Euler's number Euler $$e$$ — the base of the natural logarithm — can be calculated as the sum of the following sequence: \[ e = \sum_{i=0}^\infty \frac{1}{i!} = 1 + 1 + \frac12 + \frac16 + \dots \]

Input

No input.

Output

Write the first $$n$$ partial sums from the sequence that delivers the Euler's number, each on a separate line. These are the sums $$1$$, $$1+1$$, $$1+1+\frac12$$, …. Round off all results to 7 digits after the comma and choose $$n$$ so the last line that is written describes the exact value of e ($$e\cong 2{,}7182818$$), equal to the precision of the description.

Example

Output:

1.0
2.0
2.5
...
2.7182818