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).

Specifications

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.

Problem information

Time Limit: 1 seconds
Memory Limit: 64 MB
Balls for the passed test: 0.666667
Complexity: 37% 154/243
Classes: Geometry

Example

Example input

Sample 1
0 0
1 0
1 0
1 1

Sample 2
0 0
1 0
2 0
3 0

Example output

Sample 1
Yes

Sample 2
No

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