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)

macro_rules! input {
    ($t : ty) => {{
        use std::io::BufRead;
        let tmp_handle = std::io::stdin();
        let mut handle = tmp_handle.lock();
        let mut buf = String::new();
        handle.read_line(&mut buf).unwrap();
        let tmp_var: $t = buf.trim().parse().unwrap(); 
        buf.clear();
        tmp_var
    }};
    ($t : ty, $size : expr) => {{
        use std::io::BufRead;
        let tmp_handle = std::io::stdin();
        let mut handle = tmp_handle.lock();
        let mut buf = String::new();
        handle.read_line(&mut buf).unwrap();
        let tmp_var: $t = buf.trim().split_whitespace()
            .map(|a| a.parse().unwrap()).collect();
        buf.clear();
        tmp_var
    }};
}
#[derive(Debug)]
pub struct UnionFind {
    parents: Vec<usize>,
    rank: Vec<usize>,
}
impl UnionFind {
    pub fn new(n: usize) -> Self {
        let mut parents: Vec<usize> = Vec::with_capacity(n);
        for i in 0..n {
            parents.push(i);
        }
        let rank = vec![1; n];
        UnionFind {
            parents: parents,
            rank: rank,
        }
    }
    pub fn find(&mut self, x: usize) -> usize {
        if self.parents[x] == x {
            x
        } else {
            let par = self.parents[x];
            let root = self.find(par);
            self.parents[x] = root;
            root
        }
    }
    // union x and y
    pub fn union(&mut self, x: usize, y: usize) {
        let x_root = self.find(x);
        let y_root = self.find(y);
        // if x_root == y_root, do nothing
        if x_root == y_root { return (); }
        if self.rank[x_root] > self.rank[y_root] {
            // x <--- y
            self.parents[y_root] = x_root;
        } else {
            // y <--- x
            self.parents[x_root] = y_root;
            if self.rank[x_root] == self.rank[y_root] {
                self.rank[y_root] += 1;
            }
        }
    }
}
fn main() {
    let config = input!(Vec<usize>, 2);
    let nums: Vec<usize> = input!(Vec<usize>, config[0]).into_iter().map(|a| a - 1).collect();
    let mut uf = UnionFind::new(config[0]);
    for _ in 0..config[1] {
        let change = input!(Vec<usize>, 2);
        uf.union(change[0]-1, change[1]-1);
    }
    let mut count = 0;
    for (i, num) in nums.into_iter().enumerate() {
        if uf.find(i) == uf.find(num) { count += 1; }
    }
    println!("{}", count);
}