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: Accepted)

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

namespace Contest
{
  class Program
  {
    static void Main(string[] args)
    {
      ABC168.E();
    }
    class ABC168
    {
      public static void A()
      {
        var N = Read.Int();
        switch (N % 10)
        {
          case 0:
          case 1:
          case 6:
          case 8:
            Console.WriteLine("pon");return;
          case 3:
            Console.WriteLine("bon");return;
          case 2:
          case 4:
          case 5:
          case 7:
          case 9:
            Console.WriteLine("hon");return;
        }
      }
      public static void B()
      {
        var K = Read.Int();
        var S = Read.Str();
        Console.WriteLine(S.Length <= K ? S : S.Substring(0, K) + "...");
      }
      public static void C()
      {
        var A = Read.Int();
        var B = Read.Int();
        var H = Read.Int();
        var M = Read.Int();
        var r1 = Math.PI * (H * 60 + M) / 360;
        var r2 = Math.PI * M / 30;
        var x1 = Math.Cos(r1) * A;
        var y1 = Math.Sin(r1) * A;
        var x2 = Math.Cos(r2) * B;
        var y2 = Math.Sin(r2) * B;
        Console.WriteLine(Math.Sqrt(Math.Max(0, (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2))));
      }
      public static void D()
      {
        var N = Read.Int();
        var M = Read.Int();
        var Adj = Read.AdjacencyList(N, M);
        var ans = Enumerable.Range(0, N + 1).Select(i => -1).ToArray();
        var queue = new Queue<int>();
        queue.Enqueue(1);
        while (queue.Count > 0)
        {
          var v = queue.Dequeue();
          foreach(var w in Adj[v])
          {
            if (ans[w] >= 0) { continue; }
            ans[w] = v;
            queue.Enqueue(w);
          }
        }
        if (ans.Skip(2).Count(x => x < 0) > 0) { Console.WriteLine("No"); return; }
        Console.WriteLine("Yes");
        Console.WriteLine(String.Join(Environment.NewLine, ans.Skip(2)));
      }
      public static void E()
      {
        var N = Read.Int();
        var AB = Read.TupleLong(N);
        var Zero = new List<Tuple<long, long>>();
        var D1 = new List<Tuple<long, long>>();
        var D2 = new List<Tuple<long, long>>();

        var count1 = new Dictionary<long, Dictionary<long, long>>();
        var count2 = new Dictionary<long, Dictionary<long, long>>();

        foreach (var t in AB)
        {
          var X = t.Item1;
          var Y = t.Item2;
          if (X == 0 && Y == 0) { Zero.Add(new Tuple<long, long>(0, 0)); continue; }
          if (Y < 0)
          {
            X *= -1;
            Y *= -1;
          }
          var gcd = Util.GCD(Math.Abs(X), Y);
          X /= gcd;
          Y /= gcd;
          if (Y == 0) { X = 1; }
          if (X == 0) { Y = 1; }
          if (X > 0)
          {
            if (!count1.ContainsKey(X)) { count1.Add(X, new Dictionary<long, long>()); }
            if (!count1[X].ContainsKey(Y)) { count1[X].Add(Y, 0); }
            count1[X][Y]++;
          }
          else
          {
            if (!count2.ContainsKey(X)) { count2.Add(X, new Dictionary<long, long>()); }
            if (!count2[X].ContainsKey(Y)) { count2[X].Add(Y, 0); }
            count2[X][Y]++;
          }
        }

        MOD two = 2;
        MOD ans = 1;
        foreach(var kvp1 in count1)
        {
          foreach(var kvp2 in kvp1.Value)
          {
            var X = kvp1.Key;
            var Y = kvp2.Key;
            var C = kvp2.Value;
            if (count2.ContainsKey(-Y) && count2[-Y].ContainsKey(X))
            {
              var C2 = count2[-Y][X];
              count2[-Y][X] = 0;
              ans = ans * (two.Power(C) + two.Power(C2) - 1);
            }
            else
            {
              ans = ans * (two.Power(C) - 0);
            }
          }
        }
        foreach (var kvp1 in count2)
        {
          foreach (var kvp2 in kvp1.Value)
          {
            ans = ans * two.Power(kvp2.Value);
          }
        }
        Console.WriteLine((ans + Zero.Count - 1).V);
      }
      public static void F()
      {

      }
    }


    class Util
    {
      public static long[] ASum(long[] array)
      {
        var res = new long[array.Length + 1];
        for (int i = 0; i < array.Length; ++i)
        {
          res[i + 1] = res[i] + array[i];
        }
        return res;
      }
      public static Dictionary<T, long> Frequency<T>(T[] array)
      {
        var dict = new Dictionary<T, long>();
        foreach (var a in array)
        {
          if (!dict.ContainsKey(a)) { dict.Add(a, 0); }
          dict[a]++;
        }
        return dict;
      }
      public static long GCD(long a, long b)
      {
        while (b > 0)
        {
          var c = a % b;
          a = b;
          b = c;
        }
        return a;
      }
    }
    struct MOD
    {
      public static long P = 1000000007;
      public readonly long V;

      public MOD(long a) { this.V = a % P; }
      public static implicit operator MOD(long a) { return new MOD(a); }
      public static MOD operator +(MOD a, MOD b) { return new MOD((a.V + b.V) % P); }
      public static MOD operator -(MOD a, MOD b) { return new MOD((a.V - b.V + P) % P); }
      public static MOD operator *(MOD a, MOD b) { return new MOD((a.V * b.V) % P); }
      public static MOD operator /(MOD a, MOD b) { return new MOD((a.V * b.Inverse().V) % P); }
      public MOD Inverse()
      {
        long a = V, p = P; long b = p, c = 1, d = 0, e = 0, f = 0;
        while (b != 0) { e = a / b; f = b; b = a - e * b; a = f; f = d; d = c - e * d; c = f; }
        c %= p;
        return c + (c < 0 ? p : 0);
      }
      public MOD Power(long n)
      {
        long a = V, p = P; long res = 1; long mult = a;
        for (int i = 0; i < 63; ++i) { if ((n & ((long)1 << i)) > 0) { res = (res * mult) % p; } mult = (mult * mult) % p; }
        return res;
      }
      public override string ToString() { return V.ToString(); }
    }


    static class Read
{
static Queue<string> queue = new Queue<string>();
static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
public static string[] StrN() { return Console.ReadLine().Split(' '); }
public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
public static long[,] LongMatrix(int r, int c) { var mat = new long[r, c]; for (int i = 0; i < r; ++i) { var x = Read.LongN(); for (int j = 0; j < c; ++j) { mat[i, j] = x[j]; } } return mat; }
public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
{
Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
        for (int i = 0; i < M; ++i) { var ab = Read.IntN(); if (!dict[ab[0]].Contains(ab[1])) { dict[ab[0]].Add(ab[1]); } if (!isDirectional && !dict[ab[1]].Contains(ab[0])) { dict[ab[1]].Add(ab[0]); } }
        return dict;
}
public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
{
Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>(); for (int i = 0; i <= N; ++i) { dict.Add(i, new Dictionary<int, long>()); }
for (int i = 0; i < M; ++i) { var ab = Read.IntN(); dict[ab[0]].Add(ab[1], ab[2]); dict[ab[1]].Add(ab[0], ab[2]); }
return dict;
}
}
    }
}