NFA 0’s near end or 1 at end: Write a nondeterministic finite automaton with at most 10 states that decides whether its input is contained in the following set: {x ∈ {0, 1}∗ | x[|x| − 5] = x[|x| − 2] = 0 or x[|x|] = 1}. We index strings starting at 1, so x[1] is the first symbol, and x[|x|] is the last symbol.

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