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: Wrong Answer)

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

class Solution
{
    static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var n = vals[0];
        var m = vals[1];
        var p = Console.ReadLine().Split(' ').Select(int.Parse).ToList();
        p.Insert(0, 0);
        var swaps = new int[m][];
        for (int i = 0; i < m; i++)
        {
            swaps[i] = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        var sets = new List<HashSet<int>>();
        foreach (var swap in swaps)
        {
            var currentSets = new HashSet<int>[2];
            for (int i = 0; i < 2; i++)
            {
                bool find = false;
                foreach (var set in sets)
                {
                    if (set.Contains(swap[i]))
                    {
                        set.Add(swap[i]);
                        currentSets[i] = set;
                        find = true;
                        break;
                    }
                }

                if (!find)
                {
                    var set = new HashSet<int> { swap[i] };
                    sets.Add(set);
                    currentSets[i] = set;
                }
            }

            if (currentSets[0] != currentSets[1])
            {
                currentSets[0].UnionWith(currentSets[1]);
                sets.Remove(currentSets[1]);
            }
        }

        int result = 0;
        foreach (var set in sets)
        {
            var list = set.Select(i => p[i]).ToList();
            foreach (var i in list)
            {
                if (set.Contains(i))
                {
                    result++;
                }
            }
        }

        Console.WriteLine(result);
    }
}