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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        final int N = sc.nextInt();
        int M = sc.nextInt();
        int[] P = new int[N+1];
        for(int i = 1;i <= N;i++){
            int pi = sc.nextInt();
            P[pi] = i;
        }
        int[] par = new int[N+1];
        int[] rank = new int[N+1];
        init(N, par, rank);
        for(int i = 0;i < M;i++){
            int xi = sc.nextInt();
            int yi = sc.nextInt();
            unite(xi, yi, par, rank);
        }
        int ans = 0;
        for(int i = 1;i <= N;i++){
            if(same(i, P[i], par, rank))    ans++;
        }
        System.out.println(ans);
    }
    /**
     *  initialization
     */
    public static void init(int n, int[] par, int[] rank){
        for(int i = 1;i <= n;i++){
            par[i] = i;
            rank[i] = 0;
        }
    }
    /**
     *  find the root
     */
    public static int find(int x, int[] par, int[] rank){
        if(par[x] == x) return x;
        else    return par[x] = find(par[x], par, rank);
    }
    /**
     *  unite x and y
     */
    public static void unite(int x, int y, int[] par, int[] rank){
        x = find(x, par, rank);
        y = find(y, par, rank);
        if(x == y)  return;
        if(rank[x] < rank[y]){
            par[x] = y;
        }else{
            par[y] = x;
            if(rank[x] == rank[y])  rank[x]++;
        }
    }
    public static boolean same(int x, int y, int[] par, int[] rank){
        return find(x, par, rank) == find(y, par, rank);
    }
}