I. Parallelogram Dissection
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given is a strictly convex polygon, that is, it is convex and no three vertices are collinear. Check if it is possible to cut it into 2017 parallelograms.

Input

First line of the input contains one integer n (3 ≤ n ≤ 100).

Next n lines contains coordinates of the vertices of the polygon in clockwise order. i-th of those lines contains two integers xi and yi — coordinates of i-th vertice ( - 109 ≤ xi, yi ≤ 109).

Output

Print "yes", if it is possible to cut the given polygon into 2017 parallelograms, or "no" otherwise.

Examples
Input
4
0 0
0 1
1 1
1 0
Output
yes
Input
3
0 0
0 1
1 0
Output
no