# code festival 2014 上海

## C - Regular Polygon

Time limit時間制限 : 2sec / Memory limitメモリ制限 : 256MB

### 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.