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.Globalization;
using System.IO;
using System.Linq;
using System.Text;
using static System.Math;

namespace CSharpSpiral {
	class Program {
		static void Main(string[] args) {
			var sw = new StreamWriter(Console.OpenStandardOutput()) {
				AutoFlush=
#if DEBUG
			true
#else
			false
#endif
			};
			Console.SetOut(sw);
			new Program().Solve(new ConsoleInput(
#if DEBUG
			new StreamReader("../../../inputData.txt")
#else
			Console.In
#endif
			, ' '));
			Console.Out.Flush();
		}
		public void Solve(ConsoleInput cin) {
			var N = cin.ReadInt;
			var M = cin.ReadInt;
			var P = cin.ReadIntArray(N);
			var G = new UnionFindForest(N);
			for(int i = 0; i<M; i++) {
				var XY = cin.ReadIntArray(2);
				var x = XY[0]-1;
				var y = XY[1]-1;
				G.Union(x, y);
			}
			Console.WriteLine(Enumerable.Range(0,N).Count(i => G.Find(i, P[i]-1)));
		}
	}
	static class ExtendClass {
		public static string Join<T>(this IEnumerable<T> X, string separator = " ") => string.Join(separator, X);
	}
	class ConsoleInput {
		private readonly TextReader _stream;
		private readonly char _separator = ' ';
		private readonly Queue<string> inputStream;
		public ConsoleInput(TextReader stream, char separator = ' ') {
			this._separator=separator;
			this._stream=stream;
			inputStream=new Queue<string>();
		}
		public string Read {
			get {
				if(inputStream.Count!=0) return inputStream.Dequeue();
				string[] tmp = _stream.ReadLine().Split(_separator);
				for(int i = 0; i<tmp.Length; ++i)
					inputStream.Enqueue(tmp[i]);
				return inputStream.Dequeue();
			}
		}
		public string ReadLine { get { return _stream.ReadLine(); } }
		public int ReadInt { get { return int.Parse(Read); } }
		public long ReadLong { get { return long.Parse(Read); } }
		public double ReadDouble { get { return double.Parse(Read); } }
		public string[] ReadStrArray(long N) {
			var ret = new string[N];
			for(long i = 0; i<N; ++i)
				ret[i]=Read;
			return ret;
		}
		public int[] ReadIntArray(long N) { var ret = new int[N]; for(long i = 0; i<N; ++i) ret[i]=ReadInt; return ret; }
		public long[] ReadLongArray(long N) { var ret = new long[N]; for(long i = 0; i<N; ++i) ret[i]=ReadLong; return ret; }
		public double[] ReadDoubleArray(long N) { var ret = new double[N]; for(long i = 0; i<N; ++i) ret[i]=ReadDouble; return ret; }
		public bool isEOF {
			get { return _stream.Peek()==-1; }
		}
	}
	class UnionFindForest {
		public class Node {
			public int value { get; set; }
			public virtual Node parent { get; set; }
			public virtual Node root {
				get {
					var path = new Queue<Node>();
					var res = this;
					while(res.parent!=res) {
						path.Enqueue(res);
						res=res.parent;
					}
					while(path.Any())
						path.Dequeue().parent=res;
					return res;
				}
			}
			public int rank { get; private set; }    //meanful iff root
			public void rankIncrement() => rank++;
			public Node(int _value) {
				value=_value;
				parent=this;
				rank=1;
			}
		}

		private readonly Dictionary<int, Node> Registry = new Dictionary<int, Node>();
		public UnionFindForest(int N) {
			for(int i = 0; i<N; i++) Add(i);
		}
		public void Union(int x, int y) => Union(Registry[x], Registry[y]);
		public void Union(Node X, Node Y) {
			var RX = X.root;
			var RY = Y.root;
			switch(RX.rank.CompareTo(RY.rank)) {
				case 1:
					RY.parent=RX;
					break;
				case -1:
					RX.parent=RY;
					break;
				default:
					RX.parent=RY;
					RY.rankIncrement();
					break;
			}
		}
		public bool Find(int x, int y) => Find(Registry[x], Registry[y]);
		public bool Find(Node X, Node Y) => X.root==Y.root;
		public virtual void Add(int id) {
			var N = new Node(id);
			Registry.Add(id, N);
		}
		public Dictionary<Node, int> TallyDegrees() {
			var Roots = new Dictionary<Node, int>();
			foreach(var node in Registry.Values) {
				if(Roots.Keys.Contains(node))
					Roots[node]++;
				else
					Roots.Add(node, 1);
			}
			return Roots;
		}
		public int[] Degrees() {
			var D = TallyDegrees();
			var res = new int[Registry.Count];
			for(int i = 0; i<Registry.Count; i++)
				res[i]=D[Registry[i]];
			return res;
		}
		public int TreeCount() {
			var D = TallyDegrees();
			return D.Count;
		}
	}
}