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)

#[test]
fn test_solve() {
    assert_eq!(solve("5 2\n5 3 1 4 2\n1 3\n5 4\n"), "2\n");
    assert_eq!(solve("3 2\n3 2 1\n1 2\n2 3\n"), "3\n");
    assert_eq!(
        solve("10 8\n5 3 6 8 7 10 9 1 2 4\n3 1\n4 1\n5 9\n2 5\n6 5\n3 5\n8 9\n7 9\n"),
        "8\n"
    );
    assert_eq!(solve("5 1\n1 2 3 4 5\n1 5\n"), "5\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let n: usize = sc.read();
    let m: usize = sc.read();
    let p: Vec<usize> = (0..n).map(|_| sc.read()).collect();
    let xy: Vec<(usize, usize)> = (0..m).map(|_| (sc.read(), sc.read())).collect();
    
    let mut djs = DisjointSet::new(n);
    for &(x,y) in &xy {
        djs.unite(x-1, y-1);
    }
    let ans = (0..n).filter(|&i| {
        djs.find(i) == djs.find(p[i] - 1)
    }).count();
    
    format!("{}\n", ans)
}
struct DisjointSet {
    prt: Vec<usize>,
    rnk: Vec<usize>,
}
impl DisjointSet {
    fn new(n: usize) -> DisjointSet {
        DisjointSet {
            prt: (0..n).collect(),
            rnk: vec![0; n],
        }
    }
    fn unite(&mut self, x: usize, y: usize) {
        let x = self.find(x);
        let y = self.find(y);
        if x == y {
            return;
        }
        use std::cmp::Ordering;
        match self.rnk[x].cmp(&self.rnk[y]) {
            Ordering::Less => self.prt[x] = y,
            Ordering::Greater => self.prt[y] = x,
            Ordering::Equal => {
                self.prt[y] = x;
                self.rnk[x] += 1;
            }
        };
    }
    fn find(&mut self, x: usize) -> usize {
        if self.prt[x] == x {
            x
        } else {
            let xrt = self.prt[x];
            self.prt[x] = self.find(xrt);
            self.prt[x]
        }
    }
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}