Bichrome Tree

AtCoder

IDarc083_c

Time2000ms

Memory256MB

Difficulty—

We have a tree with $N$ vertices. Vertex $1$ is the root of the tree, and the parent of Vertex $i$ ($2 \leq i \leq N$) is Vertex $P_i$. To each vertex in the tree, Snuke will allocate a color, either black or white, and a non-negative integer weight. Snuke has a favorite integer sequence, $X_1, X_2, ..., X_N$, so he wants to allocate colors and weights so that the following condition is satisfied for all $v$. * The total weight of the vertices with the same color as $v$ among the vertices contained in the subtree whose root is $v$, is $X_v$. Here, _the subtree whose root is_ $v$ is the tree consisting of Vertex $v$ and all of its descendants. Determine whether it is possible to allocate colors and weights in this way. ## Constraints * $1 \leq N \leq 1$ $000$ * $1 \leq P_i \leq i - 1$ * $0 \leq X_i \leq 5$ $000$ ## Inputs Input is given from Standard Input in the following format: $N$ $P_2$ $P_3$ $...$ $P_N$ $X_1$ $X_2$ $...$ $X_N$ [samples]

Samples

Input #1

3
1 1
4 3 2

Output #1

POSSIBLE

For example, the following allocation satisfies the condition:

*   Set the color of Vertex $1$ to white and its weight to $2$.
*   Set the color of Vertex $2$ to black and its weight to $3$.
*   Set the color of Vertex $3$ to white and its weight to $2$.

There are also other possible allocations.

Input #2

3
1 2
1 2 3

Output #2

IMPOSSIBLE

If the same color is allocated to Vertex $2$ and Vertex $3$, Vertex $2$ cannot be allocated a non-negative weight.
If different colors are allocated to Vertex $2$ and $3$, no matter which color is allocated to Vertex $1$, it cannot be allocated a non-negative weight.
Thus, there exists no allocation of colors and weights that satisfies the condition.

Input #3

8
1 1 1 3 4 5 5
4 1 6 2 2 1 3 3

Output #3

POSSIBLE

Input #4

1

0

Output #4

POSSIBLE

API Response (JSON)

{
  "problem": {
    "name": "Bichrome Tree",
    "description": {
      "content": "We have a tree with $N$ vertices. Vertex $1$ is the root of the tree, and the parent of Vertex $i$ ($2 \\leq i \\leq N$) is Vertex $P_i$. To each vertex in the tree, Snuke will allocate a color, either ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc083_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a tree with $N$ vertices. Vertex $1$ is the root of the tree, and the parent of Vertex $i$ ($2 \\leq i \\leq N$) is Vertex $P_i$.\nTo each vertex in the tree, Snuke will allocate a color, either ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments