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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main{
    static MyReader in = new MyReader();
    static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args){
        int N, M;
        {int[] a = in.ii(); N = a[0]; M = a[1];}
        int[] p = in.ii();
        UnionFind uf = new UnionFind(N+1);
        for(int i = 0; i < M; i++){
            int[] a = in.ii();
            uf.unite(a[0], a[1]);
        }
        ArrayList<ArrayList<Integer>> list = new ArrayList<>();
        list.add(null);
        int[] id = new int[N+1];
        for(int i = 1; i <= N; i++){
            int root = uf.root(i);
            if(id[root] == 0){
                id[root] = list.size();
                ArrayList<Integer> lst = new ArrayList<>();
                lst.add(i);
                list.add(lst);
            } else {
                list.get(id[uf.par[i]]).add(i);
            }
        }
        int ans = 0;
        int K = list.size();
        for(int i = 1; i < K; i++){
            ArrayList<Integer> lst = list.get(i);
            HashSet<Integer> hs = new HashSet<>(lst);
            int k = lst.size();
            for(int j = 0; j < k; j++){
                hs.add(p[lst.get(j)-1]);
            }
            ans += 2*k-hs.size();
        }
        out.println(ans);
        out.flush();
    }
    
    static class UnionFind{
        int[] par, rank, size;
        private final int MAX_N;
        UnionFind(int n){
            MAX_N = n;
            par = new int[n];
            size = new int[n];
            for(int i = 1; i < MAX_N; i++)
                par[i] = i;
            Arrays.fill(size, 1);
            rank = new int[n];
        }

        int root(int x){
            return par[x] == x ? x : (par[x] = root(par[x]));
        }
        
        boolean isRoot(int x){
            return par[x] == x;
        }

        boolean same(int x, int y){
            return root(x) == root(y);
        }

        void unite(int x, int y){
            x = root(x);
            y = root(y);
            if(x == y)
                return;
            if(rank[x] < rank[y]){
                par[x] = y;
                size[y] += size[x];
            }else{
                par[y] = x;
                size[x] += size[y];
                if(rank[x] == rank[y])
                    rank[x]++;
            }
        }

        int size(int x){
            return size[root(x)];
        }
    }

    static class MyReader extends BufferedReader{
        MyReader(){
            super(new InputStreamReader(System.in));
        }

        String s(){
            try{return readLine();}catch(IOException e){return "";}
        }

        String[] ss(){
            return s().split(" ");
        }

        int i(){
            return Integer.parseInt(s());
        }

        int[] ii(){
            String[] ss = ss();
            int[] ii = new int[ss.length];
            for(int j = 0; j < ss.length; j++) ii[j] = Integer.parseInt(ss[j]);
            return ii;
        }

        ArrayList<Integer> li(){
            String[] ss = ss();
            ArrayList<Integer> li = new ArrayList<>();
            for(int j = 0; j < ss.length; j++) li.add(Integer.parseInt(ss[j]));
            return li;
        }

        long l(){
            return Long.parseLong(s());
        }

        long[] ll(){
            String[] ss = ss();
            long[] ll = new long[ss.length];
            for(int j = 0; j < ss.length; j++) ll[j] = Long.parseLong(ss[j]);
            return ll;
        }
    }
}