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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

    public void Proc()
    {

		int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
		this.Num = inpt[0];
		int roadNum = inpt[1];
		this.NumList = Reader.ReadLine().Split(' ').Select(a => int.Parse(a) - 1).ToArray();
		this.NodeList = new TreeNode[this.Num];
		List<int[]> road = new List<int[]>();
		for (int i = 0; i < roadNum; i++) {
			inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a) - 1).OrderBy(a=>a).ToArray();
			road.Add(inpt);
		}
		road.Sort((a, b) =>
		{
			if(a[0]==b[0]) {
				return a[1].CompareTo(b[1]);
			} else {
				return a[0].CompareTo(b[0]);
			}
		});

		for (int i = 0; i < road.Count; i++) {
			int a = road[i][0];
			int b = road[i][1];
			if(NodeList[a] == null) {
				NodeList[a] = new TreeNode(a);
				if(NodeList[b] == null) {
					NodeList[b] = new TreeNode(b);
					NodeList[a].Add(NodeList[b]);
				} else {
					NodeList[b].Parent.Add(NodeList[a]);
				}

			} else {
				if (NodeList[b] == null)
                {
                    this.NodeList[b] = new TreeNode(b);
					NodeList[a].Parent.Add(NodeList[b]);
				} else if(NodeList[a].Parent.Idx != NodeList[b].Parent.Idx) {
					NodeList[a].Parent.Add(NodeList[b].Parent);
				}
			}
		}
		int[] pos = new int[this.Num];
		for (int i = 0; i < this.Num; i++) {
			pos[NumList[i]] = i;
		}
		int ans = 0;
		for (int i = 0; i < this.Num; i++) {
			if(pos[i] == i) {
				ans++;
				continue;
			}
			int idx1 = pos[i];
			int idx2 = i;

			int num1 = i;
			int num2 = NumList[idx2];
		
			if(NodeList[idx1] == null || NodeList[idx2] == null) {
				continue;
			}
			if(NodeList[idx1].Parent.Idx != NodeList[idx2].Parent.Idx) {
				continue;
			}
			NumList[idx2] = i;
			NumList[idx1] = num2;
			pos[i] = i;
			pos[num2] = idx1;
			ans++;
		}
		Console.WriteLine(ans);
    }

	private int[] NumList;

	private int Num;

	private TreeNode[] NodeList;
	private class TreeNode {
		public int Idx;
		public TreeNode Parent;
		public List<TreeNode> Childs = new List<TreeNode>();
		public TreeNode(int id) {
			this.Parent = this;
			this.Idx = id;
		}
		public void Add(TreeNode child) {
			this.Childs.Add(child);
			child.Parent = this.Parent;
			child.Refresh();
		}
		public void Refresh() {
			if(this.Parent != this) {
				this.Parent = this.Parent.Parent;
				this.Childs.ForEach(a => a.Refresh());
			}
		}
	}


    public class Reader
    {
        static StringReader sr;
        public static bool IsDebug = false;
        public static string ReadLine()
        {
            if (IsDebug)
            {
                if (sr == null)
                {
                    sr = new StringReader(InputText.Trim());
                }
                return sr.ReadLine();
            }
            else
            {
                return Console.ReadLine();
            }
        }
        private static string InputText = @"
 
 
 
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 
 
";
    }

    public static void Main(string[] args)
    {
#if DEBUG
        Reader.IsDebug = true;
#endif
        Program prg = new Program();
        prg.Proc();
    }
}