Problem Description

Input Format

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 Format

On the first line, output $ m $, the number of points you chose to make a regular polygon which has the most vertices possible.

On the following $ m $ lines, output the index($ 1 $-indexed) of each point you chose in ascending order.

If you cannot make any regular polygon from the given points, just output a single line containing $ 0 $.

Sample Input and Output

Sample Input #1

6
1 0
-1 0
0 1
0 -1
1 2
-1 2

Sample Output #1

4
1
2
3
4

Sample Input #2

4
0 0
1 0
2 0
3 0

Sample Output #2

0

Notes/Hints

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 the most vertices possible. If there are more than one possible answers, you may choose any one of them.

Sample Explanation 1

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 vertices 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.

Sample Explanation 2

The given points are on a straight line. You cannot make any regular polygon from them.

见题面 Input 部分

见题面 Output 部分