Formulate the following as a search problem: You have three jugs that can contain 3, 8 and 12 gallons of water respectively. Yo u also have a water faucet. You can fill the jugs completely, empty them completely or transfer water from one jug to another (always up to the amount that the receiving jug holds). You need a jug to contain exactly one gallon of water. The cost of an action is the amount of water being moved.

Design a good heuristic for the problem above so A* running with your heuristic will quickly find a solution. Explain the reasoning process behind your design.