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;

class Program{
    static void Main(string[] args)
    {
        int[] nm = Scan.IntArray(2);
        int cnt = 0;
        int n, m;
        n = nm[0]; m = nm[1];
        int[] p = Scan.IntArray(n);
        for (int i = 0; i < n; i++)
        {
            p[i]--;
        }
        UnionFind uf = new UnionFind();
        uf.Init(n);
        for (int i = 0; i < m; i++)
        {
            int[] xy = Scan.IntArray(2);
            int x = xy[0] - 1;
            int y = xy[1] - 1;
            uf.Unite(x, y, 0);
        }

        for (int i = 0; i < n; i++)
        {
            if(uf.Same(i, p[i]))
            {
                cnt++;
            }
        }
        Out.Num(cnt);
    }
}

public class Scan
{
    public static int Int()
    {
        return int.Parse(Console.ReadLine());
    }

    public static int[] IntArray(int t)
    {
        string[] str = Console.ReadLine().Split(' ');
        int[] ar = new int[t];
        for (int i = 0; i < t; i++)
        {
            ar[i] = int.Parse(str[i]);
        }
        return ar;
    }
}

public class Out
{
    public static void Num<T>(T a)
    {
        Console.WriteLine(a);
    }
}

public class UnionFind
{
    public int[] parent;
    public int[] rank;
    public long[] weightDiff;

    public void Init(int size)
    {
        parent = new int[size + 5];
        rank = new int[size + 5];
        weightDiff = new long[size + 5];
        for (int i = 0; i < size; i++)
        {
            parent[i] = i;
            rank[i] = 0;
            weightDiff[i] = 0;
        }
    }

    public int Root(int x)
    {
        if(parent[x] == x)
        {
            return x;
        }
        else
        {
            int r = Root(parent[x]);
            weightDiff[x] += weightDiff[parent[x]];
            return parent[x] = r;
        }
    }

    public bool Unite(int x, int y, long w) // Add edge x <- y (weight: w)
    {
        w = w + GetWeight(x) - GetWeight(y);
        x = Root(x);
        y = Root(y);
        if (x == y) return false;
        if(rank[x] < rank[y])
        {
            int tmp = x; x = y; y = tmp;
            w *= -1;
        }
        if(rank[x] == rank[y])
        {
            ++rank[x];
        }
        parent[y] = x;
        weightDiff[y] = w;
        return true;
    }
  
      public long GetWeight(int x)
    {
        Root(x);
        return weightDiff[x];
    }


    public bool Same(int x, int y)
    {
        return Root(x) == Root(y);
    }
}