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.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using static System.Math;

class P
{
    static void Main()
    {
        int[] nm = Console.ReadLine().Split().Select(int.Parse).ToArray();
        //1~nまでを並び替えた
        int[] p = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
        //規定の並び替え動作を複数回行い、12345と一致している数を最大化
        Pair[] ps = Enumerable.Repeat(0, nm[1]).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).OrderBy(x => x).ToArray()).Select(x => new Pair(x[0], x[1])).ToArray();
        //同じグループに属している奴らは自由に並び替え可能
        //席と数字が与えられ、マッチング
        UnionFind uf = new UnionFind(nm[0]);
        foreach (var item in ps)
        {
            uf.Union(item.x, item.y);
        }
        //親,(親にひっついてる数,親達の席)
        Dictionary<int, Tuple<List<int>, List<int>>> dict = new Dictionary<int, Tuple<List<int>, List<int>>>();
        for (int i = 0; i < nm[0]; i++)
        {
            int parent = uf.Parent(i);
            if (!dict.ContainsKey(parent)) dict.Add(parent, new Tuple<List<int>, List<int>>(new List<int>(), new List<int>()));
            dict[parent].Item1.Add(p[i]);
            dict[parent].Item2.Add(i);
        }
        int count = 0;
        foreach (var item in dict.Values)
        {
            count += item.Item1.Intersect(item.Item2).Count();
        }
        Console.WriteLine(count);
    }
}


class UnionFind
{
    int[] data;
    public UnionFind(int count)
    {
        data = Enumerable.Range(0, count).ToArray();
    }
    public void Union(int x, int y)
    {
        int xp = Parent(x);
        int yp = Parent(y);
        if (xp != yp)
        {
            data[yp] = xp;
        }
    }
    public bool IsSameGroup(int x, int y) => Parent(x) == Parent(y);
    public int[] AllParents() => data.Where((x, y) => x == y).ToArray();
    public int Parent(int x)
    {
        form(x);
        return data[x];
    }
    private void form(int x)
    {
        while (data[x] != data[data[x]])
        {
            data[x] = data[data[x]];
        }
    }
}

struct Pair
{
    public int x;
    public int y;

    public Pair(int x, int y)
    {
        this.x = x;
        this.y = y;
    }
}