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;
using static System.Console;
using static System.Int32;

class Program
{
    static void Main(string[] args)
    {
        label:
        var line1 = ReadLine().Split();
        int pairCount = Parse(line1[1]);
        var line2 = ReadLine().Split();
        var chunkList = new HashSet<HashSet<int>>();
        foreach (int i in Enumerable.Range(0, pairCount))
        {
            var sp = ReadLine().Split();
            int num1 = Parse(sp[0]), num2 = Parse(sp[1]);
            var set1 = chunkList.FirstOrDefault(s => s.Contains(num1));
            var set2 = chunkList.FirstOrDefault(s => s.Contains(num2));
            if (set1 == null)
            {
                if (set2 == null)
                {
                    chunkList.Add(new HashSet<int>() { num1, num2 });
                }
                else
                {
                    set2.Add(num1);
                }
            }
            else
            {
                if (set2 == null)
                {
                    set1.Add(num2);
                }
                else if (set1 != set2)
                {
                    set1.UnionWith(set2);
                    chunkList.Remove(set2);
                }
            }
        }
        var dic = new Dictionary<int, HashSet<int>>();
        foreach (var set in chunkList)
        {
            foreach (var num in set)
            {
                dic[num] = set;
            }
        }
        int result = 0;
        for (int i = 0; i < line2.Length; ++i)
        {
            int num = Parse(line2[i]);
            int index = i + 1;
            if (index == num)
            {
                ++result;
            }
            else
            {
                HashSet<int> set;
                if (dic.TryGetValue(index, out  set) && set.Contains(num)) ++result;
            }
        }
        WriteLine(result);
    }
}