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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

func lcm(a, b int) int {
	return (a*b)/gcd(a,b)
}
func calc(arr []string, times int) {
	tmpLcm, _ := strconv.Atoi(arr[0])
	for i := 1; i < len(arr); i++ {
		b, _ := strconv.Atoi(arr[i])
		tmpLcm = lcm(tmpLcm, b)
	}
	count := 0
	for i := 0; i < len(arr); i++ {
		tmp, _ := strconv.Atoi(arr[i])
		count += tmpLcm/tmp
	}
	fmt.Println(float64(tmpLcm)/float64(count))
}

func main() {

	reader := bufio.NewReaderSize(os.Stdin, 1024*1024)
	times, _:= strconv.Atoi(readLine(reader))
	arr := strings.Split(readLine(reader), " ")
	calc(arr, times)
}

func readLine(reader *bufio.Reader) string {
	str, _, err := reader.ReadLine()
	if err == io.EOF {
		return ""
	}
	return strings.TrimRight(string(str), "\r\n")
}