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, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let m: usize = sc.cin();
    let p: Vec<usize> = sc.vec::<usize>(n).iter().map(|&x| x - 1).collect();
    let mut uf = UnionFind::new(n);
    for _ in 0..m {
        let x = sc.cin::<usize>() - 1;
        let y = sc.cin::<usize>() - 1;
        uf.merge(x, y);
    }
    let mut gs = DefaultMap::new(vec![]);
    for i in 0..n {
        gs[uf.root(i)].push(i);
    }
    let mut ans = 0;
    for &g in gs.keys() {
        let s: std::collections::HashSet<usize> = gs[g].iter().map(|&x| x).collect();
        for &x in s.iter() {
            if s.contains(&p[x]) {
                ans += 1;
            }
        }
    }
    put!(ans);
}

struct DefaultMap<S, T> {
    data: std::collections::HashMap<S, T>,
    default: T,
}
impl<S: Eq + std::hash::Hash, T> DefaultMap<S, T> {
    fn new(default: T) -> DefaultMap<S, T> {
        DefaultMap {
            data: std::collections::HashMap::new(),
            default: default
        }
    }
    fn keys(&self) -> std::collections::hash_map::Keys<S, T> { self.data.keys() }
    fn iter(&self) -> std::collections::hash_map::Iter<S, T> { self.data.iter() }
    fn len(&self) -> usize { self.data.len() }
}
impl<S: Eq + std::hash::Hash, T> std::ops::Index<S> for DefaultMap<S, T> {
    type Output = T;
    fn index(&self, key: S) -> &Self::Output {
        if let Some(val) = self.data.get(&key) {
            val
        } else {
            &self.default
        }
    }
}
impl<S: Eq + std::hash::Hash + Clone, T: Clone> std::ops::IndexMut<S> for DefaultMap<S, T> {
    fn index_mut(&mut self, key: S) -> &mut Self::Output {
        self.data.entry(key.clone()).or_insert(self.default.clone());
        self.data.get_mut(&key).unwrap()
    }
}

#[derive(Debug, Clone)]
enum UF { Root(usize), Child(usize) }

#[derive(Debug)]
struct UnionFind { table: Vec<UF> }
impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind { table: vec![UF::Root(1); n], }
    }
    fn root(&mut self, x: usize) -> usize {
        match self.table[x] {
            UF::Root(_) => x,
            UF::Child(parent) => {
                let root = self.root(parent);
                self.table[x] = UF::Child(root);
                root
            }
        }
    }
    fn is_same(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
    fn size(&mut self, x: usize) -> usize {
        let r = self.root(x);
        match self.table[r] {
            UF::Root(size) => size,
            UF::Child(_) => 0
        }
    }
    fn merge(&mut self, x: usize, y: usize) {
        let root_x = self.root(x);
        let root_y = self.root(y);
        if root_x != root_y {
            let size_x = self.size(root_x);
            let size_y = self.size(root_y);
            let (i, j) = if size_x > size_y {
                (root_x, root_y)
            } else {
                (root_y, root_x)
            };
            self.table[i] = UF::Root(size_x + size_y);
            self.table[j] = UF::Child(i);
        }
    }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}