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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main{
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int N=sc.nextInt();
    int[] bricknumber=new int[N];
    int[] index=new int[N+2];//iのあったbricknumberのindex
    int[] check=new int[N+2];
    int last=N;
    
    for(int h=0;h<N;h++){
      bricknumber[h]=sc.nextInt();
    }
    
    check[1]=0;//check[i]はi－1番目の数を見つけたインデックス。そこからiを探し始める
    for(int k=0;k<=N;k++){
      index[k]=-1;
    }
    
    for(int i=1;i<=N;i++){
      for(int j=check[i];j<N;j++){
        if(bricknumber[j]==i){
          index[i]=j;
          check[i+1]=j;
          break;
        }
      }
      if(index[i]==-1){
        last=i-1;
        break;
      }
      
    }
    if(last==0){
      last=N+1;
    }
    
    System.out.println(N-last);
    
  }
}