Common Prefixes

AtCoder

IDabc213_f

Time3000ms

Memory256MB

Difficulty—

Let the **similarity** $f(X,Y)$ between two strings $X$ and $Y$ be the length of their longest common prefix. For example, the similarity between `abc` and `axbc` is $1$, and the similarity between `aaa` and `aaaa` is $3$. You are given a string $S$ of length $N$. Let $S_i$ be the suffix of $S$ beginning with the $i$\-th character of $S$. For each $k=1,\ldots,N$, find $f(S_k,S_1)+f(S_k,S_2)+\ldots+f(S_k,S_N)$. ## Constraints * $1 \leq N \leq 10^6$ * $S$ is a string of length $N$ consisting of lowercase English letters. ## Input Input is given from Standard Input in the following format: $N$ $S$ [samples]

Samples

Input #1

3
abb

Output #1

3
3
2

$S_1$ is `abb`, $S_2$ is `bb`, and $S_3$ is `b`.

*   For $k=1$: $f(S_1,S_1)+f(S_1,S_2)+f(S_1,S_3)=3+0+0=3$.
*   For $k=2$: $f(S_2,S_1)+f(S_2,S_2)+f(S_2,S_3)=0+2+1=3$.
*   For $k=3$: $f(S_3,S_1)+f(S_3,S_2)+f(S_3,S_3)=0+1+1=2$.

Input #2

11
mississippi

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Common Prefixes",
    "description": {
      "content": "Let the **similarity** $f(X,Y)$ between two strings $X$ and $Y$ be the length of their longest common prefix.   For example, the similarity between `abc` and `axbc` is $1$, and the similarity between ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc213_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let the **similarity** $f(X,Y)$ between two strings $X$ and $Y$ be the length of their longest common prefix.  \nFor example, the similarity between `abc` and `axbc` is $1$, and the similarity between ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments