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;
class Program
{
	static void Main(string[] args)
	{
		string[] s = Console.ReadLine().Split(' ');
		int N = int.Parse(s[0]);
		int M = int.Parse(s[1]);
		string[] t = Console.ReadLine().Split(' ');
		int [] P = new int[N];
		for(var i=0;i<N;i++){
			P[i] = int.Parse(t[i]);
		}
		int [,] Q = new int[M,2];
		for(var i=0;i<M;i++){
			string[] u = Console.ReadLine().Split(' ');
			for(var j=0;j<=1;j++){
				int K = int.Parse(u[j]);
				Q[i, j] = K;
			}
		}
		int [] G = new int[N];
		int c = 1;
		for(var i=0;i<M;i++){
			if(G[Q[i,0]-1] == 0){
				if(G[Q[i,1]-1] == 0){
					G[Q[i,0]-1] = c;
					G[Q[i,1]-1] = c;
					c += 1;
				} else {
					G[Q[i,0]-1] = G[Q[i,1]-1];
				}
			} else if(G[Q[i,1]-1] == 0){
				G[Q[i,1]-1] = G[Q[i,0]-1];
			} else if(G[Q[i,0]-1] != G[Q[i,1]-1]){
				int min = Math.Min(G[Q[i,0]-1],G[Q[i,1]-1]);
				int max = Math.Max(G[Q[i,0]-1],G[Q[i,1]-1]);
				G[Q[i,0]-1] = min;
				G[Q[i,1]-1] = min;
				for(var j=0;j<N;j++){
					if(G[j] == max){
						G[j] = min;
					}
				}
			}
		}
		int count = 0;
		for(var i=0;i<N;i++){
			if(P[i]-1 == i){
				count += 1;
			} else if(G[i] == G[P[i]-1] && G[i] > 0){
				count += 1;
			}
		}
		Console.WriteLine(count);
	}
}