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"
	"io"
	"os"
	"strconv"
)

type UnionFindTree struct {
	parent []int
	rank   []int
}

func NewUnionFindTree(n int) *UnionFindTree {
	u := &UnionFindTree{}
	u.parent = make([]int, n)
	u.rank = make([]int, n)
	for i := 0; i < n; i++ {
		u.parent[i] = i
	}
	return u
}

func (u *UnionFindTree) Find(x int) int {
	p := u.parent[x]
	if p == x {
		return p
	} else {
		u.parent[x] = u.Find(p)
		return u.parent[x]
	}
}

func (u *UnionFindTree) Union(x, y int) {
	p := u.Find(x)
	q := u.Find(y)
	if u.rank[p] > u.rank[q] {
		u.parent[q] = p
	} else {
		u.parent[p] = q
		if u.rank[p] == u.rank[q] {
			u.rank[q]++
		}
	}
}

func (u *UnionFindTree) IsSameSet(x, y int) bool {
	return u.Find(x) == u.Find(y)
}

func main() {
	defer stdout.Flush()
	N := readInt()
	M := readInt()
	p := make([]int, N+1)
	uf := NewUnionFindTree(N + 1)
	for i := 1; i < N+1; i++ {
		p[i] = readInt()
	}
	for i := 0; i < M; i++ {
		x := readInt()
		y := readInt()
		uf.Union(p[x], p[y])
	}
	count := 0
	for i := N; i > 0; i-- {
		if uf.IsSameSet(p[i], i) {
			count++
		}
	}
	println(count)
}

var (
	readString func() string
	stdout     *bufio.Writer
)

func init() {
	readString = newReadString(os.Stdin)
	stdout = bufio.NewWriter(os.Stdout)
}

func newReadString(ior io.Reader) func() string {
	r := bufio.NewScanner(ior)
	r.Split(bufio.ScanWords)

	return func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
}

func readInt() int {
	i, err := strconv.Atoi(readString())
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readIntSlice(n int) []int {
	b := make([]int, n)
	for i := 0; i < n; i++ {
		b[i] = readInt()
	}
	return b
}

func readLengthAndSlice() []int {
	n := readInt()
	return readIntSlice(n)
}

func printf(f string, args ...interface{}) (int, error) {
	return fmt.Fprintf(stdout, f, args...)
}

func println(args ...interface{}) (int, error) {
	return fmt.Fprintln(stdout, args...)
}