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::collections::{BTreeMap, BTreeSet};

use io::*;
use union_find::*;

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

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

    let ps: Vec<usize> = (0..n).map(|_| sc.next::<usize>() - 1).collect();

    let xys: Vec<(usize, usize)> = (0..m)
        .map(|_| {
            let x: usize = sc.next();
            let y: usize = sc.next();
            (x - 1, y - 1)
        })
        .collect();

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

    for &(x, y) in xys.iter() {
        uf.union(x, y);
    }

    let mut unions: BTreeMap<usize, Vec<usize>> = BTreeMap::new();

    for i in 0..n {
        let parent = uf.find(i);
        unions.entry(parent).or_insert(Vec::new()).push(i);
    }

    let mut ans = 0;
    for (_, v) in unions {
        let mut ss = BTreeSet::new();
        for &ix in v.iter() {
            ss.insert(ps[ix]);
        }

        for ix in v {
            if ss.contains(&ix) {
                ans += 1;
            }
        }
    }

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

//----------

pub mod io {
    use std;

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

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

        pub 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::<T>().unwrap()
        }
    }

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

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

    pub fn read_line() -> String {
        let mut s = String::new();
        std::io::stdin().read_line(&mut s).unwrap();
        s.trim_right().to_owned()
    }
}

pub mod union_find {
    pub struct UnionFind(Vec<usize>);

    impl UnionFind {
        pub fn new(n: usize) -> UnionFind {
            UnionFind((0..n).collect())
        }

        pub fn find(&mut self, i: usize) -> usize {
            if self.0[i] == i {
                i
            } else {
                let p = self.0[i];
                self.0[i] = self.find(p);
                self.0[i]
            }
        }

        pub fn union(&mut self, i: usize, j: usize) {
            let ni = self.find(i);
            let nj = self.find(j);
            self.0[ni] = nj;
        }
    }
}