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: Time Limit Exceeded)

// Package main provides
//
// File:  main.go
// Author: ymiyamoto
//
// Created on Sun Jan 27 15:07:05 2019
//
package main

import (
	"fmt"
	"sort"
)

type unionFind struct {
	roots  []int
	depths []int
}

func new(n int) unionFind {
	uf := unionFind{}
	uf.roots = make([]int, n+1)
	uf.depths = make([]int, n+1)

	for i := range uf.roots {
		uf.roots[i] = i
		uf.depths[i] = 0
	}

	return uf
}

func (uf unionFind) root(n int) int {
	root := n
	for uf.roots[root] != root {
		root = uf.roots[root]
	}
	return root
}

func (uf unionFind) union(n, m int) {
	if uf.depths[n] == uf.depths[m] {
		uf.roots[uf.root(m)] = uf.root(n)
		uf.depths[m]++
	} else if uf.depths[n] < uf.depths[m] {
		uf.roots[uf.root(m)] = uf.root(n)
	} else {
		uf.roots[uf.root(n)] = uf.root(m)
	}
}

func scanSlice(slice []int) {
	for i := range slice {
		fmt.Scan(&slice[i])
	}
}

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

	arr := make([]int, N)
	scanSlice(arr)

	uf := new(N)
	for i := 0; i < M; i++ {
		var n, m int
		fmt.Scan(&n, &m)
		uf.union(n, m)
	}

	m1 := map[int][]int{}
	m2 := map[int][]int{}
	for i := range arr {
		m1[uf.root(arr[i])] = append(m1[uf.root(arr[i])], i+1)
		m2[uf.root(arr[i])] = append(m2[uf.root(arr[i])], arr[i])
	}

	ans := 0
	for k, v := range m1 {
		sort.Ints(v)
		sort.Ints(m2[k])

		index := 0
		for i := range v {
			for v[i] > m2[k][index] {
				if index < len(m2[k])-1 {
					index++
				} else {
					break
				}
			}

			if v[i] == m2[k][index] {
				ans++
			}
		}
	}
	fmt.Println(ans)
}