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;
class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner() {
        s = new string[0];
        i = 0;
    }

    public string next() {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int Int() {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0) {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++) {
            Array[i] = Int() + add;
        }
        return Array;
    }

    public long Long() {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0) {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++) {
            Array[i] = Long() + add;
        }
        return Array;
    }
}
public class UnionFind {
    private int[] par, rank; //親、木の深さ

    public UnionFind(int size) { //初期化
        par = new int[size];
        rank = new int[size];
        for (int i = 0; i < size; i++) {
            par[i] = i;
            rank[i] = 0;
        }
    }

    public void Unite(int x, int y) { //xが属しているグループとyが属しているグループを統合する
        //親が同じなら何もしない
        x = Find(x);
        y = Find(y);
        if (x == y) return;

        if (rank[x] < rank[y]) {
            par[x] = y;
        }
        else {
            par[y] = x;
            if (rank[x] == rank[y]) rank[x]++;
        }    
    }

    public bool IsSameGroup(int x, int y) { //xとyが同じグループに属しているかどうか
        return Find(x) == Find(y);
    }

    public int Find(int x) { //ノードxの根を求める
        if(par[x] == x) {
            return x;
        }
        else {
            return par[x] = Find(par[x]);
        }
    }

    public int Size(int x) => -par[Find(x)];
}

class Program {
    static Scanner cin = new Scanner();
    static void Main() {
        int N = cin.Int();
        int M = cin.Int();
        var p = cin.ArrayInt(N);

        var uf = new UnionFind(N);
        for (int i = 0; i < M; i++) {
            int x = cin.Int() - 1;
            int y = cin.Int() - 1;
            if(!uf.IsSameGroup(x, y)) {
                uf.Unite(x, y);
            }
        }

        int ans = 0;
        for (int i = 0; i < N; i++) {
            if(uf.IsSameGroup(p[i] - 1, i)) {
                ans++;
            }
        }

        Console.WriteLine(ans);
        Console.ReadLine();
    }
}