Online JudgeProblem SetAuthorsOnline ContestsUser
Web Board
Home Page
F.A.Qs
Statistical Charts
Problems
Submit Problem
Online Status
Prob.ID:
Register
Update your info
Authors ranklist
Current Contest
Past Contests
Scheduled Contests
Award Contest
User ID:
Password:
  Register
Language:
Doors and... more doors
Time Limit: 2000MSMemory Limit: 65536K
Total Submissions: 458Accepted: 184Special Judge

Description

When wondering through the labyrinth, the goal is usually to find some kind of door. Well, not this time.

A labyrinth consists of N × N cells, each 1 × 1 meter in size. Cells are separated by doors. Each door opens in a specific direction (as shown on the picture):

1. left outwards;
2. left inwards;
3. right outwards;
4. right inwards.

So a cell can be represented by two numbers describing doors on its eastern and southern sides according to the list above. The doors are just slightly less then 1 meter in width. The traveler in the labyrinth is also slightly less then 1 meter in diameter, so he has following limitations:

* He can not pull doors, only push them.
* After opening the door and entering the cell it leads to, he can not take a turn in the direction where the door opened, because the passage is blocked by the door. Doors have springs and close automatically when traveler leaves the cell.

Your program must find the shortest path for the traveler from north-western cell (1, 1) to south-eastern cell (N, N).

Input

Input file contains labyrinth size N followed by 2 × N2 numbers describing doors for each cell row by row. As there are no doors leading outside of labyrinth, values for eastern doors in the last column and southern doors in the last row are zero.

Constraints

1 ≤ N ≤ 1000

Output

Output file must contain the shortest path as a list of cell coordinates (column number, then row number), including both (1, 1) and (N, N) cells. If there are several solutions with the same length, output any one of them. If it is impossible to get to a destination cell, output a singe zero.

Sample Input

Sample Input 1
2
2 3 0 4
1 0 0 0
Sample Input 2
3
4 3  1 4  0 1
3 3  2 3  0 4
2 0  1 0  0 0

Sample Output

Sample Output 1
1 1
1 2
2 2
Sample Output 2
1 1
1 2
2 2
2 1
3 1
3 2
2 2
2 3
3 3

Hint

Bold texts appearing in the sample sections are informative and do not form part of the actual data.

Source

Northeastern Europe 2006, Far-Eastern Subregion

[Submit]   [Go Back]   [Status]   [Discuss]

Home Page   Go Back  To top


All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di
Any problem, Please Contact Administrator