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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.io.PrintWriter

fun main(args: Array<String>) {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}


fun solve(out: PrintWriter) {
    val (n, m) = readIntegerList()
    val pList = readIntegerList()

    val unionFind = UnionFind(n)
    repeat(m) {
        val (x, y) = readIntegerList()
        unionFind.unite(x - 1, y - 1)
    }

//    var ans = 0
//    for (i in pList.indices) {
//        if (unionFind.sameRoot(i, pList[i] - 1)) {
//            ans++
//        }
//    }
//    println(ans)
    
    pList.withIndex()
        .count { unionFind.sameRoot(it.index, it.value - 1) }
        .let(::println)
}

/**　Union find 0 ~ (n - 1)　*/
class UnionFind(n: Int) {
    val parent = IntArray(n) { it }
    val rank = IntArray(n)
    val size = IntArray(n) { 1 }

    /** O(α(n)) */
    fun findRoot(x: Int): Int {
        if (parent[x] == x) return x

        parent[x] = findRoot(parent[x])
        return parent[x]
    }

    /** O(α(n)) */
    fun sameRoot(x: Int, y: Int) = findRoot(x) == findRoot(y)

    /** O(α(n)) */
    fun unite(x: Int, y: Int) {
        val x = findRoot(x)
        val y = findRoot(y)
        if (x == y) return

        if (rank[x] < rank[y]) {
            parent[x] = y
            size[y] += size[x]
        } else {
            parent[y] = x
            if (rank[x] == rank[y]) rank[x]++

            size[x] += size[y]
        }
    }

    /** O(α(n)) */
    fun getSize(x: Int) = size[findRoot(x)]
}


fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)