Problem B

Bank (Not Quite O.C.R.)

Banks, always trying to increase their profit, asked their computer experts to come up with a system that can read bank cheques; this would make the processing of cheques cheaper. One of their ideas was to use optical character recognition (ocr) to recognize bank accounts printed using 7 line-segments.

Once a cheque has been scanned, some image processing software would convert the horizontal and vertical bars to ASCII bars '|' and underscores '_'.

The ASCII 7-segment versions of the ten digits look like this:

A bank account has a 9-digit account number with a checksum. For a valid account number, the following equation holds: (d₁ + 2 × d₂ + 3 × d₃ + . . . + 9 × d₉) mod 11 = 0. Digits are numbered from right to left like this: d₉d₈d₇d₆d₅d₄d₃d₂d₁.

Unfortunately, the scanner sometimes makes mistakes: some line-segments may be missing. Your task is to write a program that deduces the original number, assuming that:

when the input represents a valid account number, it is the original number;
at most one digit is garbled;
the scanned image contains no extra segments.

For example, the following input

    _  _     _  _  _  _  _ 
  | _| _||_||_ |_   ||_||_|
  ||_  _|  | _||_|  ||_| _|

used to be "123456789".

Input Specification

The input file starts with a line with one integer specifying the number of account numbers that have to be processed. Each account number occupies 3 lines of 27 characters.

Output Specification

For each test case, the output contains one line with 9 digits if the correct account number can be determined, the string "failure" if no solutions were found and "ambiguous" if more than one solution was found.

Example Input

4
    _  _     _  _  _  _  _ 
  | _| _||_||_ |_   ||_||_|
  ||_  _|  | _||_|  ||_| _|
    _  _  _  _  _  _     _ 
|_||_|| || ||_   |  |  ||  
  | _||_||_||_|  |  |  | _|
 _  _  _  _  _  _  _  _  _ 
|_||_||_||_||_||_||_||_||_|
|_||_||_||_||_||_||_||_||_|
 _     _  _  _  _  _  _  _ 
|_|  ||_||_||_||_||_||_||_|
|_|  ||_||_||_||_||_||_||_|

Example Output

123456789
ambiguous
failure
878888888

This page maintained by Ed Karrels.
Last updated January 3, 1998