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2
Background
Given a set of rectangles {R1, R2, …, Rn}, compute the area of their common intersection. i.e.,
Area(R1∩R2∩…∩Rn)
The edges of the rectangles R1, R2, …, Rn, are either vertical or horizontal lines.
For example, the intersection of 4 rectangles, R1, R2, R3, and R4, in the following figure is the shaded rectangle.
Input
The input contains (N + 1) lines. The first line specifies the number of rectangles N, where 1 < N < 1000. Since the sides of the rectangles are parallel to the x-axis and y-axis, each rectangle is bounded by the lines x = x1, x = x2, y = y1 and y = y2 and each subsequent line of the input file thus specifies one rectangle in the following format:
x1 x2 y1 y2
such that 0 <= x1 < x2 <= 10000 and 0 <= y1 < y2 <= 10000, and x1, x2, y1 and y2 are integers.
Output
The output file contains the area of the intersection of all the rectangles.
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