Based on the same settings and constraints of the Water Jug Puzzle discussed in class. Please draw a search tree to find all the optimal solution$($s$)$ for the following instance:

The game starts from the situation where the $4-$gallon jug is empty and the $3-$gallon jug is full. The desired result is making the $4-$gallon jug have exactly $1$ gallon of water in the $3-$gallon jug is full.