Problem:
Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 ≤ i ≤ N) such that p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

Find the maximum possible number of i such that p_i = i after operations.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.
Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation.

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp;
#[allow(unused_imports)]
use std::cmp::Ordering;

// Input macro from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
  (source = $s:expr, $($r:tt)*) => {
    let mut iter = $s.split_whitespace();
    input_inner!{iter, $($r)*}
  };
  ($($r:tt)*) => {
    #[allow(unused_mut)]
    let mut s = {
      use std::io::Read;
      let mut s = String::new();
      std::io::stdin().read_to_string(&mut s).unwrap();
      s
    };
    let mut iter = s.split_whitespace();
    input_inner!{iter, $($r)*}
  };
}

macro_rules! input_inner {
  ($iter:expr) => {};
  ($iter:expr, ) => {};

  ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
    let $var = read_value!($iter, $t);
    input_inner!{$iter $($r)*}
  };
}

macro_rules! read_value {
  ($iter:expr, ( $($t:tt),* )) => {
    ( $(read_value!($iter, $t)),* )
  };

  ($iter:expr, [ $t:tt ; $len:expr ]) => {
    (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
  };

  ($iter:expr, chars) => {
    read_value!($iter, String).chars().collect::<Vec<char>>()
  };

  ($iter:expr, usize1) => {
    read_value!($iter, usize) - 1
  };

  ($iter:expr, $t:ty) => {
    $iter.next().unwrap().parse::<$t>().expect("Parse error")
  };
}

struct UnionFind {
  par: Vec<usize>,
  rank: Vec<usize>,
}

impl UnionFind {
  fn new(n: usize) -> Self {
    let mut uf = UnionFind {par: vec![0; n], rank: vec![0; n]};
    for (i, item) in uf.par.iter_mut().enumerate() {
      *item = i;
    }
    uf
  }
  fn find(&mut self, x: usize) -> usize {
    if self.par[x] == x {
      x
    } else {
      let px = self.par[x];
      self.par[x] = self.find(px);
      self.par[x]
    }
  }
  fn unite(&mut self, x: usize, y: usize) {
    let x = self.find(x);
    let y = self.find(y);
    match self.rank[x].cmp(&self.rank[y]) {
      Ordering::Less => self.par[x] = y,
      Ordering::Greater => self.par[y] = x,
      Ordering::Equal => {
        self.par[y] = x;
        self.rank[x] += 1;
      }
    }
  }
  fn same(&mut self, x: usize, y: usize) -> bool {
    self.find(x) == self.find(y)
  }
}

fn main() {
  input!{
    n: usize,
    m: usize,
    p: [usize1; n],
    xy: [(usize1, usize1); m]
  }
  let mut uf = UnionFind::new(n);
  for (x, y) in xy {
    uf.unite(x, y);
  }
  let ans = p.iter().enumerate()
    .filter(|&(i, &x)| uf.same(i, x))
    .count();
  println!("{}", ans);
}