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;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var nm = Add.ar;
        var ps = Add.ar;
        var un = new UnionFind<int>();
        for (var i = 0; i < nm[0]; i++)
            un.MakeSet(i + 1);
        for(var i = 0; i < nm[1]; i++)
        {
            var input = Add.ar;
            un.Union(input[0], input[1]);
        }
        var res = 0;
        for (var i = 0; i < nm[0]; i++)
            if (un.IsSame(i + 1, ps[i]))
                res++;
        WriteLine(res);
    }
}

public class Add
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public  static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class UnionFind<T>
{
    private class Vertex
    {
        public T Key { get; set; }
        public Vertex Parent { get; set; }
        public int Rank { get; set; }

        public Vertex(T key) : this(key, null, 0)
        {

        }
        public Vertex(T key, Vertex Parent, int rank)
        {
            this.Key = key;
            this.Parent = Parent;
            this.Rank = rank;
        }
    }
    private readonly Dictionary<T, Vertex> dics;
    private readonly Vertex NIL;

    public int Count { get; private set; }

    public UnionFind()
    {
        NIL = new Vertex(default(T));
        dics = new Dictionary<T, Vertex>();
    }
    
    public T parent(T key)
        => FindSet(dics[key].Parent).Key;

    public bool IsSame(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            throw new ArgumentException("対応する頂点が存在しません");
        return ReferenceEquals(FindSet(dics[key1]),FindSet(dics[key2]));
    }

    public bool MakeSet(T key)
    {
        if (dics.ContainsKey(key))
            throw new ArgumentException($"{key}をキーとして持つ頂点が既に存在します");
        dics[key] = new Vertex(key, NIL, 0);
        dics[key].Parent = dics[key];
        Count++;
        return true;
    }

    public bool Union(T key1, T key2)
    {
        if (!dics.ContainsKey(key1) || !dics.ContainsKey(key2))
            throw new ArgumentException("対応する頂点が存在しません");
        if (IsSame(key1, key2)) return false;
        Link(FindSet(dics[key1]), FindSet(dics[key2]));
        Count--;
        return true;
    }

    private bool Link(Vertex vex1, Vertex vex2)
    {
        if (vex1.Rank > vex2.Rank)
            vex2.Parent = vex1;
        else
        {
            vex1.Parent = vex2;
            if (vex1.Rank == vex2.Rank)
                vex2.Rank++;
        }
        return true;
    }

    private Vertex FindSet(Vertex vex)
    {
        if (!ReferenceEquals(vex.Parent, vex))
            vex.Parent = FindSet(vex.Parent);
        return vex.Parent;
    }
}