First n strange numbers X76141

A positive number $n > 0$ is “strange” if when adding each of its digits raised to the number of digits that make it up, we obtain the number itself.

For example, 153 (which has three digits) is “strange”, $153 = 1^{3} + 5^{3} + 3^{3}$.

Make a program that returns the first $n$ “strange” numbers.

Input

A positive integer, $n > 0$, asking for the first $n$ “strange” numbers.

Output

Prints the list with the first $n$ “strange” numbers.

Observation

It is forbidden to use any external function except cin and cout, and also the program must be well documented if not it will be invalidated.