Lexicographic constraints

AtCoder

IDagc029_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, $S_1<S_2<...<S_N$ holds lexicographically, where $S_i$ is the $i$\-th string from the left. At least how many different characters are contained in $S_1,S_2,...,S_N$, if the length of $S_i$ is known to be $A_i$? ## Constraints * $1 \leq N \leq 2\times 10^5$ * $1 \leq A_i \leq 10^9$ * $A_i$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples] ## Note The strings do not necessarily consist of English alphabet; there can be arbitrarily many different characters (and the lexicographic order is defined for those characters).

Samples

Input #1

3
3 2 1

Output #1

2

The number of different characters contained in $S_1,S_2,...,S_N$ would be $3$ when, for example, $S_1=$`abc`, $S_2=$`bb` and $S_3=$`c`.
However, if we choose the strings properly, the number of different characters can be $2$.

Input #2

5
2 3 2 1 2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Lexicographic constraints",
    "description": {
      "content": "There are $N$ strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, $S_1<S_2<...<S_N$ ho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc029_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, $S_1<S_2<...<S_N$ ho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments