Minimum Cost Sort

AtCoder

IDarc194_b

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P = (P_1, P_2, \ldots, P_N)$ of $(1, 2, \ldots, N)$. Takahashi can repeatedly perform the following operation on $P$ (possibly zero times): * Choose an integer $i$ satisfying $1 \leq i \leq N-1$. Pay a cost of $i$, and swap $P_i$ and $P_{i+1}$. Find the minimum total cost required to sort $P$ in ascending order. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $(P_1, P_2, \ldots, P_N)$ is a permutation of $(1, 2, \ldots, N)$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\ldots$ $P_N$ [samples]

Samples

Input #1

3
3 2 1

Output #1

4

Takahashi can sort $P$ in ascending order as follows:

*   Pay a cost of $1$ and swap $P_1 = 3$ and $P_2 = 2$. Now, $P = (2, 3, 1)$.
*   Pay a cost of $2$ and swap $P_2 = 3$ and $P_3 = 1$. Now, $P = (2, 1, 3)$.
*   Pay a cost of $1$ and swap $P_1 = 2$ and $P_2 = 1$. Now, $P = (1, 2, 3)$.

The total cost for these operations is $4$, which is the minimum possible.

Input #2

5
2 4 1 3 5

Output #2

Input #3

2
1 2

Output #3

API Response (JSON)

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    "name": "Minimum Cost Sort",
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      "content": "You are given a permutation $P = (P_1, P_2, \\ldots, P_N)$ of $(1, 2, \\ldots, N)$. Takahashi can repeatedly perform the following operation on $P$ (possibly zero times): *   Choose an integer $i$ sati",
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      "statement_type": "Markdown",
      "content": "You are given a permutation $P = (P_1, P_2, \\ldots, P_N)$ of $(1, 2, \\ldots, N)$. Takahashi can repeatedly perform the following operation on $P$ (possibly zero times):\n\n*   Choose an integer $i$ sati...",
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