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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var D = new Dictionary<(long a, long b), (int posi, int nega)>();
			var bad = 0;
			for(int i = 0; i<N; i++) {
				var A = cin.ReadLong;
				var B = cin.ReadLong;
				var g = Abs(gcd(A, B));
				if(B==0&&A==0) {
					bad++;
					continue;
				} else if(B==0) A=1;
				else if(A==0) B=1;
				else {
					A/=g; B/=g;
					if(A<0) {
						A=-A; B=-B;
					}
				}
				var arg = B<0 ? (-B, A) : (A, B);
				var nega = B<0;
				if(D.ContainsKey(arg)) {
					var da = D[arg];
					D[arg]=nega ? (da.posi, da.nega+1) : (da.posi+1, da.nega);
				} else {
					D.Add(arg, nega ? (0, 1) : (1, 0));
				}
			}
			var F = new QuotientRing();
			var Res = 1L;
			if(D.Count>0) {
				foreach(var v in D.Values) {
					Res=F.Mul(Res, F.Pow(2, v.posi)+F.Pow(2, v.nega)-1);
				}
			}
			if(bad>0) Res=F.Add(Res, bad);
			Console.WriteLine(F.Sub(Res,1));
		}
		private static long gcd(long a, long b) {
			if(b==0) 
				return a;
			return gcd(b, a%b);
		}
	}
	static class ExtendClass {
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}
	class UnionFindForest {
		public class Node {
			public int value { get; set; }
			public virtual Node parent { get; set; }
			public virtual Node root {
				get {
					var path = new Queue<Node>();
					var res = this;
					while(res.parent!=res) {
						path.Enqueue(res);
						res=res.parent;
					}
					while(path.Any())
						path.Dequeue().parent=res;
					return res;
				}
			}
			public int rank { get; private set; }    //meanful iff root
			public void rankIncrement() => rank++;
			public Node(int _value) {
				value=_value;
				parent=this;
				rank=1;
			}
		}

		private readonly Dictionary<int, Node> Registry = new Dictionary<int, Node>();
		public UnionFindForest(int N) {
			for(int i = 0; i<N; i++) Add(i);
		}
		public void Union(int x, int y) => Union(Registry[x], Registry[y]);
		public void Union(Node X, Node Y) {
			var RX = X.root;
			var RY = Y.root;
			switch(RX.rank.CompareTo(RY.rank)) {
				case 1:
					RY.parent=RX;
					break;
				case -1:
					RX.parent=RY;
					break;
				default:
					RX.parent=RY;
					RY.rankIncrement();
					break;
			}
		}
		public bool Find(int x, int y) => Find(Registry[x], Registry[y]);
		public bool Find(Node X, Node Y) => X.root==Y.root;
		public virtual void Add(int id) {
			var N = new Node(id);
			Registry.Add(id, N);
		}
		public Dictionary<Node, int> TallyDegrees() {
			var Roots = new Dictionary<Node, int>();
			foreach(var node in Registry.Values) {
				if(Roots.Keys.Contains(node))
					Roots[node]++;
				else
					Roots.Add(node, 1);
			}
			return Roots;
		}
		public int[] Degrees() {
			var D = TallyDegrees();
			var res = new int[Registry.Count];
			for(int i = 0; i<Registry.Count; i++)
				res[i]=D[Registry[i]];
			return res;
		}
		public int TreeCount() {
			var D = TallyDegrees();
			return D.Count;
		}
	}
	class ResidueField: QuotientRing {
		public ResidueField(int _modulo = 1000*1000*1000+7) : base(_modulo) { }
		private static long extgcd(long a, long b, ref long x, ref long y) {
			if(b==0) {
				x=1; y=0; return a;
			}
			var q = a/b;
			var g = extgcd(b, a-q*b, ref x, ref y);
			var z = x-q*y;
			x=y; y=z;
			return g;
		}
		public long Inv(long a) {
			if(a==0) throw new DivideByZeroException();
