Avoid Straight Line

AtCoder

IDabc312_g

Time2000ms

Memory256MB

Difficulty—

You are given a tree with $N$ vertices. The vertices are numbered from $1$ through $N$, and the $i$\-th edge connects vertex $A_i$ and vertex $B_i$. Find the number of tuples of integers $(i,j,k)$ such that: * $1 \leq i < j < k \leq N$; and * the given tree does not contain a simple path that contains all of vertices $i$, $j$, and $k$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $1 \leq A_i, B_i \leq N$ * The given graph is a tree. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $B_1$ $\vdots$ $A_{N-1}$ $B_{N-1}$ [samples]

Samples

Input #1

Output #1

2

Two tuples satisfy the conditions: $(i,j,k) = (1,3,4),(3,4,5)$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Avoid Straight Line",
    "description": {
      "content": "You are given a tree with $N$ vertices. The vertices are numbered from $1$ through $N$, and the $i$\\-th edge connects vertex $A_i$ and vertex $B_i$.   Find the number of tuples of integers $(i,j,k)$ s",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc312_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a tree with $N$ vertices. The vertices are numbered from $1$ through $N$, and the $i$\\-th edge connects vertex $A_i$ and vertex $B_i$.  \nFind the number of tuples of integers $(i,j,k)$ s...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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