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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
int n,a[200005];
bool check(int x){
    int t=1;
    for(int k=1;k<=n;k++){
            if(x==t && t==a[k])
            return true;
        if(a[k]==t)
            t++;

    }
    return false;
}
int main(){
cin>>n;
for(int k=1;k<=n;k++)
    cin>>a[k];
int l=1,r=n;
while(r-l>1){
   int mid=(l+r)/2;
   if(!check(mid))
        r=mid;
   else l=mid;
}
int pas=-1;
if(check(l))
    pas=l;
if(check(r))
    pas=r;
    if(pas==-1)
        cout<<pas;
    else
cout<<n-pas;
return 0;
}