E - ∙ (Bullet)

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 $1000000007$.

3
1 2
-1 1
2 -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

10
3 2
3 2
-1 1
2 -1
-3 -9
-8 12
7 7
8 1
8 2
8 4

479