Squeezing Slimes

AtCoder

IDcode_festival_2017_quala_f

Time2000ms

Memory256MB

Difficulty—

There are $A$ slimes lining up in a row. Initially, the sizes of the slimes are all $1$. Snuke can repeatedly perform the following operation. * Choose a positive even number $M$. Then, select $M$ consecutive slimes and form $M / 2$ pairs from those slimes as follows: pair the $1$\-st and $2$\-nd of them from the left, the $3$\-rd and $4$\-th of them, $...$, the $(M-1)$\-th and $M$\-th of them. Combine each pair of slimes into one larger slime. Here, the size of a combined slime is the sum of the individual slimes before combination. The order of the $M / 2$ combined slimes remain the same as the $M / 2$ pairs of slimes before combination. Snuke wants to get to the situation where there are exactly $N$ slimes, and the size of the $i$\-th ($1 ≤ i ≤ N$) slime from the left is $a_i$. Find the minimum number of operations required to achieve his goal. Note that $A$ is not directly given as input. Assume $A = a_1 + a_2 + ... + a_N$. ## Constraints * $1 ≤ N ≤ 10^5$ * $a_i$ is an integer. * $1 ≤ a_i ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

2
3 3

Output #1

2

One way to achieve Snuke's goal is as follows. Here, the selected slimes are marked in bold.

*   (1, **1**, **1**, **1**, **1**, 1) → (1, **2**, **2**, 1)
*   (**1**, **2**, **2**, **1**) → (**3**, **3**)

Input #2

4
2 1 2 2

Output #2

2

One way to achieve Snuke's goal is as follows.

*   (**1**, **1**, 1, 1, 1, 1, 1) → (**2**, 1, 1, 1, 1, 1)
*   (2, 1, **1**, **1**, **1**, **1**) → (2, 1, **2**, **2**)

Input #3

1
1

Output #3

Input #4

10
3 1 4 1 5 9 2 6 5 3

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Squeezing Slimes",
    "description": {
      "content": "There are $A$ slimes lining up in a row. Initially, the sizes of the slimes are all $1$. Snuke can repeatedly perform the following operation. *   Choose a positive even number $M$. Then, select $M$ ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "code_festival_2017_quala_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $A$ slimes lining up in a row. Initially, the sizes of the slimes are all $1$.\nSnuke can repeatedly perform the following operation.\n\n*   Choose a positive even number $M$. Then, select $M$ ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments