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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Linq.Enumerable;
using static System.Math;

class Program
{
    static void Main()
    {
        var (N, M) = ReadLine().Split(' ').Select(int.Parse).ToArray();
        var p = ReadLine().Split(' ').Select(int.Parse).ToArray();
        var xy = Range(0, M).Select(i => ReadLine().Split(' ').Select(int.Parse).ToArray());

        var uf = new UnionFind(N);
        foreach (var (x, y) in xy)
            uf.Unite(x - 1, y - 1);

        var group = new Dictionary<int, (HashSet<int> n, HashSet<int> i)>();

        for (int i = 0; i < N; i++)
        {
            var g = uf.Find(i);
            if (!group.ContainsKey(g))
                group.Add(g, (new HashSet<int>(), new HashSet<int>()));

            group[g].n.Add(p[i] - 1);
            group[g].i.Add(i);
        }

        var ans = 0;

        foreach (var (n, i) in group.Select(g => g.Value))
        {
            n.IntersectWith(i);
            ans += n.Count;
        }

        WriteLine(ans);
    }
}

class UnionFind
{
    private int[] d;
    public UnionFind(int n) => d = Enumerable.Repeat(-1, n).ToArray();
    public int Find(int x) => (d[x] < 0) ? x : d[x] = Find(d[x]);
    public bool Unite(int x, int y)
    {
        (x, y) = (Find(x), Find(y));
        if (x == y)
            return false;
        if (-d[x] < -d[y])
            (x, y) = (y, x);
        (d[x], d[y]) = (d[x] + d[y], x);
        return true;
    }
    public bool Same(int x, int y) => Find(x) == Find(y);
    public int Size(int x) => -d[Find(x)];
}

static class ArrayDeconstructExtensions
{
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2) => (i1, i2) = (a[0], a[1]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3) => (i1, i2, i3) = (a[0], a[1], a[2]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4) => (i1, i2, i3, i4) = (a[0], a[1], a[2], a[3]);
    public static void Deconstruct<T>(this T[] a, out T i1, out T i2, out T i3, out T i4, out T i5) => (i1, i2, i3, i4, i5) = (a[0], a[1], a[2], a[3], a[4]);
}