Yet Another Sigma Problem

AtCoder

IDabc353_e

Time2000ms

Memory256MB

Difficulty—

For strings $x$ and $y$, define $f(x, y)$ as follows: * $f(x, y)$ is the length of the longest common prefix of $x$ and $y$. You are given $N$ strings $(S_1, \ldots, S_N)$ consisting of lowercase English letters. Find the value of the following expression: $\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(S_i,S_j)$. ## Constraints * $2 \leq N \leq 3\times 10^5$ * $S_i$ is a string consisting of lowercase English letters. * $1 \leq |S_i|$ * $|S_1|+|S_2|+\ldots+|S_N|\leq 3\times 10^5$ * All input numbers are integers. ## Input The input is given from Standard Input in the following format: $N$ $S_1$ $\ldots$ $S_N$ [samples]

Samples

Input #1

3
ab abc arc

Output #1

4

*   $f(S_1,S_2)=2$
*   $f(S_1,S_3)=1$
*   $f(S_2,S_3)=1$

Thus, the answer is $f(S_1,S_2) + f(S_1,S_3) + f(S_2,S_3) = 4$.

Input #2

11
ab bb aaa bba baba babb aaaba aabbb a a b

Output #2

API Response (JSON)

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  "problem": {
    "name": "Yet Another Sigma Problem",
    "description": {
      "content": "For strings $x$ and $y$, define $f(x, y)$ as follows: *   $f(x, y)$ is the length of the longest common prefix of $x$ and $y$. You are given $N$ strings $(S_1, \\ldots, S_N)$ consisting of lowercase ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc353_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For strings $x$ and $y$, define $f(x, y)$ as follows:\n\n*   $f(x, y)$ is the length of the longest common prefix of $x$ and $y$.\n\nYou are given $N$ strings $(S_1, \\ldots, S_N)$ consisting of lowercase ...",
      "is_translate": false,
      "language": "English"
    }
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}

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