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)

use std::io::prelude::*;

fn input<T: std::str::FromStr>() -> T {
    let stdin = std::io::stdin();
    let it = stdin.lock().bytes().map(|c| c.unwrap() as char);
    let (fs, ft) = (|c: &char| c.is_whitespace(), |c: &char| !c.is_whitespace());
    let token = it.skip_while(fs).take_while(ft).collect::<String>();
    token.parse().ok().unwrap()
}
#[allow(dead_code)]
fn with_stdout_lock<F: FnOnce(std::io::BufWriter<std::io::StdoutLock>)>(f: F) {
    let out = std::io::stdout();
    f(std::io::BufWriter::new(out.lock()));
}
#[allow(unused_macros)]
macro_rules! debug {
    ($($var:expr),*) => { #[cfg(debug_assertions)] {
        $({ match &$var { v => eprint!("{}={:?} ", stringify!($var), v) } })*
        eprintln!();
    }};
}

fn main() {
    let n: usize = input();
    let m: usize = input();
    let p: Vec<i32> = (0..n).map(|_| input()).collect();
    let xy: Vec<(usize, usize)> = (0..m).map(|_| (input(), input())).collect();

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

    let mut ans = 0;
    for i in 0..n {
        let p = p[i] as usize - 1;
        if p == i || uf.find(i) == uf.find(p) {
            ans += 1;
        }
    }
    println!("{}", ans);
}

struct UnionFind {
    parent: Vec<usize>,
    size: Vec<usize>,
}
#[allow(dead_code)]
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind {
            parent: (0..n).collect(),
            size: vec![1; n],
        }
    }
    fn find(&mut self, x: usize) -> usize {
        if self.parent[x] == x {
            x
        } else {
            let p = self.parent[x];
            self.parent[x] = self.find(p);
            self.parent[x]
        }
    }
    fn union(&mut self, x: usize, y: usize) -> bool {
        let mut x = self.find(x);
        let mut y = self.find(y);
        if x == y {
            false
        } else {
            if self.size[x] < self.size[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.parent[y] = x;
            self.size[x] += self.size[y];
            true
        }
    }
    fn size(&mut self, x: usize) -> usize {
        let p = self.find(x);
        self.size[p]
    }
}