Segments intersection

Two segments are given in the plane with integer coordinates of its endpoints in Cartesian coordinate system. Determine whether they intersect (have a common point).

Input

The first line contains the coordinates of the first endpoint of the first segment, the second line - the second endpoint of the first segment. The third and fourth lines - the corresponding coordinates of the second segment. The coordinates are integer, their absolute value do not exceed 10000.

Output

Print the word "Yes", if segments have common point, or "No" otherwise.

Examples