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 Atcoder;
using System.Threading.Tasks;
using System.ComponentModel;

public class Hello
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int[] NM = IntLine();
        int N = NM[0], M = NM[1];
        int[] p = IntLine();
        UnionFind uf = new UnionFind(N + 1);
        for (int i = 0; i < M; i++)
        {
            int[] a = IntLine();
            uf.Unite(p[a[0] - 1], p[a[1] - 1]);
        }
        long ans = 0;
        for (int i = 1; i <= N; i++) {
            if (uf.Same(i, p[i - 1])) ans++;
        }
        Console.WriteLine(ans);
    }
}

public class UnionFind
{
    public List<int> parent = new List<int>();

    public UnionFind(int N)
    {
        for (int i = 0; i < N; i++) parent.Add(i);
    }

    private int Root(int a)
    {
        if (parent[a] == a) return a;
        else return parent[a] = Root(parent[a]);
    }

    public void Unite(int a, int b)
    {
        a = Root(a);
        b = Root(b);
        if (a == b) return;
        parent[a] = parent[b];
    }

    public bool Same(int a, int b) { return (Root(a) == Root(b)); }
}

public class Permutation
{
    private static List<int> line;
    public List<List<int>> PermList { get; set; }

    public Permutation(List<int> list)
    {
        line = new List<int>(list);
        PermList = new List<List<int>>();
    }

    public void Run()
    {
        Calc(new List<int>());
    }

    public void Calc(List<int> list)
    {
        if (list.Count == line.Count())
        {
            PermList.Add(list);
            return;
        }
        foreach (int i in line)
        {
            if (!list.Contains(i))
            {
                List<int> nextlist = new List<int>(list);
                nextlist.Add(i);
                Calc(nextlist);
            }
        }
    }

    public void Draw()
    {
        foreach (var l in PermList)
        {
            l.ForEach(v => Console.Write(v + " "));
            Console.WriteLine();
        }
    }
}

public class Atcoder
{
    public static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
    public static long LCM(long a, long b)
    {
        long c = a * b;
        if (a < b) Swap(ref a, ref b);
        long d = a % b;
        while (d != 0)
        {
            a = b;
            b = d;
            d = a % b;
        }
        return c / b;
    }
    public static string StrReverce(string s)
    {
        return new string(s.Reverse().ToArray());
    }
    public static bool IsPrime(int n)
    {
        if (n < 2) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;

        //double sqrtNum = Math.Sqrt(n);
        for (int i = 3; i < n; i += 2)
        {
            if (n % i == 0) return false;
        }
        return true;
    }
    public static string[] SpRead(char c)
    {
        return Console.ReadLine().Split(c);
    }
    public static int[] SpIntRead(char c)
    {
        return Console.ReadLine().Split(c).Select(int.Parse).ToArray();
    }
    public static string ToConvertBit(int N, int e)
    {
        string ret = "";
        int r = 0;
        while (N != 0)
        {
            r = N % e;
            ret += r.ToString();
            N -= r;
            N /= e;
        }
        ret = StrReverce(ret);
        return ret;
    }
    public static int IntRead()
    {
        return int.Parse(Console.ReadLine());
    }
    public static long LongRead()
    {
        return long.Parse(Console.ReadLine());
    }
    public static long[] LongLine()
    {
        return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
    }
    public static int[] IntLine()
    {
        return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
    }
}