COCI '23 Contest 1 #1 Sudoku

Points: 5 (partial)

Time limit: 1.0s

Memory limit: 512M

Problem type

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 $9 \times 9$ ~9 \times 9~ grid with digits from $1$ ~1~ to $9$ ~9~ in such a way that the following statements hold:

Each row contains exactly one occurrence of each digit from $1$ ~1~ to $9$ ~9~.
Each column contains exactly one occurrence of each digit from $1$ ~1~ to $9$ ~9~.
Each of the nine $3 \times 3$ ~3 \times 3~ subgrids contains exactly one occurrence of each digit from $1$ ~1~ to $9$ ~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.

Input Specification

The input describes the sudoku grid.

The characters |, - and + frame the $3 \times 3$ ~3 \times 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.

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 $5$ ~5~ appears twice; and there is also a mistake in the lower right $3 \times 3$ ~3 \times 3~ subgrid: the digit $5$ ~5~ 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 $2$ ~2~ appears twice in the second column, and the digit $6$ ~6~ appears twice in the seventh column.

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