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)

#[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 mut $var = read_value!($next, $t);
        input_inner!{$next $($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>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
use std::hash::{Hash, Hasher};

// ---------- begin ModInt ----------

#[derive(Clone, Copy)]
struct ModInt(usize);
impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + MODu - rhs.0;
        if d >= MODu {
            d -= MODu;
        }
        ModInt(d)
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> Self::Output {
        ModInt((self.0 as u64 * rhs.0 as u64 % MODu as u64) as usize)
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> Self::Output {
        ModInt(if self.0 == 0 {0} else {MODu - self.0})
    }
}

impl std::fmt::Display for ModInt {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<usize>()?;
        Ok(ModInt::new(val))
    }
}
impl PartialEq for ModInt {
    fn eq(&self, other: &Self) -> bool {
        self.0 == other.0
    }
}
impl Hash for ModInt {
    fn hash<H: Hasher>(&self, state: &mut H) {
        self.0.hash(state);
        self.0.hash(state);
    }
}
impl Eq for ModInt {}
#[allow(dead_code)]
impl ModInt {
    pub fn new(n: usize) -> ModInt {
        ModInt(n % MODu)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: usize) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        self.pow(MODu - 2)
    }
}
// ---------- end ModInt ----------

/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, x:&T) -> usize;
    fn upper_bound(&self, x:&T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for VecDeque<T>{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
impl<T: Ord> BinarySearch<T> for [T]{
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}

fn matmul(A:&Vec<Vec<i64>>, B:&Vec<Vec<i64>>) -> Vec<Vec<i64>>{
    let mut C = vec![vec![0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
                C[i][j] %= MOD;
            }
        }
    }
    return C;
}
fn matpow(A:&mut Vec<Vec<i64>>, n:usize) -> Vec<Vec<i64>>{
    let mut B = vec![vec![0;A.len()];A.len()];
    for i in 0..A.len(){
        B[i][i] = 1;
    }
    let mut n = n;
    let mut tmp = A.clone();
    while(n>0){
        if n&1 == 1{B = matmul(&B, &tmp);}
        tmp = matmul(&tmp, &tmp);
        n>>=1;
    }
    return B;
}

 
 
 

fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}
struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    size_edge:Vec<usize>,
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        UnionFind{
            par:par,
            rank:vec![0;n],
            size:vec![1;n],
            size_edge:vec![0;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
                self.size_edge[y] += self.size_edge[x];
                self.size_edge[y] += 1;
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                self.size_edge[x] += self.size_edge[y];
                self.size_edge[x] += 1;
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
            
        }
        else{
            self.size_edge[x] += 1;
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s
    }
}
pub struct Scanner<R> {
    stdin: R,
}
 
impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        std::str::from_utf8(&buf).unwrap()
            .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()
    }
}
struct LazySegTree<BiOp> {
    n: usize,
    val: Vec<i64>,
    ma:Vec<i64>,
    op: BiOp,
    e: i64,
    upe:i64,
    inf:i64,
}

impl<BiOp> LazySegTree<BiOp>
    where BiOp: Fn(i64, i64) -> i64{
    pub fn new(n_: usize, op: BiOp, e: i64, upe:i64, inf:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2

        LazySegTree {n: n, val: vec![e; 2 * n ], ma:vec![upe;2*n], op: op, e: e, upe:upe, inf:inf}
    }
    pub fn query(&self, x:usize, y:usize, l:usize, r:usize, k:usize) -> i64 {
        if (r<=x || y<=l) {return self.inf;}
        if (x<=l && r<=y) {return self.ma[k];}
        let mut L = self.query(x,y,l,(l+r)/2, k*2);
        let mut R = self.query(x,y,(l+r)/2,r, k*2+1);
        return self.val[k] + (self.op)(L, R);

    }
    
    pub fn update(&mut self, x:usize, y:usize, v:i64, l:usize,r:usize, k:usize) {
        if (l>=r) {return;}
        if (x<=l && r<=y){
            self.val[k]+=v;
            self.ma[k]+=v;
        }
        else if(l<y && x<r){
            self.update(x, y, v, l, (l+r)/2, k*2);
            self.update(x,y,v,(l+r)/2,r, k*2+1);
            self.ma[k] = self.val[k] + (self.op)(self.ma[k*2], self.ma[k*2+1]);
        }
    }
}
fn modinv(a:ModInt)->ModInt{
    let mut a = a.0 as usize;
    let mut b = MODu as i64;
    let mut u = 1 as i64;
    let mut v = 0 as i64;
    let mut a = a as i64;
    let mut m = MODu as i64;
    while(b>0){
        let mut t = a/b;
        a -= t*b;
        mem::swap(&mut a, &mut b);
        u-=t*v;
        mem::swap(&mut u, &mut v);    
    }
    u%=m;
    if u<0{u+=m;}
    return ModInt(u as usize);

}
fn modpow(x:ModInt, n:ModInt) -> ModInt{
        let mut ans = ModInt(1);
        let mut n = n.0 as usize;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x;}
            x = x*x;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<ModInt>, ifac:&Vec<ModInt>)->ModInt{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return ModInt(1);}
        if a<b || a<0{return ModInt(0);}
        let mut tmp = ifac[a-b]*ifac[b];
        return tmp * fac[a];
}

fn invs()->(Vec<ModInt>, Vec<ModInt>){
    let mut fac = vec![ModInt(0);300001];
    let mut ifac = vec![ModInt(0);300001];
    fac[0] = ModInt(1);
    ifac[0] = ModInt(1);
    for i in 0..300000{

        fac[i+1] = fac[i] * ModInt(i+1);
        ifac[i+1] = ifac[i] * modpow(ModInt(i+1), ModInt(MODu - 2));
    }
    (fac, ifac)
}

struct ConvexHallTrick {
    Q: Vec<(i64, i64)>,
}

impl ConvexHallTrick{
    pub fn new() -> Self {

        ConvexHallTrick {Q: Vec::new()}
    }
    pub fn calc(&self, p:(i64, i64), x:i64)->i64{
        return p.0 * x + p.1;
    }
    pub fn dodo(& self, A:(i64, i64), B:(i64, i64), C:(i64, i64)) -> bool{
        //max or min
        (A.1 - C.1) * (B.0 - A.0) <= (A.1 - B.1)*(C.0 - A.0)
    }
    pub fn add(&mut self, a:i64, b:i64){
        self.Q.push((a, b));
        let mut v = self.Q.len();
        while(v >=3 && self.dodo(self.Q[v-3], self.Q[v-2], self.Q[v-1])){
            self.Q[v-2] = self.Q[v-1];
            self.Q.pop();
            v = self.Q.len();
        }
    }
    pub fn query(& self, x:i64) -> i64{
        let mut L = -1;
        let mut R = (self.Q.len() - 1) as i64;
        while(R-L>1){
            let mut m = (L+R)/2;
            if self.calc(self.Q[m as usize], x)>=self.calc(self.Q[m as usize+1], x){
                L=m;
            }
            else{
                R=m;
            }

        }
        return self.calc(self.Q[R as usize], x);
    }
}
#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);
impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}
impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}
fn sieve(n:usize) -> (Vec<bool>, Vec<usize>){
    let mut p:usize = 0;
    let mut is_prime = vec![false; n+1];
    let mut prime = Vec::new();
    for i in 0..n+1{
        is_prime[i] = true;
    }
    is_prime[0] = false;
    is_prime[1] = false;
    for i in 2..n+1{
        if is_prime[i]{
            prime.push(i as usize);
            let mut j = 2*i;
            while(j<=n){
                is_prime[j] = false;
                j+=i;
            }
        }
    }
    (is_prime, prime)
    
}
fn nHr(n:usize, r:usize, fac:&Vec<ModInt>, ifac:&Vec<ModInt>) -> ModInt{
    comb(n + r - 1, r, fac, ifac)
}
fn gcd(a:usize, b:usize)->usize{
    if b==0{return a;}
    return gcd(b, a%b);
}
fn lcm(a:usize, b:usize)->usize{
    return (b/gcd(a, b))*a;
}
struct SegTree_MOD<BiOp> {
    n: usize,
    dat: Vec<i64>,
    op: BiOp,
    e: i64,
    mod_:i64,
}
impl<BiOp> SegTree_MOD<BiOp>
    where BiOp: Fn(i64, i64) -> i64 
          {
    pub fn new(n_: usize, op: BiOp, e: i64, mod_:i64) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree_MOD {n: n, dat: vec![e; 2 * n - 1], op: op, e: e, mod_:mod_}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: i64) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
            self.dat[k] %= self.mod_;
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> i64 {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
                left %= self.mod_;
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
                right %= self.mod_;
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        let mut res = (self.op)(left, right);
        res %= self.mod_;
        res
        
