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 provides
//
// File:  d.go
// Author: ymiyamoto
//
// Created on Wed Dec 26 21:40:31 2018
//
package main

import (
	"fmt"
	"sort"
)

type node struct {
	index  int
	parent int
}

type unionFind struct {
	nodes []node
	rank  []int
}

func new(n int) unionFind {
	u := unionFind{}
	u.nodes = make([]node, n)
	u.rank = make([]int, n)
	for i := range u.nodes {
		u.nodes[i].index = i
		u.nodes[i].parent = i
	}
	return u
}

func (u unionFind) top(a int) int {
	p := u.nodes[a].parent
	for p != u.nodes[p].parent {
		p = u.nodes[p].parent
	}

	return p
}

func (u unionFind) union(a, b int) {
	ap := u.top(a)
	bp := u.top(b)
	if u.rank[ap] == u.rank[bp] {
		u.nodes[ap].parent = bp
		u.rank[bp]++
	} else if u.rank[ap] < u.rank[bp] {
		u.nodes[ap].parent = bp
	} else {
		u.nodes[bp].parent = ap
	}
}

func (u unionFind) find(a int) int {
	return u.top(a)
}

func (u unionFind) sets() map[int][]int {
	m := map[int][]int{}
	for i := range u.nodes {
		if _, ok := m[u.top(i)]; ok {
			m[u.top(i)] = append(m[u.top(i)], i)
		} else {
			m[u.top(i)] = []int{i}
		}
	}

	return m
}

func main() {
	var N, M int
	fmt.Scan(&N, &M)

	ps := make([]int, N)
	for i := range ps {
		fmt.Scan(&ps[i])
	}

	u := new(N)
	for i := 0; i < M; i++ {
		var x, y int
		fmt.Scan(&x, &y)
		x--
		y--
		u.union(x, y)
	}

	ans := 0
	for _, set := range u.sets() {
		var vals, indexs []int
		for _, i := range set {
			vals = append(vals, ps[i]-1)
			indexs = append(indexs, i)
		}
		sort.Ints(vals)
		sort.Ints(indexs)
		i := 0
		j := 0
		for i < len(vals) && j < len(indexs) {
			if vals[i] == indexs[j] {
				ans++
				i++
				j++
			} else if vals[i] < indexs[j] {
				i++
			} else {
				j++
			}
		}
	}

	fmt.Println(ans)
}