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 Rust (1.42.0) (judge verdict: Wrong Answer)

#[allow(unused_imports)]
use proconio::{input, marker::*};

#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};

#[allow(unused_imports)]
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        #[cfg(debug_assertions)]
        writeln!(&mut std::io::stderr(), concat!("[DEBUG] ", $(stringify!($a), "={:?} "),*), $($a),*).unwrap();
    }
}

fn gcd(a: usize, b: usize) -> usize {
    if a == usize::default() {
        b
    } else {
        gcd(b % a, a)
    }
}

use self::modint::ModInt;
mod modint {
    use std;
    #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt(usize);
    impl ModInt {
        pub fn new(value: usize) -> Self {
            ModInt(value % Self::modulo())
        }
        fn modulo() -> usize {
            1_000_000_007
        }
        pub fn pow(&self, n: usize) -> Self {
            let mut res = ModInt::new(1);
            let mut beki = *self;
            let mut n = n;
            while n > 0 {
                if n % 2 == 1 {
                    res *= beki;
                }
                beki *= beki;
                n /= 2;
            }
            res
        }
    }
    impl std::ops::Add for ModInt {
        type Output = Self;
        fn add(self, other: Self) -> Self {
            let mut value = self.0 + other.0;
            if value > Self::modulo() {
                value -= Self::modulo();
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Add<usize> for ModInt {
        type Output = Self;
        fn add(self, other: usize) -> Self {
            let other = ModInt::new(other);
            self + other
        }
    }
    impl std::ops::Sub for ModInt {
        type Output = Self;
        fn sub(self, other: Self) -> Self {
            let mut value = self.0;
            if value < other.0 {
                value += Self::modulo();
            }
            value -= other.0;
            ModInt::new(value)
        }
    }
    impl std::ops::Sub<usize> for ModInt {
        type Output = Self;
        fn sub(self, other: usize) -> Self {
            let other = ModInt::new(other);
            self - other
        }
    }
    impl std::ops::Mul for ModInt {
        type Output = Self;
        fn mul(self, other: Self) -> Self {
            let value = self.0 * other.0 % Self::modulo();
            ModInt::new(value)
        }
    }
    impl std::ops::Mul<usize> for ModInt {
        type Output = Self;
        fn mul(self, other: usize) -> Self {
            let other = ModInt::new(other);
            self * other
        }
    }
    impl std::ops::Mul<ModInt> for usize {
        type Output = ModInt;
        fn mul(self, other: ModInt) -> Self::Output {
            let value = ModInt::new(self);
            value * other
        }
    }
    impl std::ops::Div for ModInt {
        type Output = Self;
        fn div(self, other: Self) -> Self {
            let mut exp = Self::modulo() - 2;
            let mut value = self.0;
            let mut ovalue = other.0;
            while exp > 0 {
                if exp % 2 == 1 {
                    value = value * ovalue % Self::modulo();
                }
                ovalue = ovalue * ovalue % Self::modulo();
                exp /= 2;
            }
            ModInt::new(value)
        }
    }
    impl std::ops::Div<usize> for ModInt {
        type Output = Self;
        fn div(self, other: usize) -> Self {
            let other = ModInt::new(other);
            self / other
        }
    }
    impl std::ops::AddAssign for ModInt {
        fn add_assign(&mut self, other: Self) {
            *self = *self + other;
        }
    }
    impl std::ops::AddAssign<usize> for ModInt {
        fn add_assign(&mut self, other: usize) {
            *self = *self + other;
        }
    }
    impl std::ops::SubAssign for ModInt {
        fn sub_assign(&mut self, other: Self) {
            *self = *self - other;
        }
    }
    impl std::ops::SubAssign<usize> for ModInt {
        fn sub_assign(&mut self, other: usize) {
            *self = *self - other;
        }
    }
    impl std::ops::MulAssign for ModInt {
        fn mul_assign(&mut self, other: Self) {
            *self = *self * other;
        }
    }
    impl std::ops::MulAssign<usize> for ModInt {
        fn mul_assign(&mut self, other: usize) {
            *self = *self * other;
        }
    }
    impl std::ops::DivAssign for ModInt {
        fn div_assign(&mut self, other: Self) {
            *self = *self / other;
        }
    }
    impl std::ops::DivAssign<usize> for ModInt {
        fn div_assign(&mut self, other: usize) {
            *self = *self / other;
        }
    }
    impl std::fmt::Debug for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
    impl std::fmt::Display for ModInt {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }
}

fn main() {
    input! {
        n: usize,
        ab: [(isize,isize);n],
    }

    let ab = ab
        .into_iter()
        .filter(|&(a, b)| a != 0 || b != 0)
        .collect::<Vec<_>>();

    let mut map = BTreeMap::new();
    for (a, b) in ab.into_iter() {
        let g = gcd(a.abs() as usize, b.abs() as usize) as isize;
        let (a, b) = if g > 0 { (a / g, b / g) } else { (a, b) };
        *map.entry((a, b)).or_insert(0) += 1;
    }
    let mut checked = BTreeSet::new();
    let mut res = ModInt::new(1);
    for (&(a, b), &left) in &map {
        if checked.contains(&(a, b)) {
            continue;
        }
        checked.insert((b, -a));
        checked.insert((-b, a));
        let right =
            map.get(&(b, -a)).cloned().unwrap_or(0) + map.get(&(-b, a)).cloned().unwrap_or(0);
        debug!(a, b, left, right);
        res *= ModInt::new(2).pow(left) + ModInt::new(2).pow(right) - 1;
    }
    println!("{}", res - 1);
}