Intersection of line segments

Input

The input consists of eight integers, each not exceeding 10^4 in absolute value. These integers are the coordinates of points $A$, $B$, $C$, and $D$. Points may coincide, including endpoints of the same segment.

Output

If the segments do not intersect, output Empty. If the segments intersect at a single point, output two numbers—the coordinates of the intersection point. If the intersection is a segment, output four numbers—the coordinates of the endpoints of the segment in lexicographical order (first, the point with the smaller $x$ coordinate; if $x$ coordinates are equal, the point with the smaller $y$ coordinate). All numbers must be printed with a precision of at least $6$ decimal places.

Examples