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 Yorukatsu023.Questions;
using Yorukatsu023.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu023.Questions
{
    /// <summary>
    /// ABC097 D
    /// </summary>
    public class QuestionE : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            var n = nm[0];
            var m = nm[1];

            var p = inputStream.ReadIntArray().Select(i => i - 1).ToArray();
            var groups = p.Select(i => new UnionFindNode<int>(i)).ToArray();

            for (int i = 0; i < m; i++)
            {
                var xy = inputStream.ReadIntArray();
                var x = xy[0] - 1;
                var y = xy[1] - 1;
                groups[x].Unite(groups[y]);
            }

            var count = Enumerable.Range(0, n).Count(i => groups[i].IsInSameGroup(groups[p[i]]));
            yield return count;
        }
    }

    // See https://kumikomiya.com/competitive-programming-with-c-sharp/
    public class UnionFindNode<T>
    {
        private int _height;        // rootのときのみ有効
        private int _groupSize;     // 同上
        private UnionFindNode<T> _parent;
        public T Item { get; }

        public UnionFindNode(T item)
        {
            _height = 0;
            _groupSize = 1;
            _parent = this;
            Item = item;
        }

        private UnionFindNode<T> FindRoot()
        {
            if (_parent != this) // not ref equals
            {
                var root = _parent.FindRoot();
                _parent = root;
            }

            return _parent;
        }

        public int GetGroupSize() => FindRoot()._groupSize;

        public void Unite(UnionFindNode<T> other)
        {
            var thisRoot = this.FindRoot();
            var otherRoot = other.FindRoot();

            if (thisRoot == otherRoot)
            {
                return;
            }

            if (thisRoot._height < otherRoot._height)
            {
                thisRoot._parent = otherRoot;
                otherRoot._groupSize += thisRoot._groupSize;
                otherRoot._height = Math.Max(thisRoot._height + 1, otherRoot._height);
            }
            else
            {
                otherRoot._parent = thisRoot;
                thisRoot._groupSize += otherRoot._groupSize;
                thisRoot._height = Math.Max(otherRoot._height + 1, thisRoot._height);
            }
        }

        public bool IsInSameGroup(UnionFindNode<T> other) => this.FindRoot() == other.FindRoot();

        public override string ToString() => $"{Item} root:{FindRoot().Item}";
    }

}

namespace Yorukatsu023
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionE();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu023.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu023.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion