frog is trapped in a maze. The maze is infinitely large and divided into grids. It also consists of $n$ obstacles, where the $i$-th obstacle lies in grid $(x_i, y_i)$.

frog is initially in grid $(0, 0)$, heading grid $(1, 0)$. She moves according to The Law of Right Turn: she keeps moving forward, and turns right encountering a obstacle.

The maze is so large that frog has no chance to escape. Help her find out the number of turns she will make.

Input

The input consists of multiple tests. For each test:

The first line contains $1$ integer $n$ ($0 \leq n \leq 10^3$). Each of the following $n$ lines contains $2$ integers $x_i, y_i$. ($|x_i|, |y_i| \leq 10^9, (x_i, y_i) \neq (0, 0)$, all $(x_i, y_i)$ are distinct)

Output

For each test, write $1$ integer which denotes the number of turns, or -1 if she makes infinite turns.

Sample Input

2
1 0
0 -1
1
0 1
4
1 0
0 1
0 -1
-1 0

Sample Output

2
0
-1