Let's Get a Perfect Score

AtCoder

IDabc282_b

Time2000ms

Memory256MB

Difficulty—

$N$ participants, numbered $1$ to $N$, will participate in a contest with $M$ problems, numbered $1$ to $M$. For an integer $i$ between $1$ and $N$ and an integer $j$ between $1$ and $M$, participant $i$ can solve problem $j$ if the $j$\-th character of $S_i$ is `o`, and cannot solve it if that character is `x`. The participants must be in pairs. Print the number of ways to form a pair of participants who can collectively solve all the $M$ problems. More formally, print the number of pairs $(x,y)$ of integers satisfying $1\leq x < y\leq N$ such that for any integer $j$ between $1$ and $M$, at least one of participant $x$ and participant $y$ can solve problem $j$. ## Constraints * $N$ is an integer between $2$ and $30$, inclusive. * $M$ is an integer between $1$ and $30$, inclusive. * $S_i$ is a string of length $M$ consisting of `o` and `x`. ## Input The input is given from Standard Input in the following format: $N$ $M$ $S_1$ $S_2$ $\vdots$ $S_N$ [samples]

Samples

Input #1

5 5
ooooo
oooxx
xxooo
oxoxo
xxxxx

Output #1

5

The following five pairs satisfy the condition: participants $1$ and $2$, participants $1$ and $3$, participants $1$ and $4$, participants $1$ and $5$, and participants $2$ and $3$.
On the other hand, the pair of participants $2$ and $4$, for instance, does not satisfy the condition because they cannot solve problem $4$.

Input #2

3 2
ox
xo
xx

Output #2

Input #3

2 4
xxxx
oxox

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Let's Get a Perfect Score",
    "description": {
      "content": "$N$ participants, numbered $1$ to $N$, will participate in a contest with $M$ problems, numbered $1$ to $M$. For an integer $i$ between $1$ and $N$ and an integer $j$ between $1$ and $M$, participant ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc282_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ participants, numbered $1$ to $N$, will participate in a contest with $M$ problems, numbered $1$ to $M$.\nFor an integer $i$ between $1$ and $N$ and an integer $j$ between $1$ and $M$, participant ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments