There are two separate, n-element sets of points of a two dimensional map: R and W. None triple of points from the set RUW is collinear. Rockets earth-to-earth are located on points from the set R. Enemy objects, which should be destroyed, are located on points from the set W. The rockets may fly only in the straight line and their trajectories cannot intersect. We are about to find for each rocket a target to destroy.

Task

Write a program which:

• reads from the text file RAK.IN coordinates of the points from the sets R and W,
• finds the set of n pairwise not-intersecting segments, so that one end of each segment belongs to the set R, while the other belongs to the set W,
• writes the result into the text file RAK.OUT.

Input

In the first line of the file RAK.IN there is written one integer n, 1<=n<=10000, equal to the number of elements of the sets R and W.

In each of the following 2n lines of the file RAK.IN one pair of integer numbers from the interval [-10000, 10000] is written. Numbers in each pair are separated by a single space. They are coordinates of the point on a map (first coordinate x, then y). The first n lines comprise coordinates of the points from the set R, the last n lines comprise the points from the set W. In the (i+1)-th line there are coordinates of the point r_i, in the (i+n+1)-th line there are coordinates of the point w_i, 1<= i<= n. 

Output

The file RAK.OUT should consist of n lines. In the i-th line there should be one integer k(i), such that the segment r_i w_k(i) belongs to the set of segments which your program found. (This means that the rocket from the point r_i destroys an object in the point w_k(i)).

Example

For the input file RAK.IN:

4
0 0
1 5
4 2
2 6
1 2
5 4
4 5
3 1

2
1
4
3