{"problem":{"name":"Summation By Construction","description":{"content":"There is a graph with $N$ vertices $v_1, \\ldots, v_N$ on the left, and $N + 1$ vertices $u_1, \\ldots, u_{N + 1}$ on the right. Each vertex $v_i$ ($1 \\leq i \\leq N$) is connected to each vertex $u_j$ (","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc061_b"},"statements":[{"statement_type":"Markdown","content":"There is a graph with $N$ vertices $v_1, \\ldots, v_N$ on the left, and $N + 1$ vertices $u_1, \\ldots, u_{N + 1}$ on the right. Each vertex $v_i$ ($1 \\leq i \\leq N$) is connected to each vertex $u_j$ ($1 \\leq j \\leq N + 1$), that is, the graph contains $N(N + 1)$ edges.\nWe color every edge with one of the $N$ colors $1, \\ldots, N$. A coloring is **suitable** if for each $k = 1, \\ldots, N$ there are exactly $2k$ edges of color $k$, and those edges form a simple path.\nFormally, for each $k = 1, \\ldots, N$ there should exist a sequence of distinct vertices $w_0, \\ldots, w_{2k}$ such that all of the following is true:\n\n*   For each $i = 0, \\ldots, 2k - 1$, vertices $w_i$ and $w_{i + 1}$ are connected with an edge of color $k$,\n*   No other edges of color $k$ exist.\n\nFind any suitable coloring, or determine that it doesn't exist.\nFor each input file, solve $T$ test cases.\n\n## Constraints\n\n*   $1 \\leq T \\leq 100$\n*   $1 \\leq N \\leq 100$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$T$\n$case_1$\n$case_2$\n$\\vdots$\n$case_T$\n\nEach case is in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc061_b","tags":[],"sample_group":[["2\n1\n2","Yes\n1 1\nNo"]],"created_at":"2026-03-03 11:01:14"}}