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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest.D_Challenge
{
    class ABC_097
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] nm = ReadInts();
            int[] ps = ReadInts();
            var xy = new int[nm[1]][];
            for(int i = 0; i < nm[1]; i++)
            {
                xy[i] = ReadInts();
                Array.Sort(xy[i]);
            }
            Array.Sort(xy, (a, b) => a[1] - b[1]);
            Array.Sort(xy, (a, b) => a[0] - b[0]);
            for(int i = 0; i < nm[1]; i++)
            {
                Console.WriteLine(xy[i][0] + "," + xy[i][1]);
            }
            var unionFind = new int[nm[0]];
            for(int i = 0; i < nm[0]; i++)
            {
                unionFind[i] = i;
            }
            for (int i = 0; i < nm[1]; i++)
            {
                //親取得
                int indexL = xy[i][0] - 1;
                while (unionFind[indexL] != indexL)
                {
                    indexL = unionFind[indexL];
                }
                int indexR = xy[i][1] - 1;
                while (unionFind[indexR] != indexR)
                {
                    indexR = unionFind[indexR];
                }
                if(indexL< indexR)
                {
                    unionFind[indexR] = indexL;
                }
                else
                {
                    unionFind[indexL] = indexR;
                }
            }
            /*for (int i = 0; i < nm[0]; i++)
            {
                Console.WriteLine(unionFind[i]);
            }*/

            for (int i = 0; i < nm[0]; i++)
            {
                int index = i;
                while (unionFind[index] != index)
                {
                    index = unionFind[index];
                }
                unionFind[i] = index;
            }

            /*for (int i = 0; i < nm[0]; i++)
            {
                Console.WriteLine(unionFind[i]);
            }*/
            var groupDict = new Dictionary<int, Dictionary<int,bool>>();
            for(int i = 0; i < nm[0]; i++)
            {
                if (!groupDict.ContainsKey(unionFind[i]))
                {
                    groupDict.Add(unionFind[i],
                        new Dictionary<int, bool>());
                }
                groupDict[unionFind[i]].Add(ps[i]-1, true);
            }
            int cnt = 0;
            for(int i = 0; i < nm[0]; i++)
            {
                if (groupDict[unionFind[i]].ContainsKey(i))
                {
                    cnt++;
                }
            }

            Console.WriteLine(cnt);
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}