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.PrintStream;
import java.util.Scanner;

public class Main {
    private static final PrintStream ps = System.out;
    private static final Scanner     sc = new Scanner(System.in);

    public static void main(String[] args) {
        int n = sc.nextInt();
        int m = sc.nextInt();

        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = sc.nextInt();
        
        DisjointSet ds = new DisjointSet(n+1);
        for (int i = 0; i < m; i++) 
            ds.unite(sc.nextInt(), sc.nextInt());
        
        int count = 0;
        for (int i = 1; i <= n; i++)
            if (ds.same(i, a[i])) count++;
        
        ps.println(count);
   }
    
    static class DisjointSet {
        public int[] rank;
        public int[] p;
        
        DisjointSet(int size) {
            rank = new int[size];
            p = new int[size];
            for (int i = 0; i < size; i++) makeSet(i);
        }
        
        void makeSet(int x) {
            p[x] = x;
            rank[x] = 0;
        }
        
        boolean same(int x, int y) {
            return findSet(x) == findSet(y);
        }
        
        int findSet(int x) {
            if (x != p[x])
                p[x] = findSet(p[x]);
            return p[x];
        }
        
        void unite(int x, int y) {
            link(findSet(x), findSet(y));
        }
        
        void link(int x, int y) {
            if (rank[x] > rank[y]) {
                p[y] = x;
            } else {
                p[x] = y;
                if (rank[x] == rank[y])
                    rank[y]++;
            }
        }
    }
}