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 dfs(vector<vector<int> > &v, int node, vector<int> &val, vector<int> &a,
        int parent, int psum, int d) {
  int n = v[node].size();
  if (d % 2 && a[node] < psum)
    return 0;
  else if (d % 2)
    val[node] = a[node] - psum;
  else {
    int minimum = INT_MAX;
    for (int i = 0; i < n; i++) minimum = min(minimum, a[v[node][i]] - psum);
    if (minimum >= 0 && n) val[node] = minimum;
  }
  for (int i = 0; i < n; i++) {
    if (dfs(v, v[node][i], val, a, node, psum + val[node], d + 1) == 0)
      return 0;
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  vector<vector<int> > v(n);
  for (int i = 1; i <= n - 1; i++) {
    int parent;
    cin >> parent;
    parent--;
    v[parent].push_back(i);
  }
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<int> val(n);
  if (dfs(v, 0, val, a, 0, 0, 1) == 0)
    cout << -1 << endl;
  else {
    long long int sum = 0;
    for (int i = 0; i < n; i++) sum = sum + val[i];
    cout << sum << endl;
  }
  return 0;
}
