Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
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A. Sum in the tree

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMitya 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.

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.

Examples

Input

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

Output

1

Input

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

Output

2

Input

3 1 2 2 -1 1

Output

-1

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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