Decimal Sequences

Time Limit : 1 sec, Memory Limit : 262144 KB

Problem A Decimal Sequences

Hanako learned the conjecture that all the non-negative integers appear in the infinite digit sequence of the decimal representation of $\pi$ = 3.14159265..., the ratio of a circle's circumference to its diameter. After that, whenever she watches a sequence of digits, she tries to count up non-negative integers whose decimal representations appear as its subsequences.

For example, given a sequence "3 0 1", she finds representations of five non-negative integers 3, 0, 1, 30 and 301 that appear as its subsequences.

Your job is to write a program that, given a finite sequence of digits, outputs the smallest non-negative integer not appearing in the sequence. In the above example, 0 and 1 appear, but 2 does not. So, 2 should be the answer.

Input

The input consists of a single test case.

$n$
$d_1$ $d_2$ ... $d_n$

$n$ is a positive integer that indicates the number of digits. Each of $d_k$'s $(k = 1, ... , n)$ is a digit. There is a space or a newline between $d_k$ and $d_{k+1}$ $(k = 1, ..., n - 1)$.

You can assume that $1 \leq n \leq 1000$.

Output

Print the smallest non-negative integer not appearing in the sequence.

Sample Input 1

3
3 0 1

Sample Output 1

2

Sample Input 2

11
9 8 7 6 5 4 3 2 1 1 0

Sample Output 2

12

Sample Input 3

10
9 0 8 7 6 5 4 3 2 1

Sample Output 3

10

Sample Input 4

100
3 6 7 5 3 5 6 2 9 1 2 7 0 9 3 6 0 6 2
6 1 8 7 9 2 0 2 3 7 5 9 2 2 8 9 7 3 6
1 2 9 3 1 9 4 7 8 4 5 0 3 6 1 0 6 3 2
0 6 1 5 5 4 7 6 5 6 9 3 7 4 5 2 5 4 7
4 4 3 0 7 8 6 8 8 4 3 1 4 9 2 0 6 8 9
2 6 6 4 9

Sample Output 4

11

Sample Input 5

100
7 2 7 5 4 7 4 4 5 8 1 5 7 7 0 5 6 2 0
4 3 4 1 1 0 6 1 6 6 2 1 7 9 2 4 6 9 3
6 2 8 0 5 9 7 6 3 1 4 9 1 9 1 2 6 4 2
9 7 8 3 9 5 5 2 3 3 8 4 0 6 8 2 5 5 0
6 7 1 8 5 1 4 8 1 3 7 3 3 5 3 0 6 0 6
5 3 2 2 2

Sample Output 5

86

Sample Input 6

1
3

Sample Output 6

0

Source: ACM International Collegiate Programming Contest , Asia Regional Tsukuba, Tsukuba, Japan, 2015-11-29
http://icpc.iisf.or.jp/2015-tsukuba/