Problems

# Segments intersection

# 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 data

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 data

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

## Examples

Input example #1

0 0 1 0 1 0 1 1

Output example #1

Yes

Input example #2

0 0 1 0 2 0 3 0

Output example #2

No