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_rules !read_value {($iter :expr ,($($t :tt ) ,*) ) =>{($(read_value !($iter ,$t ) ) ,*) } ;($iter :expr ,[$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |read_value !($iter ,$t ) ) .collect ::<Vec <_ >>() } ;($iter :expr ,{chars :$base :expr } ) =>{read_value !($iter ,String ) .chars () .map (|c |(c as u8 -$base as u8 ) as usize ) .collect ::<Vec <usize >>() } ;($iter :expr ,{char :$base :expr } ) =>{read_value !($iter ,{chars :$base } ) [0 ] } ;($iter :expr ,chars ) =>{read_value !($iter ,String ) .chars () .collect ::<Vec <char >>() } ;($iter :expr ,char ) =>{read_value !($iter ,chars ) [0 ] } ;($iter :expr ,usize1 ) =>{read_value !($iter ,usize ) -1 } ;($iter :expr ,$t :ty ) =>{$iter .next () .unwrap () .parse ::<$t >() .unwrap () } ;}
macro_rules !input_inner {($iter :expr ) =>{} ;($iter :expr ,) =>{} ;($iter :expr ,mut $var :ident :$t :tt $($r :tt ) *) =>{let mut $var =read_value !($iter ,$t ) ;input_inner !{$iter $($r ) *} } ;($iter :expr ,mut $var :ident $($r :tt ) *) =>{input_inner !{$iter ,mut $var :usize $($r ) *} } ;($iter :expr ,$var :ident :$t :tt $($r :tt ) *) =>{let $var =read_value !($iter ,$t ) ;input_inner !{$iter $($r ) *} } ;($iter :expr ,$var :ident $($r :tt ) *) =>{input_inner !{$iter ,$var :usize $($r ) *} } ;}
macro_rules !input {(source =$s :expr ,$($r :tt ) *) =>{let mut iter =$s .split_whitespace () ;input_inner !{iter ,$($r ) *} } ;(iter =$iter :ident ,$($r :tt ) *) =>{let s ={use std ::io ::Read ;let mut s =String ::new () ;std ::io ::stdin () .read_to_string (&mut s ) .unwrap () ;s } ;let mut $iter =s .split_whitespace () ;input_inner !{$iter ,$($r ) *} } ;($($r :tt ) *) =>{let s ={use std ::io ::Read ;let mut s =String ::new () ;std ::io ::stdin () .read_to_string (&mut s ) .unwrap () ;s } ;let mut iter =s .split_whitespace () ;input_inner !{iter ,$($r ) *} } ;}
pub trait Modulo: Copy {
    const MODULO: u32;
    #[inline]
    fn modulo(x: u32) -> u32 {
        x % Self::MODULO
    }
}
pub mod modulos {
    use super::*;
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo1000000007 {}
    impl Modulo for Modulo1000000007 {
        const MODULO: u32 = 1_000_000_007;
    }
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo1000000009 {}
    impl Modulo for Modulo1000000009 {
        const MODULO: u32 = 1_000_000_009;
    }
    #[derive(Clone, Copy, Debug, Default, Eq, Hash, Ord, PartialEq, PartialOrd)]
    pub struct Modulo998244353 {}
    impl Modulo for Modulo998244353 {
        const MODULO: u32 = 998_244_353;
    }
}
#[derive(Copy, Clone, Debug, Default, PartialEq, Eq, Hash)]
pub struct Modu32<M = modulos::Modulo1000000007>
where
    M: Modulo,
{
    x: u32,
    phantom: std::marker::PhantomData<M>,
}
impl<M: Modulo> Modu32<M> {
    #[inline]
    pub fn new(x: u32) -> Self {
        Self {
            x: M::modulo(x),
            phantom: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn new_unchecked(x: u32) -> Self {
        Self {
            x,
            phantom: std::marker::PhantomData,
        }
    }
    #[inline]
    pub fn one() -> Self {
        Self::new_unchecked(1)
    }
    #[inline]
    pub fn zero() -> Self {
        Self::new_unchecked(0)
    }
    #[inline]
    pub fn get_mod() -> u32 {
        M::MODULO
    }
    #[inline]
    pub fn pow(mut self, mut y: usize) -> Self {
        let mut x = Self::one();
        while y > 0 {
            if y & 1 == 1 {
                x *= self;
            }
            self *= self;
            y >>= 1;
        }
        x
    }
    #[inline]
