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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Set;

class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		Solver solver = new Solver();
		solver.init();
		solver.readHead(in.readLine());
		for (; solver.hasNext();) {
			solver.readBody(in.readLine());
		}
		solver.solve();
	}
}

class Solver {
	int N;
	int M;
	int cnt;

	public void init() {
		N = 0;
		M = 0;
		cnt = 0;
	}

	public void readHead(String str) {
		String[] strArr = str.split(" ");
		N = Integer.parseInt(strArr[0]);
		M = Integer.parseInt(strArr[1]);
		// System.out.println(N);
	}

	public boolean hasNext() {
		return cnt < M + 1;
	}

	public void readBody(String str) {
		// System.out.println(str);
		if (cnt == 0) {
			P = new int[N + 1];
			SwapTab = new HashMap<Integer, Set<Integer>>();
			String[] strArr = str.split(" ");
			for (int i = 0; i < N; i++) {
				P[i + 1] = Integer.parseInt(strArr[i]);
			}
		} else {
			String[] strArr = str.split(" ");
			int a = Integer.parseInt(strArr[0]);
			int b = Integer.parseInt(strArr[1]);
			addSwapTab(a, b);
			addSwapTab(b, a);
		}
		cnt++;
	}

	private int[] P;
	private HashMap<Integer, Set<Integer>> SwapTab;

	private void addSwapTab(int left, int right) {
		if (!SwapTab.containsKey(left))
			SwapTab.put(left, new HashSet<Integer>());
		SwapTab.get(left).add(right);
	}

	public void solve() {
		int ans = 0;
		Path = new HashSet<Integer>();
		NG = new HashMap<Integer, Set<Integer>>();
		// print();
		for (int i = 1; i <= N; i++) {
			Path.clear();
			if (i == P[i] || isSwapable(i, P[i])) {
				ans++;
			}
		}
		// print();
		System.out.println(ans);
	}

	Set<Integer> Path;
	private HashMap<Integer, Set<Integer>> NG;

	private boolean isSwapable(int left, int right) {
		if (SwapTab.containsKey(left) && SwapTab.get(left).contains(right))
			return true;
		if (NG.containsKey(left) && NG.get(left).contains(right))
			return false;

		boolean ans = false;
		if (SwapTab.containsKey(left)) {
			Path.add(left);
			for (int nextLeft : SwapTab.get(left)) {
				if (Path.contains(nextLeft))
					continue;
				ans = isSwapable(nextLeft, right);
				if (ans)
					break;
			}
			Path.remove(left);
		}

		if (ans) {
			addSwapTab(left, right);
			addSwapTab(right, left);
		} else {
			addNG(left, right);
			addNG(right, left);
		}
		return ans;
	}

	private void addNG(int left, int right) {
		if (!NG.containsKey(left))
			NG.put(left, new HashSet<Integer>());
		NG.get(left).add(right);
	}

	private void print() {
		for (int i = 1; i <= N; i++)
			System.out.print(" " + P[i]);
		System.out.println();
		System.out.println("SwapTab");
		for (int left : SwapTab.keySet()) {
			System.out.print(left + ":");
			for (int num : SwapTab.get(left))
				System.out.print(" " + num);
			System.out.println();
		}
		System.out.println("NG");
		for (int left : NG.keySet()) {
			System.out.print(left + ":");
			for (int num : NG.get(left))
				System.out.print(" " + num);
			System.out.println();
		}
	}

}