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)

pub fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

pub fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

pub fn read_vec2<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

pub fn read_col<T: std::str::FromStr>(n: usize) -> Vec<T> {
    (0..n).map(|_| read()).collect()
}

fn f(u: usize, p: usize, c: u64, edges: &Vec<Vec<(usize, u64)>>, depth: &mut Vec<u64>) {
    depth[u as usize] = c;
    for v in &edges[u] {
        if v.0 == p {
            continue;
        }
        f(v.0, u, c + v.1, edges, depth);
    }
}

fn dist(a: u32, b: u32) -> u32 {
    if a > b {
        a - b
    } else {
        b - a
    }
}

use std::collections::BTreeSet;

fn fun(
    u: usize,
    pvec: &Vec<usize>,
    edges: &Vec<Vec<usize>>,
    vals: &mut BTreeSet<usize>,
    nodes: &mut BTreeSet<usize>,
    checked: &mut BTreeSet<usize>,
) {
    if checked.contains(&u) {
        return;
    }
    checked.insert(u);
    nodes.insert(u);
    vals.insert(pvec[u]);
    for v in &edges[u] {
        fun(*v, pvec, edges, vals, nodes, checked);
    }
}

fn main() {
    let nm: Vec<usize> = read_vec();
    let n = nm[0];
    let m = nm[1];
    let ptmp: Vec<usize> = read_vec();
    let mut pvec: Vec<usize> = vec![1000000];
    for p in ptmp {
        pvec.push(p);
    }

    let mut edges: Vec<Vec<usize>> = vec![vec![]; n + 1];

    for _ in 0..m {
        let xy: Vec<usize> = read_vec();
        let x = xy[0];
        let y = xy[1];
        edges[x].push(y);
        edges[y].push(x);
    }

    let mut checked: BTreeSet<usize> = BTreeSet::new();

    let mut ans: u32 = 0;
    for i in 0..n {
        if checked.contains(&i) {
            continue;
        }
        let mut vals: BTreeSet<usize> = BTreeSet::new();
        let mut nodes: BTreeSet<usize> = BTreeSet::new();
        fun(i, &pvec, &edges, &mut vals, &mut nodes, &mut checked);
        for v in vals {
            if nodes.contains(&v) {
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}