Wandering TKHS

AtCoder

IDagc029_e

Time2000ms

Memory256MB

Difficulty—

Takahashi's office has $N$ rooms. Each room has an ID from $1$ to $N$. There are also $N-1$ corridors, and the $i$\-th corridor connects Room $a_i$ and Room $b_i$. It is known that we can travel between any two rooms using only these corridors. Takahashi has got lost in one of the rooms. Let this room be $r$. He decides to get back to his room, Room $1$, by repeatedly traveling in the following manner: * Travel to the room with the smallest ID among the rooms that are adjacent to the rooms already visited, but not visited yet. Let $c_r$ be the number of travels required to get back to Room $1$. Find all of $c_2,c_3,...,c_N$. Note that, no matter how many corridors he passes through in a travel, it still counts as one travel. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq a_i,b_i \leq N$ * $a_i \neq b_i$ * The graph given as input is a tree. ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $b_1$ $:$ $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

5 5 5 1 5

For example, if Takahashi was lost in Room $2$, he will travel as follows:

*   Travel to Room $6$.
*   Travel to Room $3$.
*   Travel to Room $4$.
*   Travel to Room $5$.
*   Travel to Room $1$.

Input #2

Output #2

1 2 3 4 5

Input #3

Output #3

7 5 3 1 3 4 7 4 5

API Response (JSON)

{
  "problem": {
    "name": "Wandering TKHS",
    "description": {
      "content": "Takahashi's office has $N$ rooms. Each room has an ID from $1$ to $N$. There are also $N-1$ corridors, and the $i$\\-th corridor connects Room $a_i$ and Room $b_i$. It is known that we can travel betwe",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc029_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi's office has $N$ rooms. Each room has an ID from $1$ to $N$. There are also $N-1$ corridors, and the $i$\\-th corridor connects Room $a_i$ and Room $b_i$. It is known that we can travel betwe...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments