/ 
Time Limit: 2 sec / Memory Limit: 256 MB
Problem
You are given N points of integer lattice on a rectangular coordinate plane, You want to choose some points from them to make a regular polygon by connecting the chosen points with straight lines. Also, you want to choose as many points as possible to make a regular polygon.
Determine the points you should choose to make a regular polygon which has most vertices possible. If there are more than one possible answers, you may choose any one of them.
Input
Input is given in the following format.
N x_1 y_1 x_2 y_2 : x_N y_N
- On the first line, you will be given an integer N (1 \leq N \leq 1,000), the number of integer lattice points given.
- On the following N lines, you will be given the coordinates of each lattice. The i-th (1 \leq i \leq N) line consists of two integers x_i,y_i (-10^9 \leq x_i,y_i \leq 10^9), the x,y coordinate of the i-th lattice, respectively.
- Each given lattice is guaranteed to be distinct. In other words, for any 2 integers i,j(1 \leq i,j \leq N), if i \neq j then (x_i,y_i)≠(x_j,y_j) holds.
Output
On the first line, output m, the number of points you chose to make a regular polygon which has most vertices possible.
On the following m lines, output the index(1-indexed) of each points you chose in ascending order .
If you cannot make any regular polygon from the given points, just output a single line containing 0.
Input Example 1
6 1 0 -1 0 0 1 0 -1 1 2 -1 2
Output Example 1
4 1 2 3 4
Among the given 6 points, you can choose 4 points (1,0),(-1,0),(0,1),(0,-1) to make a regular square, which has the most vertex possible. So the answer is 4 and the indices of those points.
The 4 points (-1,0),(1,0),(1,2),(-1,2) can also make a regular square. So, the indices of them, {1,2,5,6}, will be considered correct too.
Input Example 2
4 0 0 1 0 2 0 3 0
Output Example 2
0
The given points are on a straight line. You cannot make any regular polygon from them.