Tessellate S.T.E.M.S. (2019) - Computer Science - College - Set 2 - Objective Problem 3

Given a language $L$ , define $L^i$ as follows:

$L^0 = \{ \epsilon \} \\ L^i = L^{i-1} \cdot i \text { for all } i > 0$

The order of the language is the smallest $k$ such that $L^k = L^{k+1}$ . Consider the language $L$ , accepted by the following automaton.

What is it's order?

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This problem is a part of Tessellate S.T.E.M.S (2019)