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Problem C
Euler's Number

Euler’s number (you may know it better as just $e$ ) has a special place in mathematics. You may have encountered $e$ in calculus or economics (for computing compound interest), or perhaps as the base of the natural logarithm, $\ln x$ , on your calculator.

While $e$ can be calculated as a limit, there is a good approximation that can be made using discrete mathematics. The formula for $e$ is:

\begin{aligned} e & = \sum_{i = 0}^{n} \frac{1}{i!} \\ = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \dots \end{aligned}

Note that $0! = 1$ . Now as $n$ approaches $\infty$ , the series converges to $e$ . When $n$ is any positive constant, the formula serves as an approximation of the actual value of $e$ . (For example, at $n = 10$ the approximation is already accurate to $7$ decimals.)

You will be given a single input, a value of $n$ , and your job is to compute the approximation of $e$ for that value of $n$ .

Input

A single integer $n$ , ranging from $0$ to $10 000$ .

Output

A single real number – the approximation of $e$ computed by the formula with the given $n$ . All output must be accurate to an absolute or relative error of at most $10^{- 12}$ .

Sample Input 1	Sample Output 1
3	2.6666666666666665

Sample Input 2	Sample Output 2
15	2.718281828458995

Problem CEuler's Number

Input

Output

Problem C
Euler's Number