Summation By Construction

AtCoder

IDagc061_b

Time2000ms

Memory256MB

Difficulty—

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. We 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. Formally, 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: * For each $i = 0, \ldots, 2k - 1$, vertices $w_i$ and $w_{i + 1}$ are connected with an edge of color $k$, * No other edges of color $k$ exist. Find any suitable coloring, or determine that it doesn't exist. For each input file, solve $T$ test cases. ## Constraints * $1 \leq T \leq 100$ * $1 \leq N \leq 100$ ## Input Input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each case is in the following format: $N$ [samples]

Samples

Input #1

2
1
2

Output #1

Yes
1 1
No

API Response (JSON)

{
  "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 $u_j$ (...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments