Problem:
Score : 200 points

Problem Statement

There are N + 1 squares arranged in a row, numbered 0, 1, ..., N from left to right.

Initially, you are in Square X.
You can freely travel between adjacent squares. Your goal is to reach Square 0 or Square N.
However, for each i = 1, 2, ..., M, there is a toll gate in Square A_i, and traveling to Square A_i incurs a cost of 1.
It is guaranteed that there is no toll gate in Square 0, Square X and Square N.

Find the minimum cost incurred before reaching the goal.

Constraints

1 \leq N \leq 100

1 \leq M \leq 100

1 \leq X \leq N - 1

1 \leq A_1 < A_2 < ... < A_M \leq N

A_i \neq X

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M X
A_1 A_2 ... A_M

Output

Print the minimum cost incurred before reaching the goal.

Sample Input 1

5 3 3
1 2 4

Sample Output 1

1

The optimal solution is as follows:

First, travel from Square 3 to Square 4. Here, there is a toll gate in Square 4, so the cost of 1 is incurred.

Then, travel from Square 4 to Square 5. This time, no cost is incurred.

Now, we are in Square 5 and we have reached the goal.

In this case, the total cost incurred is 1.

Sample Input 2

7 3 2
4 5 6

Sample Output 2

0

We may be able to reach the goal at no cost.

Sample Input 3

10 7 5
1 2 3 4 6 8 9

Sample Output 3

3

Solution in Perl (v5.18.2) (judge verdict: Accepted)

#!/usr/bin/perl

my ($n,$m,$x) = map {$_ - 0} split(/\s+/o,<STDIN>);
my @a = map {$_ - 0} split(/\s+/o,<STDIN>);

my $res = 0;
if( $n > 2 ){
  my @aa = ();
  $#aa = $n;
  $aa[$_] = 1 foreach (@a);
  my @l = @aa[0..($x-1)];
  my $l = 0;
  $l += $_ foreach @l;
  my @r = @aa[($x+1)..$n];
  my $r = 0;
  $r += $_ foreach @r;
  $res = ($l<$r) ? $l : $r;
}
print "$res\n";

exit(0);