Write a data type Interval that implements the following API:An interval is defined to be...

Write a data type Interval that implements the following API:

An interval is defined to be the set of all points on the line greater than or equal to left and less than or equal to right. In particular, an interval with right less than left is empty. Write a client that is a filter that takes a floating-point command-line argument x and prints all of the intervals on standard input (each defined by a pair of double values) that contain x.