''' mbinary
#########################################################################
# File : Astar.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-05-19  23:06
# Description:
#########################################################################
'''

from random import shuffle
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()


def info():
    print('input a 3x3 matrix in one line')
    print('from left to right,from up to down')
    print('such as 56831247x  represent matrix as follow')
    print('5  6  8\n3  1  2\n4  7  x')
    print('then, if it has, I will print the path of moving x to reach state as follows')
    print('1  2  3\n4  5  6\n7  8  x')
    print('print q to quit')


case = list('12345678x')


def genCase():
    tmp = case.copy()
    shuffle(tmp)
    print(f'Using random data: {tmp}')
    index = -1
    for i, j in enumerate(tmp):
        if j == 'x':
            index = i
            break
    tmp[index] = '9'
    return tmp, index


def isValid(li):
    for i in '123456789':
        if not i in li:
            print('Invalid Input')
            return False
    return True


def run():
    while 1:
        print('\n\n'+'-'*10+'Game Begins' + '-'*10)
        info()
        s = input('input: ')
        if s == 'q' or s == 'Q' or s == 'quit':
            break
        index = s.find('x')
        li = list(s)
        if index != -1:
            li[index] = '9'
        if not isValid(li):
            li, index = genCase()
        if solvable(li):
            print(''.join(getPath(li, index)))
        else:
            print('unsolvable')


if __name__ == '__main__':
    run()