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: Time Limit Exceeded)

use std::io::*;
use std::collections::HashSet;

fn read<T: std::str::FromStr>() -> T {
    let stdin = stdin();
    let mut buf = String::new();
	stdin.lock().read_line(&mut buf);
	buf.trim().parse().ok().unwrap()
}

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

fn read_vec_char() -> Vec<char> {
    read::<String>().chars().collect()
}

fn read_mat<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

fn read_mat_char(n: usize) -> Vec<Vec<char>> {
    (0..n).map(|_| read_vec_char()).collect()
}

fn find(uf: &mut Vec<(usize,usize,HashSet<usize>)>, x: usize) -> usize {
    let p = uf[x].0;
    if p != x {
        let r = find(uf, p);
        uf[x].0 = r;
    }
    uf[x].0
}

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

    let mut uf: Vec<(usize,usize,HashSet<usize>)> = (0..n).map(|x| {let mut s = HashSet::new(); s.insert(x); (x,0,s)}).collect();
    for i in 0..m {
        let xy = read_vec::<usize>();
        let (x,y) = (xy[0]-1,xy[1]-1);
        let xr = find(&mut uf,x);
        let yr = find(&mut uf,y);
        if xr == yr { continue; }
        if uf[xr].1 < uf[yr].1 {
            uf[xr].0 = yr;
            uf[yr].2 = uf[yr].2.union(&uf[xr].2).map(|x| *x).collect();
        } else {
            uf[yr].0 = xr;
            uf[xr].2 = uf[xr].2.union(&uf[yr].2).map(|x| *x).collect();
            if uf[xr].1 == uf[yr].1 {
                uf[xr].1 += 1;
            }
        }
    }
    let mut ans = 0;
    for i in 0..n {
        let s1 = &uf[i].2;
        if uf[i].0 == i {
            let s2 = s1.iter().clone().map(|j| p[*j]-1).collect();
            ans += s1.intersection(&s2).collect::<HashSet<_>>().len();
        }
    }
    println!("{}",ans);
}