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:
For example, the following input
_ _ _ _ _ _ _ | _| _||_||_ |_ ||_||_| | _ _| | _||_| ||_| _|
used to be ''123456789''.
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.
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.
4 _ _ _ _ _ _ _ | _| _||_||_ |_ ||_||_| | _ _| | _||_| ||_| _| _ _ _ _ _ _ _ |_||_|| || ||_ | | ||_ | _||_||_||_| | | | _| _ _ _ _ _ _ _ _ _ |_||_||_||_||_||_||_||_||_| |_||_||_||_||_||_||_||_||_| _ _ _ _ _ _ _ _ |_| ||_||_||_||_||_||_||_| |_| ||_||_||_||_||_||_||_|
123456789 ambiguous failure 878888888