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: Time Limit Exceeded)

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

class D
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var h = read();
		var n = h[0];
		var p = read();
		var map = new int[n + 1].Select(_ => new List<int>()).ToArray();
		foreach (var r in new int[h[1]].Select(_ => read()))
		{
			map[r[0]].Add(r[1]);
			map[r[1]].Add(r[0]);
		}

		var c = 0;
		var used = new bool[n + 1];
		var q = new Queue<int>();
		var l = new List<int>();

		for (int i = 1; i <= n; i++)
		{
			if (used[i]) continue;
			used[i] = true;
			q.Enqueue(i);
			l.Add(i);

			while (q.Any())
				foreach (var np in map[q.Dequeue()])
				{
					if (used[np]) continue;
					used[np] = true;
					q.Enqueue(np);
					l.Add(np);
				}
			var z = new int[n + 1];
			foreach (var k in l)
			{
				z[k]++;
				z[p[k - 1]]++;
			}
			c += z.Count(x => x == 2);
			l.Clear();
		}
		Console.WriteLine(c);
	}
}