Suppose we use a heuristic f$($state$)=$ depth$($state$)+$ h$($state$)$ for guiding the search algorithm, where h$($n$)$ counts the number of letter positions in state that do not have the desired value. $$

For instance, h$("$BATCH$")=2$: since positions $0,1,$ and $4$ contain the desired letters in their proper positions $($B$,$ C$,$ H$),$ and positions $2$ and $3$ do not contain the desired letters in their proper positions $($E$,$ A$).$

Is this an admissible heuristic? $$Explain why or why not.$$