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.Diagnostics;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Reflection.Emit;
using System.Text;
using static System.Console;
using static System.Math;

//using CS_Contest.Graph;
using CS_Contest.Loop;
using CS_Contest.Utils;
using static Nakov.IO.Cin;
using static CS_Contest.IO.IO;
using static CS_Contest.Utils.MyMath;


namespace CS_Contest {
    using bint=BigInteger;
	using Li = List<int>;
	using LLi = List<List<int>>;
	using Ll = List<long>;
	using ti3 = Tuple<int, int, int>;
	using ti2 = Tuple<int, int>;
    using tl3=Tuple<long,long,long>;
	internal class Program {
		private static void Main(string[] args) {
			var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
			SetOut(sw);
			new Calc().Solve();
			Out.Flush();
		}

	    public class Calc
	    {
	        public void Solve() {
	            int N = NextInt(), M = NextInt();
	            var P = NextIntList();

                var uf=new UnionFind(N);
                M.REP(i => { uf.Unite(NextInt()-1, NextInt()-1); });

	            var cnt = 0;
                
                N.REP(i => {
                    if (uf.IsSameGroup(P[i]-1, i)) cnt++;
                });

                cnt.WL();
	        }
	        /// <summary>
	        /// UnionFind
	        /// </summary>
	        public struct UnionFind {
	            private readonly int[] _data;

	            public UnionFind(int size) {
	                _data = new int[size];
	                for (var i = 0; i < size; i++) _data[i] = -1;
	            }

	            public bool Unite(int x, int y) {
	                x = Root(x);
	                y = Root(y);

	                if (x == y) return x != y;
	                if (_data[y] < _data[x]) {
	                    var tmp = y;
	                    y = x;
	                    x = tmp;
	                }
	                _data[x] += _data[y];
	                _data[y] = x;
	                return x != y;
	            }

	            public bool IsSameGroup(int x, int y) {
	                return Root(x) == Root(y);
	            }

	            public int Root(int x) {
	                return _data[x] < 0 ? x : _data[x] = Root(_data[x]);
	            }
	        }

        }
    }
}
namespace Nakov.IO {
	using System;
	using System.Text;
	using System.Globalization;

	public static class Cin {
		public static string NextToken() {
			var tokenChars = new StringBuilder();
			var tokenFinished = false;
			var skipWhiteSpaceMode = true;
			while (!tokenFinished) {
				var nextChar = Read();
				if (nextChar == -1) {
					tokenFinished = true;
				} else {
					var ch = (char)nextChar;
					if (char.IsWhiteSpace(ch)) {
					    if (skipWhiteSpaceMode) continue;
					    tokenFinished = true;
					    if (ch == '\r' && (Environment.NewLine == "\r\n")) {
					        Read();
					    }
					} else {
						skipWhiteSpaceMode = false;
						tokenChars.Append(ch);
					}
				}
			}

			var token = tokenChars.ToString();
			return token;
		}

		public static int NextInt() {
			var token = NextToken();
			return int.Parse(token);
		}
		public static long NextLong() {
			var token = NextToken();
			return long.Parse(token);
		}
		public static double NextDouble(bool acceptAnyDecimalSeparator = true) {
			var token = NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				var result = double.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				var result = double.Parse(token);
				return result;
			}
		}
		public static decimal NextDecimal(bool acceptAnyDecimalSeparator = true) {
			var token = NextToken();
			if (acceptAnyDecimalSeparator) {
				token = token.Replace(',', '.');
				var result = decimal.Parse(token, CultureInfo.InvariantCulture);
				return result;
			} else {
				var result = decimal.Parse(token);
				return result;
			}
		}

	    public static BigInteger NextBigInteger(bool acceptAnyDecimalSeparator = true) {
	        var token = NextToken();
	        if (!acceptAnyDecimalSeparator) return BigInteger.Parse(token);
	        token = token.Replace(',', '.');
	        return BigInteger.Parse(token, CultureInfo.InvariantCulture);
	    }

	}
}

namespace CS_Contest.Loop {
	[DebuggerStepThrough]
	public static class Loop {
		public static void REP(this int n, Action<int> act) {
			for (var i = 0; i < n; i++) {
				act(i);
			}
		}

		public static void ForeachWith<T>(this IEnumerable<T> ie, Action<int, T> act) {
			var i = 0;
			foreach (var item in ie) {
				act(i, item);
				i++;
			}
		}

		public static void Foreach<T>(this IEnumerable<T> ie, Action<T> act) {
			foreach (var item in ie) {
				act(item);
			}
		}