    }
}
fn modpow2(x:usize, n:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%MODu;}
            x = x*x%MODu;
            n = n>>1;
        }
        ans
}
#[derive(Clone)]
struct PPUnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    time:Vec<usize>,
    now:usize,
    history:Vec<(usize, usize)>,
}
impl PPUnionFind{
    fn init(n:usize) -> PPUnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;
        }
        PPUnionFind{
            par:par,
            rank:vec![0;n],
            time:vec![INF as usize;n],
            now:0,
            history:vec![],
        }
    }
    fn find(&mut self, t:usize, x:usize) ->usize{
        if self.time[x] > t{return x;}
        else { let tt = self.par[x]; return self.find(t, tt);}
    }
    fn unite(&mut self, x:usize, y:usize) -> usize{
        self.now+=1;
        let mut x = x;
        let mut y = y;
        let nc = self.now;
        x = self.find(nc, x);
        y = self.find(nc, y);
        if x == y{return self.now;}
        if self.par[x] < self.par[y] {mem::swap(&mut x, &mut y);}
        self.par[x] += self.par[y];
        self.history.push((self.now, self.par[x]));
        self.par[y] = x;
        self.time[y] = self.now;
        return self.now;
    }
}

fn prim(cost:&Vec<Vec<(usize, i64)>>, vs:usize)->i64{
    let mut used = vec![false; vs];
    let mut bh = BinaryHeap::new();
    for j in 0..cost[0].len(){
            bh.push((cost[0][j].1, cost[0][j].0));
    }
    used[0] = true;
    let mut res = 0;
    while(bh.len()!=0){
        let mut m = bh.pop().unwrap();
        if used[m.1]{continue;}
        used[m.1] = true;
        for e in 0..cost[m.1].len(){
            if used[cost[m.1][e].0] == false{
                bh.push((cost[m.1][e].1, cost[m.1][e].0));
            }
        }
        res += m.0;
    }
    return res;
}
fn kruscal(cost:&mut Vec<(i64, usize, usize)>, vs:usize)->i64{
    cost.sort();
    let mut uf = UnionFind::init(vs);
    let mut res = 0;

    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res += e.0;
        }
    }
    return res;
}
fn kruscal3(cost:&mut Vec<(f64, usize, usize, usize)>, vs:usize)->(UnionFind, Vec<usize>) {
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    let mut rv = Vec::new();
    let mut c = 0.0;
    let mut t = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            rv.push(e.3);
        }
    }
    return (uf,rv);
}
fn kruscal2(cost:&mut Vec<(f64, usize, usize)>, vs:usize)->f64{
    cost.sort_by(|a, b| (&a.0).partial_cmp(&b.0).unwrap());
    let mut uf = UnionFind::init(vs);
    let mut res = 0.0;
    for i in 0..cost.len(){
        let e = cost[i].clone();
        if uf.find(e.1) != uf.find(e.2){
            uf.unite(e.1, e.2);
            res+= e.0;
        }
    }
    return res;
}

struct segtree<I, Op>{
    n: usize,
    dat: Vec<I>,
    op:Op,
    e:I,
}
impl<I, Op> segtree<I, Op>


