Simple Polygon

A *polygon* $P$
determined by points $p_1, p_2,
\ldots , p_ n$ is a closed chain of line segments
(called edges) $p_1 p_2, p_2 p_3,
\ldots , p_ n p_1$ in the plane. Polygon $P$ is simple, if no two edges have
any points in common, with the obvious exception of two
consecutive segments having one common point (called vertex).
Note however, that if a vertex is part of any other (third)
edge, the polygon is no longer simple.

Any polygon that is not simple is called
*self-intersecting*. In two example figures below, the
first polygon is simple, the second one is
self-intersecting.

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

The input contains at most $150$ test cases. Each test case corresponds to one polygon. First line of the test case contains $N$, the number of points ($1 \leq N \leq 40\ 000$). Each of the following $N$ lines contains coordinates of point $P_ i$, that is $X_ i$, $Y_ i$ separated by space, $1 \leq X_ i, Y_ i \leq 30\ 000$.

The last test case is followed by a line containing zero.

For each test case output either “`YES`” (the polygon is simple) or “`NO`” (the polygon is self-intersecting).

Sample Input 1 | Sample Output 1 |
---|---|

5 1 6 5 7 9 4 2 3 6 1 7 1 6 5 7 9 4 4 3 7 4 4 6 3 1 7 1 1 1 4 1 3 2 2 3 1 3 2 2 2 0 |
NO YES NO |