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;
class Program
{

static string[] input = Console.ReadLine().Split(' ');
static int n = int.Parse(input[0]);
static int m = int.Parse(input[1]);
static int[] nums = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
static int[] parents = new int[n];//親
  
	static void Main()
	{
    int answer = 0;
    
    for(int i = 1; i < n; i++)
    {
    parents[i] = i;
    }
  
    for(int i = 0; i < m; i++)
    {
      int[] edges = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
      
        if(whatParent(edges[0]-1) != whatParent(edges[1]-1))
          parents[whatParent(edges[0]-1)] = whatParent(edges[1]-1);//親を結合して統一。親が2人できることはない。
      
    }

    for(int i = 0; i < n; i++)
    {
      if(whatParent(nums[i]-1) == whatParent(nums[nums[i]-1]-1)) answer++;
    }

    Console.WriteLine(answer);
    
	}

  static int whatParent(int child)
  {
    if(parents[child] == child) return child;
    else return parents[child] = whatParent(parents[child]);
  }
  
}