Appending Mex
Description
Initially Ildar has an empty array. He performs $n$ steps. On each step he takes a subset of integers already added to the array and appends the mex of this subset to the array.
The mex of an multiset of integers is the smallest non-negative integer not presented in the multiset. For example, the mex of the multiset $[0, 2, 3]$ is $1$, while the mex of the multiset $[1, 2, 1]$ is $0$.
More formally, on the step $m$, when Ildar already has an array $a_1, a_2, \ldots, a_{m-1}$, he chooses some subset of indices $1 \leq i_1 < i_2 < \ldots < i_k < m$ (possibly, empty), where $0 \leq k < m$, and appends the $mex(a_{i_1}, a_{i_2}, \ldots a_{i_k})$ to the end of the array.
After performing all the steps Ildar thinks that he might have made a mistake somewhere. He asks you to determine for a given array $a_1, a_2, \ldots, a_n$ the minimum step $t$ such that he has definitely made a mistake on at least one of the steps $1, 2, \ldots, t$, or determine that he could have obtained this array without mistakes.
The first line contains a single integer $n$ ($1 \leq n \leq 100\,000$) — the number of steps Ildar made.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i \leq 10^9$) — the array Ildar obtained.
If Ildar could have chosen the subsets on each step in such a way that the resulting array is $a_1, a_2, \ldots, a_n$, print $-1$.
Otherwise print a single integer $t$ — the smallest index of a step such that a mistake was made on at least one step among steps $1, 2, \ldots, t$.
Input
The first line contains a single integer $n$ ($1 \leq n \leq 100\,000$) — the number of steps Ildar made.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \leq a_i \leq 10^9$) — the array Ildar obtained.
Output
If Ildar could have chosen the subsets on each step in such a way that the resulting array is $a_1, a_2, \ldots, a_n$, print $-1$.
Otherwise print a single integer $t$ — the smallest index of a step such that a mistake was made on at least one step among steps $1, 2, \ldots, t$.
Samples
4
0 1 2 1
-1
3
1 0 1
1
4
0 1 2 239
4
Note
In the first example it is possible that Ildar made no mistakes. Here is the process he could have followed.
- $1$-st step. The initial array is empty. He can choose an empty subset and obtain $0$, because the mex of an empty set is $0$. Appending this value to the end he gets the array $[0]$.
- $2$-nd step. The current array is $[0]$. He can choose a subset $[0]$ and obtain an integer $1$, because $mex(0) = 1$. Appending this value to the end he gets the array $[0,1]$.
- $3$-rd step. The current array is $[0,1]$. He can choose a subset $[0,1]$ and obtain an integer $2$, because $mex(0,1) = 2$. Appending this value to the end he gets the array $[0,1,2]$.
- $4$-th step. The current array is $[0,1,2]$. He can choose a subset $[0]$ and obtain an integer $1$, because $mex(0) = 1$. Appending this value to the end he gets the array $[0,1,2,1]$.
Thus, he can get the array without mistakes, so the answer is $-1$.
In the second example he has definitely made a mistake on the very first step, because he could not have obtained anything different from $0$.
In the third example he could have obtained $[0, 1, 2]$ without mistakes, but $239$ is definitely wrong.