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