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Approximation of e P11916

Statement

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The Taylor series of the function e^x is

e^x =

∑

i ≥ 0

xⁱ

⁠ ⁠ .

Note that this series has an infinite number of terms. However, for any x we can get an approximation of e^x by adding some of the first terms of the series (of course, the more terms, the better the result). In particular, chosing x = 1 gives us a method to compute e ≃ 2′71828182845904523536:

e =

∑

i ≥ 0

⁠ ⁠ .

Write a program that, for every given natural number n, prints the approximation of e that we get by adding the n first terms of the series above.

Input

Input consists of several natural numbers n between 0 and 20.

Output

For every given n, print with 10 digits after the decimal point the approximation of e that we get by adding the n first terms of the series above.

Observation

Because of overflow reasons, do all the computations for this exercise using real numbers.

Public test cases

Input

Output

With 0 term(s) we get 0.0000000000.
With 1 term(s) we get 1.0000000000.
With 3 term(s) we get 2.5000000000.
With 20 term(s) we get 2.7182818285.

Information

Author: Salvador Roura
Language: English
Translator: Carlos Molina
Original language: Catalan
Other languages: Catalan
Official solutions: C++ Java Python
User solutions: C C++ Java Python