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;

namespace AtCoder
{
    class Node<T>
    {
        private int m_height;
        private Node<T> m_parent;
        public T Item { get; private set; }
        public Node(T item)
        {
            m_height = 0;
            m_parent = this;
            Item = item;
        }
        public Node<T> Find()
        {
            if (m_parent == this) { return this; }

            Node<T> parent = m_parent.Find();
            m_parent = parent;
            return parent;
        }
        public static void Unite(Node<T> a, Node<T> b)
        {
            Node<T> p = a.Find();
            Node<T> q = b.Find();
            if (p.m_height < q.m_height)
            {
                p.m_parent = q;
                q.m_height = Math.Max(p.m_height + 1, q.m_height);
            }
            else
            {
                q.m_parent = p;
                p.m_height = Math.Max(q.m_height + 1, p.m_height);
            }
        }
    }
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static int Solve(int N, int[] P, Tuple<int, int>[] tuples)
        {
            var nodes = new Node<int>[N];
            for (int i = 0; i < N; ++i) { nodes[i] = new Node<int>(i); }
            foreach (var tuple in tuples)
            {
                int a = tuple.Item1;
                int b = tuple.Item2;
                Node<int>.Unite(nodes[a], nodes[b]);
            }
            int count = 0;
            for (int i = 0; i < N; ++i)
            {
                if (nodes[i].Find().Item == nodes[P[i]].Find().Item) { ++count; }
            }
            return count;
        }
        static void Main(string[] args)
        {
            var V1 = ReadInts();
            int N = V1[0];
            int M = V1[1];
            var P = ReadInts().Select(p => p - 1).ToArray();
            var tuples = new Tuple<int, int>[M];
            for (int i = 0; i < M; ++i)
            {
                var V2 = ReadInts();
                tuples[i] = new Tuple<int, int>(V2[0] - 1, V2[1] - 1);
            }
            Console.WriteLine(Solve(N, P, tuples));
        }
    }
}