    where Op: Fn(I, I) -> I, I:Copy{
        
        pub fn new(n_:usize, op: Op, e:I)->Self{
            let mut n = 1;
            while(n<n_){n*=2;}
            segtree{n: n, dat:vec![e; 2*n-1], op:op, e:e}
        }
        pub fn update(&mut self, k:usize, a:I){
            let mut k = k;
            k += self.n-1;
            self.dat[k] = a;
            while(k>0){
                k = (k-1)/2;
                self.dat[k] = (self.op)(self.dat[k*2 + 1], self.dat[k*2+2]);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> I{
            if r<=a || b<=l{return self.e;}
            if a<=l && r<=b{return self.dat[k];}
            else{
                let mut vl = self.query(a, b, k*2+1, l, (l+r)/2);
                let mut vr = self.query(a, b, k*2+2, (l+r)/2, r);
                return (self.op)(vl, vr);
            }
        }
    }
struct BIT<I, Op>{
    n:usize,
    bit:Vec<I>,
    op:Op,
    e:I,
    ini:I,
}
impl <I, Op>  BIT<I, Op>
    /* 1-index*/  
    where Op: Fn(I, I) -> I, I:Copy{
        pub fn new(n_:usize, op:Op, e:I, ini:I)->Self{
            BIT{n:n_, bit:vec![e;n_+1], op:op, e:e, ini:ini}
        }
        pub fn sum(&self, i:usize)->I{
            let mut s = self.ini;
            let mut i = i as i64;
            while(i>0){
                s = (self.op)(s, self.bit[i as usize]);
                i -= i & -i;
            }
            return s;
        }
        pub fn add(&mut self, i:usize, x:I){
            let mut i = i as i64;
            while(i<=self.n as i64){
                self.bit[i as usize] = (self.op)(self.bit[i as usize], x);
                i += i & -i;
            }
        }
    }
struct Dsegtree{
    n: usize,
    datA: Vec<i64>,
    datB:Vec<i64>,
    e:i64,
}
impl Dsegtree{
        pub fn new(n_:usize, e:i64)->Self{

            Dsegtree{n:n_, datA:vec![e; 1<<22 - 1], datB:vec![e;1<<22 - 1], e:e}
        }
        pub fn update(&mut self,a:usize, b:usize, x:i64,  k:usize, l:usize, r:usize){
            //println!("{} {} {} {} {} {}", a, b, x, k , l, r);
            if a<=l && r<=b{
                self.datA[k] += x;
            }
            else if (l<b && a<r){
                self.datB[k] += (cmp::min(b, r) as i64 - cmp::max(a, l) as i64) * x;
                self.update(a, b, x, k*2+1, l, (l+r)/2);
                self.update(a, b, x, k*2+2, (l+r)/2, r);
            }
        }
        pub fn query(&self, a:usize, b:usize, k:usize, l:usize, r:usize) -> i64{
            if (b<=l || r<=a){
                return 0;
            }
            else if (a<=l && r<=b){
                return self.datA[k] * ((r as i64-l as i64)) + self.datB[k];
            }
            else{
                let mut res = (cmp::min(b, r) as i64 - cmp::max(a, l) as i64)* self.datA[k];
                res += self.query(a, b, k*2+1, l, (l+r)/2);
                res += self.query(a, b, k*2+2, (l+r)/2, r);
                return res;
            }
        }
    }
/*
unwrap_or_else
*/
fn prime_factor(n:usize)->HashMap<usize, usize>{
    let mut res = HashMap::new();
    let mut n = n;
    for i in 2..n{
        if i*i>n{break;}
        while(n%i==0){
            *res.entry(i).or_insert(0)+=1;
            n/=i;
        }
    }
    if n != 1{
        res.insert(n, 1);
    }
    res
}
struct rollinghash{
    base:Vec<i64>,
    Mod:Vec<i64>,
    hash:Vec<Vec<i64>>,
    power:Vec<Vec<i64>>,
}
impl rollinghash{
    pub fn new(s:&Vec<usize>)->Self{
        let mut n = s.len();
        let mut base = vec![1007, 2009];
        let mut hash = vec![vec![0;n+1];2];
        let mut power = vec![vec![1;n+1];2];
        let mut Mod = vec![1000000007, 1000000009];
        for iter in 0..2{
            let mut ht = vec![0;n+1];
            let mut pt = vec![1;n+1];
            for i in 0..n{
                hash[iter][i+1] = (hash[iter][i] * base[iter] + s[i] as i64) % Mod[iter];
                power[iter][i+1] = power[iter][i] * base[iter] % Mod[iter];
            }
        }
        return rollinghash{base:base, Mod:Mod, hash:hash, power:power}
   
    }
    pub fn get(&self, l:usize, r:usize)->(i64, i64){
        let mut res = self.hash[0][r] - self.hash[0][l] * self.power[0][r-l] % self.Mod[0];
        if res<0{
            res += self.Mod[0];
        }
        let mut res2 = self.hash[1][r] - self.hash[1][l] * self.power[1][r-l] % self.Mod[1];
        if res2<0{
            res2 += self.Mod[1];
        }
        return (res, res2);
    }

}
struct LCA{
    G:Vec<Vec<i64>>,
    parent:Vec<Vec<i64>>,
    depth:Vec<i64>,
    root:i64,
}
impl LCA{
    pub fn new(G:Vec<Vec<i64>>, N:i64,R:i64)->Self{
        let D = (f64::log2(N as f64)) as i64 + 2;
        LCA{G:G, parent:vec![vec![0;N as usize];1+D as usize], depth:vec![0;N as usize], root:R}
    }
    pub fn getP(&mut self, v:i64, p:i64, d:i64){
        self.parent[0][v as usize] = p;
        self.depth[v as usize] = d;
        for i in 0..self.G[v as usize].len(){
            if self.G[v as usize][i as usize] != p{
                let n = self.G[v as usize][i as usize];
                self.getP(n, v, d+1);
            }
        }
    }
    pub fn init(&mut self){
        let root = self.root;
        self.getP(root, -1, 0);
        let V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            for v in 0..V{
                if self.parent[k as usize][v as usize] <0{
                    self.parent[k as usize+1][v as usize] = -1;
                }
                else{
                    self.parent[k as usize+1][v as usize] = self.parent[k as usize][ (self.parent[k as usize][v as usize]) as usize];
                }
            }
        }
    }
    fn ft(&self, f:i64, d:i64)->i64{
        let mut now = f;
        let mut now2 = 0;
        let V = self.depth.len();

        let logN = f64::log2(V as f64) as i64 + 2;
        let mut v = f;
        for k in 0..logN{
            if (d >> k) & 1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }

        return v;
    }

    fn lca(&mut self,u:i64, v:i64)->i64{
        let mut u = u;
        let mut v = v;
        if self.depth[u as usize] > self.depth[v as usize]{
            mem::swap(&mut u, &mut v);
        }
        let mut V = self.depth.len();
        let logN = f64::log2(V as f64) as i64 + 2;
        for k in 0..logN{
            if ((self.depth[v as usize] - self.depth[u as usize]) >> k)&1 == 1{
                v = self.parent[k as usize][v as usize];
            }
        }
        if u == v{return u;}
        for k in (0..logN).rev(){
            if self.parent[k as usize][u as usize] != self.parent[k as usize][v as usize]{
                u = self.parent[k as usize][u as usize];
                v = self.parent[k as usize][v as usize];
            }
        }
        return self.parent[0][u as usize];
    }

    fn dist(&mut self,u:i64, v:i64)->i64{
        let lc = self.lca(u, v);
        return self.depth[u as usize] + self.depth[v as usize] - 2* self.depth[lc as usize];
    }

}
fn fast_prime_factor_table(ma:usize)->Vec<usize>{
    let mut p = sieve(1001);
    let mut minf = vec![0;ma];
    for j in 0..p.1.len(){
        let P = p.1[j];
        let mut now = P;
        for i in 2..ma{
            if minf[now] ==0{
                minf[now] = P;
            }
            now+=P;
            if now>=ma{
                break;
            }
        }
    }
    return minf;
}
fn area_rectanble(x1:f64, x2:f64, x3:f64, y1:f64, y2:f64, y3:f64)->f64{
    let tmp = x1*y2 + x2*y3 + x3*y1 - y1*x2 - y2*x3 - y3*x1;
    tmp.abs()/2.0
}
#[derive(PartialEq, Clone)]
struct FW(f64);

impl Eq for FW {}

impl PartialOrd for FW {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        self.0.partial_cmp(&other.0)
    }
}

impl Ord for FW {
    fn cmp(&self, other: &FW) -> Ordering {
        other.partial_cmp(self).unwrap()

    }
}
/* parsing
    fn expr(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = term(s, i);
        while(*i<s.len() && (s[*i] == '+' || s[*i] == '-')){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = term(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn term(s:&Vec<char>, i:&mut usize) -> Vec<usize>{
        let mut val = factor(s, i);
        while(*i<s.len() && s[*i] == '*'){
            let mut op = encode(s[*i]);
            *i+=1;
            let mut val2 = factor(s, i);
            val = cal(val, val2, op);
        }
        return val;
    }
    fn factor(s:&Vec<char>, i:&mut usize)->Vec<usize>{
        if s[*i] == 'R' || s[*i] == 'S' || s[*i] == 'P' || s[*i] == '?'{
            let mut res = encode(s[*i]);
            *i+=1;
            return res;
        }
        *i+=1;
        let mut ret = expr(s, i);
        *i+=1;
        return ret;
    }
*/
fn matmulf64(A:&Vec<Vec<f64>>, B:&Vec<Vec<f64>>) -> Vec<Vec<f64>>{
    let mut C = vec![vec![0.0;B[0].len()];A.len()];
    for i in 0..A.len(){
        for k in 0..B.len(){
            for j in 0..B[0].len(){
                C[i][j] += A[i][k]*B[k][j];
            }
        }
    }
    return C;
}
//sort_by_key(|a| vec![a[0], -a[1]]);
//sort_by_key(|a| vec![a[0], -a[1]]);
////v.sort_by(|a, b| a.partial_cmp(b).unwrap());
struct UnionFind2 {
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind2 {
    fn new(n: usize) -> UnionFind2 {
        let mut vec = vec![0;n];
        for i in 0..n {
            vec[i] = i;
        }
        UnionFind2 {
            par : vec,
            rank : vec![0;n],
        }
    }

    fn find(&mut self, x: usize) -> usize {
        if x == self.par[x] {
            x
        }else{
            let par = self.par[x];
            let res = self.find(par);
            self.par[x] = res;
            res
        }
    }

    fn same(&mut self, a: usize, b: usize) -> bool {
        self.find(a) == self.find(b)
    }

    fn unite(&mut self, a: usize, b: usize){
        let apar = self.find(a);
        let bpar = self.find(b);
        if self.rank[apar] > self.rank[bpar] {
            self.par[bpar] = apar;
        }else{
            self.par[apar] = bpar;
            if self.rank[apar] == self.rank[bpar] {
                self.rank[bpar] += 1;
            }
        }
    }
}





#[macro_use]
fn solve(){
    let sssss = std::io::stdin();
    let mut sc = Scanner { stdin: sssss.lock() };
    /*
    let mut N:usize = sc.read();
    let mut M:usize = sc.read();
    let mut prob = vec![vec![INF as i64;N];M];
    let mut c = vec![];
    for i in 0..M{
        let mut x:usize = sc.read();
        let mut C:usize = sc.read();
        c.push(C);
        for j in 0..x{
            let mut w:usize = sc.read();
            let mut p:i64 = sc.read();
            prob[i][w-1] = p;
        }
    }
    */
    let mut N:usize = sc.read();
    let mut h = HashMap::new();
    let mut z = 0;
    for i in 0..N{
        let mut a:i64 = sc.read();
        let mut b:i64 = sc.read();
        if a == 0 || b == 0{
            if a== 0 && b != 0{
                *h.entry(vec![0,0, 1, 1, 0]).or_insert(0usize)+=1;
            }
            else if a != 0&&b==0{
                *h.entry(vec![1,1, 0, 0, 1]).or_insert(0usize)+=1;
            }
            else{
                z+=1;
            }
        }
        else{
            let mut flag = {if (a>0 && b>0) ||(a<0 && b<0){0}else{1}};
            let mut g=  gcd(a.abs() as usize, b.abs() as usize) as i64;
            let mut x = a.abs()/g;
            let mut y = b.abs()/g;
            let mut xx = b.abs()/g;
            let mut yy = a.abs()/g;
            *h.entry(vec![flag,x , y, xx, yy]).or_insert(0usize)+=1;
        }
    }
    let mut nu = HashSet::new();
    let mut dp = vec![0; h.len()+1];
    dp[0] = 1;
    let mut n = 0;
    for (i, j) in &h{
        if nu.contains(i){
            continue;
        }
        dp[n+1] = (dp[n] + (dp[n]*(modpow2(2, *j)-1))%MODu)%MODu;
        n+=1;
        let mut key = vec![(i[0]+1)%2, i[3], i[4], i[1], i[2]];
        nu.insert(i.clone());
        if h.contains_key(&key){
            dp[n+1] = (dp[n]+(dp[n-1]*(modpow2(2, h[&key])-1))%MODu)%MODu;
            n+=1;
            nu.insert(key.clone());
        }
    }
    let mut res = dp[n];
    res = MODu+res-1;
    res %= MODu;
    res += z;
    res %= MODu;

    println!("{}", res);














}






fn main(){
    solve();
}
const PI:f64 = std::f64::consts::PI;
pub static MOD:i64 = 998244353;
pub static MODu:usize = 1000000007;
pub static eps:f64 = 1e-6;
const INF: i64 = 1 << 60;