log

AtCoder

IDarc109_b

Time2000ms

Memory256MB

Difficulty—

Snuke is visiting a shop in Tokyo called 109 to buy some logs. He wants $n$ logs: one of length $1$, one of length $2$, $...$, and one of length $n$. The shop has $n+1$ logs in stock: one of length $1$, one of length $2$, $\dots$, and one of length $n+1$. Each of these logs is sold for $1$ yen (the currency of Japan). He can cut these logs as many times as he wants after buying them. That is, he can get $k$ logs of length $L_1, \dots, L_k$ from a log of length $L$, where $L = L_1 + \dots + L_k$. He can also throw away unwanted logs. Snuke wants to spend as little money as possible to get the logs he wants. Find the minimum amount of money needed to get $n$ logs of length $1$ to $n$. ## Constraints * $1 \leq n \leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $n$ [samples]

Samples

Input #1

Output #1

3

One way to get the logs he wants with $3$ yen is:

*   Buy logs of length $2$, $4$, and $5$.
*   Cut the log of length $5$ into two logs of length $1$ each and a log of length $3$.
*   Throw away one of the logs of length $1$.

Input #2

109109109109109109

Output #2

109109108641970782

API Response (JSON)

{
  "problem": {
    "name": "log",
    "description": {
      "content": "Snuke is visiting a shop in Tokyo called 109 to buy some logs. He wants $n$ logs: one of length $1$, one of length $2$, $...$, and one of length $n$. The shop has $n+1$ logs in stock: one of length $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": "arc109_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke is visiting a shop in Tokyo called 109 to buy some logs. He wants $n$ logs: one of length $1$, one of length $2$, $...$, and one of length $n$. The shop has $n+1$ logs in stock: one of length $1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments