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;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    partial class Program
    {
        static long mod = 1000000007;
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            Solve();
            Console.Out.Flush();
            Console.ReadKey();
        }

        //ここから
        static void Solve()
        {
            int N;int M;
            Multi(out N, out M);
            var A = GetIntArray();
            var uf = new UnionFind(N);
            for(int i = 0; i < M; i++)
            {
                var cin = GetIntArray();
                uf.Union(cin[0] - 1, cin[1] - 1);
            }
            var ans = 0;
            for(int i = 0; i < N; i++)
            {
                if (uf.Same(i, A[i] - 1)) ans++;
            }
            Console.WriteLine(ans);
        }

    }

    //Union Find
    //Find(logN)
    //Union(1)
    class UnionFind
    {
        // 親要素のインデックスを保持する
        // 親要素が存在しない(自身がルートである)とき、マイナスでグループの要素数を持つ
        public int[] Parents { get; set; }
        public UnionFind(int n)
        {
            this.Parents = new int[n];
            for (int i = 0; i < n; i++)
            {
                // 初期状態ではそれぞれが別のグループ(ルートは自分自身)
                // ルートなのでマイナスで要素数(1個)を保持する
                this.Parents[i] = -1;
            }
        }

        // 要素xのルート要素はどれか
        public int Find(int x)
        {
            // 親がマイナスの場合は自分自身がルート
            if (this.Parents[x] < 0) return x;
            // ルートが見つかるまで再帰的に探す
            // 見つかったルートにつなぎかえる
            this.Parents[x] = Find(this.Parents[x]);
            return this.Parents[x];
        }

        // 要素xの属するグループの要素数を取得する
        public int Size(int x)
        {
            // ルート要素を取得して、サイズを取得して返す
            return -this.Parents[this.Find(x)];
        }

        // 要素x, yが同じグループかどうか判定する
        public bool Same(int x, int y)
        {
            return this.Find(x) == this.Find(y);
        }

        // 要素x, yが属するグループを同じグループにまとめる
        public bool Union(int x, int y)
        {
            // x, y のルート
            x = this.Find(x);
            y = this.Find(y);
            // すでに同じグループの場合処理しない
            if (x == y) return false;

            // 要素数が少ないグループを多いほうに書き換えたい
            if (this.Size(x) < this.Size(y))
            {
                var tmp = x;
                x = y;
                y = tmp;
            }
            // まとめる先のグループの要素数を更新
            this.Parents[x] += this.Parents[y];
            // まとめられるグループのルートの親を書き換え
            this.Parents[y] = x;
            return true;
        }
    }



    //拡張メソッド
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.Ordinal); return s.ToList(); }
        public static string yesno(this bool b) { return b ? "yes" : "no"; }
        public static string YesNo(this bool b) { return b ? "Yes" : "No"; }
        public static string YESNO(this bool b) { return b ? "YES" : "NO"; }
    }

    partial class Program
    {
        static public string GetStr() { return Console.ReadLine().Trim(); }
        static public char GetChar() { return Console.ReadLine().Trim()[0]; }
        static public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        static public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        static public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        static public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        static public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        static public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        static public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        static public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        static public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        static public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        static public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        static public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        static public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }

        static public void WriteObjects<T>(IReadOnlyCollection<T> values) { var array = values.ToArray(); var num = array.Length; Console.Write(array[0]); for (int i = 1; i < num; i++) { Console.Write(" "+array[i]);} Console.WriteLine(); }

        static bool eq<T, U>() => typeof(T).Equals(typeof(U));
        static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        static T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        static void Multi<T>(out T a) => a = cv<T>(GetStr());
        static void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        static void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        static void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        static void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        static void Multi<T, U, V, W, X,Y>(out T a, out U b, out V c, out W d, out X e,out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);f = cv<Y>(ar[5]);
        }
    }
}