CF1722E Counting Rectangles

You have $ n $ rectangles, the $ i $ -th rectangle has height $ h_i $ and width $ w_i $ . You are asked $ q $ queries of the form $ h_s \ w_s \ h_b \ w_b $ . For each query output, the total area of rectangles you own that can fit a rectangle of height $ h_s $ and width $ w_s $ while also fitting in a rectangle of height $ h_b $ and width $ w_b $ . In other words, print $ \sum h_i \cdot w_i $ for $ i $ such that $ h_s < h_i < h_b $ and $ w_s < w_i < w_b $ . Please note, that if two rectangles have the same height or the same width, then they cannot fit inside each other. Also note that you cannot rotate rectangles. Please note that the answer for some test cases won't fit into 32-bit integer type, so you should use at least 64-bit integer type in your programming language (like long long for C++).

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In the first test case, there is only one query. We need to find the sum of areas of all rectangles that can fit a $ 1 \times 1 $ rectangle inside of it and fit into a $ 3 \times 4 $ rectangle. Only the $ 2 \times 3 $ rectangle works, because $ 1 < 2 $ (comparing heights) and $ 1 < 3 $ (comparing widths), so the $ 1 \times 1 $ rectangle fits inside, and $ 2 < 3 $ (comparing heights) and $ 3 < 4 $ (comparing widths), so it fits inside the $ 3 \times 4 $ rectangle. The $ 3 \times 2 $ rectangle is too tall to fit in a $ 3 \times 4 $ rectangle. The total area is $ 2 \cdot 3 = 6 $ .