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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoder
{
	public class ABC
	{
		static public void Main(string[] args)
		{
			Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
			Solve();
			Console.Out.Flush();
		}

		const int mod = 1000000007;  // 10^9+7
		static int Mod(long x, int m) { return (int)((x % m + m) % m); }
		static long Mod(long x, long m) { return (x % m + m) % m; }

		static public void Solve()
		{
			//string s = Console.ReadLine();
			//int n = int.Parse(Console.ReadLine());
			//long x = long.Parse(Console.ReadLine());
			//int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			//long[] vs = Console.ReadLine().Split().Select(long.Parse).ToArray();

			int[] vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int n = vs[0];
			int m = vs[1];
			int[] p = Console.ReadLine().Split().Select(int.Parse).ToArray();
			int[] q = new int[n];
			for (int i = 0; i < n; i++) {
				int x = p[i] - 1;
				q[x] = i;
			}

			UnionFind union = new UnionFind(n);
			for (int i = 0; i < m; i++) {
				vs = Console.ReadLine().Split().Select(int.Parse).ToArray();
				int x = vs[0] - 1;
				int y = vs[1] - 1;
				union.Unite(x, y);
			}

			int ans = 0;
			for (int x = 0; x < n; x++) {
				int i = q[x];
				if (union.Same(i, x)) {
					ans++;
				}
			}
			Console.WriteLine(ans);

		}
	}

	#region Union-Find木 UnionFind
	public class UnionFind
	{
		private readonly UnionFindNode[] _Parent;

		/// <summary>
		/// Union-Find木
		/// </summary>
		/// <param name="n">サイズ</param>
		public UnionFind(int n)
		{
			_Parent = new UnionFindNode[n];
			for (int i = 0; i < n; i++) {
				_Parent[i] = new UnionFindNode(i, 1);
			}
		}

		public int Find(int x)
		{
			if (_Parent[x].Parent == x) {
				return _Parent[x].Parent;
			}
			return _Parent[x].Parent = Find(_Parent[x].Parent);
		}

		public int Size(int x)
		{
			return _Parent[Find(x)].Size;
		}

		/// <summary>
		/// xとyの木を併合
		/// </summary>
		/// <param name="x"></param>
		/// <param name="y"></param>
		public void Unite(int x, int y)
		{
			int rx = Find(x);
			int ry = Find(y);
			if (rx != ry) {
				_Parent[ry].Parent = rx;
				_Parent[rx].Size += _Parent[ry].Size;
			}
		}

		/// <summary>
		/// x, yが同じ木に属している
		/// </summary>
		/// <param name="x"></param>
		/// <param name="y"></param>
		/// <returns></returns>
		public bool Same(int x, int y)
		{
			int rx = Find(x);
			int ry = Find(y);
			return rx == ry;
		}

		public override string ToString()
		{
			return string.Join(" ", _Parent.Select(p => $"({p.Parent},{p.Size})"));
		}
	}
	public class UnionFindNode
	{
		public int Parent;
		public int Size;
		public UnionFindNode(int parent, int size)
		{
			Parent = parent;
			Size = size;
		}
	}
	#endregion

}