    pub fn inv(self) -> Self {
        let mut a = self.x;
        let (mut b, mut u, mut s) = (M::MODULO, 1, 0);
        let k = a.trailing_zeros();
        a >>= k;
        for _ in 0..k {
            if u & 1 == 1 {
                u += M::MODULO;
            }
            u /= 2;
        }
        while a != b {
            if b < a {
                std::mem::swap(&mut a, &mut b);
                std::mem::swap(&mut u, &mut s);
            }
            b -= a;
            if s < u {
                s += M::MODULO;
            }
            s -= u;
            let k = b.trailing_zeros();
            b >>= k;
            for _ in 0..k {
                if s & 1 == 1 {
                    s += M::MODULO;
                }
                s /= 2;
            }
        }
        Self::new_unchecked(s)
    }
}
pub mod modu32_impl {
    use super::*;
    use std::{
        fmt,
        iter::{Product, Sum},
        num::ParseIntError,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
        str::FromStr,
    };
    impl<M: Modulo> From<u32> for Modu32<M> {
        #[inline]
        fn from(x: u32) -> Self {
            Self::new(x)
        }
    }
    impl<M: Modulo> From<u64> for Modu32<M> {
        #[inline]
        fn from(x: u64) -> Self {
            Self::new_unchecked((x % M::MODULO as u64) as u32)
        }
    }
    impl<M: Modulo> Add for Modu32<M> {
        type Output = Self;
        #[inline]
        fn add(self, rhs: Self) -> Self::Output {
            let mut x = self.x + rhs.x;
            if x >= M::MODULO {
                x -= M::MODULO;
            }
            Self::new_unchecked(x)
        }
    }
    impl<M: Modulo> Sub for Modu32<M> {
        type Output = Self;
        #[inline]
        fn sub(self, rhs: Self) -> Self::Output {
            if self.x < rhs.x {
                Self::new_unchecked(self.x + M::MODULO - rhs.x)
            } else {
                Self::new_unchecked(self.x - rhs.x)
            }
        }
    }
    impl<M: Modulo> Mul for Modu32<M> {
        type Output = Self;
        #[inline]
        fn mul(self, rhs: Self) -> Self::Output {
            Self::new_unchecked((self.x as u64 * rhs.x as u64 % M::MODULO as u64) as u32)
        }
    }
    impl<M: Modulo> Div for Modu32<M> {
        type Output = Self;
        #[inline]
        fn div(self, rhs: Self) -> Self::Output {
            self * rhs.inv()
        }
    }
    impl<M: Modulo> Neg for Modu32<M> {
        type Output = Self;
        #[inline]
        fn neg(self) -> Self::Output {
            if self.x == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(M::MODULO - self.x)
            }
        }
    }
    impl<M: Modulo> Sum for Modu32<M> {
        #[inline]
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<M: Modulo> Product for Modu32<M> {
        #[inline]
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<'a, M: Modulo + 'a> Sum<&'a Modu32<M>> for Modu32<M> {
        #[inline]
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::zero(), Add::add)
        }
    }
    impl<'a, M: Modulo + 'a> Product<&'a Modu32<M>> for Modu32<M> {
        #[inline]
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::one(), Mul::mul)
        }
    }
    impl<M: Modulo> fmt::Display for Modu32<M> {
        fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
            write!(f, "{}", self.x)
        }
    }
    impl<M: Modulo> FromStr for Modu32<M> {
        type Err = ParseIntError;
        #[inline]
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            s.parse::<u32>().map(Self::new_unchecked)
