Simple Polygon

A polygon $P$ defined by points $p_1, p_2, \dots, p_n$ in the plane is the closed chain of line segments (called edges) $p_1p_2, p_2p_3, \dots, p_np_1$. The polygon $P$ is simple if no two edges share any point, with the single exception that two consecutive edges may share their one common point (called a vertex). However, if a vertex also lies on any other (third) edge, the polygon is no longer simple.

A polygon that is not simple is called self-intersecting.

Your task is to determine whether a given polygon is simple or self-intersecting.

The input contains several test cases; each test case describes one polygon. The first line of a test case contains $N$, the number of points ($1 \le N \le 40\,000$). Each of the next $N$ lines contains the coordinates of a point $P_i$, namely $X_i$ and $Y_i$ separated by a space ($1 \le X_i, Y_i \le 30\,000$). The points are given in the order they appear along the polygon.

The last test case is followed by a line containing a single $0$, which marks the end of the input.

For each test case, print YES on its own line if the polygon is simple, or NO if it is self-intersecting.