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: Runtime Error)

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};
#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let cin = stdin();
    let cin = cin.lock();
    let s: String = cin
        .bytes() // Bytes
        .map(|c| c.expect("failed reading char") as char)
        .skip_while(|c| c.is_whitespace()) // c が whitespace である限り skip
        .take_while(|c| !c.is_whitespace()) // c が whitespace でない限り要素を返す
        .collect();
    s.parse().ok().expect("failed parsing")
}

fn gcd(x: usize, y: usize) -> usize {
    if y > 0 {
        gcd(y, x % y)
    } else {
        x
    }
}

mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy {
        fn m() -> i64;
    }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> {
        pub x: i64,
        phantom: ::std::marker::PhantomData<M>,
    }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self {
            ModInt::new_internal(x % M::m())
        }
        fn new_internal(x: i64) -> Self {
            ModInt {
                x: x,
                phantom: ::std::marker::PhantomData,
            }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 {
                    sum *= cur;
                }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self {
            self.pow(M::m() - 2)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() {
                sum -= M::m();
            }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 {
                sum += M::m();
            }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self {
            ModInt::new(self.x * other.into().x % M::m())
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) {
            *self = *self + other;
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) {
            *self = *self - other;
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) {
            *self = *self * other;
        }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self {
            ModInt::new(0) - self
        }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self {
            Self::new(x)
        }
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        struct $struct_name {}
        impl mod_int::Mod for $struct_name {
            fn m() -> i64 {
                $modulo
            }
        }
    };
}
const MOD: i64 = 1000000007;
define_mod!(P, MOD);
type ModInt = mod_int::ModInt<P>;

#[allow(non_snake_case)]
fn main() {
    input! {
        N:usize,
        AB:[(isize,isize);N]
    }
    let mut x = HashMap::new();
    for (a, b) in &AB {
        let g = gcd(a.abs() as usize, b.abs() as usize);
        let a = a / g as isize;
        let b = b / g as isize;
        if a as i128 * b as i128 > 0 {
            *x.entry((1, a.abs(), b.abs())).or_insert(0) += 1;
        } else {
            *x.entry((-1, b.abs(), a.abs())).or_insert(0) += 1;
        }
    }
    let mut ans = ModInt::new(1);
    let mut vis = HashSet::new();
    for ((f, a, b), v) in &x {
        if vis.contains(&(*f, *a, *b)) {
            continue;
        }
        vis.insert((*f, *a, *b));
        vis.insert((-*f, *a, *b));
        let mut t = ModInt::new(0);
        t += ModInt::new(2).pow(*x.get(&(*f, *a, *b)).unwrap() as i64);
        if x.contains_key(&(-*f, *a, *b)) {
            t += ModInt::new(2).pow(*x.get(&(-*f, *a, *b)).unwrap() as i64);
            t -= 1;
        }
        ans *= t;
    }
    ans -= 1;
    println!("{}", ans);
}