Sumdoku

*Sumdoku* is a variant of the game *Sudoku*.
As in *Sudoku*, the aim is to fill in a $9$-by-$9$ grid with the digits $1$ through $9$ so that each digit $1$ through $9$ occurs exactly once in each row,
exactly once in each column and exactly once in each of the
$9$ $3$-by-$3$ sub-squares subject to constraints
on the choices. In Sudoku, the constraints are that certain
squares must contain fixed values. In *Sumdoku*, the
constraints are on the sum of adjacent squares within each
$3$-by-$3$ sub-square. In the illustration
below, the symbols $<$,
$=$ and $>$ indicate that the sum of the
values on either side (or above and below) the symbol must have
sum less than $10$, equal
to $10$ or greater than
$10$, respectively.

Write a program to solve Sumdoku problems.

The input consists of a single data set containing
$15$ lines of input, each
line consisting of the characters `<`, `=` or `>`. Rows $1$, $3$, $5$, $6$, $8$, $10$, $11$, $13$ and $15$ contain $6$ characters corresponding to
constraints on the sum of values to the left and right of the
symbol. Rows $2$,
$4$, $7$, $9$, $12$ and $14$ contain $9$ characters corresponding to
constraints on the sum of values above and below the symbol.
**Note:** Solutions of some problems may
not be unique. The judging program will just check whether your
solution satisfies the constraints of the problem (row, column,
$3$-by-$3$ box and inequality
constraints).

Output $9$ lines consisting of $9$ decimal digits each, separated by a single space. The value in the $j^\text {th}$ position in the $i^{\text {th}}$ line of the $9$ output lines is the solution value in column $j$ of row $i$.

Sample Input 1 | Sample Output 1 |
---|---|

<==<=> ><>><<><= >=<==< ><<><>><< <<>==< =<=>=> >><<>=<>< ><>>>< =====<<>> <><<>> <><><< <>><>><>= =>><=> <><<><><> <>=>=< |
5 3 7 8 2 1 6 4 9 9 6 4 5 3 7 8 2 1 8 1 2 9 4 6 7 3 5 6 4 5 3 7 8 1 9 2 7 8 1 4 9 2 5 6 3 3 2 9 6 1 5 4 7 8 2 7 8 1 6 9 3 5 4 1 9 3 7 5 4 2 8 6 4 5 6 2 8 3 9 1 7 |