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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports)]
#![cfg_attr(feature = "cargo-clippy", allow(redundant_field_names))]

use std::{cmp, fmt};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::io::{self, BufWriter, Read, Write};
use std::ops::{Add, Div, Mul, Sub};
use std::str::{self, FromStr};

fn main() {
    let (n, m, x, a): (usize, usize, usize, Vec<usize>) = {
        let mut sc = InputScanOnce::new(io::stdin(), 1024);
        let (n, m, x) = (sc.next(), sc.next(), sc.next());
        (n, m, x, sc.vec(m))
    };
    let mut w = vec![false; n + 1];
    for &i in &a {
        w[i] = true;
    }
    let r1 = w[1..x].iter().filter(|&&p| p).count();
    let r2 = w[x + 1..n + 1].iter().filter(|&&p| p).count();
    println!("{}", cmp::min(r1, r2));
}

struct InputScanOnce {
    buf: Vec<u8>,
    pos: usize,
}

#[allow(dead_code)]
impl InputScanOnce {
    fn new<R: Read>(mut reader: R, estimated: usize) -> Self {
        let mut buf = Vec::with_capacity(estimated);
        let _ = io::copy(&mut reader, &mut buf).unwrap();
        InputScanOnce { buf: buf, pos: 0 }
    }

    #[inline]
    fn next<T: FromStr>(&mut self) -> T
    where
        T::Err: fmt::Debug,
    {
        let mut start = None;
        loop {
            match (self.buf[self.pos], start.is_some()) {
                (b' ', true) | (b'\n', true) => break,
                (_, true) | (b' ', false) | (b'\n', false) => self.pos += 1,
                (_, false) => start = Some(self.pos),
            }
        }
        let target = &self.buf[start.unwrap()..self.pos];
        unsafe { str::from_utf8_unchecked(target) }.parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        T::Err: fmt::Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<T1: FromStr, T2: FromStr>(&mut self, n: usize) -> Vec<(T1, T2)>
    where
        T1::Err: fmt::Debug,
        T2::Err: fmt::Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<T1: FromStr, T2: FromStr, T3: FromStr>(&mut self, n: usize) -> Vec<(T1, T2, T3)>
    where
        T1::Err: fmt::Debug,
        T2::Err: fmt::Debug,
        T3::Err: fmt::Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        T::Err: fmt::Debug,
    {
        (0..m).map(|_| self.vec(n)).collect()
    }

    fn strings_as_mat<T, F: FnMut(u8) -> T>(&mut self, h: usize, mut f: F) -> Vec<Vec<T>> {
        (0..h)
            .map(|_| {
                let l = self.next::<String>();
                l.as_bytes().iter().cloned().map(&mut f).collect()
            })
            .collect()
    }
}