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.util.*;
import java.util.stream.Collectors;



public class Main {
    public static void main(String[] args) {
        Scanner scanner=new Scanner(System.in);
        final int N=scanner.nextInt();
        final int M=scanner.nextInt();
        final int[] pArray=new int[N];
        for(int i=0;i<N;i++){
            pArray[i]=scanner.nextInt();
        }
        UnionFind unionFind=new UnionFind(N);
        for(int i=0;i<M;i++){
            int x=scanner.nextInt();
            int y=scanner.nextInt();
            unionFind.union(x-1,y-1);
        }
        int result=0;
        for(int i=0;i<N;i++){
            if(unionFind.same(i,pArray[i]-1)) result++;
        }
        System.out.println(result);
    }
}
class UnionFind{
    int n;
    int[] ints;
    public UnionFind(int n) {
        this.n = n;
        ints = new int[n];
        for(int i=0;i<n;i++){
            ints[i]=i;
        }
    }
    public int root(int x){
        if(ints[x]==x){
            return x;
        }else{
            int root=root(ints[x]);
            ints[x]=root;
            return root;
        }
    }
    public boolean same(int x,int y){
        return root(x)==root(y);
    }
    public void union(int x,int y){
        ints[root(x)]=ints[root(y)];
    }
    @Override
    public String toString(){
        return Arrays.stream(ints).mapToObj(i->String.format("%d",i)).collect(Collectors.joining(","));
    }
}