{"raw_statement":[{"iden":"statement","content":"You are given a set of n points S = {p1, p2, ..., pn} on the plane. A triple (pi, pj, pk) is called #cf_span(class=[tex-font-style-underline], body=[good]) if no point in S is strictly inside the circumference of these three points. If it is possible, find a good triple!\n\nThe first line contains an integer n, the number of the points (3 ≤ n ≤ 106). The i-th of the next n lines contains two integer numbers xi and yi, the coordinates of pi ( - 104 ≤ xi, yi ≤ 104). No two given points will be equal. \n\nIf a good triple exists, output \"_Yes_\" in the first line. In the next line output three space-separated integers, the numbers of the three points as they appeared in the input.\n\nIf no good triple exists, output \"_No_\" in a single line.\n\n"},{"iden":"input","content":"The first line contains an integer n, the number of the points (3 ≤ n ≤ 106). The i-th of the next n lines contains two integer numbers xi and yi, the coordinates of pi ( - 104 ≤ xi, yi ≤ 104). No two given points will be equal. "},{"iden":"output","content":"If a good triple exists, output \"_Yes_\" in the first line. In the next line output three space-separated integers, the numbers of the three points as they appeared in the input.If no good triple exists, output \"_No_\" in a single line."},{"iden":"examples","content":"Input40 10 0-1 -11 -1OutputYes3 1 2Input3-1 -10 01 1OutputNoInput4-2 -22 -2-2 22 2OutputYes1 3 2"}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ S = \\{p_1, p_2, \\dots, p_n\\} \\subset \\mathbb{R}^2 $ be a set of $ n \\geq 3 $ distinct points in the plane.  \nFor a triple $ (p_i, p_j, p_k) \\in S^3 $ with $ i < j < k $, let $ C(p_i, p_j, p_k) $ denote the unique circle passing through $ p_i, p_j, p_k $ (if non-collinear).  \n\n**Constraint**  \nA triple $ (p_i, p_j, p_k) $ is *good* if:  \n- $ p_i, p_j, p_k $ are not collinear, and  \n- No point $ p_\\ell \\in S \\setminus \\{p_i, p_j, p_k\\} $ lies strictly inside $ C(p_i, p_j, p_k) $.  \n\n**Objective**  \nDetermine whether there exists a good triple in $ S $. If yes, output \"Yes\" followed by the 1-based indices of any such triple; otherwise, output \"No\".","simple_statement":"Given n points on a plane, find three points such that no other point lies inside the circle passing through them. If found, output \"Yes\" and the three point indices; otherwise, output \"No\".","has_page_source":false}