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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use proconio::input;
use proconio::marker::*;
use std::collections::{HashSet, HashMap};

fn size(
  parents: &mut Vec<isize>,
  i: isize
) -> isize {
  let ii = find(parents, i) as usize;
  -1 * parents[ii]
}

fn find(
  parents: &mut Vec<isize>,
  i: isize
) -> isize {
  let ui = i as usize;
  if -1 < parents[ui] {
    parents[ui] = find(parents, parents[ui]);
    parents[ui]
  } else {
    i
  }
}

fn connect(
  parents: &mut Vec<isize>,
  a: isize,
  b: isize,
) -> bool {
  let pa = find(parents, a);
  let pb = find(parents, b);
  
  if pa == pb { return false }
  
  let av = size(parents, pa);
  let bv = size(parents, pb);
  
  let upa = pa as usize;
  let upb = pb as usize;
  if av < bv {
    parents[upb] += parents[upa];
    parents[upa] = pb;
  } else {
    parents[upa] += parents[upb];
    parents[upb] = pa;
  }
  true
}

fn main() {
  input! {
    n: usize,
    m: usize,
    vals: [Usize1;n],
    queries: [(Isize1, Isize1);m]
  }
  
  let mut parents: Vec<isize> = vec![-1;n];
  for (a, b) in queries.iter() {
    connect(&mut parents, *a, *b);
  }
  for (a, b) in queries {
    connect(&mut parents, a, b);
  }
  
  let mut map: HashMap<usize, HashSet<usize>> = HashMap::new();
  
  for i in 0..n {
    let v = parents[i];
    if v < 0 {
      let entry = map.entry(i).or_insert(HashSet::new());
      entry.insert(i);
    } else {
      let uv = v as usize;
      let entry = map.entry(uv).or_insert(HashSet::new());
      entry.insert(i);
    }
  }
  
  let mut result = 0;
  for (_, v) in map {
    for vv in v.iter() {
      let vvv = vals[*vv];
      if v.contains(&vvv) {
        result += 1;
      }
    }
  }
  
  println!("{}", result);
}