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A specialist in VLSI design testing must decide if there are some components that cover each other for a given design. A component is represented as a rectangle. Assume that each rectangle is rectilinearly oriented (sides parallel to the x and y axis), so that the representation of a rectangle consists of its minimum and maximum x and y coordinates.
Write a program that counts the rectangles that are entirely covered by another rectangle.
The input contains the text description of several sets of rectangles. The specification of a set consists of the number of rectangles in the set and the list of rectangles given by the minimum and maximum x and y coordinates separated by white spaces, in the format:
xmin1 xmax1 ymin1 ymax1
xmin2 xmax2 ymin2 ymax2
xminn xmaxn yminn ymaxn
For each set,there will be less than 5000 rectangles.
The output should be printed on the standard output. For each given input data set, print one integer number in a single line that gives the result (the number of rectangles that are covered).
3 100 101 100 101 0 3 0 101 20 40 10 400 4 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20
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