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: Wrong Answer)

import java.util.ArrayList;
import java.util.*;


class Main{
	public static void main(String[] args){

		//permutation
		List<Integer> perm = new ArrayList<>();
		//swap pair
		//List<Integer> pair = new ArrayList<>();
		Pair pairs = new Pair();

		//Count
		int count = 0;

		Scanner scan = new Scanner(System.in);

		//permutation size
		int permMax = Integer.parseInt(scan.next());
		//pair size
		int pairMax = Integer.parseInt(scan.next());

		//string to int
		for(int i = 0; i < permMax; i++){
			perm.add(Integer.parseInt(scan.next()));
		}

		//set pair
		for(int i = 0; i < pairMax; i++){

			pairs.setPair(Integer.parseInt(scan.next()), 
					Integer.parseInt(scan.next()));
		}

		//join same pair
		pairs.joinSamePair();

		//sum
		for(int i = 0; i < perm.size(); i++){

			//添字の要素と一致した場合
			if(i + 1 == perm.get(i)){
				count++;
				//System.out.println("i:" + (i+1) + " 添字と同じ");
				continue;

			}

			//一致しなかった場合
			//swap可能な範囲がある場合に検索	
			if(!pairs.getPair(i + 1).isEmpty()){
				for(Integer value : pairs.getPair(i + 1)){
					//
					if(i + 1 == perm.get(value - 1)){
						count++;
						//System.out.println("i:" + (i+1) + "");
						break;
					}
				}	
			}

		}

		System.out.println(count);

		//pairs.printAll();


	}
}

class Pair{
	private List<Set<Integer>> swapPair;

	public Pair(){
		swapPair = new ArrayList<>();
		swapPair.add(new HashSet<Integer>());
	}

	//ペアをチェックして追加していく
	public void setPair(int a, int b){

		//入力した数値がペアリストが含まれていた場合片方を追加
		for(Set<Integer> set : this.swapPair){
			if(set.contains(a)){
				set.add(b);
				return;
			}else if (set.contains(b)){
				set.add(a);
				return;
			}
		}	

		//入力した数値がペアリストに無かった時両方追加
		Set<Integer> set = new HashSet<>();
		set.add(a);
		set.add(b);
		this.swapPair.add(set);
	}

	public List<Set<Integer>> getPair(){
		return this.swapPair;
	}

	//添字を含むペアのSetを返す
	public Set<Integer> getPair(int i){
		Set<Integer> setPair = new HashSet<>();

		for(Set<Integer> set : this.swapPair){
			if(set.contains(i)){
				setPair = set;	
			}
		}

		return setPair;
	}

	//同じ添字がある場合結合
	public void joinSamePair(){
		boolean flag = true;
		while(flag){
			for(int i = 0; i < swapPair.size() - 1; i++){
				Set<Integer> set1 = swapPair.get(i);
				Set<Integer> set2 = swapPair.get(i + 1);
				//set1とset2に同じ要素がある場合
				if(set1.stream().anyMatch(set2::contains)){
					swapPair.get(i).addAll(set2);
					swapPair.remove(i + 1);
					break;
				}
				//最後の要素であれば終了
				flag = false;
			}	
		}	
	}

	//データ確認用
	public void printAll(){
		for(Set<Integer> set : swapPair){
			for(Integer i : set){
				System.out.print(i + " ");
			}
			System.out.println();
		}
	}
}