			long x = 0, y = 0;
			extgcd(a, modulo, ref x, ref y);
			return mod(x);
		}
		public long Div(long a, long b) => Mul(a, Inv(b));
		public long Combination(int n, int k) {
			if(k<0||k>n) return 0;
			if(n-k<k) k=n-k;
			return Div(Permutation(n, k), Factorial(k));
		}
		public override long Calculate(params object[] RPN) {
			var S = new Stack<long>();
			foreach(var token in RPN) {
				var type = token.GetType();
				if(type==typeof(int)) {
					S.Push((int)token);
				} else if(type==typeof(long)) {
					S.Push((long)token);
				} else if(type==typeof(char)) {
					long v1 = 0L, v2 = 0L;
					v2=S.Pop();
					HashSet<char> unaries = new HashSet<char>() { '!' };
					if(!unaries.Contains((char)token))
						v1=S.Pop();
					long res;
					switch((char)token) {
						case '+': res=Add(v1, v2); break;
						case '-': res=Sub(v1, v2); break;
						case '*': res=Mul(v1, v2); break;
						case '/': res=Div(v1, v2); break;
						case '^': res=Pow(v1, v2); break;
						case '!': res=Factorial((int)v2); break;
						case 'C': res=Combination((int)v1, (int)v2); break;
						case 'P': res=Permutation((int)v1, (int)v2); break;
						default: throw new InvalidOperationException();
					}
					S.Push(res);
				} else throw new InvalidOperationException();
			}
			return S.Peek();
		}
	}
	class QuotientRing {
		public readonly long modulo;
		public QuotientRing(int mModulo = 1000*1000*1000+7) {
			modulo=mModulo;
		}
		private long[] factorialTable = { 1 };
		private int factorialTableLastIndex { get { return factorialTable.Length-1; } }
		public long mod(long x) => x<0 ? x%modulo+modulo : x%modulo;
		public long Add(long a, long b) => mod(a+b);
		public long Sub(long a, long b) => mod(a-b);
		public long Mul(long a, long b) => mod(a*b);
		public long Pow(long a, long n) {
			if(n==0) return 1;
			var R = 1L;
			n=n<0 ? n%(modulo-1)+(modulo-1) : n%(modulo-1);
			for(; n>0; a=Mul(a, a), n>>=1) {
				if((n&1)!=0) R=Mul(R, a);
			}
			return R;
		}
		private void ExpandFactorialTable(int N) {
			var k = factorialTableLastIndex;
			Array.Resize(ref factorialTable, N+1);
			for(int i = k+1; i<=N; i++) {
				if(i==0) { factorialTable[i]=1; continue; }
				factorialTable[i]=Mul(factorialTable[i-1], i);
			}
		}
		public long Factorial(int n) {
			if(n>factorialTableLastIndex)
				ExpandFactorialTable(n);
			return factorialTable[n];
		}
		public long Permutation(int n, int k) {
			if(k<0||k>n) return 0;
			var Res = 1L;
			for(int i = 0; i<k; i++)
				Res=Mul(Res, n-i);
			return Res;
		}
		public virtual long Calculate(params object[] RPN) {
			var S = new Stack<long>();
			foreach(var token in RPN) {
				var type = token.GetType();
				if(type==typeof(int)||type==typeof(long)) {
					S.Push((long)token);
				} else if(type==typeof(char)) {
					long v1 = 0L, v2 = 0L;
					v2=S.Pop();
					HashSet<char> unaries = new HashSet<char>() { '!' };
					if(!unaries.Contains((char)token))
						v1=S.Pop();
					long res;
					switch((char)token) {
						case '+': res=Add(v1, v2); break;
						case '-': res=Sub(v1, v2); break;
						case '*': res=Mul(v1, v2); break;
						case '^': res=Pow(v1, v2); break;
						case '!': res=Factorial((int)v2); break;
						default: throw new InvalidOperationException();
					}
					S.Push(res);
				} else throw new InvalidOperationException();
			}
			return S.Peek();
		}
	}
}