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: Time Limit Exceeded)

use std::io;
use std::cmp;
use std::collections::HashMap;


/// https://beta.atcoder.jp/contests/arc097/tasks/arc097_b
fn main() {
    let (n, m) = {
        let i = read::<usize>();
        (i[0], i[1])
    };

    let p = read::<usize>();
    let mut xy = Vec::new();
    for _ in 0..m {
        let i = read::<usize>();
        xy.push((i[0], i[1]));
    }

    let mut uf = UnionFind::new(n + 1);
    for &(x, y) in &xy {
        uf.unite(x, y);
    }

    let mut hm = HashMap::new();
    for i in &p {
        hm.entry(uf.find(*i))
            .or_insert(Vec::new()).push(i);
    }

    let mut ans = 0;
    for i in 0..p.len() {
        let g = &hm[&uf.find(i + 1)];
        if g.contains(&&p[i]) { ans += 1; }
    }
    println!("{}", ans);
}


#[derive(Debug)]
struct UnionFind {
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            par: (0..n).collect(),
            rank: vec![0; n],
        }
    }

    fn find(&mut self, x: usize) -> usize {
        if self.par[x] == x { x }
        else {
            let p = self.par[x];
            let pp = self.find(p);
            self.par[x] = pp;
            pp
        }
    }

    fn unite(&mut self, x: usize, y: usize) {
        let x = self.find(x);
        let y = self.find(y);
        if x == y { return; }

        match self.rank[x].cmp(&self.rank[y]) {
            cmp::Ordering::Equal => {
                self.par[y] = x;
                self.rank[x] += 1;
            },
            cmp::Ordering::Less => {
                self.par[x] = y;
            },
            cmp::Ordering::Greater => {
                self.par[y] = x;
            }
        }
    }
}


#[allow(dead_code)]
fn read<T>() -> Vec<T>
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.split_whitespace()
        .map(|s| s.trim().parse().unwrap())
        .collect()
}

#[allow(dead_code)]
fn read_one<T>() -> T
where T:
    std::str::FromStr,
    T::Err: std::fmt::Debug {

    let mut buf = String::new();
    io::stdin().read_line(&mut buf).unwrap();
    buf.trim().parse().unwrap()
}