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: Runtime Error)

using System.Collections;
using System.Text;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System;
using System.Numerics;
using System.IO.Pipes;

class Program
{
    #region Reader
    //static Vector2Int ReadVec2Int
    //{
    //    get
    //    {
    //        string[] s = Console.ReadLine().Split(' ');
    //        return new Vector2Int(int.Parse(s[0]), int.Parse(s[1]));
    //    }
    //}
    //static Vector2Int[] ReadVec2Ints(int n)
    //{
    //    List<Vector2Int> list = new List<Vector2Int>();
    //    for (int i = 0; i < n; ++i)
    //    {
    //        var ab = ReadInts;
    //        list.Add(new Vector2Int(ab[0], ab[1]));
    //    }
    //    return list.ToArray();
    //}
    //static HashSet<Vector2Int> ReadVec2IntHash(int n)
    //{
    //    HashSet<Vector2Int> hash = new HashSet<Vector2Int>();
    //    for (int i = 0; i < n; ++i)
    //    {
    //        var ab = ReadInts;
    //        hash.Add(new Vector2Int(ab[0], ab[1]));
    //    }
    //    return hash;
    //}
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine());
    static int[] ReadInts => Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine());
    static long[] ReadLongs => Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    static long[,] ReLongMatrix(int r, int c)
    {
        var mat = new long[r, c];
        for (int i = 0; i < r; ++i)
        {
            var x = ReadLongs;
            for (int j = 0; j < c; ++j)
            {
                mat[i, j] = x[j];
            }
        }
        return mat;
    }
    static Tuple<string, string>[] ReTupleStr(int n)
    {
        List<Tuple<string, string>> list = new List<Tuple<string, string>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadStrs;
            list.Add(new Tuple<string, string>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<long, long>[] ReTupleLong(int n)
    {
        List<Tuple<long, long>> list = new List<Tuple<long, long>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<long, long>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<int, int>[] ReadTupleInt(int n)
    {
        List<Tuple<int, int>> list = new List<Tuple<int, int>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            list.Add(new Tuple<int, int>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<double, double>[] ReTupleDouble(int n)
    {
        List<Tuple<double, double>> list = new List<Tuple<double, double>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<double, double>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Dictionary<int, HashSet<int>> ReAdjacencyList(int N, int M)
    {
        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 = ReadInts;
            dict[ab[0]].Add(ab[1]);
            dict[ab[1]].Add(ab[0]);
        }
        return dict;
    }
    #endregion
    static void Swap<T>(ref T a, ref T b)
    {
        T temp = a;
        a = b;
        b = temp;
    }
    static int mod = (int)Pow(10, 9) + 7;


    public static long GetInv(long a, long mod = 1000000007)
    {
        return PowerMod(a, mod - 2, mod);
    }
    public static long Combination(long a, long b, long mod = 1000000007)
    {
        if (b < 0 || b > a) return 0;
        if (b > a / 2) b = a - b;
        long numerator = Factorial(a, mod);
        long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

        return (numerator * GetInv(denominator, mod)) % mod;
    }
    public static long Factorial(long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return 1;
        long ans = n;
        for (int i = 2; i < n; i++)
        {
            ans = (ans * i) % mod;
        }

        return ans;
    }
    private static long PowerMod(long a, long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return a;

        long p = PowerMod(a, n / 2, mod);
        if (n % 2 == 1) return ((p * p) % mod * a) % mod;
        else return (p * p) % mod;
    }

    /// <summary>
    /// 最小公倍数
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long Lcm(long a, long b)
    {
        return a * b / Gcd(a, b);
    }


    /// <summary>
    /// 最大公約数
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }

    public struct Fish
    {
        public Fish(long a,long b)
        {
            A = a;
            B = b;
        }
        public long A;
        public long B;

    }

    static void Main()
    {
        int N = ReadInt;
        long[][] fish = new long[N][];

        Dictionary<Fish, int> fishMap = new Dictionary<Fish, int>();

        HashSet<Fish> set = new HashSet<Fish>();

        for (int i = 0; i < N; i++)
        {
            long[] AB = ReadLongs;
            if (AB[0] < -1)
            {
                AB[0] *= -1;
                AB[1] *= -1;
            }

            long g = Gcd(Abs(AB[0]), Abs(AB[1]));
            AB[0] /= g;
            AB[1] /= g;

            Fish f = new Fish(AB[0], AB[1]);

            if (fishMap.ContainsKey(f)) fishMap[f]++;
            else
            {
                fishMap.Add(f, 1);

                Fish ortho = new Fish(AB[1], AB[0] * -1);

                if (ortho.A < 0)
                {
                    ortho.A *= -1;
                    ortho.B *= -1;
                }

                if (fishMap.ContainsKey(ortho))
                {
                    if (!set.Contains(ortho))
                    {
                        set.Add(f);
                    }
                }
            }
        }


        List<long[]> pairs = new List<long[]>();

        foreach (Fish f in set)
        {
           
            Fish ortho = new Fish(f.B, f.A * -1);

            if (ortho.A < 0)
            {
                ortho.A *= -1;
                ortho.B *= -1;
            }

            pairs.Add(new long[2] { fishMap[f], fishMap[ortho] });
        }


        long ans = PowerMod(2, N)-1;
        for (int i = 0; i < pairs.Count; i++)
        {
            ans -= ((PowerMod(2, pairs[i][0] - 1) * PowerMod(2, pairs[i][1] - 1) * (N - pairs[i][0] - pairs[i][1])))%mod;
            if (ans < 0) ans += mod;
        }

        WriteLine(ans-1);
    }

}