Problem 3 (Search . In HW6, you wrote a C program that performs state-space search for the 15-Puzzle simi- lar in principle to those used in game engines. This search consists of a main loop that operates on two major lists open and closed and a small list, successors. Write a C program that performs A* search using open, closed, suce, expand(node), fil- ter(succ, list), merge(1st1,1st2). Write the main loop and merge(). DO NOT write filter() and expand(). Again, use the same structure used in the homework. Assume the values used for node selection are computed and insertion functions listed below are available: struct node *insert_by_h(node,lst), *insert_by_g(node,lst), *insert_by_f(node,lst); /* insert a node to list */ struct node { int loc[N+1][N]; struct node *next; } *start, *goal; struct node *initialize(), *expand(),*merge(), *filter(); int main(int arge,char **argv) { struct node *tsucc, *csucc,*copen, *topen,*open, *closed,*succ; open-closed-suce=NULL; start-initialize(arge,argv); /* init initial and goal states */ open-start; /* the last row holds the three values used for node selection */ /* you may use any and all of the insert functons listed above */ struct node *merge(struct node *succ,struct node *open,int flag) { struct node *csucc,*copen; return open;