Sudoku

문제

Sudoku is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9 × 9 grid with digits from 1 to 9 in such a way that the following statements hold:

• Each row contains exactly one occurrence of each digit from 1 to 9.
• Each column contains exactly one occurrence of each digit from 1 to 9.
• Each of the nine 3 × 3 subgrids contains exactly one occurrence of each digit from 1 to 9.

For a given not yet finished sudoku grid, determine if there is a mistake in it.

Note: It is not necessary to check whether the sudoku grid is solvable.

입력

The input describes the sudoku grid.

The characters ’|’, ’-’ and ’+’ frame the 3 × 3 subgrids.

The character ’.’ represents an empty cell.

All the other characters in the input will be digits from ’1’ to ’9’.

See the examples for clarification.

출력

Output the word GRESKA if there is a mistake in the sudoku board. Otherwise, output the word OK.

힌트

Clarification of the first example:

There is no mistake, so the output is OK.

Clarification of the second example:

There is a mistake in the ninth column: the digit 5 appears twice; and there is also a mistake in the lower right 3 × 3 subgrid: the digit 5 appears twice.

Clarification of the third example:

There are two mistakes: the digit 2 appears twice in the second column, and the digit 6 appears twice in the seventh column.

+---+---+---+
|52.|...|.81|
|.39|58.|...|
|.8.|.9.|...|
+---+---+---+
|24.|...|1.3|
|1..|43.|86.|
|.63|..7|.24|
+---+---+---+
|...|1.9|35.|
|..8|.74|6..|
|31.|86.|7.9|
+---+---+---+

OK

+---+---+---+
|3..|6..|..4|
|4.9|8.1|..7|
|..7|.49|6..|
+---+---+---+
|946|157|8.2|
|.2.|3..|745|
|.7.|28.|...|
+---+---+---+
|...|4..|..5|
|8.5|.6.|.2.|
|734|..8|5..|
+---+---+---+

GRESKA

+---+---+---+
|5..|98.|67.|
|6..|...|.31|
|.2.|613|.4.|
+---+---+---+
|.96|8.2|1.7|
|.28|..5|.9.|
|7.3|19.|6..|
+---+---+---+
|962|.7.|.1.|
|1.5|...|76.|
|.7.|5..|9..|
+---+---+---+

GRESKA