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::HashMap;
// use std::collections::HashSet;


fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let n = sc.read();
    let m = sc.read();
    let mut ps = Vec::new();
    for _ in 0..n {
        let p: usize = sc.read();
        ps.push(p - 1);
    }
    let ps = ps;

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

    for _ in 0..m {
        let x = sc.read::<usize>() - 1;
        let y = sc.read::<usize>() - 1;

        uf.merge(x, y);
        // xs.push(x);
        // ys.push(y);
    }

    let mut ans = 0;
    for i in 0..n {
        if uf.class(i) == uf.class(ps[i]) {
            ans += 1;
        }
    }
    println!("{}", ans);
}


struct UnionFind {
    parent_or_size: Vec<isize>,
}


impl UnionFind {
    fn new(size: usize) -> UnionFind {
        UnionFind { parent_or_size: vec![-1; size] }
    }

    fn class(&self, index: usize) -> usize {
        let mut index = index;
        while self.parent_or_size[index] >= 0 {
            index = self.parent_or_size[index] as usize;
        }
        index
    }

    fn merge(&mut self, index0: usize, index1: usize) -> bool {
        let a = self.class(index0);
        let b = self.class(index1);
        if a == b {
            false
        } else {
            if self.parent_or_size[a] < self.parent_or_size[b] {
                self.parent_or_size[a] += self.parent_or_size[b];
                self.parent_or_size[b] = a as isize;
            } else {
                self.parent_or_size[b] += self.parent_or_size[a];
                self.parent_or_size[a] = b as isize;
            }
            true
        }
    }
}


// thanks, ir5
use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

struct Scanner<'a> {
    cin: StdinLock<'a>,
}

impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read1<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin
            .by_ref()
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn read<T: FromStr>(&mut self) -> T {
        self.read1().unwrap()
    }
}