Limited Insertion

AtCoder

IDagc032_a

Time2000ms

Memory256MB

Difficulty—

Snuke has an empty sequence $a$. He will perform $N$ operations on this sequence. In the $i$\-th operation, he chooses an integer $j$ satisfying $1 \leq j \leq i$, and insert $j$ at position $j$ in $a$ (the beginning is position $1$). You are given a sequence $b$ of length $N$. Determine if it is possible that $a$ is equal to $b$ after $N$ operations. If it is, show one possible sequence of operations that achieves it. ## Constraints * All values in input are integers. * $1 \leq N \leq 100$ * $1 \leq b_i \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $b_1$ $\dots$ $b_N$ [samples]

Samples

Input #1

3
1 2 1

Output #1

1
1
2

In this sequence of operations, the sequence $a$ changes as follows:

*   After the first operation: $(1)$
*   After the second operation: $(1,1)$
*   After the third operation: $(1,2,1)$

Input #2

2
2 2

Output #2

\-1

$2$ cannot be inserted at the beginning of the sequence, so this is impossible.

Input #3

9
1 1 1 2 2 1 2 3 2

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Limited Insertion",
    "description": {
      "content": "Snuke has an empty sequence $a$. He will perform $N$ operations on this sequence. In the $i$\\-th operation, he chooses an integer $j$ satisfying $1 \\leq j \\leq i$, and insert $j$ at position $j$ in $a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc032_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has an empty sequence $a$.\nHe will perform $N$ operations on this sequence.\nIn the $i$\\-th operation, he chooses an integer $j$ satisfying $1 \\leq j \\leq i$, and insert $j$ at position $j$ in $a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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