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: Accepted)

#[macro_use]
mod input_mcr {
    // ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
    // diff: using Parser
    #[macro_export(local_inner_macros)]
    macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

    #[macro_export(local_inner_macros)]
    macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, line) => {
        $parser.next_line()
    };
    ($parser:ident, line_) => {
        $parser.next_line().chars().collect::<Vec<char>>()
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

    use std::io;
    use std::io::BufRead;
    use std::str;

    // ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
    // ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
    // diff: using std::io::BufRead::fill_buf()
    pub struct Parser<R> {
        pub reader: R,
        buf: Vec<u8>,
        pos: usize,
    }

    impl Parser<io::Empty> {
        pub fn from_str(s: &str) -> Parser<io::Empty> {
            Parser {
                reader: io::empty(),
                buf: s.as_bytes().to_vec(),
                pos: 0,
            }
        }
    }

    impl<R: BufRead> Parser<R> {
        pub fn new(reader: R) -> Parser<R> {
            Parser {
                reader: reader,
                buf: vec![],
                pos: 0,
            }
        }
        pub fn update_buf(&mut self) {
            self.buf.clear();
            self.pos = 0;
            loop {
                let (len, complete) = {
                    let buf2 = self.reader.fill_buf().unwrap();
                    self.buf.extend_from_slice(buf2);
                    let len = buf2.len();
                    (len, buf2[len - 1] <= 0x20)
                };
                self.reader.consume(len);
                if complete {
                    break;
                }
            }
        }
        pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn next_line(&mut self) -> String {
            loop {
                let mut begin = self.pos;
                if begin < self.buf.len() && (self.buf[begin] < 0x20) {
                    begin += 1;
                }
                let mut end = begin;
                while end < self.buf.len() && (self.buf[end] >= 0x20) {
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.to_string();
                } else {
                    self.update_buf();
                }
            }
        }
        pub fn fast_i64(&mut self) -> i64 {
            loop {
                let mut begin = self.pos;
                while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                    begin += 1;
                }
                if begin == self.buf.len() {
                    self.update_buf();
                    continue;
                }
                let mut res = 0;
                let (is_positive, mut end) = match self.buf[begin] {
                    b'+' => (true, begin + 1),
                    b'-' => (false, begin + 1),
                    _ => (true, begin),
                };
                while end < self.buf.len() && (self.buf[end] > 0x20) {
                    res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                    end += 1;
                }
                if begin != self.buf.len() {
                    self.pos = end;
                    return if is_positive { res } else { -res };
                } else {
                    self.update_buf();
                }
            }
        }
    }
}

mod modular {
    use std::marker::PhantomData;
    use std::ops::*;

    pub trait ModP {
        fn as_u64() -> u64;
    }

    #[allow(non_camel_case_types)]
    #[derive(Clone, Copy, Debug)]
    pub struct Mod_1_000_000_007();
    impl ModP for Mod_1_000_000_007 {
        fn as_u64() -> u64 {
            1_000_000_007
        }
    }

    #[allow(non_camel_case_types)]
    #[derive(Clone, Copy, Debug)]
    pub struct Mod_998_244_353();
    impl ModP for Mod_998_244_353 {
        fn as_u64() -> u64 {
            998_244_353
        }
    }

    #[derive(Clone, Copy, PartialEq, Debug)]
    pub struct Modular<P: ModP + Copy>(u32, PhantomData<P>);

    impl<P: ModP + Copy> Modular<P> {
        pub fn new(x: u32) -> Modular<P> {
            Modular((x as u64 % P::as_u64()) as u32, PhantomData)
        }
        pub fn pow(self, n: u64) -> Modular<P> {
            if n == 0 {
                return Modular(1, PhantomData);
            }
            let t = self.pow(n / 2);
            if n % 2 == 0 {
                t * t
            } else {
                t * t * self
            }
        }
        pub fn as_u32(self) -> u32 {
            self.0
        }
    }

    impl<P: ModP + Copy> Add for Modular<P> {
        type Output = Self;
        fn add(self, rhs: Self) -> Self::Output {
            let t = (self.0 + rhs.0) as u64;
            let u = if t < P::as_u64() { t } else { t - P::as_u64() };
            Modular(u as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> AddAssign for Modular<P> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<P: ModP + Copy> Sub for Modular<P> {
        type Output = Self;
        fn sub(self, rhs: Self) -> Self::Output {
            let t = if self.0 >= rhs.0 {
                self.0 as u64 - rhs.0 as u64
            } else {
                self.0 as u64 + P::as_u64() - rhs.0 as u64
            };
            assert!(t < P::as_u64());
            Modular(t as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> SubAssign for Modular<P> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<P: ModP + Copy> Neg for Modular<P> {
        type Output = Modular<P>;
        fn neg(self) -> Modular<P> {
            Modular((P::as_u64() - self.0 as u64) as u32, PhantomData)
        }
    }

    impl<P: ModP + Copy> Mul for Modular<P> {
        type Output = Self;
        fn mul(self, rhs: Self) -> Self::Output {
            Modular(
                ((self.0 as u64 % P::as_u64()) * (rhs.0 as u64 % P::as_u64()) % P::as_u64()) as u32,
                PhantomData,
            )
        }
    }

    impl<P: ModP + Copy> MulAssign for Modular<P> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<P: ModP + Copy> Div for Modular<P> {
        type Output = Self;
        fn div(self, rhs: Self) -> Self::Output {
            if rhs.0 == 0 {
                loop {}
            }
            assert!(rhs.0 != 0);
            self * rhs.pow(P::as_u64() - 2)
        }
    }

    impl<P: ModP + Copy> DivAssign for Modular<P> {
        fn div_assign(&mut self, rhs: Self) {
            *self = *self / rhs;
        }
    }

    pub fn gen_fact_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
        let mut res = vec![Modular::<P>::new(1); n + 1];
        for i in 0..n {
            res[i + 1] = res[i] * Modular::<P>::new((i + 1) as u32);
        }
        res
    }

    pub fn gen_inv_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
        let mut res = vec![Modular::<P>::new(0); n + 1];
        res[1] = Modular::<P>::new(1);
        for i in 2..n + 1 {
            res[i] =
                -res[P::as_u64() as usize % i] * Modular::<P>::new((P::as_u64() / i as u64) as u32);
        }
        res
    }

    /*
    #[test]
    fn test_modular_1_000_000_007() {
        type Mod = Modular<Mod_1_000_000_007>;
        assert_eq!(Mod::new(2).pow(1_000_000).as_u32(), 235_042_059)
    }

    #[test]
    fn test_modular_998_244_353() {
        type Mod = Modular<Mod_998_244_353>;
        assert_eq!(Mod::new(2).pow(1_000_000).as_u32(), 421_273_117);
    }
    */
}

mod gcd {
    use std;

    pub fn gcd<T>(x: T, y: T) -> T
    where
        T: PartialEq + Copy + std::ops::Rem<Output = T> + std::convert::From<u8>,
    {
        if y == T::from(0u8) {
            x
        } else {
            gcd(y, x % y)
        }
    }
}

use input_mcr::*;
use std::cmp::*;

use modular::*;
type Mod = Modular<Mod_1_000_000_007>;

use gcd::*;
use std::collections::BTreeMap;

fn main() {
    input! {
        n: usize,
        xs: [(i64,i64); n],
    }
    let mut map: BTreeMap<(i64, i64), (i64, i64)> = BTreeMap::new();
    let mut left_zero = 0;
    let mut right_zero = 0;
    let mut zero_zero = 0;
    for &(s, t) in &xs {
        if (s > 0 && t > 0) || (s < 0 && t < 0) {
            let u = gcd(s.abs(), t.abs());
            map.entry((s.abs() / u, t.abs() / u)).or_insert((0, 0)).0 += 1;
        } else if (s > 0 && t < 0) || (s < 0 && t > 0) {
            let u = gcd(s.abs(), t.abs());
            map.entry((t.abs() / u, s.abs() / u)).or_insert((0, 0)).1 += 1;
        } else {
            if s == 0 && t != 0 {
                left_zero += 1;
            }
            if s != 0 && t == 0 {
                right_zero += 1;
            }
            if s == 0 && t == 0 {
                zero_zero += 1;
            }
        }
    }
    // eprintln!("{:?}", map);
    let mut res = Mod::new(1);
    for (key, &(s, t)) in &map {
        res *= Mod::new(2).pow(s as u64) + Mod::new(2).pow(t as u64) - Mod::new(1);
    }
    res *= Mod::new(2).pow(left_zero as u64) + Mod::new(2).pow(right_zero as u64) - Mod::new(1);
    res -= Mod::new(1);
    res += Mod::new(zero_zero as u32);
    println!("{}", res.as_u32());
}