        }
    }
    macro_rules! modu32_ref_binop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<'a, M: Modulo> $imp<$t> for &'a $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, other)
                }
            }
            impl<M: Modulo> $imp<&$t> for $t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(self, *other)
                }
            }
            impl<M: Modulo> $imp<&$t> for &$t {
                type Output = <$t as $imp<$t>>::Output;
                #[inline]
                fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
                    $imp::$method(*self, *other)
                }
            }
        };
    }
    modu32_ref_binop!(Add, add, Modu32<M>);
    modu32_ref_binop!(Sub, sub, Modu32<M>);
    modu32_ref_binop!(Mul, mul, Modu32<M>);
    modu32_ref_binop!(Div, div, Modu32<M>);
    macro_rules! modu32_ref_unop {
        ($imp :ident ,$method :ident ,$t :ty ) => {
            impl<M: Modulo> $imp for &$t {
                type Output = <$t as $imp>::Output;
                #[inline]
                fn $method(self) -> <$t as $imp>::Output {
                    $imp::$method(*self)
                }
            }
        };
    }
    modu32_ref_unop!(Neg, neg, Modu32<M>);
    macro_rules! modu32_ref_op_assign {
        ($imp :ident ,$method :ident ,$t :ty ,$fromimp :ident ,$frommethod :ident ) => {
            impl<M: Modulo> $imp<$t> for $t {
                #[inline]
                fn $method(&mut self, rhs: $t) {
                    *self = $fromimp::$frommethod(*self, rhs);
                }
            }
            impl<M: Modulo> $imp<&$t> for $t {
                #[inline]
                fn $method(&mut self, other: &$t) {
                    $imp::$method(self, *other);
                }
            }
        };
    }
    modu32_ref_op_assign!(AddAssign, add_assign, Modu32<M>, Add, add);
    modu32_ref_op_assign!(SubAssign, sub_assign, Modu32<M>, Sub, sub);
    modu32_ref_op_assign!(MulAssign, mul_assign, Modu32<M>, Mul, mul);
    modu32_ref_op_assign!(DivAssign, div_assign, Modu32<M>, Div, div);
}
pub fn gcd(mut a: i64, mut b: i64) -> i64 {
    while b != 0 {
        a %= b;
        std::mem::swap(&mut a, &mut b);
    }
    a
}
type M = Modu32<modulos::Modulo1000000007>;
fn main() {
    input! { n, ab: [(i64, i64); n] };
    let mut mp = std::collections::HashMap::new();
    let mut zz = 0;
    let mut az = 0;
    let mut zb = 0;
    for t in ab.iter().map(|&(a, b)| {
        let (a, t1) = if a < 0 { (-a, true) } else { (a, false) };
        let (b, t2) = if b < 0 { (-b, true) } else { (b, false) };
        let g = gcd(a, b);
        if g == 0 {
            (0, 0, false)
        } else {
            (a / g, b / g, t1 ^ t2)
        }
    }) {
        if t.0 == 0 && t.1 == 0 {
            zz += 1;
        } else if t.0 == 0 {
            zb += 1;
        } else if t.1 == 0 {
            az += 1;
        } else {
            *mp.entry(t).or_insert(0) += 1;
        }
    }
    let mut ans = M::new(2).pow(az as usize) + M::new(2).pow(zb as usize) - M::one();
    let k = M::new(zz);
    let mut used = std::collections::HashSet::new();
    for (&(a, b, t), &v) in mp.iter() {
        if used.contains(&(a, b, t)) {
            continue;
        }
        if let Some(&v2) = mp.get(&(b, a, !t)) {
            ans *= M::new(2).pow(v as usize) + M::new(2).pow(v2 as usize) - M::one();
            used.insert((b, a, !t));
        } else {
            ans *= M::new(2).pow(v as usize);
        }
    }
    println!("{}", ans - M::one() + k);
}