Problem Description

Sudoku is a logic puzzle game. The player’s task is to fill a $9\times9$ grid with the digits $1\sim9$ so that the following conditions are satisfied:

• The digits $1\sim 9$ appear exactly once in each row.
• The digits $1\sim 9$ appear exactly once in each column.
• The grid is divided into $9$ subgrids of size $3\times3$, and the digits $1\sim 9$ appear exactly once in each subgrid.

You are given an unfinished Sudoku grid. You need to determine whether there is currently an error. A grid has an error if and only if there exists a row, a column, or a subgrid in which at least one digit appears $2$ times or more.

The figure shows a Sudoku grid with no errors.

Input Format

Input a $13\times 13$ character matrix representing the Sudoku grid, where:

• The characters -, |, + represent the grid framework, which divides the grid into $9$ subgrids of size $3\times 3$.
• The character . represents an empty cell.
• A digit from $1\sim9$ means that the corresponding cell has already been filled with that digit.

See the samples for the exact format.

Output Format

Output one line with a string: if this grid has an error, output GRESKA, otherwise output OK.

+---+---+---+
|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

Hint

Sample Explanation #1

This grid has no errors, so output OK.

Sample Explanation #2

In column $9$, the digit $5$ appears $2$ times, and in the bottom-right subgrid, the digit $5$ also appears $2$ times.

Sample Explanation #3

In column $2$, the digit $2$ appears $2$ times, and in column $7$, the digit $6$ appears $2$ times.

Constraints

For $100\%$ of the testdata, the character matrix contains only digits $1\sim9and the characters-, |, +, ., and the positions of -, |, +` are the same as in the sample.

This problem uses bundled tests.

Notes

The scoring of this problem follows the original COCI problem setting, with a full score of $50$.

Translated from COCI2023-2024 CONTEST #1 T1 Sudoku.

Translated by ChatGPT 5