{"raw_statement":[{"iden":"problem statement","content":"A triangle $ABC$ on the $xy$\\-plane is said to be a good triangle when it satisfies all of the following conditions.\n\n*   Each of the vertices $A$, $B$, and $C$ is a lattice point whose $x$\\- and $y$\\-coordinates are between $0$ and $10^{8}$, inclusive.\n*   The triangle $ABC$ (**including** the perimeter and vertices) wholly contains exactly one square of area $1$ whose vertices are all lattice points.\n\nYou are given a positive integer $S$.\nDetermine if there is a good triangle of area $\\frac{S}{2}$, and construct one if it exists.\nFor each input file, you have $T$ test cases to solve."},{"iden":"constraints","content":"*   $1\\leq T\\leq 10^{5}$\n*   $1\\leq S\\leq 10^{8}$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$T$\n$\\text{case}_{1}$\n$\\text{case}_{2}$\n$\\vdots$\n$\\text{case}_{T}$\n\nEach case is given in the following format:\n\n$S$"},{"iden":"sample input 1","content":"3\n1\n4\n15"},{"iden":"sample output 1","content":"No\nYes\n1 1 1 3 3 3\nYes\n5 1 7 8 4 5\n\n![image](https://img.atcoder.jp/arc167/d6986726412312ca9a6e022bc8e722ce.png)\nIn the figure, the left and right triangles correspond to the second and third test cases, respectively."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}