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.Text;
using System.Threading.Tasks;

namespace ConsoleApp15
{
    class Class368
    {
        static void Main()
        {
            var NM = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int N = NM[0], M = NM[1];
            var p = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

            var uni = new Union_Find(N);
            for (int i = 0; i < M; i++)
            {
                var r = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                uni.Unite(--r[0], --r[1]);
            }
            int count = 0;
            for(int i = 0; i < N; i++)
            {
                if (uni.IsSameGroup(--p[i], i))
                    count++;
            }
            Console.WriteLine(count);
        }
    }

    public class Union_Find
    {
        private int[] data;
        public Union_Find()
        {
            int size = 200000;
            data = new int[size];
            for (int i = 0; i < size; i++) data[i] = -1;
        }
        public Union_Find(int size)
        {
            data = new int[size];
            for (int i = 0; i < size; i++) data[i] = -1;
        }
        public bool Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x != y)
            {
                if (data[y] < data[x])
                {
                    var tmp = y;
                    y = x;
                    x = tmp;
                }
                data[x] += data[y];
                data[y] = x;
            }
            return x != y;
        }
        public bool IsSameGroup(int x, int y) => Root(x) == Root(y);
        public int Root(int x) => data[x] < 0 ? x : data[x] = Root(data[x]);
        public int getMem(int x) => -data[Root(x)];
    }
}