Negative Doubling

AtCoder

IDcaddi2018_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ positive integers $A_1, A_2, ..., A_N$. Takahashi can perform the following operation on these integers any number of times: * Choose $1 \leq i \leq N$ and multiply the value of $A_i$ by $-2$. Notice that he multiplies it by **minus** two. He would like to make $A_1 \leq A_2 \leq ... \leq A_N$ holds. Find the minimum number of operations required. If it is impossible, print `-1`. ## Constraints * $1 \leq N \leq 200000$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

4
3 1 4 1

Output #1

3

One possible solution is:

*   Choose $i=4$ and multiply the value of $A_4$ by $-2$. $A_1, A_2, A_3, A_4$ are now $3, 1, 4, -2$.
*   Choose $i=1$ and multiply the value of $A_1$ by $-2$. $A_1, A_2, A_3, A_4$ are now $-6, 1, 4, -2$.
*   Choose $i=4$ and multiply the value of $A_4$ by $-2$. $A_1, A_2, A_3, A_4$ are now $-6, 1, 4, 4$.

Input #2

5
1 2 3 4 5

Output #2

0

$A_1 \leq A_2 \leq ... \leq A_N$ holds before any operation is performed.

Input #3

8
657312726 129662684 181537270 324043958 468214806 916875077 825989291 319670097

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Negative Doubling",
    "description": {
      "content": "There are $N$ positive integers $A_1, A_2, ..., A_N$. Takahashi can perform the following operation on these integers any number of times: *   Choose $1 \\leq i \\leq N$ and multiply the value of $A_i$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "caddi2018_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ positive integers $A_1, A_2, ..., A_N$. Takahashi can perform the following operation on these integers any number of times:\n\n*   Choose $1 \\leq i \\leq N$ and multiply the value of $A_i$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments