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-----
3
1 2
-1 1
2 -1

-----Sample Output-----
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

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