CF1194E Count The Rectangles
Description
There are $ n $ segments drawn on a plane; the $ i $ -th segment connects two points ( $ x_{i, 1} $ , $ y_{i, 1} $ ) and ( $ x_{i, 2} $ , $ y_{i, 2} $ ). Each segment is non-degenerate, and is either horizontal or vertical — formally, for every $ i \in [1, n] $ either $ x_{i, 1} = x_{i, 2} $ or $ y_{i, 1} = y_{i, 2} $ (but only one of these conditions holds). Only segments of different types may intersect: no pair of horizontal segments shares any common points, and no pair of vertical segments shares any common points.
We say that four segments having indices $ h_1 $ , $ h_2 $ , $ v_1 $ and $ v_2 $ such that $ h_1 < h_2 $ and $ v_1 < v_2 $ form a rectangle if the following conditions hold:
- segments $ h_1 $ and $ h_2 $ are horizontal;
- segments $ v_1 $ and $ v_2 $ are vertical;
- segment $ h_1 $ intersects with segment $ v_1 $ ;
- segment $ h_2 $ intersects with segment $ v_1 $ ;
- segment $ h_1 $ intersects with segment $ v_2 $ ;
- segment $ h_2 $ intersects with segment $ v_2 $ .
Please calculate the number of ways to choose four segments so they form a rectangle. Note that the conditions $ h_1 < h_2 $ and $ v_1 < v_2 $ should hold.
Input Format
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Output Format
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Explanation/Hint
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