Tree Game

AtCoder

IDagc010_f

Time2000ms

Memory256MB

Difficulty—

There is a tree with $N$ vertices, numbered $1$ through $N$. The $i$\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$. Currently, there are $A_i$ stones placed on vertex $i$. Takahashi and Aoki will play a game using this tree. First, Takahashi will select a vertex and place a piece on it. Then, starting from Takahashi, they will alternately perform the following operation: * Remove one stone from the vertex currently occupied by the piece. * Then, move the piece to a vertex that is adjacent to the currently occupied vertex. The player who is left with no stone on the vertex occupied by the piece and thus cannot perform the operation, loses the game. Find all the vertices $v$ such that Takahashi can place the piece on $v$ at the beginning and win the game. ## Constraints * $2 ≦ N ≦ 3000$ * $1 ≦ a_i,b_i ≦ N$ * $0 ≦ A_i ≦ 10^9$ * The given graph is a tree. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ … $A_N$ $a_1$ $b_1$ : $a_{N-1}$ $b_{N-1}$ [samples]

Samples

Input #1

Output #1

2

The following is one possible progress of the game when Takahashi places the piece on vertex $2$:

*   Takahashi moves the piece to vertex $1$. The number of the stones on each vertex is now: $(1,1,3)$.
*   Aoki moves the piece to vertex $2$. The number of the stones on each vertex is now: $(0,1,3)$.
*   Takahashi moves the piece to vertex $1$. The number of the stones on each vertex is now: $(0,0,3)$.
*   Aoki cannot take a stone from the vertex, and thus Takahashi wins.

Input #2

Output #2

1 2

Input #3

Output #3

Note that the correct output may be an empty line.

API Response (JSON)

{
  "problem": {
    "name": "Tree Game",
    "description": {
      "content": "There is a tree with $N$ vertices, numbered $1$ through $N$. The $i$\\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$. Currently, there are $A_i$ stones placed on vertex $i$. Takahashi and Aok",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc010_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a tree with $N$ vertices, numbered $1$ through $N$. The $i$\\-th of the $N-1$ edges connects vertices $a_i$ and $b_i$.\nCurrently, there are $A_i$ stones placed on vertex $i$. Takahashi and Aok...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments