6. (10%) Given a received vector (1,2,..., 6) = (1,-1,-1,-2,-2,1), please use the A* algorithm to find a path from the root of the following code tree to a goal node such that the cost of the path is minimum among all paths from the root to a goal node (2%), where the cost of the edge from a node at level t-1 to level t is (re-(-1))2, where ct is the label of the edge. Note that you need also to define the cost function of the nodes in your search (3%) and draw your searching tree (5%) in your answer. 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 000000 001011 010101 011110 100110 101101 110011 111000