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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.util.*

class Scanner(`in`: java.io.InputStream) {
    private val reader = java.io.BufferedReader(java.io.InputStreamReader(`in`))
    private var tokenizer: StringTokenizer? = null

    fun next(): String {
        if (tokenizer?.hasMoreTokens() != true) {
            tokenizer = StringTokenizer(reader.readLine())
        }
        return tokenizer!!.nextToken()
    }

    fun nextInt() = next().toInt()

    fun nextLong() = next().toLong()

    fun nextLine(): String {
        return if (tokenizer?.hasMoreTokens() != true) {
            reader.readLine()
        } else tokenizer!!.nextToken("\n")
    }
}

fun main(args: Array<String>) {
    val pw = java.io.PrintWriter(System.out)
    Problem.solve(Scanner(System.`in`), pw)
    pw.flush()
}

fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)

data class P(val a: Long, val b: Long)

data class ModInt(var value: Long) {
    init {
        assert(value in 0 until MOD)
    }

    override fun toString(): String = value.toString()

    // 加減乗算は結果を毎回 mod P すれば良い
    operator fun plus(b: Long): ModInt =
        ModInt((this.value + b) % MOD)

    operator fun plus(b: Int): ModInt =
        ModInt((this.value + b) % MOD)

    operator fun plus(b: ModInt): ModInt =
        ModInt((this.value + b.value) % MOD)

    operator fun plusAssign(b: Long) {
        this.value += b
        this.value %= MOD
    }

    operator fun plusAssign(b: Int) {
        this.value += b
        this.value %= MOD
    }

    operator fun plusAssign(b: ModInt) {
        this.value += b.value
        this.value %= MOD
    }

    operator fun minus(b: Long): ModInt =
        ModInt((this.value + MOD - b) % MOD)

    operator fun minus(b: Int): ModInt =
        ModInt((this.value + MOD - b) % MOD)

    operator fun minus(b: ModInt): ModInt =
        ModInt((this.value + (MOD - b.value)) % MOD)

    operator fun minusAssign(b: Long) {
        this.value += MOD - b
        this.value %= MOD
    }

    operator fun minusAssign(b: Int) {
        this.value += MOD - b
        this.value %= MOD
    }

    operator fun minusAssign(b: ModInt) {
        this.value += MOD - b.value
        this.value %= MOD
    }

    operator fun times(b: Long): ModInt =
        ModInt((this.value * b) % MOD)

    operator fun times(b: Int): ModInt =
        ModInt((this.value * b) % MOD)

    operator fun times(b: ModInt): ModInt =
        ModInt((this.value * b.value) % MOD)

    operator fun timesAssign(b: Long) {
        this.value *= b
        this.value %= MOD
    }

    operator fun timesAssign(b: Int) {
        this.value *= b
        this.value %= MOD
    }

    operator fun timesAssign(b: ModInt) {
        this.value *= b.value
        this.value %= MOD
    }

    // b で割る = 1/b を掛ける
    // フェルマーの小定理から、b の逆数 1/b (mod P) = b^(P-2)
    operator fun div(b: Long): ModInt =
        this * ModInt(b).pow(MOD - 2)

    operator fun div(b: Int): ModInt =
        this * ModInt(b.toLong()).pow(MOD - 2)

    operator fun div(b: ModInt): ModInt =
        this * b.pow(MOD - 2)

    operator fun divAssign(b: Long) {
        this *= ModInt(b).pow(MOD - 2)
    }

    operator fun divAssign(b: Int) {
        this *= ModInt(b.toLong()).pow(MOD - 2)
    }

    operator fun divAssign(b: ModInt) {
        this *= b.pow(MOD - 2)
    }

    fun inv() = pow(MOD - 2)

    // 累乗 (mod P)
    // 計算量は O(log p)
    fun pow(p: Long): ModInt = when {
        p == 0L -> ModInt(1)
        p % 2 == 1L -> this * this.pow(p - 1)
        else -> {
            val half = this.pow(p / 2)
            half * half
        }
    }

    companion object {
        const val MOD = 1000000007L
    }
}

object Problem {
    fun toP(a0: Long, b0: Long): Pair<P, Boolean> {
        var a = a0
        var b = b0
        when {
            b == 0L -> a = 1 // (x, 0) => (1, 0)
            a == 0L -> b = 1 // (0, x) => (0, 1)
            b < 0 -> { // b は必ず正にそろえる
                a = -a; b = -b
            }
        }
        val rot = a <= 0
        if (rot) {
            val tmp = -a
            a = b
            b = tmp
        }
        val g = Math.abs(gcd(a, b))
        return Pair(P(a / g, b / g), rot)
    }

    fun solve(sc: Scanner, pw: java.io.PrintWriter) {
        val N = sc.next().toInt()
        var z = 0L
        val count = mutableMapOf<P, Pair<Long, Long>>()
        repeat(N) {
            val a = sc.next().toLong()
            val b = sc.next().toLong()
            if (a == 0L && b == 0L) {
                // (0,0) だけ特別
                z++
            } else {
                val (p, rot) = toP(a, b)
                if (!count.containsKey(p)) count[p] = Pair(0L, 0L)
                var (c1, c2) = count[p]!!
                if (!rot) c1++ else c2++
                count[p] = Pair(c1, c2)
            }
        }
//        dprint(count)
        val ans = ModInt(1L)
        count.forEach { c ->
            val n = ((ModInt(2L).pow(c.value.first)) - 1) +
                    ((ModInt(2L).pow(c.value.second)) - 1) + 1
            ans *= n
        }
        ans += z
        ans -= 1
        pw.println(ans)
    }
}