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.Linq;

namespace ARC097D
{
    internal class Program
    {
        public static void Main(string[] args)
        {
            int[] input = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
            int n = input[0];
            int m = input[1];

            int[] p = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);

            int[] x = new int[m];
            int[] y = new int[m];
            for (int i = 0; i < m; i++)
            {
                int[] line = Array.ConvertAll(Console.ReadLine().Split(' '), int.Parse);
                x[i] = line[0];
                y[i] = line[1];
            }

            UnionFind union = new UnionFind(n);
            for (int i = 0; i < m; i++)
            {
                union.Unite(x[i], y[i]);
            }

            Point[] points = new Point[n + 1];
            for (int i = 0; i <= n; i++)
            {
                points[i] = new Point(i);
            }

            for (int i = 1; i <= n; i++)
            {
                points[union.Root(i)].Add(i);
            }

            int score = 0;
            foreach (Point point in points)
            {
                score += point.Score(p);
            }

            Console.WriteLine(score);
        }

        class Point
        {
            private List<int> X;
            public int M;
            private bool _on;

            public Point(int m)
            {
                M = m;
                X = new List<int>();
            }

            public void Add(int x)
            {
                X.Add(x);
                _on = true;
            }

            private List<int> all()
            {
                List<int> list = new List<int>();
                foreach (int i in X)
                {
                    list.Add(i);
                }

                list.Add(M);
                return list.Distinct().ToList();
            }

            public int Score(int[] p)
            {
                if (!_on)
                {
                    return 0;
                }

                if (M == 0)
                {
                    return 0;
                }

                int[] indexes = all().ToArray();
                var values = new Dictionary<int, bool>();
                for (int i = 0; i < indexes.Length; i++)
                {
                    values[p[indexes[i] - 1]] = true;
                }

                int score = 0;
                for (int i = 0; i < indexes.Length; i++)
                {
                    if (values.ContainsKey(indexes[i]))
                    {
                        score++;
                    }
                }

                return score;
            }
        }
    }

    public class UnionFind
    {
        private int[] par;

        public UnionFind(int maxN)
        {
            par = new int[maxN + 1];
            Init(maxN);
        }

        void Init(int n)
        {
            for (int i = 1; i <= n; i++)
            {
                par[i] = i;
            }
        }

        public int Root(int x)
        {
            if (par[x] == x)
            {
                return x;
            }

            return par[x] = Root(par[x]);
        }

        public bool Same(int x, int y)
        {
            return Root(x) == Root(y);
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y)
            {
                return;
            }

            par[x] = y;
        }
    }
}