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.Linq;

namespace arc097_b
{
    public class Unionfind
    {
        public static int[] par;//親
        public static int[] rank; //深さ
        public void init(int n)//初期化
        {
            par = new int[n]; rank = new int[n];
            for (int i = 0; i < n; i++)
            {
                par[i] = i;
                rank[i] = 0;
            }
        }
        public int root(int x)//根を求める
        {
            if (par[x] == x) return x;
            else return par[x] = root(par[x]);
        }
        public void unite(int x, int y)//集合を併合
        {
            x = root(x); y = root(y);
            if (x == y) return;
            else
            {
                if (rank[x] < rank[y]) par[x] = y;
                else
                {
                    par[y] = x;
                    if (rank[x] == rank[y]) rank[x]++;
                }
            }
        }
        public bool issame(int x, int y)//同じ集合に属しているか
        {
            return root(x) == root(y);
        }
    }
    class Program
    {
        static void Main(string[] args)
        {
            int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            Unionfind find = new Unionfind();
            find.init(a[0]);
            for (int i = 0; i < a[1]; i++)
            {
                int[] y = Console.ReadLine().Split().Select(int.Parse).ToArray();
                find.unite(y[0] - 1, y[1] - 1);
            }
            int ret = 0;
            for (int i = 0; i < a[0]; i++)
            {
                if (find.issame(i, x[i] - 1)) ret++;
            }
            Console.WriteLine(ret);
        }
    }
}