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.Arrays;
import java.util.Scanner;

public class Main {
	
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = Integer.parseInt(sc.next());
		int m = Integer.parseInt(sc.next());
		
		int []p = new int [n];
		
		for(int i = 0 ;i < n ;i++) {
			p[i] = Integer.parseInt(sc.next())-1;
		}
		Unionfind uf = new Unionfind(n);
		
		for(int i = 0 ;i < m ;i++) {
			int x = Integer.parseInt(sc.next())-1;
			int y = Integer.parseInt(sc.next())-1;
			
			uf.union(x, y);
		}
		
		int ans = 0;
		
		for(int i = 0 ;i < n ;i++) {
			if(uf.root(i) == uf.root(p[i])) {
				ans++;
			}
		}
		
		System.out.println(ans);
		
		
	}

}

class Unionfind {

	private int[] data;
	
	public Unionfind(int size) {
		this.data = new int [size];
		clear();
	}
	
	public void clear() {
		Arrays.fill(data, -1);
	}
	
	public void union(int x , int y ) {
		if((x = root(x)) != (y = root(y))) {
			if(data[y] < data[x]) {
				final int t = x;
				x = y;
				y = t;
			}
			data[x] += data[y];
			data[y] = x;
		}
	}
	
	public int root(int x) {
		if(data[x] < 0) {
			return x;
		}
		else {
			return data[x] = root(data[x]);
		}
	}
	
	public boolean same(int x, int y) {
		return root(x) == root(y);
	}
	

}