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)

use std::io::Read;
use std::collections::{VecDeque, HashSet};

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let m: usize = iterator.next().unwrap().parse().unwrap();
    let p: Vec<usize> = (0..n).map(|_| iterator.next().unwrap().parse::<usize>().unwrap() - 1).collect();
    let mut graph: Vec<Vec<usize>> = vec![Vec::new(); n];
    for _ in 0..m {
        let xi: usize = iterator.next().unwrap().parse().unwrap();
        let yi: usize = iterator.next().unwrap().parse().unwrap();
        graph[xi - 1].push(yi - 1);
        graph[yi - 1].push(xi - 1);
    }

    let mut ans: usize = 0;
    let mut visited: Vec<bool> = vec![false; n];
    for i in 0..n {
        if visited[i] {
            continue;
        }
        let mut q: VecDeque<usize> = VecDeque::new();
        q.push_back(i);
        visited[i] = true;
        let mut nodes = HashSet::new();
        let mut numbers = HashSet::new();
        nodes.insert(i);
        numbers.insert(p[i]);
        if i == p[i] {
            ans += 1;
        }
        while let Some(u) = q.pop_front() {
            for &node in &graph[u] {
                if visited[node] {
                    continue;
                }
                q.push_back(node);
                visited[node] = true;
                let number = p[node];
                if node == number {
                    ans += 1;
                }
                if numbers.contains(&node) {
                    ans += 1;
                }
                if nodes.contains(&number) {
                    ans += 1;
                }
                numbers.insert(number);
                nodes.insert(node);
            }
        }
    }
    ans.to_string()
}