Problem Statement

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

Outputs

If it is possible to allocate colors and weights to the vertices so that the condition is satisfied, print POSSIBLE; otherwise, print IMPOSSIBLE.