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::*;
use std::str::FromStr;

pub fn read<t: FromStr>() -> t {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

struct UnionFind {
    parent: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        // initialize
        let mut v: Vec<usize> = vec![];
        for i in 0..n + 1 {
            v.push(i)
        }
        let mut s: Vec<usize> = vec![1; n + 1];

        UnionFind { parent: v, size: s }
    }

    fn root(&self, x: usize) -> usize {
        if self.parent[x] == x {
            return x;
        } else {
            return self.root(self.parent[x]);
        }
    }

    fn size(&self, a: usize) -> usize {
        let ra = self.root(a);
        self.size[ra]
    }

    fn unite(&mut self, a: usize, b: usize) {
        let mut ra = self.root(a);
        let mut rb = self.root(b);
        if ra == rb {
            return;
        }
        if self.size[ra] < self.size[rb] {
            std::mem::swap(&mut ra, &mut rb)
        };
        self.size[ra] += self.size[rb];
        self.parent[rb] = ra;
    }

    fn same(&self, a: usize, b: usize) -> bool {
        let ra = self.root(a);
        let rb = self.root(b);
        ra == rb
    }
}

fn main() {
    let n: usize = read();
    let m: usize = read();
    let mut p: Vec<i64> = vec![];
    let mut uf = UnionFind::new(n);
    for _ in 0..n {
        p.push(read());
    }
    let mut xy: Vec<(i64, i64)> = vec![];
    for _ in 0..m {
        let x: i64 = read();
        let y: i64 = read();
        xy.push((x, y));
        uf.unite(x as usize, y as usize);
    }
    let mut ans = 0;

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