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)

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()
}

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

struct UnionFindTree {
    n: usize,
    par: Vec<usize>,
    rank: Vec<usize>,
}

impl UnionFindTree {
    pub fn new(n: usize) -> UnionFindTree {
        let mut par: Vec<usize> = Vec::new();
        for i in 0..n {
            par.push(i);
        }
        let rank = vec![0; n];
        UnionFindTree{
            n: n,
            par: par,
            rank: rank,
        }
    }

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

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

    fn unite(&mut self, x: usize, y: usize) {
        if self.same(x, y) {
            return;
        }
        let mut x = self.find(x);
        let mut y = self.find(y);
        if self.rank[y] > self.rank[x] {
            std::mem::swap(&mut x, &mut y);
        }
        self.par[x] = y;
        if self.rank[x] == self.rank[y] {
          self.rank[x] = self.rank[y] + 1;
      }
    }
}

fn main() {
    let nm: Vec<usize> = read_vec();
    let (n, m) = (nm[0], nm[1]);
    let mut p: Vec<usize> = read_vec();
    let mut uft = UnionFindTree::new(n + 1);
    for _i in 0..m {
        let xy = read_vec::<usize>();
        let (x, y) = (xy[0] - 1, xy[1] - 1);
        uft.unite(x, y);
    }

    let mut ans:i32 = 0;
    for i in 0..p.len() {
        p[i] -= 1;
    }
    for i in 0..p.len() {
        if uft.same(p[i], i) {
            ans += 1;
        }
    }
    println!("{:?}", ans);
}