Jono has been working hard on his AI project. He has been tasked with designing an LLM that generates a list of points that are in a straight line. Jono created his LLM using an LLM, and it keeps hallucinating points that are not, in fact, in a straight line.

Jono's project is due in 3 hours, and he doesn't have time to get the LLM working. Jono needs you to check if the list of points the LLM has generated is actually in a straight line, so if it isn't, he can silently re-run the LLM.

Input

The first line contains an integer ~n\ (1 \leq n \leq 1000)~, the number of points.

Each of the next ~n~ lines contains two integers ~x_i~ and ~y_i\ (-10^4 \leq x_i, y_i \leq 10^4)~, representing the coordinates of the ~i^{th}~ point.

Output

Print "YES" if all the given points lie perfectly on a single straight line. Otherwise, print "NO", so Jono knows his LLM has once again creatively reinterpreted geometry.

Example

Input

3
1 1
2 2
3 3

Output

YES

Explanation

The points are in a straight line.