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 (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	N, M := ReadInt(), ReadInt()
	Ps := ReadInts(N)
	uf := InitUnionFind(N)
	for m := 0; m < M; m++ {
		x, y := ReadInt(), ReadInt()
		uf.Unite(x-1, y-1)
	}
	ans := 0
	for i := 0; i < N; i++ {
		if uf.Connected(Ps[i]-1, i) {
			ans++
		}
	}
	fmt.Println(ans)
}

func InitUnionFind(size int) UnionFind {
	parent := make([]int, size)
	for i := 0; i < size; i++ {
		parent[i] = i
	}
	return parent
}

type UnionFind []int

func (uf UnionFind) Unite(x, y int) {
	x = uf.Root(x)
	y = uf.Root(y)
	if x != y {
		uf[x] = y
	}
}

func (uf UnionFind) Connected(x, y int) bool {
	return uf.Root(x) == uf.Root(y)
}

func (uf UnionFind) Root(x int) int {
	if uf[x] == x {
		return x
	}
	uf[x] = uf.Root(uf[x])
	return uf[x]
}

func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int) { Scan(&i); return }