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 System.Text;
using System.Threading.Tasks;

namespace ConsoleApp4
{
    class Program
    {
        struct table
        {
            public int 所属;
            public bool チェック済み;
            public table(int a)
            {
                this.所属 = 0;
                this.チェック済み = false;
            }
        }
        struct taple
        {
            public int x;
            public int y;
            public taple(int a, int b)
            {
                this.x = a;
                this.y = b;
                
            }
        }
        public static void Main(string[] args)
        {
            var read = Console.ReadLine();
            int N = int.Parse(read.Split(' ')[0]);
            int M = int.Parse(read.Split(' ')[1]);
            int[] p = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            taple[] choice = new taple[M];
            for (int i = 0; i < M; i++)
            {
                int[] temp = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                if (temp[0] < temp[1])
                {
                    choice[i] = new taple(temp[0], temp[1]);
                }
                else
                {
                    choice[i] = new taple(temp[1], temp[0]);
                }
            }
            ;
            table[] table = new table[N + 1];
            table[1].所属 = 1;
            int groups = 1;
            for (int i = 1; i<= N; i++)
            {
                if (table[i].チェック済み == true) continue;
                var lista=choice.Where(x => x.x == i).ToArray();
                for (int counter = 0; counter < lista.Count(); counter++)
                {
                    if (table[i].所属 == 0)
                    {
                        groups++;
                        table[i].所属 = groups;
                    }
                    if (table[lista[counter].y].所属 == 0)
                    {
                        table[lista[counter].y].所属 = table[i].所属;
                    }
                    else
                    {
                        int big = Math.Max(table[lista[counter].y].所属, table[i].所属);
                        int small = Math.Min(table[lista[counter].y].所属, table[i].所属);
                        for (int changer = 0; changer < table.Length; changer++)
                        {
                            if (table[changer].所属 == big) table[changer].所属 = small;
                        }
                    }
                }
                
            }
            ;

            string[] islands = new string[groups + 1];
            for (int i = 1; i <table.Length;i++)
            {
                islands[table[i].所属] += "," +p[i-1]+",";
            }
            int score = 0;

            for (int i = 1; i <= N; i++)
            {
                if (table[i].所属 != 0)
                {
                    if (islands[table[i].所属].IndexOf("," + i+ ",") != -1) score++;

                }
                else
                {
                    if (p[i - 1] == i) score++;
                }
            }
            Console.WriteLine(score);
        }
        
    }
}