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 {
    static int n, m;
    static int[] p;
    static int modP = 1000000007;
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        m = in.nextInt();
        p = new int[n];

        UF uf = new UF(n);
        for(int i = 0; i < n; i++) p[i] = in.nextInt();
        for(int i = 0; i < m; i++) {
            int x = in.nextInt()-1;
            int y = in.nextInt()-1;
            uf.union(x, y);
        }

        int cnt = 0;
        for(int i = 0; i < n; i++) {
            if(uf.same(i, p[i]-1)) cnt++;
        }
        print(cnt);
    }

    static void print(String s) {
        System.out.println(s);
    }

    static void print(int i) {
        System.out.println(i);
    }
}

class UF {
    int[] table, ranks;

    UF(int s) {
        table = new int[s];
        ranks = new int[s];
        for(int i = 0; i < s; i++) {
            table[i] = i;
        }
    }

    public int find(int x) {
        if(table[x] != x) table[x] = find(table[x]);

        return table[x];
    }

    public void union(int x , int y) {
        int xR = find(x);
        int yR = find(y);
        if(xR == yR) return;

        if(ranks[xR] < ranks[yR]) {
            table[xR] = yR;
        }else{
            table[yR] = xR;
            if(ranks[xR] == ranks[yR]) ranks[xR]++;
        }
    }

    public boolean same(int x, int y) {
        return find(x) == find(y);
    }
}