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: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        List<Set<Integer>> nums = new ArrayList<>();
        int n = sc.nextInt(), m = sc.nextInt();
        int[] p = new int[n];
        for (int i = 0; i < n; i++) {
            p[i] = sc.nextInt();
        }
        outer: for (int i = 0; i < m; i++) {
            int x = sc.nextInt(), y = sc.nextInt();
            for (int a = 0; a < nums.size(); a++) {
                Set<Integer> as = nums.get(a);
                if (as.contains(x)) {
                    for (int b = 0; b < nums.size(); b++) {
                        Set<Integer> bs = nums.get(b);
                        if (bs.contains(y)) {
                            as.addAll(bs);
                            nums.set(b, as);
                            continue outer;
                        }
                    }
                    as.add(y);
                    continue outer;
                } else if (as.contains(y)) {
                    for (int b = 0; b < nums.size(); b++) {
                        Set<Integer> bs = nums.get(b);
                        if (bs.contains(x)) {
                            as.addAll(bs);
                            nums.set(b, as);
                            continue outer;
                        }
                    }
                    as.add(x);
                    continue outer;
                }
            }
            HashSet<Integer> hs = new HashSet<>();
            hs.add(x);
            hs.add(y);
            nums.add(hs);
        }
        int counter = 0;
        System.out.println(nums);
        outer: for (int i = n; i >= 1; i--) {
            if (p[i - 1] == i) {
                counter++;
                continue;
            }
            for (Set<Integer> s : nums) {
                for (int num : s) {
                    if (p[num - 1] == i && s.contains(i)) {
                        counter++;
                        continue outer;
                    }
                }
            }
        }
        System.out.println(counter);
    }



    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }

}