Daily sudoku, *New York Times*, November 1, 2023, Difficulty: Hard

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

- Each row contains exactly one occurrence of each digit from to .
- Each column contains exactly one occurrence of each digit from to .
- Each of the nine subgrids contains exactly one occurrence of each digit from to .

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.

#### Input Specification

The input describes the sudoku grid.

The characters `|`

, `-`

and `+`

frame the 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.

#### Output Specification

Output the word `GRESKA`

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

.

#### Constraints

Subtask | Points | Constraints |
---|---|---|

1 | 11 | It's possible to determine whether there is a mistake by only checking the first rule. |

2 | 12 | It's possible to determine whether there is a mistake by only checking the second rule. |

3 | 13 | It's possible to determine whether there is a mistake by only checking the third rule. |

4 | 14 | No additional constraints. |

#### Sample Input 1

```
+---+---+---+
|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|
+---+---+---+
```

#### Sample Output 1

`OK`

#### Explanation for Sample 1

There is no mistake, so the output is `OK`

.

#### Sample Input 2

```
+---+---+---+
|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..|
+---+---+---+
```

#### Sample Output 2

`GRESKA`

#### Explanation for Sample 2

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

#### Sample Input 3

```
+---+---+---+
|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..|
+---+---+---+
```

#### Sample Output 3

`GRESKA`

#### Explanation for Sample 3

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

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