Problem:
Score : 400 points

Problem Statement

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

Output

Print the minimum number of bricks that need to be broken to satisfy Snuke's desire, or print -1 if his desire is unsatisfiable.

Sample Input 1

3
2 1 2

Sample 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.

Sample Input 2

3
2 2 2

Sample Output 2

-1

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

Sample Input 3

10
3 1 4 1 5 9 2 6 5 3

Sample Output 3

7

Sample Input 4

1
1

Sample Output 4

0

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

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
  $n = intval(fgets(STDIN));
  $a = explode(" ", trim(fgets(STDIN)));

  $result = -1;

  $idx=0;
  $count = 0;
  $max = $n;
  while($idx<$max){
    if($a[$idx]==$idx+1){
      //現在地が一致したので次へ
      $idx++;
    }else{
      //現在地を砕く
      array_splice($a, $idx, 1);
      $count++;
      //砕いたのでループ数を減らす
      $max--;
    }
  }
  if($count==$n){
    $result = -1;
  }else{
    $result = $count;
  }

/*  
  for($i=0; $i<$n; $i++){
    if($a[$i]==$i+1){
      //初期位置のままでOK
      $result = 0;
      break;
    }
    //前にあるブロック数＝砕ける数
    $breakable = $i;
    
    if($a[$i]>$i+1){
      //数値＞位置なら、砕いても調整不可なので次へ
    }else{
      //位置-値=砕かないといけない回数
      $tmpResult = $i+1-$a[$i];
      
      if($tmpResult<=$breakable && ($result==-1 || $tmpResult < $result)){
        $result = $tmpResult;
      }
    }
  }
*/
  echo $result."\n";