Divide String

AtCoder

IDarc163_a

Time2000ms

Memory256MB

Difficulty—

You are given a string $S$ of length $N$ consisting of lowercase English letters. Determine whether it is possible to divide $S$ into two or more consecutive substrings so that they are strictly increasing in lexicographical order. To be precise, determine whether there is a sequence of strings $t=(t_1,t_2,\dots,t_k)$ that satisfies all of the following conditions. * The length of the sequence $k$ is at least $2$. * $t_i$ is not empty. ($1 \le i \le k$) * Concatenating $t_1,t_2,\dots,t_k$ in this order results in $S$. * $t_i$ is lexicographically smaller than $t_{i+1}$ for every integer $i$ such that $1 \le i < k$. You are given $T$ test cases. Find the answer for each of them. What is lexicographical order?A string $S = S_1S_2\ldots S_{|S|}$ is said to be **lexicographically smaller** than a string $T = T_1T_2\ldots T_{|T|}$ if either 1. or 2. below holds. Here, $|S|$ and $|T|$ represent the lengths of $S$ and $T$, respectively. 1. $|S| \lt |T|$ and $S_1S_2\ldots S_{|S|} = T_1T_2\ldots T_{|S|}$. 2. There is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold. * $S_1S_2\ldots S_{i-1} = T_1T_2\ldots T_{i-1}$. * The character $S_i$ comes before $T_i$ in alphabetical order. ## Constraints * $1 \le T \le 2000$ * $2 \le N \le 2000$ * $S$ is a string of length $N$ consisting of lowercase English letters. * The sum of $N$ over all test cases in a single input does not exceed $2000$. ## Input The input is given from Standard Input in the following format: $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Here, $\mathrm{case}_i$ represents the $i$\-th test case. Each test case is given in the following format: $N$ $S$ [samples]

Samples

Input #1

5
4
abac
3
cac
2
ab
12
abababababab
5
edcba

Output #1

Yes
No
Yes
Yes
No

For the first test case, you can divide $S$ into `a`, `ba`, `c`.
For the second test case, there is no way to divide $S$ into substrings so that they are strictly increasing in lexicographical order.

API Response (JSON)

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  "problem": {
    "name": "Divide String",
    "description": {
      "content": "You are given a string $S$ of length $N$ consisting of lowercase English letters. Determine whether it is possible to divide $S$ into two or more consecutive substrings so that they are strictly incre",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc163_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a string $S$ of length $N$ consisting of lowercase English letters. Determine whether it is possible to divide $S$ into two or more consecutive substrings so that they are strictly incre...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments