Missing Numbers

Source: Kattis

Version: Phuoc Hung OJ Extended

Problem

The child recites strictly increasing integers $a_1<\cdots<a_n$. Let $M=\{x\in\mathbb Z:1\le x\le a_n,\ x\notin\{a_1,\ldots,a_n\}\}$. Print every missing number in increasing order; if $M$ is empty, print good job.

Input

The first line contains $n$. The next $n$ lines contain strictly increasing values in $[1,200]$.

Output

Print missing numbers one per line, or good job when none are missing.

Subtask

Subtask 1 (20 points): $a_n\le20$.

Subtask 2 (30 points): $a_n\le100$.

Subtask 3 (50 points): $1\le n\le100$, $a_n\le200$.

Example

Input

5
1
2
4
5
7

Output

3
6

Explanation

Numbers 3 and 6 are missing from 1 through 7.