A polygon P determined by points p₁, p₂, . . . , p_n is a closed chain of line segments (called edges) p₁p₂, p₂p₃, . . . , p_np₁ 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.</p>

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.

입력 형식

The input contains several test cases. Each test case corresponds to one polygon. First line of the test case contains N, the number of points (1 ≤ N ≤ 40 000). Each of the following N lines contains coordinates of point P_i, that is X_i, Y_i separated by space, 1 ≤ X_i,Y_i ≤ 30 000.</p>

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

출력 형식

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

예제 입력

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 3
2 2
0

예제 출력

NO
YES
NO