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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"math/big"
	"os"
	"strconv"
	"strings"
)

var sc = bufio.NewScanner(os.Stdin)

var mod int64 = 1000000007

func modPow2(num int64) int64 {
	if num == 0 {
		return 1
	}

	var rtn int64
	rtn = 1
	for i := 0; int64(i) < num; i++ {
		rtn = (rtn << 1) % mod
	}
	return rtn
}

func main() {
	N := getStdinInt()
	hash1 := make(map[string]int64)
	hash2 := make(map[string]string)
	var zero int64 = 0
	for i := 0; i < N; i++ {
		list := getStdinIntArr()
		A := int64(list[0])
		B := int64(list[1])
		if A == 0 && B == 0 {
			zero++
		} else if B == 0 {
			hash1["1/0"]++
			hash2["1/0"] = "0/1"
		} else if A == 0 {
			hash1["0/1"]++
			hash2["0/1"] = "1/0"
		} else {
			rat1 := big.NewRat(A, B)
			rat2 := big.NewRat(-B, A)
			hash1[fmt.Sprint(rat1)]++
			hash2[fmt.Sprint(rat1)] = fmt.Sprint(rat2)
		}
	}

	var ans int64 = 1
	for idx, val1 := range hash1 {
		if val1 == -1 {
			continue
		}
		var val2 int64 = hash1[hash2[idx]]	// 仲の悪い相方
		var tmp1 int64 = (modPow2(val1) - 1) % mod
		var tmp2 int64 = (modPow2(val2) - 1) % mod
		var tmp3 int64 = 1
		hash1[idx] = -1			// 重複を避ける
		hash1[hash2[idx]] = -1
		ans = (ans * (tmp1 + tmp2 + tmp3)) % mod
	}
	ans = (ans + zero - 1) % mod
	fmt.Printf("%d", ans)

	fmt.Printf("\n")
}

func getStdin() string {
	sc.Scan()
	return sc.Text()
}
func getStdinInt() int {
	sc.Scan()
	rtn, _ := strconv.Atoi(sc.Text())
	return rtn
}
func getStdinIntArr() []int {
	sc.Scan()
	str := sc.Text()
	list := strings.Split(str, " ")
	rtn := make([]int, len(list))
	for idx, val := range list {
		rtn[idx], _ = strconv.Atoi(val)
	}
	return rtn
}