Printed Circuit Board

A printed circuit board (PCB) mechanically supports and electrically connects electronic components using conductive pathways etched from copper sheets that are laminated onto a nonconductive substrate.

Your company wants to build a new electronic device on a PCB. The design is partially finished and has the shape of a closed polygon with $N$ nodes numbered from $1$ to $N$. For every $i$, node $i$ and node $i+1$ are joined by a straight wire segment, and node $N$ is joined back to node $1$. The wire segments are non-crossing: if two segments share a point, that point is an endpoint of both segments, and every node is the endpoint of exactly two segments. Each node has integer coordinates $(x, y)$, and the origin $(0, 0)$ is the lower-left corner of the board, which lies outside the polygon.

Write a program that determines every node that can be joined to the origin by a straight wire segment whose only common point with the polygon is that node itself.

The first line contains one integer $N$ ($1 \le N \le 200000$), the number of nodes.

Each of the next $N$ lines contains two integers $x$ and $y$ ($0 < x, y \le 1000000$): line $i+1$ gives the coordinates of node $i$.

On the first line, print one integer $M$: the number of nodes that can be joined to the origin by a straight wire segment meeting the polygon only at that node.

On the second line, print those node numbers in increasing order, separated by single spaces.