1270E · Divide Points

Problem: You are given a set of $n\ge 2$ pairwise different points with integer coordinates. Your task is to partition these points into two nonempty groups $A$ and $B$, such that the following condition holds:

For every two points $P$ and $Q$, write the Euclidean distance between them on the blackboard: if they belong to the same group — with a yellow pen, and if they belong to different groups — with a blue pen. Then no yellow number is equal to any blue number.

It is guaranteed that such a partition exists for any possible input. If there exist multiple partitions, you are allowed to output any of them.

Input Format: The first line contains one integer $n$ $(2 \le n \le 10^3)$ — the number of points.

The $i$-th of the next $n$ lines contains two integers $x_i$ and $y_i$ ($-10^6 \le x_i, y_i \le 10^6$) — the coordinates of the $i$-th point.

It is guaranteed that all $n$ points are pairwise different.

Output Format: In the first line, output $a$ ($1 \le a \le n-1$) — the number of points in a group $A$.

In the second line, output $a$ integers — the indexes of points that you include into group $A$.

If there are multiple answers, print any.

Note: In the first example, we set point $(0, 0)$ to group $A$ and points $(0, 1)$ and $(1, 0)$ to group $B$. In this way, we will have $1$ yellow number $\sqrt{2}$ and $2$ blue numbers $1$ on the blackboard.

In the second example, we set points $(0, 1)$ and $(0, -1)$ to group $A$ and points $(-1, 0)$ and $(1, 0)$ to group $B$. In this way, we will have $2$ yellow numbers $2$, $4$ blue numbers $\sqrt{2}$ on the blackboard.