Intersection |

You are to write a program that has to decide whether a given line segment intersects a given rectangle.

line: start point: (4,9)end point: (11,2)

rectangle: left-top: (1,5)

right-bottom: (7,1)

**Figure:** Line segment does not intersect rectangle

The line is said to intersect the rectangle if the line and the rectangle have at least one point in common. The rectangle consists of four straight lines and the area in between. Although all input values are integer numbers, valid intersection points do not have to lay on the integer grid.

The input consists of *n* test cases. The first line of the input file
contains the number *n*. Each following line contains one test case
of the format:

where (*xstart*, *ystart*) is the start and (*xend*, *yend*)
the end point of the line and (*xleft*, *ytop*) the top left and
(*xright*, *ybottom*) the bottom right corner of the rectangle.
The eight numbers are separated by a blank. The terms and
do not imply any ordering of coordinates.

For each test case in the input file, the output file should contain a line
consisting either of the letter "`T`" if the line segment intersects
the rectangle or the letter "`F`" if the line segment does not intersect
the rectangle.

1 4 9 11 2 1 5 7 1

F