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;

class Program
{
	static void Main() => new Program().Solve();

	void Solve()
	{
		var n = ReadLong();

		var d1 = new Dictionary<string, long>();
		var d2 = new Dictionary<string, long>();
		var size00 = 0L;

		for (var i = 0; i < n; i++) {
			var t = ReadLongArray();
			if (t[0] == 0 && t[1] == 0) {
				size00++;
				continue;
			}
			var a = Math.Abs(t[0]);
			var b = Math.Abs(t[1]);
			var key = "";
			if (a == 0) {
				key = "0/1";
			} else if (b == 0) {
				key = "1/0";
			} else {
				var k = (a > b) ? gcd(a, b) : gcd(b, a);
				key = (a / k) + "/" + (b / k);
			}
			if (t[0] > 0 ^ t[1] > 0) {
				if (!d1.ContainsKey(key)) d1[key] = 0;
				d1[key]++;
			} else {
				if (!d2.ContainsKey(key)) d2[key] = 0;
				d2[key]++;
			}
		}

		modlong size = 1;

		foreach (var key in d1.Keys) {
			var ab = key.Split('/');
			var rev = ab[1] + "/" + ab[0];
			if (d2.ContainsKey(rev)) {
				size *= modlong.Pow(2, d1[key]) + modlong.Pow(2, d2[rev]) - 1;
				d2.Remove(rev);
			} else {
				size *= modlong.Pow(2, d1[key]);
			}
		}

		foreach (var key in d2.Keys) {
			size *= modlong.Pow(2, d2[key]);
		}

		Console.WriteLine((long)size - 1 + size00);
	}

	/// <summary>最大公約数</summary>
	long gcd(long a, long b) => (a == 0) ? b : gcd(b % a, a);

	#region Console.Read 関係
	long[] ReadLongArray() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
	long ReadLong() => long.Parse(Console.ReadLine());
	#endregion
}

class modlong
{
	const long M = 1000000007;
	long value;
	modlong(long a) => value = a;
	public static modlong Pow(long a, long n)
	{
		var res = 1L;
		while (n > 0) {
			if ((n & 1) != 0) res = res * a % M;
			a = a * a % M;
			n >>= 1;
		}
		return res;
	}
	public static implicit operator modlong(long a) => new modlong(a);
	public static explicit operator long(modlong a) => a.value;
	public static modlong operator +(modlong a, modlong b) => (a.value + b.value) % M;
	public static modlong operator -(modlong a, modlong b) => (a.value + M - b.value) % M;
	public static modlong operator *(modlong a, modlong b) => (a.value * b.value) % M;
}