Description

A simple mathematical formula for e is

e=Σ_0<=i<=n1/i!

where n is allowed to go to infinity. This can actually yield very accurate approximations of e using relatively small values of n.

Input

No input

Output

Output the approximations of e generated by the above formula for the values of n from 0 to 9. The beginning of your output should appear similar to that shown below.

no input

n e
- -----------
0 1
1 2
2 2.5
3 2.666666667
4 2.708333333
...

Source

Greater New York 2000