Problem B. Better security

Author:A. Klenin, I. Ludov   Time limit:2 sec
Input file:input.txt   Memory limit:64 Mb
Output file:output.txt  

Statement

Young black-hat hacker Vasya routinely installs key loggers on every computer he can get his hands on. Browsing the logs collected, he sometimes can glance passwords of unaware users.

The IT department of the university where Vasya studies noticed suspicious activity and introduced a new, more secure way to enter passwords. Instead of password input field, window with 9 buttons is displayed. Buttons are arranged into 3 × 3 grid as shown in the table below.

789
456
123
Each button is a square of 100 by 100 pixels. There is no space between buttons. User must enter (digital) password by clicking buttons with a mouse.

To overcome this scheme, Vasya downloaded another cool program: mouse logger. It saves coordinates of clicks in a file, which Vasya is later able to browse. However, a complication has arisen: no information is saved about the position of password window on the screen. Indeed, it might even be partially off screen!

Your program must, given the series of mouse clicks, determine all possible corresponding passwords.

Input file format

Input file contains number of clicks N followed by integer coordinates x1 y1 x2 y2… xN yN.

Output file format

Output file must contain one line per possible password. Each line must consist of exactly N digits. Lines must be sorted in lexicographical order. If there are no possible combinations, output file must contain the string NONE.

Constraints

1 ≤ N ≤ 100, 0 ≤ xi yi ≤ 1000

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
2
10 12 110 12
12
23
45
56
78
89
2
2
10 12 750 12
NONE

0.123s 0.013s 13