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::str::FromStr;
use std::fmt::Debug;
use std::cmp;

#[allow(dead_code)]
fn read_as_vec<T>() -> Vec<T>
where T: FromStr, <T as FromStr>::Err : Debug{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().split_whitespace().map(|c| T::from_str(c).unwrap()).collect()

}

#[allow(dead_code)]
fn read_as_string() -> String{
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s.trim().to_string()
}

struct UnionFind{
    v: Vec<usize>
}

impl UnionFind{
    fn new(n: usize) -> UnionFind{
        let mut v: Vec<usize> = Vec::new();
        for i in 0..n{
         v.push(i);
        }
        UnionFind{v:v}
    }


    fn find(&mut self, i: usize) -> usize{
        if self.v[i] == i{
            i
        }else{
            let ni = self.v[i];
            self.v[i] = self.find(ni);
            self.v[i]
        }
    }

    fn union(&mut self, i: usize, j: usize){
        let root_i = self.find(i);
        let root_j = self.find(j);
        self.v[root_i] = root_j;
    }

}

fn main(){
    let line = read_as_vec::<usize>();
    let (n, m) = (line[0], line[1]);
    let p = read_as_vec::<usize>();

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

    for _ in 0..m{
        let line = read_as_vec::<usize>();
        let (x, y) = (line[0]-1, line[1]-1);
        uf.union(x, y);

    }


    let mut ans = 0;
    for i in 0..n{
        if uf.find(p[i]-1) == uf.find(i){
            ans += 1;
        }
    }
    println!("{}", ans);
}