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: Time Limit Exceeded)

using System;
using System.Linq;

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 par = new int[nm[0] + 1];
            for (int i = 0; i < par.Count(); i++) par[i] = i;
            for (int i = 0; i < nm[1]; i++)
            {
                var inp = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                int v1 = inp.Max();
                int v2 = inp.Min();
                while (par[v1] != v1) v1 = par[v1];
                while (par[v2] != v2) v2 = par[v2];
                par[v1] = v2;
            }
            int ans = 0;
            for (int i = 0; i < nm[0]; i++)
            {
                if (findRoot(par, p[i]) == findRoot(par, p[p[i] - 1])) ans++;
            }
            Console.WriteLine(ans);
        }
        static int findRoot(int[] par, int x)
        {
            while (par[x] != x) x = par[x];
            return x;
        }
    }
}