{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 1$ $000$\n*   $1 \\leq P_i \\leq i - 1$\n*   $0 \\leq X_i \\leq 5$ $000$"},{"iden":"inputs","content":"Input is given from Standard Input in the following format:\n\n$N$\n$P_2$ $P_3$ $...$ $P_N$\n$X_1$ $X_2$ $...$ $X_N$"},{"iden":"sample input 1","content":"3\n1 1\n4 3 2"},{"iden":"sample output 1","content":"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."},{"iden":"sample input 2","content":"3\n1 2\n1 2 3"},{"iden":"sample output 2","content":"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."},{"iden":"sample input 3","content":"8\n1 1 1 3 4 5 5\n4 1 6 2 2 1 3 3"},{"iden":"sample output 3","content":"POSSIBLE"},{"iden":"sample input 4","content":"1\n\n0"},{"iden":"sample output 4","content":"POSSIBLE"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}