{"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 black or white, and a non-negative integer weight.\nSnuke 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 $v$.\n\n*   The total weight of the vertices with the same color as $v$ among the vertices contained in the subtree whose root is $v$, is $X_v$.\n\nHere, _the subtree whose root is_ $v$ is the tree consisting of Vertex $v$ and all of its descendants.\nDetermine whether it is possible to allocate colors and weights in this way.\n\n## Constraints\n\n*   $1 \\leq N \\leq 1$ $000$\n*   $1 \\leq P_i \\leq i - 1$\n*   $0 \\leq X_i \\leq 5$ $000$\n\n## Inputs\n\nInput is given from Standard Input in the following format:\n\n$N$\n$P_2$ $P_3$ $...$ $P_N$\n$X_1$ $X_2$ $...$ $X_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc083_c","tags":[],"sample_group":[["3\n1 1\n4 3 2","POSSIBLE\n\nFor example, the following allocation satisfies the condition:\n\n*   Set the color of Vertex $1$ to white and its weight to $2$.\n*   Set the color of Vertex $2$ to black and its weight to $3$.\n*   Set the color of Vertex $3$ to white and its weight to $2$.\n\nThere are also other possible allocations."],["3\n1 2\n1 2 3","IMPOSSIBLE\n\nIf the same color is allocated to Vertex $2$ and Vertex $3$, Vertex $2$ cannot be allocated a non-negative weight.\nIf 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.\nThus, there exists no allocation of colors and weights that satisfies the condition."],["8\n1 1 1 3 4 5 5\n4 1 6 2 2 1 3 3","POSSIBLE"],["1\n\n0","POSSIBLE"]],"created_at":"2026-03-03 11:01:14"}}