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 read1<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 readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
    let s = read1::<String>();
    s.split(delimiter).map(|e| e.parse().ok().unwrap()).collect::<Vec<T>>()
}

pub struct UnionFind {
    pub par: Vec<usize>,
    pub rank: Vec<usize>,
}

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

    pub fn root(&mut self, x: usize) -> usize {
        let cand = self.par[x];
        if cand == x {
            return x;
        } else {
            let ret = self.root(cand);
            self.par[x] = ret;
            return ret;
        }
    }

    pub fn same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }

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

        if self.rank[root_x] < self.rank[root_y] {
            self.par[root_x] = self.par[root_y];
        } else {
            self.par[root_y] = self.par[root_x];
            if self.rank[root_y] == self.rank[root_x] {
                self.rank[root_x] += 1;
            }
        }
    }
}

fn main() {
    let nm = readn::<usize>(" ");
    let n = nm[0];
    let m = nm[1];
    let p = readn::<usize>(" ");
    let mut uf = UnionFind::new(n);

    for _ in 0..m {
        let xy = readn::<usize>(" ");
        let x = xy[0] - 1;
        let y = xy[1] - 1;
        uf.unite(x, y);
    }

    let root = (0..n).map(|i| uf.root(i)).collect::<Vec<usize>>();

    let mut ans = 0;
    for i in 0..n {
        if root[i] == root[p[i]-1] {
            ans += 1;
        }
    }

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