Tournament Result

AtCoder

IDabc261_b

Time2000ms

Memory256MB

Difficulty—

$N$ 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 $i$. ## Constraints * $2 \leq N \leq 1000$ * $A_{i,i}$ is `-`. * $A_{i,j}$ is `W`, `L`, or `D`, for $i\neq j$. ## Input Input is given from Standard Input in the following format: $N$ $A_{1,1}A_{1,2}\ldots A_{1,N}$ $A_{2,1}A_{2,2}\ldots A_{2,N}$ $\vdots$ $A_{N,1}A_{N,2}\ldots A_{N,N}$ [samples]

Samples

Input #1

4
-WWW
L-DD
LD-W
LDW-

Output #1

incorrect

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

Input #2

2
-D
D-

Output #2

correct

There is no contradiction.

API Response (JSON)

{
  "problem": {
    "name": "Tournament Result",
    "description": {
      "content": "$N$ 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 $A$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc261_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ players played a round-robin tournament.\nYou 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 $A$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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