{"problem":{"name":"Four TSP","description":{"content":"There is a complete graph with four vertices numbered $1, 2, 3, 4$. You will now assign weights to each of the six edges. Each weight should be a positive integer, and the sum of the six weights shoul","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc212_a"},"statements":[{"statement_type":"Markdown","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.\n\n## Constraints\n\n*   $6 \\le K \\le 5000$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc212_a","tags":[],"sample_group":[["7","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 $24$."],["2026","513760748"]],"created_at":"2026-03-03 11:01:13"}}