Given a set of rectangles in the plane, determine if it is possible to choose one diagonal from each rectangle such that none of the selected diagonals intersect. Two diagonals intersect if they share at least one point. Note that the rectangles themselves are free to intersect.
Input consists of several test cases. Each test case begins with an integer n (1<=n<=1000), representing the number of rectangles. This is followed by n lines each describing a rectangle using 8 integer numbers x1, y1, x2, y2, x3, y3, x4, y4, where each (xi, yi) is a vertex. All coordinate values are between -109 and 109. The input is terminated by a line containing "0" which should not be processed.
For each test case, output a line containing either "YES" if the selection is possible or "NO" if not.
4 0 1 1 1 1 0 0 0 1 1 2 1 2 0 1 0 2 3 5 3 5 0 2 0 2 3 3 3 3 2 2 2 7 0 10 10 10 10 0 0 0 10 10 20 10 20 0 10 0 20 30 50 30 50 0 20 0 20 30 30 30 30 20 20 20 30 10 40 10 40 0 30 0 5 0 30 0 30 -10 5 -10 0 0 5 0 5 -10 0 -10 0
YES NO
Migrated from old NTUJ.
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