There are points in a plane forming a convex polygon. The coordinates of the -th point are . You need to find three pairwise distinct indices , such that there exists a triangle satisfying

• is the anticomplementary triangle of .

• is inside or on the edge of for all .

is the anticomplementary triangle of if are the midpoints of edge respectively.

输入描述:

The first line contains an integer , indicating the number of points.
The -th of the next  lines contains two integers  and , indicating the coordinates of . The vertices are guaranteed to form a convex polygon, and are given in counterclockwise order.

输出描述:

Output three integers  and  indicating the selected indices. If there are multiple solutions, print any of them. You can output  in an arbitrary order.

4
0 0
1 0
1 1
0 1

1 2 3

5
-1 -9
3 1
5 8
-1 11
-8 -10

2 4 5

备注:

Here is the illustration for the second example.