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: Wrong Answer)


import java.util.NoSuchElementException
import java.io.IOException


fun main(args : Array<String>) {
    val fs = FastScanner()
    val n = fs.nextInt()
    val m = fs.nextInt()
    val p = (1..n).map { fs.nextInt() }
    val cg = mutableListOf<MutableSet<Int>>()
    for (i in 0 until m) {
        val e0 = fs.nextInt()
        val e1 = fs.nextInt()
        var doo = -1
        for (c in cg) {
            if (e0 in c || e1 in c) {
                if (doo != -1) {
                    c.addAll(cg[doo])
                    cg.removeAt(doo)
                    break
                } else {
                    doo = cg.indexOf(c)
                }
                if (e0 in c) {
                    c.add(e1)
                } else if (e1 in c) {
                    c.add(e0)
                }
            }
        }
        if (doo < 0) {
            cg.add(mutableSetOf(e0, e1))
        }
    }
    val cgt = mutableSetOf<Int>()
    for (c in cg) {
        cgt += c
    }

    var res = 0
    val bebe = Array<Int>(n, {-1})

    for (i in 0 until cg.size) {
        cg[i].forEach { bebe[it - 1] = i }
    }
    for (i in 0 until n) {
        if (bebe[i] == bebe[p[i] - 1]) {
            res++
        }
    }

    print(res)
}


class FastScanner() {
    private val `in` = System.`in`
    private val buffer = ByteArray(1024)
    private var ptr = 0
    private var buflen = 0
    private fun hasNextByte(): Boolean {
        if (ptr < buflen) {
            return true
        } else {
            ptr = 0
            try {
                buflen = `in`.read(buffer)
            } catch (e: IOException) {
                e.printStackTrace()
            }

            if (buflen <= 0) {
                return false
            }
        }
        return true
    }

    private fun readByte(): Int {
        return if (hasNextByte()) buffer[ptr++].toInt() else -1
    }

    private fun isPrintableChar(c: Int): Boolean {
        return c in 33..126
    }

    operator fun hasNext(): Boolean {
        while (hasNextByte() && !isPrintableChar(buffer[ptr].toInt())) ptr++
        return hasNextByte()
    }

    operator fun next(): String {
        if (!hasNext()) throw NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b)
            b = readByte()
        }
        return sb.toString()
    }

    fun nextLong(): Long {
        if (!hasNext()) throw NoSuchElementException()
        var n: Long = 0
        var minus = false
        var b = readByte()
        if (b == '-'.toInt()) {
            minus = true
            b = readByte()
        }
        if (b < '0'.toInt() || '9'.toInt() < b) {
            throw NumberFormatException()
        }
        while (true) {
            if ('0'.toInt() <= b && b <= '9'.toInt()) {
                n *= 10
                n += (b - '0'.toInt()).toLong()
            } else return if (b == -1 || !isPrintableChar(b)) {
                if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun nextInt(): Int {
        val nl = nextLong()
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun nextDouble(): Double {
        return java.lang.Double.parseDouble(next())
    }
}