Problem Statement

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.

Input

Input is given from Standard Input in the following format:
N
$A_{1,1}A_{1,2}\ldots A_{1,N}$
$A_{2,1}A_{2,2}\ldots A_{2,N}$
$\vdots$
$A_{N,1}A_{N,2}\ldots A_{N,N}$

Output

If the given table is not contradictory, print correct; if it is contradictory, print incorrect.

Constraints

• $2 \leq N \leq 1000$
• A_{i,i} is -.
• A_{i,j} is W, L, or D, for $i\neq j$.

Sample Input 1

4
-WWW
L-DD
LD-W
LDW-

Sample Output 1

incorrect

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

Sample Input 2

2
-D
D-

Sample Output 2

correct

There is no contradiction.

见题面 Input 部分

见题面 Output 部分