Two Squares

Description:

Input:

The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order.

The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees.

All the values are integer and between $$$-100$$$ and $$$100$$$.

Output:

Print "Yes" if squares intersect, otherwise print "No".

You can print each letter in any case (upper or lower).

Sample Input:

0 0 6 0 6 6 0 6
1 3 3 5 5 3 3 1

Sample Output:

YES

Sample Input:

0 0 6 0 6 6 0 6
7 3 9 5 11 3 9 1

Sample Output:

NO

Sample Input:

6 0 6 6 0 6 0 0
7 4 4 7 7 10 10 7

Sample Output:

YES

Note:

In the first example the second square lies entirely within the first square, so they do intersect.

In the second sample squares do not have any points in common.

Here are images corresponding to the samples: