Ball Redistribution

AtCoder

IDagc068_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ boxes numbered from $1$ to $N$, and $N$ balls numbered from $1$ to $N$. You have assigned Snuke the following **procedure** as homework. * Put each ball into any box he likes. Multiple balls can be placed in the same box, and there can be boxes without balls. * For $i = 1, 2, \cdots, N$ in this order, perform the following operations. * If box $i$ contains no balls, do nothing. * If box $i$ contains balls, take all of them out and arrange them in a line **in any order he likes**. Let $k$ be the number of balls taken out, and $(x_1, x_2, \cdots, x_k)$ be the ball numbers in the line. For each $1 \leq j \leq k$, put ball $x_j$ into box $x_{j+1}$. Here, $x_{k+1}$ means $x_1$. All these operations of putting balls into boxes happen simultaneously. He claims that he has completed the homework and reports the final state to you. Specifically, he says that ball $i$ is in box $A_i$ after the procedure. You doubt whether he has correctly performed the procedure. Determine whether the state he reported is a possible result of the procedure. There are $T$ test cases for each input. ## Constraints * $1 \leq T \leq 250000$ * $1 \leq N \leq 250000$ * $1 \leq A_i \leq N$ * The sum of $N$ over all test cases in each input is at most $250000$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each test case is given in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

5
3
1 1 1
3
2 2 2
5
1 2 3 4 5
10
8 3 8 10 1 5 3 1 6 4
10
1 5 1 2 4 8 8 6 7 3

Output #1

Yes
No
Yes
No
Yes

Consider the first test case. The following steps yield the state Snuke reported, so the answer is `Yes`.

*   Put balls $1, 2, 3$ into boxes $1, 1, 2$, respectively.
*   Take out the balls from box $1$ and arrange them as $(2, 1)$.
    *   Put ball $2$ into box $1$.
    *   Put ball $1$ into box $2$.
*   Take out the balls from box $2$ and arrange them as $(1, 3)$.
    *   Put ball $1$ into box $3$.
    *   Put ball $3$ into box $1$.
*   Take out the balls from box $3$ and arrange them as $(1)$.
    *   Put ball $1$ into box $1$.
*   Now, balls $1, 2, 3$ are all in box $1$.

API Response (JSON)

{
  "problem": {
    "name": "Ball Redistribution",
    "description": {
      "content": "There are $N$ boxes numbered from $1$ to $N$, and $N$ balls numbered from $1$ to $N$. You have assigned Snuke the following **procedure** as homework. *   Put each ball into any box he likes. Multipl",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc068_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ boxes numbered from $1$ to $N$, and $N$ balls numbered from $1$ to $N$.\nYou have assigned Snuke the following **procedure** as homework.\n\n*   Put each ball into any box he likes. Multipl...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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