Oddly Similar

AtCoder

IDabc348_f

Time2000ms

Memory256MB

Difficulty—

There are $N$ sequences of length $M$, denoted as $A_1, A_2, \ldots, A_N$. The $i$\-th sequence is represented by $M$ integers $A_{i,1}, A_{i,2}, \ldots, A_{i,M}$. Two sequences $X$ and $Y$ of length $M$ are said to be similar if and only if the number of indices $i (1 \leq i \leq M)$ such that $X_i = Y_i$ is odd. Find the number of pairs of integers $(i,j)$ satisfying $1 \leq i < j \leq N$ such that $A_i$ and $A_j$ are similar. ## Constraints * $1 \leq N \leq 2000$ * $1 \leq M \leq 2000$ * $1 \leq A_{i,j} \leq 999$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,M}$ $A_{2,1}$ $A_{2,2}$ $\ldots$ $A_{2,M}$ $\vdots$ $A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,M}$ [samples]

Samples

Input #1

Output #1

1

The pair $(i,j) = (1,2)$ satisfies the condition because there is only one index $k$ such that $A_{1,k} = A_{2,k}$, which is $k=1$.
The pairs $(i,j) = (1,3), (2,3)$ do not satisfy the condition, making $(1,2)$ the only pair that does.

Input #2

6 5
8 27 27 10 24
27 8 2 4 5
15 27 26 17 24
27 27 27 27 27
27 7 22 11 27
19 27 27 27 27

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Oddly Similar",
    "description": {
      "content": "There are $N$ sequences of length $M$, denoted as $A_1, A_2, \\ldots, A_N$. The $i$\\-th sequence is represented by $M$ integers $A_{i,1}, A_{i,2}, \\ldots, A_{i,M}$. Two sequences $X$ and $Y$ of length ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc348_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ sequences of length $M$, denoted as $A_1, A_2, \\ldots, A_N$. The $i$\\-th sequence is represented by $M$ integers $A_{i,1}, A_{i,2}, \\ldots, A_{i,M}$.\nTwo sequences $X$ and $Y$ of length ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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