Construct a search graph with no more than $10$ nodes for which all of

the following are true:

i$.$ Least$-$cost search returns an optimal solution.

ii$.$ Depth$-$first search returns the highest$-$cost solution.

iii. Breadth$-$first search returns a solution whose cost is strictly less than the highest$-$cost

solution and strictly more than the least$-$cost solution.