Two Choices

AtCoder

IDarc115_a

Time2000ms

Memory256MB

Difficulty—

$N$ students took a test with $M$ questions with two choices: $0$ and $1$. You are given $N$ strings of length $M$ each: $S_1, S_2, \ldots, S_N$. The $k$\-th character of $S_i$ is `0` or `1`, representing the response of the $i$\-th student to the $k$\-th question. Although we know the response of each student to each question, we do not yet know the correct answer ― $0$ or $1$ ― to each problem. Find the number of pairs $(i, j)$ satisfying $1 \leq i < j \leq N$ such that it is impossible for Student $i$ and Student $j$ to have the same number of correct answers. ## Constraints * $2 \leq N \leq 10^5$ * $1 \leq M \leq 20$ * $S_i$ is a string of length $M$ consisting of `0` and `1`. ## Input Input is given from Standard Input in the following format: $N$ $M$ $S_1$ $S_2$ $:$ $S_N$ [samples]

Samples

Input #1

Output #1

2

For example, if the correct answers to the $1$\-st and $2$\-nd questions are both $0$, Student $2$ and Student $3$ have the same number of correct answers ― $1$. On the other hand, Student $1$ and Student $2$ never have the same number of correct answers, nor do Student $1$ and Student $3$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Two Choices",
    "description": {
      "content": "$N$ students took a test with $M$ questions with two choices: $0$ and $1$. You are given $N$ strings of length $M$ each: $S_1, S_2, \\ldots, S_N$. The $k$\\-th character of $S_i$ is `0` or `1`, represen",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc115_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ students took a test with $M$ questions with two choices: $0$ and $1$. You are given $N$ strings of length $M$ each: $S_1, S_2, \\ldots, S_N$. The $k$\\-th character of $S_i$ is `0` or `1`, represen...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments