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;
class Program{
	static int b=1,ans=0;
	static int[] s,p;
	static int[,] h;
	static List<int>[] li;
	static void Main(){
		s=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
		p=Array.ConvertAll(("0 "+Console.ReadLine()).Split(),int.Parse);
		h=new int[2,s[0]+1];
		li=new List<int>[s[0]+1];
		for(int i=1;i<=s[0];i++){li[i]=new List<int>();}
		for(int i=0;i<s[1];i++){
			int[] q=Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
			li[q[0]].Add(q[1]);
			li[q[1]].Add(q[0]);
		}
		for(;b<=s[0];b++){
			if(h[0,b]==0){fu(b);}
		}
		Console.WriteLine("{0}",ans);
	}
	static void fu(int a){
		ck(a,0);
		ck(p[a],1);
		for(int i=0;i<li[a].Count;i++){
			if(h[0,li[a][i]]==0){fu(li[a][i]);}
		}
	}
	static void ck(int a,int c){
		h[c,a]=b;
		if(h[c^1,a]==b){ans++;}
	}
}