Ameba

AtCoder

IDabc274_c

Time2000ms

Memory256MB

Difficulty—

You observed amoebae and kept some records. Initially, there was one amoeba, numbered $1$. You made $N$ records. According to the $i$\-th record, the amoeba numbered $A_i$ disappeared by dividing itself into two new amoebae, which were then numbered $2i$ and $2i+1$. Here, amoeba $A_i$ is said to be the parent of amoebae $2i$ and $2i+1$. For each $k=1,\ldots,2N+1$, how many generations away is amoeba $k$ from amoeba $1$? ## Constraints * $1 \leq N \leq 2\times 10^5$ * The records are consistent. That is: * $1\leq A_i \leq 2i-1$. * $A_i$ are distinct integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

2
1 2

Output #1

0
1
1
2
2

From amoeba $1$, amoebae $2$ and $3$ were born. From amoeba $2$, amoebae $4$ and $5$ were born.

*   Amoeba $1$ is zero generations away from amoeba $1$.
*   Amoeba $2$ is one generation away from amoeba $1$.
*   Amoeba $3$ is one generation away from amoeba $1$.
*   Amoeba $4$ is one generation away from amoeba $2$, and two generations away from amoeba $1$.
*   Amoeba $5$ is one generation away from amoeba $2$, and two generations away from amoeba $1$.

Input #2

4
1 3 5 2

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Ameba",
    "description": {
      "content": "You observed amoebae and kept some records. Initially, there was one amoeba, numbered $1$. You made $N$ records. According to the $i$\\-th record, the amoeba numbered $A_i$ disappeared by dividing itse",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc274_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You observed amoebae and kept some records.\nInitially, there was one amoeba, numbered $1$.\nYou made $N$ records. According to the $i$\\-th record, the amoeba numbered $A_i$ disappeared by dividing itse...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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