Do the segments intersect - 1

Given four points (A), (B), (C), and (D), it is guaranteed that no three of these points are collinear.

Determine whether the line segments (AB) and (CD) intersect.

Input

The input consists of exactly three groups, each containing two lines (a total of six lines). The first line of each group provides the coordinates of segment (AB) in the format: (A_x) (A_y) (B_x) (B_y). The second line of each group provides the coordinates of segment (CD) in the format: (C_x) (C_y) (D_x) (D_y). All coordinates are integers, with absolute values not exceeding one million.

Output

For each group, output YES on a separate line if the segments intersect, or NO if they do not.

Examples