	}

	public class Generate
	{
	    public static IEnumerable<int> Seq(int e) => Seq(0, e, 1);
		public static IEnumerable<int> Seq(int s, int e) => Seq(s, e, 1);
		public static IEnumerable<int> Seq(int s, int e, int a) {
			while (s != e) {
				yield return s;
				s += a;
			}
		}
		public static List<T> Repeat<T>(Func<int, T> result, int range) =>
			Enumerable.Range(0, range).Select(result).ToList();
	}
}

namespace CS_Contest.IO {
	using Li = List<int>;
	using Ll = List<long>;

	public static class IO {
		public static void WL(this object obj) => WriteLine(obj);
		public static void WL(this string obj) => WriteLine(obj);
		public static void WL<T>(this IEnumerable<T> list) => list.ToList().ForEach(x => x.WL());

		public static Li NextIntList() => ReadLine().Split().Select(int.Parse).ToList();
		public static Li NextIntList(int n) => Enumerable.Repeat(0, n).Select(x => ReadLine()).Select(int.Parse).ToList();
		public static Ll NextLongList() => ReadLine().Split().Select(long.Parse).ToList();

		public static T Tee<T>(this T t, Func<T, string> formatter = null) {
			if (formatter == null) formatter = arg => arg.ToString();
			formatter(t).WL();
			return t;
		}
		public static void JoinWL<T>(this IEnumerable<T> @this, string sp = " ") => @this.StringJoin(sp).WL();
		public static void W(this object @this) => Write(@this);

	    public static T[,] GetBox<T>(int h, int w, Func<int, int, T> getFunc) {
	        var rt = new T[h, w];
	        for (var i = 0; i < h; i++) {
	            for (var j = 0; j < w; j++) {
	                rt[i, j] = getFunc(i, j);
	            }
	        }

	        return rt;
	    }

	}


}

namespace CS_Contest.Utils {
	using Li = List<int>;
	using Ll = List<long>;
    using bint = BigInteger;

    [DebuggerStepThrough]
    public static class Utils {
        public static bool AnyOf<T>(this T @this, params T[] these) where T : IComparable {
            return these.Contains(@this);
        }

        public static bool Within(int x, int y, int lx, int ly) => !(x < 0 || x >= lx || y < 0 || y >= ly);

        public static void Add<T1, T2>(this List<Tuple<T1, T2>> list, T1 t1, T2 t2) =>
            list.Add(new Tuple<T1, T2>(t1, t2));

        public static string StringJoin<T>(this IEnumerable<T> l, string separator = "") => string.Join(separator, l);

        public static Queue<T> ToQueue<T>(this IEnumerable<T> iEnumerable) {
            var rt = new Queue<T>();
            foreach (var item in iEnumerable) {
                rt.Enqueue(item);
            }

            return rt;
        }

        public static void Swap<T>(ref T x, ref T y) {
            var tmp = x;
            x = y;
            y = tmp;
        }

        public static List<Tuple<TKey, TValue>> ToTupleList<TKey, TValue>(this Map<TKey, TValue> @this) =>
            @this.Select(x => Tuple.Create(x.Key, x.Value)).ToList();


        public static Map<TKey, int> CountUp<TKey>(this IEnumerable<TKey> l) {
            var dic = new Map<TKey, int>();
            foreach (var item in l) {
                dic[item]++;
            }

            return dic;
        }

        public static int Count<T>(this IEnumerable<T> l, T target) => l.Count(x => x.Equals(target));

        public static IEnumerable<T> SkipAt<T>(this IEnumerable<T> @this, int at) {
            var enumerable = @this as T[] ?? @this.ToArray();
            for (var i = 0; i < enumerable.Count(); i++) {
                if (i == at) continue;
                yield return enumerable.ElementAt(i);
            }
        }

        public static int LowerBound<T>(this List<T> @this, T x) where T : IComparable {
            int lb = -1, ub = @this.Count;
            while (ub - lb > 1) {
                var mid = (ub + lb) >> 1;
                if (@this[mid].CompareTo(x) >= 0) ub = mid;
                else lb = mid;
            }

            return ub;
        }

        public static int UpperBound<T>(this List<T> @this, T x) where T : IComparable {
            int lb = -1, ub = @this.Count;
            while (ub - lb > 1) {
                var mid = (ub + lb) >> 1;
                if (@this[mid].CompareTo(x) > 0) ub = mid;
                else lb = mid;
            }

            return ub;
        }

        public static List<int> Imos(this IEnumerable<int> @this) {
            var rt = @this.ToList();
            for (var i = 0; i < rt.Count-1; i++) rt[i + 1] += rt[i];
            return rt;
        }

        public static bool IsOdd(this long @this) => @this % 2 == 1;
        public static bool IsOdd(this int @this) => @this % 2 == 1;
        public static bool IsOdd(this bint @this) => @this % 2 == 1;

    }



    public class Map<TKey, TValue> : Dictionary<TKey, TValue> {
		public Map() : base() { }
		public Map(int capacity) : base(capacity) { }

		public new TValue this[TKey index] {
			get {
				TValue v;
				return TryGetValue(index, out v) ? v : base[index] = default(TValue);
			}
			set { base[index] = value; }
		}
	}

	public static class MyMath {
		
		public static T EMin<T>(params T[] a) where T : IComparable<T> => a.Min();
		public static T EMax<T>(params T[] a) where T : IComparable<T> => a.Max();

	}


}