Given a language $$𝐿,$$ define $${L^i}$$ as follows: $${L^0} = \left\{ \varepsilon \right\}$$
$${L^i} = {L^{i - 1}}.\,\,L$$ for all $$i > 0$$

The order of a language $$L$$ is defined as the smallest k such that $${L^k} = {L^{k + 1}}.$$ Consider the language $${L_1}$$ (over alphabet $$0$$) accepted by the following automaton.

The order of $${L_1}$$ is _____.

“From where are they bringing their books? ________ bringing _______ books from _____.”

The words that best fill the blanks in the above sentence are

The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?

“A _________ investigation can sometimes yield new facts, but typically organized ones are more successful.”

The word that best fills the blank in the above sentence is