Increment and Swap

AtCoder

IDcf17_exhibition_b

Time2000ms

Memory256MB

Difficulty—

We have a sequence $A$ of length $N$. On this sequence, we can perform the following two kinds of operations: * Swap two adjacent elements. * Select one element, and increment it by $1$. We will repeatedly perform these operations so that $A$ will be a non-decreasing sequence. Find the minimum required number of operations. ## Constraints * $1 ≤ N ≤ 200000$ * $1 ≤ A_i ≤ 10^9$ * $A_i$ is an integer. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $:$ $A_N$ [samples]

Samples

Input #1

Output #1

2

We can turn $A$ into a non-decreasing sequence in two operations:

*   Initially, $A = {4, 1, 8, 8, 7}$.
*   Swap the first two elements. Now, $A = {1, 4, 8, 8, 7}$.
*   Increment the last element by $1$. Now, $A = {1, 4, 8, 8, 8}$.

Input #2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Increment and Swap",
    "description": {
      "content": "We have a sequence $A$ of length $N$. On this sequence, we can perform the following two kinds of operations: *   Swap two adjacent elements.      *   Select one element, and increment it by $1$.    ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "cf17_exhibition_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence $A$ of length $N$.\nOn this sequence, we can perform the following two kinds of operations:\n\n*   Swap two adjacent elements.\n    \n*   Select one element, and increment it by $1$.\n   ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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