Short complete diagnostic tests for circuits with one additional input in the standard basis

We prove that each monotone (antimonotone) Boolean function in $n$ variables can be modeled by a logic circuit with one additional input in the basis “conjunction, disjunction, negation” allowing a complete diagnostic test with length no more than $n+2$ (no more than $n+1$, respectively) relative to constant faults of type $1$ at outputs of logic gates.