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.IO;
using System.Collections.Generic;

namespace ARC097D
{
    public class Program
    {
        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var N = ss.Next(int.Parse);
            var M = ss.Next(int.Parse);
            var P = ss.Next(int.Parse, N);

            var uf = new UnionFind(N);
            for (var i = 0; i < M; i++)
            {
                uf.Unite(ss.Next(int.Parse) - 1, ss.Next(int.Parse) - 1);
            }

            var ans = 0;
            for (var i = 0; i < N; i++)
            {
                if (uf.IsSameSet(P[i] - 1, i)) ans++;
            }

            sw.WriteLine(ans);
            //---------------------------------
        }

        static void Main()
        {
            var ss = new StreamScanner(new StreamReader(Console.OpenStandardInput()));
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            new Program().Solve(ss, sw);
            sw.Flush();
        }

        static readonly Func<string, string> String = s => s;
    }

    public class UnionFind
    {
        private readonly int[] _rank;
        private readonly int[] _p;

        public UnionFind(int size)
        {
            _rank = new int[size];
            _p = new int[size];

            for (var i = 0; i < size; i++)
            {
                _rank[i] = 0;
                _p[i] = i;
            }
        }

        public void Unite(int x, int y)
        {
            x = FindSet(x);
            y = FindSet(y);

            if (_rank[x] > _rank[y]) _p[y] = x;
            if (_rank[x] < _rank[y]) _p[x] = y;
            if (_rank[x] == _rank[y])
            {
                _p[x] = y;
                _rank[y]++;
            }
        }

        public bool IsSameSet(int x, int y)
        {
            return FindSet(x) == FindSet(y);
        }

        public int FindSet(int x)
        {
            if (_p[x] == x) return x;
            return _p[x] = FindSet(_p[x]);
        }
    }

    public class StreamScanner
    {
        static readonly char[] Sep = {' '};
        readonly Queue<string> buffer = new Queue<string>();
        readonly TextReader textReader;

        public StreamScanner(TextReader textReader)
        {
            this.textReader = textReader;
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (buffer.Count != 0) return parser(buffer.Dequeue());
            var nextStrings = textReader.ReadLine().Split(Sep, StringSplitOptions.RemoveEmptyEntries);
            foreach (var nextString in nextStrings) buffer.Enqueue(nextString);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }
}