[문제요약] 폐 곡선의 각 점의 좌표가 주어질 때 원점에서 각 꼭지점으로 선을 연결할 때 폐곡선을 건들지 않는 점의 개수와 점을 구하는 문제.

점을 출력할 때 오름차순으로 출력

Your company wants to produce a new electronic device that will be manufactured using a PCB. The design of the required PCB is partially ready, and has the shape of a closed polygon. It consists of N nodes numbered from 1 to N. Node u and node u+1 are connected by a straight line wire segment and node N is connected to node 1 by a straight line wire segment. Wire segments are non-crossing, that is for any pair of wire segments if they share a common point then this point must be an endpoint of both segments, and each node is the endpoint of exactly two segments. The location of each node is given by x- and y-coordinates, and the origin (0,0) is the lower left corner of the board.

Task

입력

• The first line of the input contains one integer, N (1 ≤ N ≤ 100 000) the number of nodes of the circuit.
• Each of the next N lines contain two integers, x, y (0 < x, y ≤ 1 000 000) the x- and y-coordinates of a node. Nodes are numbered from 1 to N, the input line i+1 contains the coordinates of node i.

출력

• The first line of the output contains one integer M, the number of nodes that can be connected to the origin by a straight line wire segment so that this point is the only common point with any wire segment of the circuit.
• The second line contains these nodes separated by space in increasing order.

입출력 예

입력

11
7 6
4 4
3 2
1 3
9 9
13 4
8 1
6 4
9 5
8 3
11 5

출력

3
3 4 7

출처:ceoi 2012