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;
using System.IO;
using System.Text.RegularExpressions;
using System.Diagnostics;

//var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
namespace AtCoderSolve
{
    
    class Solve
    {
        const int mod = 1000000007;
        const int INF = 1000000000;


        static int N, M;
        static int[] p, x, y;
        
        
        public static void Input()
        {
            var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            N = input[0];
            M = input[1];
            p = Console.ReadLine().Split().Select(int.Parse).ToArray();
            x = new int[M];
            y = new int[M];
            for(var i = 0; i < M; i++)
            {
                var xy = Console.ReadLine().Split().Select(int.Parse).ToArray();
                x[i] = xy[0];
                y[i] = xy[1];
            }
        }

        static void Main(string[] args)
        {
            Input();
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            var U = new UnionFind(N);
            for(var i = 0; i < M; i++)
            {
                U.Unite(x[i] - 1, y[i] - 1);
            }

            long ans = 0;
            for(var i = 0; i < N; i++)
            {
                if (U.SameRoot(p[i] - 1, i)) 
                {
                    ans++;
                }

            }
            Console.WriteLine(ans);

            //Console.Out.Flush();
        }

        
    }

    public class UnionFind
    {
        public int[] parent;
        public int[] rank;
        public UnionFind(int size)
        {
            parent = new int[size];
            rank = new int[size];
            for(var i = 0; i < size; i++)
            {
                parent[i] = i;
                rank[i] = 0;
            }
        }

        private int Root(int x)
        {
            return parent[x] == x ? x : parent[x] = Root(parent[x]);
        }

        public bool SameRoot(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; }

            if (rank[x] < rank[y])
            {
                parent[x] = y;
            }
            else
            {
                parent[y] = x;
                if (rank[x] == rank[y]) { rank[x]++; }
            }
        }

    }



}