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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function bai(x,y) {
	var x1 = x, y1 = y;
	var temp;
	while (y1 != 0) {
		temp = y1;
		y1 = x1 % y1;
		x1 = temp;
	}
	return x*y/x1;
}

// inputに入力データ全体が入る
function Main(input) {
	console.log("main");
	// 1行目がinput[0], 2行目がinput[1], …に入る
	input = input.split("\n");
	var count = input[0]-0;
	var values = input[1].split(" ");
	var numerator = 1;
	var denominator = values[0]-0;
	console.log("for");
	for(var i = 1; i < count; i++) {
		console.log(i);
		var newDenominator = bai(denominator, values[i]-0);
		numerator *= newDenominator/denominator;
		numerator += newDenominator/values[i]-0;
	}
	
	console.log(newDenominator/numerator);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));