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

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        return UnionFind {
            par: (0..n).map(|i| i).collect::<Vec<usize>>(),
            rank: vec![0; n],
            size: vec![1; n]
        }
    }

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

    pub fn merge(&mut self, x: usize, y: usize) {
        let root_x = self.find_root(x);
        let root_y = self.find_root(y);
        if self.rank[root_x] < self.rank[root_y] {
            self.par[root_x] = root_y;
            self.size[root_y] += self.size[root_x];
        } else {
            self.par[root_y] = root_x;
            self.size[root_x] += self.size[root_y];
            if self.rank[root_x] == self.rank[root_y] {
                self.rank[root_x] += 1;
            } 
        }
    }

    pub fn issame(&mut self, x: usize, y: usize) -> bool {
        if self.find_root(x) == self.find_root(y) {
            return true;
        } else {
            return false;
        }
    }

    pub fn get_size(&mut self, x: usize) -> usize {
        let root_x = self.find_root(x);
        return self.size[root_x];
    }
}

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n = sc.read();
    let m = sc.read();
    let mut p = sc.vec(n);

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

    for _ in 0..m {
        let x: usize = sc.read();
        let y: usize = sc.read();
        uf.merge(x-1, y-1);
    }
    
    let mut ans: usize = 0;
    for i in 0..p.len() {
        p[i] -= 1;
    }

    for i in 0..p.len() {
        if uf.issame(p[i], i) {
            ans += 1;
        }
    }
    println!("{}", ans);
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n')
            .take_while(|&b| b != b' ' && b != b'\n')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}