Distance Sums 2

AtCoder

IDabc220_f

Time2000ms

Memory256MB

Difficulty—

Given is a tree with $N$ vertices. The vertices are numbered $1,2,\ldots ,N$, and the $i$\-th edge is an undirected edge connecting Vertices $u_i$ and $v_i$. For each integer $i\,(1 \leq i \leq N)$, find $\sum_{j=1}^{N}dis(i,j)$. Here, $dis(i,j)$ denotes the minimum number of edges that must be traversed to go from Vertex $i$ to Vertex $j$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq u_i < v_i \leq N$ * The given graph is a tree. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_{N-1}$ $v_{N-1}$ [samples]

Samples

Input #1

3
1 2
2 3

Output #1

3
2
3

We have:
$dis(1,1)+dis(1,2)+dis(1,3)=0+1+2=3$,
$dis(2,1)+dis(2,2)+dis(2,3)=1+0+1=2$,
$dis(3,1)+dis(3,2)+dis(3,3)=2+1+0=3$.

Input #2

2
1 2

Output #2

1
1

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Distance Sums 2",
    "description": {
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1,2,\\ldots ,N$, and the $i$\\-th edge is an undirected edge connecting Vertices $u_i$ and $v_i$. For each integer $i\\,(1 \\leq i \\leq N)$, f",
      "description_type": "Markdown"
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    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc220_f"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a tree with $N$ vertices. The vertices are numbered $1,2,\\ldots ,N$, and the $i$\\-th edge is an undirected edge connecting Vertices $u_i$ and $v_i$.\nFor each integer $i\\,(1 \\leq i \\leq N)$, f...",
      "is_translate": false,
      "language": "English"
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