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 static Assistant.Input;
using static Assistant.Debug;
using System.Linq;
using Assistant;

namespace ABC097D_2
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = ReadInt;
            var M = ReadInt;

            int[] p = ReadInts;

            UnionFind uf = new UnionFind(N + 1);
            for (int i = 0; i < M; i++)
            {
                var x = ReadInt;
                var y = ReadInt;
                uf.Unite(x, y);
            }

            int[] oya = new int[N + 1];
            for (int i = 0; i < N + 1; i++)
            {
                oya[i] = uf.Find(i);
            }

            int count = 0;
            for (int i = 0; i < N; i++)
            {
                if (oya[i + 1] == uf.Find(p[i])) count++;
            }
            Console.WriteLine(count);
        }


    }

    class UnionFind
    {
        int[] par;
        int[] rank;
        int[] count;

        public UnionFind(int n)
        {
            Init(n);
        }

        void Init(int n)
        {
            par = new int[n];
            rank = new int[n];
            count = new int[n].Select(x => 1).ToArray();

            for (int i = 0; i < n; i++)
            {
                par[i] = i;
            }
        }

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

        public bool Unite(int x, int y)
        {
            x = Find(x);
            y = Find(y);
            if (x == y) return false; //すでに要素を追加済みの場合、falseを返す。

            if (rank[x] < rank[y])
            {
                par[x] = y;
                count[y] += count[x];
            }
            else
            {
                par[y] = x;
                count[x] += count[y];
                if (rank[x] == rank[y]) rank[x]++;
            }
            return true;
        }
        public bool Same(int x, int y)
        {
            return Find(x) == Find(y);
        }

        public int Size(int x)
        {
            return count[Find(x)];
        }
    }


}

namespace Assistant
{
    static class Input
    {
        static List<string> line = new List<string>();
        static int index = 0;
        static String ReadNext()
        {
            if (line.Count <= index) line.AddRange(Console.ReadLine().Split());
            return line[index++];
        }
        public static int ReadInt => int.Parse(ReadNext());
        public static long ReadLong => long.Parse(ReadNext());
        public static int[] ReadInts => Console.ReadLine().Split().Select(int.Parse).ToArray();
        public static long[] ReadLongs => Console.ReadLine().Split().Select(long.Parse).ToArray();
    }

    static class Debug
    {
        static public void Draw2D(int[,] map, int mode = 1)
        {
#if DEBUG
            int W = map.GetLength(0);
            int H = map.GetLength(1);

            int[,] map2 = new int[W + 1, H + 1];
            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (i == 0 && j == 0) map2[i, j] = 0;
                    else if (i == 0) map2[i, j] = j - 1;
                    else if (j == 0) map2[i, j] = i - 1;
                    else map2[i, j] = map[i - 1, j - 1];
                }
            }

            for (int i = 0; i < W + 1; i++)
            {
                for (int j = 0; j < H + 1; j++)
                {
                    if (mode == 0) Console.Write(map2[i, j] % 10);
                    if (mode == 1) Console.Write(map2[i, j] + " ");
                }
                Console.WriteLine();
            }
            Console.WriteLine();
#endif
        }

        public static void Draw1D(int[] array, int mode = 0)
        {
#if DEBUG
            Console.WriteLine(string.Join(" ", array));
#endif
        }
    }
}