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.