Planar Tree

AtCoder

IDagc058_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ vertices on a circumference. The vertices are numbered $1$ to $N$ in clockwise order, and Vertex $i$ has an integer $A_i$ written on it, where $A_i$ is $1$, $2$, $3$, or $4$. Here, $A$ contains each of $1$, $2$, $3$, and $4$ at least once. Consider making a tree by adding $N-1$ edges connecting these $N$ vertices. Here, the following conditions must be satisfied. * If Vertices $x$ and $y$ are directly connected by an edge, $|A_x-A_y|=1$. * When the edges are drawn as segments, no two of them intersect except at an endpoint. For instance, the figure below shows a tree that satisfies the conditions: ![image](https://img.atcoder.jp/agc058/8ed6a07d693053455f589dff2d9dccfa.png) Determine whether it is possible to construct a tree that satisfies the conditions. Solve $T$ test cases for each input file. ## Constraints * $1 \leq T \leq 75000$ * $4 \leq N \leq 300000$ * $1 \leq A_i \leq 4$ * $A$ contains each of $1$, $2$, $3$, and $4$ at least once. * The sum of $N$ in one input file does not exceed $300000$. * All values in input are integers. ## 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: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

Output #1

Yes
Yes
No

Input #2

3
8
4 2 3 4 1 2 2 1
8
3 2 2 3 1 3 3 4
8
2 3 3 2 1 4 1 4

Output #2

Yes
Yes
No

The first test case corresponds to the figure in the Problem Statement.

API Response (JSON)

{
  "problem": {
    "name": "Planar Tree",
    "description": {
      "content": "There are $N$ vertices on a circumference. The vertices are numbered $1$ to $N$ in clockwise order, and Vertex $i$ has an integer $A_i$ written on it, where $A_i$ is $1$, $2$, $3$, or $4$. Here, $A$ c",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc058_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ vertices on a circumference. The vertices are numbered $1$ to $N$ in clockwise order, and Vertex $i$ has an integer $A_i$ written on it, where $A_i$ is $1$, $2$, $3$, or $4$. Here, $A$ c...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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