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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	//	"strings"
)

type UnionFind struct {
	p []int
}

func (u *UnionFind) init(size int) {
	u.p = make([]int, size)
	for i := 0; i < size; i++ {
		u.p[i] = i
	}
}

func (u *UnionFind) root(x int) int {
	if u.p[x] == x {
		return x
	}
	u.p[x] = u.root(u.p[x])
	return u.p[x]
}

func (u *UnionFind) unite(x, y int) {
	rx := u.root(x)
	ry := u.root(y)
	if rx != ry {
		u.p[rx] = ry
	}
}

func (u *UnionFind) same(x, y int) bool {
	rx := u.root(x)
	ry := u.root(y)
	return rx == ry
}

func solve(n, q int, data [][]int) []int {
	ans := []int{}
	return ans
}

func main() {
	sc := NewScanner()

	n := sc.NextInt()
	m := sc.NextInt()

	p := make([]int, n)
	for i := 0; i < n; i++ {
		p[i] = sc.NextInt()
		p[i]--
	}
	u := UnionFind{}
	u.init(n)

	for i := 0; i < m; i++ {
		x := sc.NextInt()
		y := sc.NextInt()
		u.unite(x-1, y-1)
	}

	ans := 0
	for i := 0; i < n; i++ {
		if p[i] == i {
			ans++
			continue
		}
		b := u.same(p[i], i)
		if b {
			ans++
		}
	}
	fmt.Printf("%v\n", ans)
}

/*
func main() {

	n := 5
	q := 12
	// command, x, y
	// command ... 0 = unite (merge)
	// command ... 1 = find (if same or not)
	data := [][]int{
		{0, 1, 4},
		{0, 2, 3},
		{1, 1, 2},
		{1, 3, 4},
		{1, 1, 4},
		{1, 3, 2},
		{0, 1, 3},
		{1, 2, 4},
		{1, 3, 0},
		{0, 0, 4},
		{1, 0, 2},
		{1, 3, 0},
	}
	ans := solve(n, q, data)
	fmt.Printf("%+v\n", ans) // output for debug

}
*/

type Scanner struct {
	r   *bufio.Reader
	buf []byte
	p   int
}

func NewScanner() *Scanner {
	rdr := bufio.NewReaderSize(os.Stdin, 1000)
	return &Scanner{r: rdr}
}
func (s *Scanner) Next() string {
	s.pre()
	start := s.p
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}
	result := string(s.buf[start:s.p])
	s.p++
	return result
}
func (s *Scanner) NextLine() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)
	return string(s.buf[start:])
}
func (s *Scanner) NextInt() int {
	v, _ := strconv.Atoi(s.Next())
	return v
}

func (s *Scanner) NextIntArray() []int {
	s.pre()
	start := s.p
	result := []int{}
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			v, _ := strconv.Atoi(string(s.buf[start:s.p]))
			result = append(result, v)
			start = s.p + 1
		}
	}
	v, _ := strconv.Atoi(string(s.buf[start:s.p]))
	result = append(result, v)

	return result
}

func (s *Scanner) NextMap() map[int]bool {
	s.pre()
	start := s.p
	mp := map[int]bool{}
	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			v, _ := strconv.Atoi(string(s.buf[start:s.p]))
			mp[v] = true
			start = s.p + 1
		}
	}
	v, _ := strconv.Atoi(string(s.buf[start:s.p]))
	mp[v] = true

	return mp
}

func (s *Scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}
func (s *Scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}