Smallest Value Appearing Exactly Once

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $a_0,a_1,\ldots,a_{n-1}$ with $0\le a_i\le1000$, define

and $U=\{v\in[0,1000]\mid f(v)=1\}$. Print $\min U$ if $U$ is nonempty; otherwise print -1.

Input

The first line contains $n$. The second line contains $n$ integers in $[0,1000]$.

Output

Print the smallest value appearing exactly once, or -1 if none exists.

Subtask

Subtask 1 (20 points): $1\le n\le 10$, $0\le a_i\le 1000$.

Subtask 2 (30 points): $1\le n\le 5000$, $0\le a_i\le 1000$.

Subtask 3 (50 points): $1\le n\le 2\cdot 10^5$, $0\le a_i\le 1000$.

Example

Input

8
5 2 9 2 7 5 4 9

Output

4

Explanation

The output follows directly from the mathematical definition above.