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::thread;
use std::io::{ self, Read };
use std::fmt;
use std::iter::Iterator;
use std::cmp::*;
use std::collections::*;
use std::str::*;

#[derive(Default)]
struct Input {
    buf: Vec<String>
}

impl Input {
    fn new() -> Input {
        Input { buf: Vec::new() }
    }

    fn read<T: FromStr>(&mut self) -> T 
    where <T as FromStr>::Err: fmt::Debug {
        self.next().unwrap().parse::<T>().unwrap()
    }

    fn read_bytes(&mut self) -> Vec<u8> {
        self.next().unwrap().into_bytes()
    }

    fn read_n<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where <T as FromStr>::Err: fmt::Debug {
        let mut v = Vec::new();
        for _ in 0..n { v.push(self.read::<T>()); }
        v
    }
}

impl Iterator for Input {
    type Item = String;
    fn next(&mut self) -> Option<String> {
        while self.buf.is_empty() {
            let mut s = String::new();
            let _res = io::stdin().read_line(&mut s);
            self.buf = s.split_whitespace().map(|s| s.to_owned()).collect::<Vec<_>>();
            self.buf.reverse();
        }
        self.buf.pop()
    }
}

struct UnionFind {
    c: Vec<(usize, usize)>
}

impl UnionFind {
    fn new(n: usize) -> UnionFind {
        UnionFind { c: (0..n).map(|u| (u, 1)).collect::<Vec<_>>() }
    }

    fn root(&self, u: usize) -> usize {
        let v = self.c[u].0;
        if u == v { u } else { self.root(v) }
    }

    fn is_same(&self, u: usize, v: usize) -> bool {
        self.root(u) == self.root(v)
    }

    fn size(&self, u: usize) -> usize {
        self.c[u].1
    }

    fn unite(&mut self, u: usize, v: usize) {
        let ru = self.root(u);
        let rv = self.root(v);
        let su = self.size(ru);
        let sv = self.size(rv);
        if su > sv {
            self.c[rv].0 = ru;
            self.c[ru].1 = su + sv;
        } else {
            self.c[ru].0 = rv;
            self.c[rv].1 = su + sv;
        }
    }
}

fn run() {
    let mut ip = Input::new();
    let n = ip.read::<usize>();
    let m = ip.read::<usize>();
    let mut p = ip.read_n::<usize>(n);
    p.insert(0, 0);
    let mut uf = UnionFind::new(n + 1);
    for _ in 0..m {
        let u = ip.read::<usize>();
        let v = ip.read::<usize>();
        uf.unite(u, v);
    }
    let mut s = 0;
    for u in 1..n + 1 {
        if uf.is_same(u, p[u]) {
            s += 1;
        }
    }
    println!("{}", s);
}

fn main() {
    let _ = thread::Builder::new()
        .stack_size(10 * 1024 * 1024)
        .spawn(run).unwrap()
        .join();
}