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
#include <bits/stdc++.h>
using namespace std;
int n;
unsigned long long int sum = 0;
bool ok = true;
class Tree {
  int V;
  list<int> *adj;
  void DFSUntil(int v, bool visited[], int *s, int *depth, int *parent);

 public:
  Tree(int V) {
    this->V = V;
    adj = new list<int>[V + 1];
  }
  void addEdge(int v, int w);
  void DFS(int v, int *s, int *depth, int *parent);
};
void Tree::addEdge(int v, int w) {
  adj[v].push_back(w);
  adj[w].push_back(v);
}
void Tree::DFSUntil(int v, bool visited[], int *s, int *depth, int *parent) {
  visited[v] = true;
  if (v == 1)
    sum += s[v];
  else if (depth[v] == 1) {
    int av = s[v] - s[parent[v]];
    if (av < 0) {
      ok = false;
      return;
    }
    sum += av;
  } else {
    if (adj[v].size() == 1) {
      s[v] = 0;
    }
    if (adj[v].size() != 1) {
      int min = 100000000, av;
      for (auto i = adj[v].begin(); i != adj[v].end(); i++) {
        if (*i != parent[v]) {
          av = s[*i] - s[parent[v]];
          if (av < 0) {
            ok = false;
            return;
          }
          if (av < min) min = av;
        }
      }
      s[v] = s[parent[v]] + min;
      sum += min;
    }
  }
  for (auto i = adj[v].begin(); i != adj[v].end(); i++) {
    if (!visited[*i]) {
      DFSUntil(*i, visited, s, depth, parent);
    }
  }
}
void Tree::DFS(int v, int *s, int *depth, int *parent) {
  bool *visited = new bool[V + 1];
  for (int i = 1; i <= V; i++) visited[i] = false;
  DFSUntil(v, visited, s, depth, parent);
  delete[] visited;
}
int main() {
  cin >> n;
  Tree g(n);
  int *parent = new int[n + 1];
  for (int i = 2; i <= n; i++) {
    int p;
    cin >> p;
    g.addEdge(p, i);
    parent[i] = p;
  }
  int *s = new int[n + 1];
  int *depth = new int[n + 1];
  for (int i = 1; i <= n; i++) {
    cin >> s[i];
    if (s[i] == -1)
      depth[i] = 0;
    else
      depth[i] = 1;
  }
  g.DFS(1, s, depth, parent);
  if (ok == false)
    cout << -1;
  else
    cout << sum;
  delete[] s, depth, parent;
  return 0;
}
