Frequency

AtCoder

IDarc069_c

Time2000ms

Memory256MB

Difficulty—

Snuke loves constructing integer sequences. There are $N$ piles of stones, numbered $1$ through $N$. The pile numbered $i$ consists of $a_i$ stones. Snuke will construct an integer sequence $s$ of length $Σa_i$, as follows: 1. Among the piles with the largest number of stones remaining, let $x$ be the index of the pile with the smallest index. Append $x$ to the end of $s$. 2. Select a pile with one or more stones remaining, and remove a stone from that pile. 3. If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process. We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers $1,2,3,...,N$, how many times does it occur in the lexicographically smallest sequence? ## Constraints * $1 ≤ N ≤ 10^{5}$ * $1 ≤ a_i ≤ 10^{9}$ ## Input The input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_{N}$ [samples]

Samples

Input #1

2
1 2

Output #1

2
1

The lexicographically smallest sequence is constructed as follows:

*   Since the pile with the largest number of stones remaining is pile $2$, append $2$ to the end of $s$. Then, remove a stone from pile $2$.
*   Since the piles with the largest number of stones remaining are pile $1$ and $2$, append $1$ to the end of $s$ (we take the smallest index). Then, remove a stone from pile $2$.
*   Since the pile with the largest number of stones remaining is pile $1$, append $1$ to the end of $s$. Then, remove a stone from pile $1$.

The resulting sequence is $(2,1,1)$. In this sequence, $1$ occurs twice, and $2$ occurs once.

Input #2

10
1 2 1 3 2 4 2 5 8 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Frequency",
    "description": {
      "content": "Snuke loves constructing integer sequences. There are $N$ piles of stones, numbered $1$ through $N$. The pile numbered $i$ consists of $a_i$ stones. Snuke will construct an integer sequence $s$ of len",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc069_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke loves constructing integer sequences.\nThere are $N$ piles of stones, numbered $1$ through $N$. The pile numbered $i$ consists of $a_i$ stones.\nSnuke will construct an integer sequence $s$ of len...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments