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)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

pub trait InputValue {
    fn parse(s: &str) -> Self;
}

pub fn read<T: InputValue>() -> T {
    let mut buf = String::new();
    let _ = stdin().read_line(&mut buf);
    T::parse(&buf.trim())
}

pub fn readn<T: InputValue>(n: usize) -> Vec<T> {
    let mut vec = vec![];
    for _ in 0..n {
        vec.push(read());
    }
    vec
}

pub fn readnc<T: InputValue>() -> Vec<T> {
    let mut vec = vec![];
    let line: String = read();
    for token in line.split_whitespace() {
        vec.push(T::parse(token));
    }
    vec
}

macro_rules! parse_single_value {
    ($($t:ty),*) => {
        $(
            impl InputValue for $t {
                fn parse(s: &str) -> $t { s.parse().unwrap() }
            }
        )*
	}
}
parse_single_value!(i32, i64, f32, f64, usize, String);

macro_rules! parse_tuple {
	($($t:ident),*) => {
		impl<$($t),*> InputValue for ($($t),*) where $($t: InputValue),* {
			fn parse(s: &str) -> ($($t),*) {
				let mut tokens = s.split_whitespace();
				let t = ($($t::parse(tokens.next().unwrap())),*);
				t
			}
		}
	}
}
parse_tuple!(A, B);

// ===

struct UnionFind {
    parent: Vec<usize>,
    rank: Vec<usize>
}

impl UnionFind {
    fn new(n: usize) -> Self {
        let mut parent = vec![0; n];
        for i in 0..n {
            parent[i] = i;
        }
        UnionFind { parent: parent, rank: vec![0; n] }
    }

    fn unite(&mut self, a: usize, b: usize) {
        let pa = self.find(a);
        let pb = self.find(b);
        if pa == pb {
            return;
        }

        let mut next_rank = 0;
        if self.rank[pa] <= self.rank[pb] {
            self.parent[pa] = pb;
            next_rank = max(self.rank[pb], self.rank[pa] + 1);
        } else {
            self.parent[pb] = pa;
            next_rank = self.rank[pa];
        }
        self.rank[pa] = next_rank;
        self.rank[pb] = next_rank;
    }

    fn find(&mut self, u: usize) -> usize {
        if self.parent[u] == u {
            return u;
        }
        let mut pu = self.parent[u];
        pu = self.find(pu);
        self.parent[u] = pu;
        return pu
    }
}

fn main() {
    let (n, m): (usize, usize) = read();
    let p: Vec<usize> = readnc::<usize>().iter().map(|u| u-1).collect();

    let mut uf = UnionFind::new(n);
    for i in 0..m {
        let (a, b): (usize, usize) = read();
        uf.unite(a-1, b-1);
    }

    let mut id_positions = vec![0; n];
    for i in 0..n {
        id_positions[i] = uf.find(i);
    }

    let mut ans = 0;
    for i in 0..n {
        if uf.find(i) == id_positions[p[i]] {
            ans += 1;
        }
    }

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