Veshy is taking a class in linear algebra! He comes across a problem about the rotations of points with respect to the origin. However, he deems this too trivial so he comes up with the following problem instead:

Veshy chooses two points located at integer coordinates, $A$ and $B$, on the 2D plane. There is initially a token at $A$. Veshy also has a sequence of $N$ points, all located at integer coordinates, on this plane, $a_1,a_2,\dots ,a_N$. One operation is defined as choosing some index $i$ and rotating the token by an arbitrary angle around $a_i$. However, if Veshy previously performed an operation on index $i$, he is only allowed to perform an operation on index $j$ if $j>i$. Determine if it's possible to move the token from $A$ to $B$, and if so, the minimum number of operations required.

Constraints

In all subtasks,
$1\le N\le 500$
The absolute value of all coordinates will be less than or equal to ${10}^9$.

Subtask 1 [5%]

$N=1$

Subtask 2 [10%]

$1\le N\le 2$

Subtask 3 [25%]

$1\le N\le 15$

Subtask 4 [60%]

No additional constraints.

Input Specification

The first line contains one integer, $N$.
The second line contains two space-separated integers, $A_x$ and $A_y$, the coordinates of point $A$.
The third line contains two space-separated integers, $B_x$ and $B_y$, the coordinates of point $B$.
The next $N$ lines contain two space-separated integers, $x_i$ and $y_i$ the coordinates of point $a_i$.

Output Specification

Output one line containing one integer, the minimum number of operations if it's possible and -1 otherwise.

Sample Input

3
0 0
4 0
1 0
2 3
3 0

Sample Output

1

Explanation for Sample Output

One sequence of operations would be to rotate the token ${180}^{\circ }$ around $a_1$ and then another ${180}^{\circ }$ around $a_3$. This sequence is shown in green. This would require two operations.
Another sequence would be rotating the token ${67.38}^{\circ }$ counter-clockwise around $a_2$. This sequence is shown in blue. This would require one operation and it can be shown that there is no shorter sequence.