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)

use crate::mod_int::ModInt;
use std::collections::{BTreeMap, BTreeSet};

const MOD: u64 = 1e9 as u64 + 7;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let mut count_map = BTreeMap::new();

    let mut zero = 0;
    let mut a_zero = 0;
    let mut b_zero = 0;

    for _ in 0..n {
        let a: i64 = sc.read();
        let b: i64 = sc.read();
        if a == 0 && b == 0 {
            zero += 1;
        } else if a == 0 {
            a_zero += 1;
        } else if b == 0 {
            b_zero += 1;
        } else {
            let a = if a >= 0 {
                ModInt::new(a as u64)
            } else {
                ModInt::new(0) - ModInt::new((-a) as u64)
            };
            let b = if b >= 0 {
                ModInt::new(b as u64)
            } else {
                ModInt::new(0) - ModInt::new((-b) as u64)
            };
            let c = a / b;
            count_map.entry(c.v).and_modify(|a| *a += 1).or_insert(1);
        }
    }

    let mut vis = BTreeSet::new();
    let mut pairs = vec![(a_zero, b_zero)];
    for (&c, &count1) in count_map.iter() {
        if vis.contains(&c) {
            continue;
        }
        let other = ModInt::new(0) - ModInt::new(1) / c;
        vis.insert(c);
        vis.insert(other.v);

        let other = *count_map.get(&other.v).unwrap_or(&0);
        pairs.push((count1, other));
    }

    let mut ans = ModInt::new(zero + 1);
    for (c1, c2) in pairs.into_iter() {
        let sum = ModInt::new(2).pow(c1) + ModInt::new(2).pow(c2) - 1;
        ans *= sum;
    }
    ans -= 1;

    println!("{}", ans.v);
}
pub mod mod_int {
    use crate::MOD;
    use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Rem, Sub, SubAssign};

    pub struct ModInt<T> {
        pub v: T,
        pub modulo: T,
    }

    impl<T> Copy for ModInt<T> where T: Copy {}
    impl<T> Clone for ModInt<T>
    where
        T: Copy,
    {
        fn clone(&self) -> Self {
            ModInt {
                v: self.v,
                modulo: self.modulo,
            }
        }
    }

    impl<T> Add<T> for ModInt<T>
    where
        T: Add<Output = T> + Sub<Output = T> + Rem<Output = T> + Copy + PartialOrd,
    {
        type Output = ModInt<T>;
        fn add(self, mut rhs: T) -> ModInt<T> {
            if rhs >= self.modulo {
                rhs = rhs % self.modulo;
            }
            let mut t = rhs + self.v;
            if t >= self.modulo {
                t = t - self.modulo;
            }
            ModInt {
                v: t,
                modulo: self.modulo,
            }
        }
    }

    impl<T> Add<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<T, Output = ModInt<T>>,
    {
        type Output = ModInt<T>;
        fn add(self, rhs: ModInt<T>) -> ModInt<T> {
            self + rhs.v
        }
    }

    impl<T> Sub<T> for ModInt<T>
    where
        T: Add<Output = T> + Sub<Output = T> + Rem<Output = T> + Copy + PartialOrd,
    {
        type Output = ModInt<T>;
        fn sub(self, rhs: T) -> ModInt<T> {
            let rhs = if rhs >= self.modulo {
                rhs % self.modulo
            } else {
                rhs
            };
            let value = if self.v < rhs {
                self.v + self.modulo
            } else {
                self.v
            };
            ModInt {
                v: value - rhs,
                modulo: self.modulo,
            }
        }
    }

    impl<T> Sub<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<T, Output = ModInt<T>>,
    {
        type Output = ModInt<T>;
        fn sub(self, rhs: ModInt<T>) -> ModInt<T> {
            self - rhs.v
        }
    }

    impl<T> AddAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<T, Output = ModInt<T>>,
    {
        fn add_assign(&mut self, other: T) {
            *self = *self + other;
        }
    }
    impl<T> AddAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Add<ModInt<T>, Output = ModInt<T>>,
    {
        fn add_assign(&mut self, other: ModInt<T>) {
            *self = *self + other;
        }
    }

    impl<T> SubAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<T, Output = ModInt<T>>,
    {
        fn sub_assign(&mut self, other: T) {
            *self = *self - other;
        }
    }

    impl<T> SubAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Sub<ModInt<T>, Output = ModInt<T>>,
    {
        fn sub_assign(&mut self, other: ModInt<T>) {
            *self = *self - other;
        }
    }

    impl<T> Div<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<T, Output = ModInt<T>>,
    {
        type Output = ModInt<T>;
        fn div(self, rhs: ModInt<T>) -> ModInt<T> {
            self / rhs.v
        }
    }

    impl<T> DivAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<T, Output = ModInt<T>>,
    {
        fn div_assign(&mut self, rhs: T) {
            *self = *self / rhs
        }
    }
    impl<T> DivAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Div<ModInt<T>, Output = ModInt<T>>,
    {
        fn div_assign(&mut self, rhs: ModInt<T>) {
            *self = *self / rhs
        }
    }

    impl<T> Mul<T> for ModInt<T>
    where
        T: Mul<Output = T> + Rem<Output = T> + Copy + PartialOrd,
    {
        type Output = ModInt<T>;

        fn mul(self, mut rhs: T) -> ModInt<T> {
            if rhs >= self.modulo {
                rhs = rhs % self.modulo;
            }
            let t = (self.v * rhs) % self.modulo;
            ModInt {
                v: t,
                modulo: self.modulo,
            }
        }
    }
    impl<T> Mul<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<T, Output = ModInt<T>>,
    {
        type Output = ModInt<T>;
        fn mul(self, rhs: ModInt<T>) -> ModInt<T> {
            self * rhs.v
        }
    }

    impl<T> MulAssign<T> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<T, Output = ModInt<T>>,
    {
        fn mul_assign(&mut self, rhs: T) {
            *self = *self * rhs;
        }
    }

    impl<T> MulAssign<ModInt<T>> for ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<ModInt<T>, Output = ModInt<T>>,
    {
        fn mul_assign(&mut self, rhs: ModInt<T>) {
            *self = *self * rhs;
        }
    }

    impl<T> ModInt<T>
    where
        T: Copy,
        ModInt<T>: Mul<ModInt<T>, Output = ModInt<T>>,
    {
        pub fn general_pow(self, e: u64, one: ModInt<T>) -> ModInt<T> {
            let mut result = one;
            let mut cur = self;
            let mut e = e;
            while e > 0 {
                if e & 1 == 1 {
                    result *= cur;
                }
                e >>= 1;
                cur *= cur;
            }
            result
        }
    }

    impl Div<u64> for ModInt<u64> {
        type Output = ModInt<u64>;
        fn div(self, mut rhs: u64) -> ModInt<u64> {
            if rhs >= self.modulo {
                rhs %= self.modulo;
            }
            self * ModInt {
                v: rhs,
                modulo: self.modulo,
            }
            .pow(self.modulo - 2)
        }
    }

    impl ModInt<u64> {
        pub fn new(v: u64) -> Self {
            Self {
                v: v % MOD,
                modulo: MOD,
            }
        }

        pub fn pow(self, e: u64) -> ModInt<u64> {
            self.general_pow(e, ModInt::new(1))
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> Self {
        Self(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}