Sum in the tree

给定一个以 $1$ 为根节点，大小为 $n$ 的树。根节点深度为 $1$。 树上原本每个节点都有一个非负权值 $a_i$，记 $s_i$ 表示从 $i$ 号节点到根节点的路径上所有点的权值和，包括根节点及其本身。 现在给你每个节点的 $s_i$。深度为偶数的节点的 $s_i$ 为 $-1$，表示该节点的 $s_i$ 未知。 请你还原树的每个节点的权值 $a_i$。使得其满足所有深度为奇数的节点的 $s_i$。并输出所有满足情况的方案中，$\sum a_i$ 的最小值。 如果无解，则输出 $-1$。

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.

5
1 1 1 1
1 -1 -1 -1 -1

1

5
1 2 3 1
1 -1 2 -1 -1

2

3
1 2
2 -1 1

-1