Brick Break

AtCoder

IDabc148_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ bricks arranged in a row from left to right. The $i$\-th brick from the left $(1 \leq i \leq N)$ has an integer $a_i$ written on it. Among them, you can break at most $N-1$ bricks of your choice. Let us say there are $K$ bricks remaining. Snuke will be satisfied if, for each integer $i$ $(1 \leq i \leq K)$, the $i$\-th of those brick from the left has the integer $i$ written on it. Find the minimum number of bricks you need to break to satisfy Snuke's desire. If his desire is unsatisfiable, print `-1` instead. ## Constraints * All values in input are integers. * $1 \leq N \leq 200000$ * $1 \leq a_i \leq N$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3
2 1 2

Output #1

1

If we break the leftmost brick, the remaining bricks have integers $1$ and $2$ written on them from left to right, in which case Snuke will be satisfied.

Input #2

3
2 2 2

Output #2

\-1

In this case, there is no way to break some of the bricks to satisfy Snuke's desire.

Input #3

10
3 1 4 1 5 9 2 6 5 3

Output #3

Input #4

1
1

Output #4

0

There may be no need to break the bricks at all.

API Response (JSON)

{
  "problem": {
    "name": "Brick Break",
    "description": {
      "content": "We have $N$ bricks arranged in a row from left to right. The $i$\\-th brick from the left $(1 \\leq i \\leq N)$ has an integer $a_i$ written on it. Among them, you can break at most $N-1$ bricks of your ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc148_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ bricks arranged in a row from left to right.\nThe $i$\\-th brick from the left $(1 \\leq i \\leq N)$ has an integer $a_i$ written on it.\nAmong them, you can break at most $N-1$ bricks of your ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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