You are given two digits represented as 3 \times 5 matrices of characters ('X' for an active pixel, '0' for an inactive pixel). Each digit is provided in a "broken" state: exactly one 'X' pixel that should be active according to the standard font is instead rendered as a '0'.
Your task is to identify the two original digits, calculate their sum, and output that sum in its perfect (unbroken) 3 \times 5 matrix format.
The following 3 \times 5 grids define the standard appearance for digits 0-9. Any "broken" input is a modification of one of these templates.
0: 1: 2: 3: 4:
XXX 00X XXX XXX X0X
X0X 00X 00X 00X X0X
X0X 00X XXX XXX XXX
X0X 00X X00 00X 00X
XXX 00X XXX XXX 00X
5: 6: 7: 8: 9:
XXX XXX XXX XXX XXX
X00 X00 00X X0X X0X
XXX XXX 00X XXX XXX
00X X0X 00X X0X 00X
XXX XXX 00X XXX XXX
Input
The input consists of two 3 \times 5 matrices, provided one after the other (10 lines total), representing two single digits (0-9). In each matrix, exactly one 'X' from the standard font has been replaced by a '0'.
Output
Identify the original digits. If the identified digits result in a unique possible sum, print the 3 \times 5 matrix (or matrices) representing that sum using the standard font.
If the sum is 0-9, output a single 3 \times 5 matrix.
If the sum is 10-18, output two 3 \times 5 matrices side-by-side, separated by a single space character.
If the original digits cannot be determined uniquely, or if they could represent multiple different sums, output -1.
Examples
| standard input | standard output |
|---|
| XXX
X0X
X0X
X0X
0XX
X0X
X0X
X0X
X0X
XXX
| XXX
X0X
X0X
X0X
XXX
|
| X0X
X0X
XXX
X0X
XXX
X0X
00X
XXX
X00
XXX
| 00X XXX
00X X0X
00X X0X
00X X0X
00X XXX
|
| XXX
X00
X0X
X0X
XXX
XXX
X00
X0X
X0X
XXX
| -1
|