Given a language 𝐿, define 𝐿𝑖 as follows: 𝐿0 = {𝜀} 𝐿𝑖 = 𝐿𝑖−1 ⋅ 𝐿…

Given a language 𝐿, define 𝐿𝑖 as follows:

𝐿0 = {𝜀}

𝐿𝑖 = 𝐿𝑖−1 ⋅ 𝐿 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑖 > 0

The order of a language 𝐿 is defined as the smallest $k$ such that 𝐿𝑘 = 𝐿𝑘+1 .

Consider the language 𝐿1 (over alphabet 0) accepted by the following automaton.

The order of 𝐿1 is _____.