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)

struct UnionFindTree {
    par: Vec<usize>,
}

impl UnionFindTree {
    fn new(n: usize) -> UnionFindTree {
        UnionFindTree {
            par: (0..n).collect(),
        }
    }

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

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

    fn unite(&mut self, x: usize, y: usize) {
        let rootx = self.root(x);
        let rooty = self.root(y);
        if rootx == rooty {
            ;
        } else {
            self.par[rootx] = rooty;
        }
    }
}

fn main() {
    let s = read_string();
    let mut sc = Scanner::new(&s);

    let n: usize = sc.next();
    let m: usize = sc.next();

    let mut ps = Vec::with_capacity(n);

    for _i in 0..n {
        let p: usize = sc.next();
        ps.push(p-1);
    }

    let mut uf = UnionFindTree::new(n);

    for _i in 0..m {
        let x: usize = sc.next();
        let y: usize = sc.next();
        uf.unite(x-1, y-1);
    }

    let mut ans = 0;

    for i in 0..n {
        if uf.same(ps[i], i) {
            ans += 1;
        }
    }

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

// 以下、たなこふ先生からぱくったやつ (´･_･`)

struct Scanner<'a> {
    iter: std::str::SplitWhitespace<'a>,
}

impl<'a> Scanner<'a> {
    fn new(s: &str) -> Scanner {
        Scanner {
            iter: s.split_whitespace(),
        }
    }

    fn next<T>(&mut self) -> T
        where T: std::str::FromStr,
              <T as std::str::FromStr>::Err: std::fmt::Debug,
    {
        let s = self.iter.next().unwrap();
        s.parse().unwrap()
    }
}

fn read_string() -> String {
    use std::io::Read;

    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    buf
}