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;

class Program
{
    static void Main(string[] args)
    {
        var sc = new Scanner();
        int n = sc.NextInt();
        int m = sc.NextInt();
        int[] p = new int[n];
        for (int i = 0; i < n; i++) p[i] = sc.NextInt() - 1;
        
        var t = new UnionFindTree(n);
        for (int i = 0; i < m; i++)
        {
            int x = sc.NextInt() - 1;
            int y = sc.NextInt() - 1;
            t.Unite(x, y);
            //if (!g.ContainsKey(x)) g.Add(x, new List<int>());
            //g[x].Add(y);
            //if (!g.ContainsKey(y)) g.Add(y, new List<int>());
            //g[y].Add(x);
        }
        int ans = 0;
        for (int i = 0; i < n; i++)
        {
            if (t.Same(i, p[i])) ans++;
        }
        Console.WriteLine(ans);
    }
}

class UnionFindTree
{
    private int[] p;
    public UnionFindTree(int size)
    {
        p = new int[size];
        for (int i = 0; i < size; i++) p[i] = i;
    }

    public int Find(int n)
    {
        while (p[n] != n) n = p[n];
        return n;
    }

    public void Unite(int a, int b)
    {
        int pa = Find(a);
        int pb = Find(b);
        if (pa == pb) return;
        p[pb] = pa;
    }

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


class Scanner
{
    int index = -1;
    string[] buf;

    public Scanner()
    {
    }

    public int NextInt()
    {
        CheckNext();
        return int.Parse(buf[index++]);
    }

    public long NextLong()
    {
        CheckNext();
        return long.Parse(buf[index++]);
    }

    public double NextDouble()
    {
        CheckNext();
        return double.Parse(buf[index++]);
    }

    public string NextString()
    {
        CheckNext();
        return buf[index++];
    }

    private void CheckNext()
    {
        if (index >= 0 && index < buf.Length) return;

        buf = Console.ReadLine().Split(' ');
        index = 0;
    }
}