{"raw_statement":[{"iden":"problem statement","content":"There is a complete graph with four vertices numbered $1, 2, 3, 4$.\nYou will now assign weights to each of the six edges. Each weight should be a positive integer, and the sum of the six weights should be exactly $K$.  \nMore formally, you choose positive integers $x_{i,j} \\ (1\\leq i<j\\leq 4)$ such that $\\sum_{1\\leq i<j\\leq 4}x_{i,j}=K$, and assign weight $x_{i,j}$ to the edge connecting $i$ and $j$.\nFor this weighted graph $G$, let $f(G)$ be the minimum sum of edge weights in a cycle that **passes through all vertices**. Find the sum, modulo $998244353$, of $f(G)$ over all possible $G$.\nWhat is a complete graph?A complete graph is a graph with an edge between every pair of two distinct vertices."},{"iden":"constraints","content":"*   $6 \\le K \\le 5000$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$K$"},{"iden":"sample input 1","content":"7"},{"iden":"sample output 1","content":"24\n\nThe possible graphs are the ones where one of the six edges has weight $2$ and the other edges have weight $1$. There are six such graphs $G$, and we have $f(G)=4$ for each of them, so the answer is $24$."},{"iden":"sample input 2","content":"2026"},{"iden":"sample output 2","content":"513760748"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}