Problem:
Score : 200 points

Problem Statement

Given is a sequence of N integers A_1, \ldots, A_N.

Find the (multiplicative) inverse of the sum of the inverses of these numbers, \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Constraints

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print a decimal number (or an integer) representing the value of \frac{1}{\frac{1}{A_1} + \ldots + \frac{1}{A_N}}.

Your output will be judged correct when its absolute or relative error from the judge's output is at most 10^{-5}.

Sample Input 1

2
10 30

Sample Output 1

7.5

\frac{1}{\frac{1}{10} + \frac{1}{30}} = \frac{1}{\frac{4}{30}} = \frac{30}{4} = 7.5.

Printing 7.50001, 7.49999, and so on will also be accepted.

Sample Input 2

3
200 200 200

Sample Output 2

66.66666666666667

\frac{1}{\frac{1}{200} + \frac{1}{200} + \frac{1}{200}} = \frac{1}{\frac{3}{200}} = \frac{200}{3} = 66.6666....

Printing 6.66666e+1 and so on will also be accepted.

Sample Input 3

1
1000

Sample Output 3

1000

\frac{1}{\frac{1}{1000}} = 1000.

Printing +1000.0 and so on will also be accepted.

Solution in Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.io.PrintWriter
import java.lang.Math.sqrt
import java.util.*

const val MOD = 1000000007L
const val INF = Long.MAX_VALUE - 1

fun main(args: Array<String>) {
    val reader = System.`in`.bufferedReader()

    val n = readInt()
    val a = readIntList()

    var total = 1L
    a.forEach {
        total *= it
    }

    val mother = a.map {
        total / it
    }.sum()

    val child = total

    val pw = PrintWriter(System.out)

    pw.println(child.toDouble() / mother.toDouble())

    pw.flush()
}

data class Edge(var num: Int, var parent: Int, var count: Int = 0)


fun readList() = readLine()!!.split(' ')
fun readInt() = readIntList().first()
fun readIntList() = readList().map(String::toInt)
fun readLong() = readLongList().first()
fun readLongList() = readList().map(String::toLong)
fun readDoubleList() = readList().map(String::toDouble)

fun <T> readClass(n: Int, body: (List<String>) -> T): List<T> {
    val ret = mutableListOf<T>()
    for (i in 0 until n) {
        ret.add(body(readList()))
    }
    return ret
}

fun readPair(): Pair<String, String> {
    val splite = readLine()!!.split(' ')
    return Pair(splite[0], splite[1])
}

fun <T> List<T>.copy() = this.map { it }

fun Long.toBinaryString(): String {
    var t = this
    var res = ""
    while (t > 0) {
        res += (t % 2).toString()
        t /= 2
    }
    return res
}

inline fun <reified T> dualArray(h: Int, w: Int, init: (Int, Int) -> T) {
    Array(h) { i ->
        return@Array Array(w) { j ->
            return@Array init(i, j)
        }
    }
}

// 速度のためforEachは避ける
inline fun Int.rep(start: Int = 0, shiftLast: Boolean = false, body: (Int) -> Unit) {
    for (i in start until if (shiftLast) this + start else this) {
        body(i)
    }
}

inline fun Long.rep(start: Long = 0, shiftLast: Boolean = false, body: (Long) -> Unit) {
    for (i in start until if (shiftLast) this + start else this) {
        body(i)
    }
}

// 約数のList
fun divisor(value: Long): List<Long> {
    val max = sqrt(value.toDouble()).toLong()
    val former = mutableListOf<Long>()
    val latter = mutableListOf<Long>()
    (1..max).filter { value % it == 0L }
        .forEach {
            former.add(it)
            latter.add(value / it)
        }
    former.addAll(latter.reversed())
    return former
}

// 範囲内の素数を取得
// fromだけ指定すると戻り値の個数で素数判定ができる
fun prime(from: Long, to: Long = from): List<Long> {
    return (from..to).filter { i ->
        val max = Math.sqrt(i.toDouble()).toLong()
        (2..max).all { j -> i % j != 0L }
    }
}

// 素因数分解
fun decom(value: Long): List<Long> {
    if (value == 1L) return listOf(1)
    val max = Math.sqrt(value.toDouble()).toLong()
    return prime(2, max).filter { value % it == 0L }
}

// 最大公約数
fun gcd(a: Long, b: Long): Long {
    return if (a % b == 0L) b else gcd(b, a % b)
}

// 文字列を入れ替え
fun swap(base: String, a: String, b: String): String {
    return base.map {
        when (it) {
            a.toCharArray()[0] -> b
            b.toCharArray()[0] -> a
            else -> it.toString()
        }
    }.joinToString()
}

// bit全探索
fun bitAllSearch(n: Int, body: (Array<Boolean>) -> Unit) {
    for (bit in 0 until (1 shl n)) {
        val s = Array(n) {
            return@Array false
        }
        for (i in 0 until n) {
            if ((bit and (1 shl i)) shr i == 1) { // i が bit に入るかどうか
                s[i] = true
            }
        }
        body(s)
    }
}

internal class UnionFindTree(size: Int) {

    private val parent = Array(size) {
        return@Array it
    }
    private val rank = Array(size) {
        return@Array 0
    }

    fun union(x: Int, y: Int): Int {
        val xRoot = find(x)
        val yRoot = find(y)

        if (xRoot == yRoot) return xRoot

        when {
            rank[xRoot] > rank[yRoot] -> parent[yRoot] = xRoot
            rank[xRoot] < rank[yRoot] -> parent[xRoot] = yRoot
            xRoot != yRoot -> {
                parent[yRoot] = xRoot
                rank[xRoot]++
            }
        }
        return parent[xRoot]
    }

    fun find(i: Int): Int {
        if (i != parent[i]) {
            parent[i] = find(parent[i])
        }
        return parent[i]
    }

    fun same(x: Int, y: Int): Boolean {
        return find(x) == find(y)
    }
}

fun <K, V> Map<K, V>.toMutableMap(): MutableMap<K, V> {
    return HashMap(this)
}