#D528. Sum in the tree
Sum in the tree
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 ≥ 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 ≤ n ≤ 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 ≤ p_i < i). The last line contains integer values s_1, s_2, ..., s_n (-1 ≤ s_v ≤ 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
inputFormat
Input
The first line contains one integer n — the number of vertices in the tree (2 ≤ n ≤ 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 ≤ p_i < i). The last line contains integer values s_1, s_2, ..., s_n (-1 ≤ s_v ≤ 10^9), where erased values are replaced by -1.
outputFormat
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
样例
3
1 2
2 -1 1
-1