A12326 | Sum in the tree

Mitya has a rooted tree with $n$ vertices indexed from $1$ to $n$ , where the root has index $1$ . Each vertex $v$ initially had an integer number $a_v \ge 0$ written on it. For every vertex $v$ Mitya has computed $s_v$ : the sum of all values written on the vertices on the path from vertex $v$ to the root, as well as $h_v$ — the depth of vertex $v$ , which denotes the number of vertices on the path from vertex $v$ to the root. Clearly, $s_1=a_1$ and $h_1=1$ .

Then Mitya erased all numbers $a_v$ , and by accident he also erased all values $s_v$ for vertices with even depth (vertices with even $h_v$ ). Your task is to restore the values $a_v$ for every vertex, or determine that Mitya made a mistake. In case there are multiple ways to restore the values, you're required to find one which minimizes the total sum of values $a_v$ for all vertices in the tree.

The first line contains one integer $n$ — the number of vertices in the tree ( $2 \le n \le 10^5$ ). The following line contains integers $p_2$ , $p_3$ , ... $p_n$ , where $p_i$ stands for the parent of vertex with index $i$ in the tree ( $1 \le p_i < i$ ). The last line contains integer values $s_1$ , $s_2$ , ..., $s_n$ ( $-1 \le s_v \le 10^9$ ), where erased values are replaced by $-1$ .

Output one integer — the minimum total sum of all values $a_v$ in the original tree, or $-1$ if such tree does not exist.