Contest: Task: Related: TaskA TaskC

Score : $200$ points

$N$ players played a round-robin tournament.

You are given an $N$-by-$N$ table $A$ containing the results of the matches. Let $A_{i,j}$ denote the element at the $i$-th row and $j$-th column of $A$.

$A_{i,j}$ is `-`

if $i=j$, and `W`

, `L`

, or `D`

otherwise.

$A_{i,j}$ is `W`

if Player $i$ beat Player $j$, `L`

if Player $i$ lost to Player $j$, and `D`

if Player $i$ drew with Player $j$.

Determine whether the given table is contradictory.

The table is said to be contradictory when some of the following holds:

- There is a pair $(i,j)$ such that Player $i$ beat Player $j$, but Player $j$ did not lose to Player $i$;
- There is a pair $(i,j)$ such that Player $i$ lost to Player $j$, but Player $j$ did not beat Player $i$;
- There is a pair $(i,j)$ such that Player $i$ drew with Player $j$, but Player $j$ did not draw with Player $i$.

- $2 \leq N \leq 1000$
- $A_{i,i}$ is
`-`

. - $A_{i,j}$ is
`W`

,`L`

, or`D`

, for $i\neq j$.

Input is given from Standard Input in the following format:

$N$ $A_{1,1}A_{1,2}\ldots A_{1,N}$ $A_{2,1}A_{2,2}\ldots A_{2,N}$ $\vdots$ $A_{N,1}A_{N,2}\ldots A_{N,N}$

If the given table is not contradictory, print `correct`

; if it is contradictory, print `incorrect`

.

4 -WWW L-DD LD-W LDW-

incorrect

Player $3$ beat Player $4$, while Player $4$ also beat Player $3$, which is contradictory.

2 -D D-

correct

There is no contradiction.