zeros[1]];
			var c2 = P2[zeros[2]];
			tot *= (c1 + c2 - 1);
		} else if(zeros[1] > 0){
			tot *= P2[zeros[1]];
		} else if(zeros[2] > 0){
			tot *= P2[zeros[2]];
		}
		
		tot -= 1;
		if(zeros[0] > 0) tot += zeros[0];
		
		Console.WriteLine(tot);
		
		
		
		
	}
	int N;
	long[] A,B;
	public Sol(){
		N = ri();
		A = new long[N];
		B = new long[N];
		for(int i=0;i<N;i++){
			var d = rla();
			A[i] = d[0];
			B[i] = d[1];
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}


struct mlong {
	
	const long mod = (long) 1e9 + 7;
	long V;
	
	public mlong(long _v = 0){
		V = _v;
	}
	
	public static mlong operator+(mlong a, mlong b){
		var v0 = a.V + b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator-(mlong a, mlong b){
		var v0 = mod + a.V - b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator-(mlong b){
		var v0 = mod - b.V; if(v0 >= mod) v0 -= mod;
		return new mlong(v0);
	}
	public static mlong operator*(mlong a, mlong b){
		var v0 = a.V * b.V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	public static mlong operator/(mlong a, mlong b){
		var v0 = a.V * inv(b.V).V; if(v0 >= mod) v0 %= mod;
		return new mlong(v0);
	}
	
	
	public static mlong inv(long x){
		long a = 0, b = 0, c = 0;
		ExtGCD(x, mod, ref a, ref b, ref c);
		return (mlong)((a + mod) % mod);
	}
	
	public static void ExtGCD(long x, long y, ref long a, ref long b, ref long c){
		long r0 = x; long r1 = y;
		long a0 = 1; long a1 = 0;
		long b0 = 0; long b1 = 1;
		long q1, r2, a2, b2;
		while(r1 > 0){
			q1 = r0 / r1;
			r2 = r0 % r1;
			a2 = a0 - q1 * a1;
			b2 = b0 - q1 * b1;
			r0 = r1; r1 = r2;
			a0 = a1; a1 = a2;
			b0 = b1; b1 = b2;
		}
		c = r0;
		a = a0;
		b = b0;
	}
	
	public static mlong ModPow(mlong a, long k){
		if(k == 0) return (mlong) 1;
		if(a == 0) return (mlong) 0;
		mlong x = a;
		mlong ret = 1;
		while(k > 0){
			if(k % 2 == 1) ret *= x;
			x *= x;
			k >>= 1;
		}
		return ret;
	}
	
	
	public static bool operator == (mlong a, mlong b){
		 return a.Equals(b);
	}
	public static bool operator != (mlong a, mlong b){
		 return !(a == b);
	}
	
	public override bool Equals(System.Object obj){
		if(obj  ==  null) return false;
		mlong p  =  (mlong) obj;
		if((System.Object) p  ==  null) return false;
		return p.V  ==  V;
	}
	public override int GetHashCode(){
		return V.GetHashCode();
	}
	
	public static implicit operator mlong(long n){
		long v = n % mod; if(v < 0) v += mod;
		return new mlong(v);
	}
	public static implicit operator mlong(int n){
		long v = n % mod; if(v < 0) v += mod;
		return new mlong(v);
	}
	public static explicit operator long(mlong n){
		return n.V;
	}
	
	public override String ToString(){
		return V.ToString();
	}
	
	
}

struct Q:IComparable<Q> {
	long num;
	long den;
	public static long gcd(long a, long b){
		return a == 0 ? b : gcd(b % a, a);
	}
	public static Q Red(Q x){
		long n = x.Num;
		long d = x.Den;
		long g = gcd(Math.Abs(n), Math.Abs(d));
		n /= g;
		d /= g;
		if(d < 0){n *= -1;d *= -1;}
		return new Q(n, d);
	}
	
	public int CompareTo(Q t){
		var d  =  num * t.den - den * t.num;
		return d > 0 ? 1 : d < 0 ? -1 : 0;
	}
	
	public long Num{
		get{return num;}
		set{this.num = value;}
	}
	public long Den{
		get{return den;}
		set{this.den = value;}
	}
	
	public Q(long n_, long d_){
		if(d_ < 0){ n_ *= -1;d_ *= -1;}
		long g = gcd(Math.Abs(n_), Math.Abs(d_));
		n_ /= g;
		d_ /= g;
		num = n_; den = d_;
	}
	
	public static implicit operator Q(long n){
		return new Q(n, 1);
	}
	
	public static explicit operator long (Q q){
		return q.num / q.den;
	}	
	
	
	public static Q operator+(Q a, Q b){
		 return (new Q(a.Num * b.Den + a.Den * b.Num, a.Den * b.Den));
	}
	public static Q operator-(Q a, Q b){
		 return (new Q(a.Num * b.Den - a.Den * b.Num, a.Den * b.Den));
	}
	public static Q operator-(Q a){
		 return (new Q(-a.Num, a.Den));
	}
	public static Q operator*(Q a, Q b){
		 return (new Q(a.Num * b.Num, a.Den * b.Den));
	}
	public static Q operator/(Q a, Q b){
		 return (new Q(a.Num * b.Den, a.Den * b.Num));
	}
	public static bool operator>(Q a, Q b){
		 return a.CompareTo(b) > 0;
	}
	public static bool operator<(Q a, Q b){
		 return a.CompareTo(b) < 0;
	}
	public static bool operator>= (Q a, Q b){
		 return a.CompareTo(b) >=  0;
	}
	public static bool operator<= (Q a, Q b){
		 return a.CompareTo(b) <=  0;
	}
	
	public static bool operator == (Q a, Q b){
		 return a.Equals(b);
	}
	public static bool operator != (Q a, Q b){
		 return !(a == b);
	}
	
	public override bool Equals(System.Object obj){
		if(obj  ==  null) return false;
		Q p  =  (Q) obj;
		if((System.Object) p  ==  null) return false;
		return den * p.num  ==  num * p.den;
	}
	public override int GetHashCode(){
		return (den ^ num).GetHashCode();
	}
	
	
	public static Q Min(Q a, Q b){
		 return a < b ? a : b;
	}
	public static Q Max(Q a, Q b){
		 return a > b ? a : b;
	}
	public override String ToString(){
		return this.Num.ToString()+"/"+this.Den.ToString();
	}
}