D - Brick Break

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.

3
2 1 2

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.

3
2 2 2

-1

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

10
3 1 4 1 5 9 2 6 5 3

7

1
1

0

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