{"raw_statement":[{"iden":"statement","content":"Given  points on a plane, output the area of a rectangle with its sides parallel with the coordinate axes that contains inside or on the sides at least  points of the  points given.\n\nThe input file *drept.in* contains on the first lines 2 numbers  and each of the following  lines contains 2 numbers  and   describing the th point. \n\nThe output file *drept.out* contains the required area.\n\n"},{"iden":"input","content":"The input file *drept.in* contains on the first lines 2 numbers  and each of the following  lines contains 2 numbers  and   describing the th point. "},{"iden":"output","content":"The output file *drept.out* contains the required area."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ n \\in \\mathbb{Z}^+ $ be the number of points.  \nLet $ P = \\{(x_i, y_i) \\mid i \\in \\{1, \\dots, n\\}\\} $ be a set of points in $ \\mathbb{R}^2 $.\n\n**Constraints**  \nEach point satisfies $ x_i, y_i \\in \\mathbb{R} $.\n\n**Objective**  \nFind the minimum area $ A $ of an axis-aligned rectangle $ R = [x_{\\min}, x_{\\max}] \\times [y_{\\min}, y_{\\max}] $ such that all $ n $ points lie inside or on the boundary of $ R $:  \n$$\nA = (x_{\\max} - x_{\\min}) \\cdot (y_{\\max} - y_{\\min})\n$$  \nwhere  \n$$\nx_{\\min} = \\min_{i} x_i, \\quad x_{\\max} = \\max_{i} x_i, \\quad y_{\\min} = \\min_{i} y_i, \\quad y_{\\max} = \\max_{i} y_i\n$$","simple_statement":"Find the smallest axis-aligned rectangle that contains at least k points, and output its area.","has_page_source":false}