Convex polygon

Input

The first line contains a single integer $N$ (3 \leq N \leq 100000). The next $N$ lines contain pairs of integers — the coordinates of the vertices of a simple polygon, given in order (either clockwise or counterclockwise). All coordinates are integers with absolute value not exceeding $10000$.

Output

Output one line with "YES" if the given polygon is convex, and "NO" otherwise.

Examples