Little C has recently been studying the structure of triangles. Given three points $A, B, C$ on a 2D plane, if the line segments $AB, BC, AC$ do not overlap, we say that these three points can form a triangle.

Now, Little C has $n$ points on a 2D plane. Can you help Little C determine if it is possible to choose three points from them such that they can form a triangle?

Input

The first line contains an integer $n$ ($3 \le n \le 10^5$), representing the number of points.

Each of the next $n$ lines contains two integers $x_i, y_i$ ($-10^9 \le x_i, y_i \le 10^9$), representing the coordinates of the $i$-th point. It is guaranteed that all point coordinates are distinct.

Output

If Little C cannot find three points that satisfy the requirements, output NO; otherwise, output YES.

Examples

Input 1

4
1 1
1 2
2 1
2 2

Output 1

YES

Input 2

3
1 1
1 2
1 3

Output 2

NO