training_2005_04_16 - Sudoku Checker

Problem F. Sudoku Checker ≡

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Author:	A. Klenin	Time limit:	2 sec
Input file:	input.txt	Memory limit:	64 Mb
Output file:	output.txt

Statement

The puzzle game of Sudoku is played on a board of N² × N² cells. The cells are grouped in N × N squares of N × N cells each. Each cell is either empty or contains a number between 1 and N².

The sudoku position is correct when numbers in each row, each column and each square are different. The goal of the game is, starting from some correct position, fill all empty cells so that the final position is still correct.

This game is fairly popular in the Internet, and there are many sites which allow visitors to solve puzzles online. Such sites always have a subroutine to determine a correctness of a given position.

You are to write such a routine.

Input file format

Input file contains integer N, followed by N⁴ integers — sudoku position. Empty cells are denoted by zeroes.

Output file format

Output file must contain a single string 'CORRECT' or 'INCORRECT'.

Constraints

1 ≤ N ≤ 10.

Sample tests

No.	Input file (`input.txt`)	Output file (`output.txt`)
1	`2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1`	`CORRECT`
2	`2 2 1 3 0 3 2 4 0 1 3 2 4 0 0 0 1`	`INCORRECT`