Approximating the Constant e

Problem Description

The natural constant $\,e=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}\cdots+\frac{1}{n!}\,(0\le n \le 50, where 0!=1 by convention)$. Given a positive integer $\,n\,$, compute the corresponding value of $\,e\,$, rounded to $\,8\,$ decimal places.

Input Format

Input a positive integer $\,n$.

Output Format

Output the approximate value of $\,e\,$.

Sample Input

13

Sample Output

2.71828183

Hint

1. The concept of factorial

$4!=4\times 3\times 2\times 1=24$

$5!=5\times (4\times 3\times 2\times 1)=5\times 4!=5\times 24=120$

$n!$ is called the factorial of $n$.

$n!=n\times(n-1)\times(n-2)\times\cdots\times 3\times 2\times 1=n\times(n-1)!$

In particular, we define $0!=1$.

2. About the value ranges

• $int$: $-2\times 10^9\sim 2\times 10^9$

• $long\ long$: $-2\times 10^{18}\sim 2\times 10^{18}$

• $double$: $-2\times 10^{308}\sim 2\times 10^{308}$; however, many numbers in this range cannot be represented exactly, and a number that cannot be represented is replaced by the representable number closest to it.

• $50!=3.0414093201713378043612608166065\times 10^{64}$