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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Runtime.CompilerServices;
using System.Net.NetworkInformation;

namespace ConsoleApp5
{
    class Program
    {

        static void Main(string[] args)
        {
            var nm = System.Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            UnionFind unionFInd = new UnionFind(nm[0]);
            var numbers = System.Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
            for (int i = 0; i < nm[1]; i++)
            {
                var xy = System.Console.ReadLine().Split(' ').Select(i => int.Parse(i)).ToArray();
                unionFInd.Union(xy[0], xy[1]);
            }

            int count = 0;

            for(int i = 0; i < numbers.Length; i++)
            {
                if(unionFInd.Some(i+1, numbers[i])){
                    count++;
                }
            }

            Console.WriteLine(count);
        }
    }

    public class UnionFind
    {
        int[] Parents { get; set; }
        int[] Rank { get; set; }
        public UnionFind(int n)
        {
            Parents = new int[n+1];
            Rank = new int[n+1];
            for (int i = 1; i < n; i++)
            {
                Parents[i] = i;
                Rank[i] = 0;
            }
        }

        public int Find(int x)
        {
            if(Parents[x] == x)  return x;

            Parents[x] = Find(Parents[x]);
            return Parents[x];
        }


        public void Union(int x, int y)
        {
            var rx = Find(x);
            var ry = Find(y);
            if (rx == ry) return;
            if(Rank[rx] < Rank[ry])
            {
                Parents[rx] = ry;
            }
            else { 
                Parents[ry] = rx;
                if (Rank[rx] == Rank[ry]) Rank[rx]++;
            }
        }

        public bool Some(int x, int y)
        {
            return Find(x) == Find(y);
        }
    }
}