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)

#![allow(unused_imports)]
#![allow(dead_code)]

use std::collections::*;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let m: usize = sc.read();
    let p: Vec<usize> = sc.vec(n);
    let mut uf: UnionFind = UnionFind::new(n);
    for _ in 0..m {
        let x: usize = sc.read();
        let y: usize = sc.read();
        uf.unite(x - 1, y - 1);
    }
    let mut ans = 0;
    for i in 0..n {
        if uf.is_same(i, p[i] - 1) {
            ans += 1;
        }
    }
    println!("{}", ans);
}

#[derive(Debug, Copy, Clone)]
enum UFdata {
    Child(usize),
    Root(usize),
}
struct UnionFind {
    data: Vec<UFdata>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        UnionFind {
            data: vec![UFdata::Root(1); n],
        }
    }
    fn root(&mut self, x: usize) -> usize {
        match self.data[x] {
            UFdata::Child(p) => {
                let res = self.root(p);
                self.data[x] = UFdata::Child(res);
                res
            }
            UFdata::Root(_) => x,
        }
    }
    pub fn size(&mut self, x: usize) -> usize {
        match self.data[x] {
            UFdata::Root(m) => m,
            UFdata::Child(_) => {
                let r = self.root(x);
                self.size(r)
            }
        }
    }
    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let (mut u, mut v) = (self.root(x), self.root(y));
        if u == v {
            false
        } else {
            if self.size(u) < self.size(v) {
                std::mem::swap(&mut u, &mut v);
            }
            self.data[u] = UFdata::Root(self.size(u) + self.size(v));
            self.data[v] = UFdata::Child(u);
            true
        }
    }
    pub fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .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()
    }
}