Chef and Dynamo

"The secret impresses no one, the trick you use it for is everything." - The Prestige **This is an interactive problem.** An $N$-perfect number is defined as a positive integer with at most $N$ digits (in decimal representation without leading zeros) ― that is, $X$ is an $N$-perfect number if $0 \lt X \lt 10^N$. Chef has a friend named Dynamo, who is a legendary magician. Chef learned a n