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 (1.42.0) (judge verdict: Accepted)

use proconio::{input, marker::Usize1};

// union-find{{{
mod union_find {
    //! union-find です。

    #[allow(dead_code)]
    #[derive(Clone, Copy, Debug)]
    enum ParentOrSize {
        Parent(usize),
        Size(usize),
    }

    /// union-find です。
    #[allow(dead_code)]
    #[derive(Clone, Debug)]
    pub struct UnionFind(Vec<ParentOrSize>);

    #[allow(dead_code)]
    impl UnionFind {
        /// 構築です。
        ///
        /// # Example
        ///
        /// ```
        /// let uf = union_find::UnionFind::new(3);
        /// ```
        pub fn new(len: usize) -> Self {
            Self(vec![ParentOrSize::Size(1); len])
        }

        /// 空かどうかです。
        ///
        /// # Example
        ///
        /// ```
        /// assert!(!union_find::UnionFind::new(3).is_empty());
        /// assert!(union_find::UnionFind::new(0).is_empty());
        /// ```
        pub fn is_empty(&self) -> bool {
            self.0.is_empty()
        }

        /// 長さです。
        ///
        /// # Example
        ///
        /// ```
        /// assert_eq!(union_find::UnionFind::new(3).len(), 3);
        /// ```
        pub fn len(&self) -> usize {
            self.0.len()
        }

        /// 親を探します。
        ///
        /// # Example
        ///
        /// ```
        /// let mut uf = union_find::UnionFind::new(3);
        /// assert_ne!(uf.find(0), uf.find(1));
        /// uf.unite(0, 1);
        /// assert_eq!(uf.find(0), uf.find(1));
        /// ```
        pub fn find(&mut self, i: usize) -> usize {
            self.find_and_size(i).0
        }

        /// 属する成分のサイズです。
        ///
        /// # Example
        ///
        /// ```
        /// let mut uf = union_find::UnionFind::new(3);
        /// assert_eq!(uf.size(0), 1);
        /// uf.unite(0, 1);
        /// assert_eq!(uf.size(0), 2);
        /// ```
        pub fn size(&mut self, i: usize) -> usize {
            self.find_and_size(i).1
        }

        fn find_and_size(&mut self, i: usize) -> (usize, usize) {
            assert!(i < self.len());
            match self.0[i] {
                ParentOrSize::Parent(p) => {
                    let ret = self.find_and_size(p);
                    self.0[i] = ParentOrSize::Parent(ret.0);
                    ret
                }
                ParentOrSize::Size(si) => (i, si),
            }
        }

        /// くっつけます。
        ///
        /// # Example
        ///
        /// ```
        /// let mut uf = union_find::UnionFind::new(3);
        /// uf.unite(0, 1);
        /// ```
        pub fn unite(&mut self, u: usize, v: usize) {
            let (mut u, su) = self.find_and_size(u);
            let (mut v, sv) = self.find_and_size(v);
            if u == v {
                return;
            }
            if su > sv {
                std::mem::swap(&mut u, &mut v);
                std::mem::swap(&mut v, &mut u);
            }
            self.0[v] = ParentOrSize::Size(su + sv);
            self.0[u] = ParentOrSize::Parent(v);
        }

        /// 同じ連結成分に入っているかどうかです。
        ///
        /// # Example
        ///
        /// ```
        /// let mut uf = union_find::UnionFind::new(3);
        /// assert!(!uf.same(0, 1));
        /// uf.unite(0, 1);
        /// assert!(uf.same(0, 1));
        /// ```
        pub fn same(&mut self, u: usize, v: usize) -> bool {
            self.find(u) == self.find(v)
        }
    }
}
//}}}

fn main() {
    input!(
        n: usize,
        m: usize,
        p: [Usize1; n],
        xy: [(Usize1, Usize1); m]
    );
    let mut uf = union_find::UnionFind::new(n);
    xy.into_iter().for_each(|(x, y)| uf.unite(x, y));
    println!("{}", (0..n).filter(|&i| uf.same(i, p[i])).count());
}