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.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        static void Main()
        {
            var nm = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            var p = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            var inp = new List<int[]>();
            var swapTree = new Dictionary<int, List<int>>();
            for (int i = 0; i < nm[1]; i++)
            {
                inp.Add(Array.ConvertAll(Console.ReadLine().Split(), int.Parse));
                int temp = inp[i][0];
                inp[i][0] = inp[i][1];
                inp[i][1] = temp;
                inp.Add(inp[i]);
            }
            inp = inp.OrderBy(x => x[1]).OrderBy(x => x[0]).ToList();
            for (int i = 0; i <= nm[0]; i++) swapTree[i] = new List<int>();
            for (int i = 0; i < inp.Count(); i++)
            {
                swapTree[inp[i][0]].Add(inp[i][1]);
            }
            for (int i = 0; i < swapTree.Count(); i++)
            {
                swapTree[swapTree.ElementAt(i).Key] = swapTree[swapTree.ElementAt(i).Key].Distinct().ToList();
                int search = swapTree.ElementAt(i).Value.Count();
                int check = 0;
                while (search != 0)
                {
                    for (int j = 0; j < search; j++)
                    {
                        swapTree[swapTree.ElementAt(i).Key].AddRange(swapTree[swapTree.ElementAt(i).Value[check + j]]);
                        swapTree[swapTree.ElementAt(i).Key] = swapTree[swapTree.ElementAt(i).Key].Distinct().ToList();
                    }
                    check = search;
                    search = swapTree.ElementAt(i).Value.Count() - search;
                }
            }
            int ans = 0;
            for (int i = 0; i < nm[0]; i++)
            {
                Console.WriteLine(string.Join(" ", swapTree[p[i]]));
                if (swapTree[p[i]].Contains(p[i])) ans++;
            }
            Console.WriteLine(ans);
        }
    }
}