Triangle

AtCoder

IDabc258_g

Time3000ms

Memory256MB

Difficulty—

You are given a simple undirected graph $G$ with $N$ vertices. $G$ is given as the $N \times N$ adjacency matrix $A$. That is, there is an edge between Vertices $i$ and $j$ if $A_{i,j}$ is $1$, and there is not if $A_{i,j}$ is $0$. Find the number of triples of integers $(i,j,k)$ satisfying $1 \le i < j < k \le N$ such that there is an edge between Vertices $i$ and $j$, an edge between Vertices $j$ and $k$, and an edge between Vertices $i$ and $k$. ## Constraints * $3 \le N \le 3000$ * $A$ is the adjacency matrix of a simple undirected graph $G$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_{1,1}A_{1,2}\dots A_{1,N}$ $A_{2,1}A_{2,2}\dots A_{2,N}$ $\vdots$ $A_{N,1}A_{N,2}\dots A_{N,N}$ [samples]

Samples

Input #1

Output #1

2

$(i,j,k)=(1,3,4),(2,3,4)$ satisfy the condition.
$(i,j,k)=(1,2,3)$ does not satisfy the condition, because there is no edge between Vertices $1$ and $2$.
Thus, the answer is $2$.

Input #2

Output #2

API Response (JSON)

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  "problem": {
    "name": "Triangle",
    "description": {
      "content": "You are given a simple undirected graph $G$ with $N$ vertices. $G$ is given as the $N \\times N$ adjacency matrix $A$. That is, there is an edge between Vertices $i$ and $j$ if $A_{i,j}$ is $1$, and th",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc258_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple undirected graph $G$ with $N$ vertices.\n$G$ is given as the $N \\times N$ adjacency matrix $A$. That is, there is an edge between Vertices $i$ and $j$ if $A_{i,j}$ is $1$, and th...",
      "is_translate": false,
      "language": "English"
    }
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}

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