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;
using System.Collections.Generic;
using System.Linq;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using System.Numerics;
using System.IO;
using System.Runtime.InteropServices;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming
{
    public void Solve()
    {
        var o = Ints;
        var N = o[0];
        var M = o[1];
        var p = Ints;
        var uf = new UnionFind(N);
        for (int i = 0; i < M; ++i)
        {
            var xy = Ints;
            var x = xy[0] - 1;
            var y = xy[1] - 1;
            uf.Merge(x, y);
        }
        int ans = 0;
        for (int i = 0; i < N; ++i)
        {
            if (uf.IsSame(i, p[i] - 1)) ++ans;
        }
        Write(ans);
    }
}

public class UnionFind
{
    int _count;
    int[] par, sizes, rank;
    public UnionFind(int N)
    {
        _count = N;
        par = new int[N];
        sizes = new int[N];
        rank = new int[N];
        for (int i = 0; i < N; ++i)
        {
            par[i] = i;
            sizes[i] = 1;
            rank[i] = 0;
        }
    }
    int Root(int X)
    {
        if (par[X] == X)
        {
            return X;
        }
        else return (par[X] = Root(par[X]));
    }
    public bool Merge(int X, int Y)
    {
        X = Root(X);
        Y = Root(Y);
        if (X == Y) return false;
        --_count;
        if (rank[X] < rank[Y])
        {
            par[X] = Y;
            sizes[Y] += sizes[X];
        }
        else
        {
            par[Y] = X;
            sizes[X] += sizes[Y];
            if (rank[X] == rank[Y]) ++rank[X];
        }
        return true;
    }
    public bool IsSame(int X, int Y) => Root(X) == Root(Y);
    public int Count => _count;
    public bool IsParent(int X) => X == Root(X);
    public int GetParent(int X) => Root(X);
    public int Size(int X) => sizes[Root(X)];
}

public static class Math2
{
    public const int INF = 1 << 29;
    public const long INFL = 1L << 60;
    public const int MOD = 1000000007;
    public const int MOD2 = 998244353;

    public static long Pow(long i, long N, long MOD = 1000000007)//i^N
    {
        long res = 1;
        while (N > 0)
        {
            if ((N & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            N >>= 1;
        }
        return res;
    }
    public static long GCD(long i, long N)
    {
        if (i > N) Swap(ref i, ref N);
        if (i == 0) return N;
        while (N != 0)
        {
            var r = i % N;
            i = N;
            N = r;
        }
        return i;
    }
    public static long LCM(long i, long N) => i * N / GCD(i, N);
    public static long Comb(long N, long R, int MOD = 1000000007)
    {
        long ret = 1;
        long x = 1;
        for (long i = N; i >= N - R + 1; --i)
        {
            ret = ret / x * i;
            ret %= MOD;
            x++;
        }
        return ret;
    }
    public static long Comb2(long N, long R)
    {
        long Nume = 1;
        long Deno = 1;

        if (R > N - R) Swap(ref N, ref R);
        for (long i = 1; i <= R; ++i)
        {
            Deno *= i;
            Nume *= N - i + 1;
        }
        return Deno / Nume;
    }
    public static Dictionary<long, int> PrimeFactorization(long N)
    {
        var ret = new Dictionary<long, int>();
        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;
        }
        if (N >= 2) ret[N] = 1;
        return ret;
    }
    public static List<long> DivisorEnumrate(long N)
    {
        var ret = new List<long>();
        for (long i = 1; i * i <= N; ++i)
        {
            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }
        }
        return ret;
    }
}
public static class Utils
{

    public static void Swap<T>(ref T A, ref T B)
    {
        T x = A;
        A = B;
        B = x;
    }
    public static int DigitSum(int N)
    {
        string s = N.ToString();
        int ret = 0;
        for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
        return ret;
    }
}
class Program
{
    static void Main(string[] args)
    {
        var CompetitiveProgramming = new CompetitiveProgramming();
        CompetitiveProgramming.Solve();
    }
}
public static class io
{
    public static string Str => Console.ReadLine();
    public static string[] Strs => Str.Split(' ');
    public static long[] Longs => Strs.Select(long.Parse).ToArray();
    public static int[] Ints => Strs.Select(int.Parse).ToArray();
    public static char[] Chars => Str.ToArray();
    public static double[] Doubles => Strs.Select(double.Parse).ToArray();
    public static long Long1 => Longs[0];
    public static int Int1 => Ints[0];
    public static char Char1 => Chars[0];
    public static double Double1 => Doubles[0];
    public static long[] VerticalRead(int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
    public static void Write(string a) => Console.WriteLine(a);
    public static void Write(params object[] i) => Write(string.Join(" ", i));
    public static void Write<T>(IEnumerable<T> a) => Write(string.Join(" ", a));
    public static void Verticalwrite<T>(IEnumerable<T> a) { foreach (var z in a) Write(z); }
    public static void YN(bool i) { if (i) Write("Yes"); else Write("No"); }
}