isVisited = [0]*362880 # 0 for not visited,1 for occured,2 for visited fac = [1,1,2,6,24,120,720,5040,40320] lf = len(fac) h = [[0,1,2,1,2,3,2,3,4], [1,0,1,2,1,2,3,2,3], [2,1,0,3,2,1,4,3,2], [1,2,3,0,1,2,1,2,3], [2,1,2,1,0,1,2,1,2], [3,2,1,2,1,0,3,2,1], [2,3,4,1,2,3,0,1,2], [3,2,3,2,1,2,1,0,1], [4,3,2,3,2,1,2,1,0]] def cantor(s): sum = 0 ls = len(s) for i in range(ls): count = 0 for j in range(i+1,ls): if s[i] > s[j]: count +=1 sum += count*fac[lf-i-1] return sum que = [] dir = {-3:'u',1:'r',3:'d',-1:'l'} class state: flag = True def __init__(self,s,x,f,step=0,last=0): self.x = x self.s = list(s) self.step = step self.path = [] self.last = last self.f = f def can(self): cans = [-1,1,3,-3] if self.last in cans : cans.remove(-self.last) if self.x<3: cans.remove(-3) if self.x>5: cans.remove(3) if self.x%3 is 0: cans.remove(-1) if self.x%3 is 2: cans.remove(1) return cans def move(self): cans = self.can() for i in cans: s = list(self.s) tmp = self.x + i s[self.x] = s[tmp] s[tmp] = '9' ct = cantor(s) if isVisited[ct] != 2 : val = int(s[self.x]) f = h[8][tmp] +h[val-1][self.x]-h[8][self.x]-h[val-1][tmp]+self.step+1 new = state(s,tmp,f,self.step +1,i) new.path = self.path + [dir[i]] if isVisited[ct] == 1: for i,node in enumerate(que): if mew.s == node.s: del que[i] break else:isVisited[ct] = 1 if que == []: que.append(new) continue for i,node in enumerate(que): if new.f<=node.f: que.insert(i,new) def solvable(s): reverse = 0 for i in range(8): if s[i] is '9':continue for j in range(i+1,9): if s[i]>s[j]:reverse +=1 if reverse % 2 is 0:return True else:return False def getPath(s,index): f = 0 for i,j in enumerate(s): f+=h[int(j)-1][i] que.append(state(s,index,f,0,0)) while que != []: cur = que.pop(0) ct = cantor(cur.s) isVisited[ct] = 2 if ct is 0: return cur.path cur.move() if __name__ == '__main__': s=input() index = s.find('x') s =list(s) s[index] = '9' if solvable(s):print(''.join(getPath(s,index))) else:print('unsolvable')