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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

public class MainClass
{
	public const long Giri = 1000000007;


	
	public static void Main(string[] args)
	{
		var u = Input().ToInt();
		var n = u[0];
		var m = u[1];
		var p = Input().ToInt();
		
		var tree = new UnionFind(n);
		for(int i = 0; i < m; i++)
		{
			u = Input().ToInt();
			var x = u[0];
			var y = u[1];
			
			tree.Unite(x-1, y-1);
		} 
		var wa = 0;
		for(int i = 0; i < n; i++)
		{
			if(tree.InSameTree(i, p[i]-1))
				wa++;
		}
		Console.WriteLine(wa);
	}

	
	static long GCD(long a, long b)
	{
		var v = new[] { a, b };
		while (v[1] != 0) { v = new[] { v[1], v[0] % v[1] }; }
		return v[0];
	}
	public static string[] Input() { return Console.ReadLine().Split(' '); }
	public static int Clamp(int val, int max, int min = 0) { return Math.Min(max, Math.Max(min, val)); }
}

public static class Smarter
{
	public static int ToInt(this string str) { return int.Parse(str); }
	public static long ToLong(this string str) { return long.Parse(str); }
	public static int[] ToInt(this string[] str)
	{
		var r = new int[str.Length];
		for(int i = 0; i < str.Length; i++) r[i] = str[i].ToInt();
		return r;
	 }
}

public class UnionFind
{
	private int[] par;
	public UnionFind(int n)
	{
		par = new int[n];
		for(int i = 0; i < n; i++)
			par[i] = i;
	}
	
	public int Root(int x)
	{
		if(par[x] == x) return x;
		return par[x] = Root(par[x]);
	}
	public void Unite(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry) return;
		par[rx] = ry;
	}
	public bool InSameTree(int x, int y)
	{
		return Root(x) == Root(y);
	}
}