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;
inline long long min(long long a, long long b, long long c) {
  return min(min(a, b), c);
}
inline long long max(long long a, long long b, long long c) {
  return max(max(a, b), c);
}
inline void fastio() {
  ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL);
}
int dx[] = {-1, 0, 1, 0, -1, -1, 1, 1};
int dy[] = {0, 1, 0, -1, -1, 1, 1, -1};
vector<long long> gr[2000006];
long long s[2000006];
long long dfs(long long src, long long par, long long grand_par, long long ht) {
  long long res = 0;
  if (ht % 2 == 0) {
    long long min_x = INT_MAX;
    for (auto child : gr[src]) {
      if (child != par) {
        res += dfs(child, src, par, ht + 1);
        res += s[child] - s[par];
        if (s[child] - s[par] < 0) {
          cout << "-1";
          exit(0);
        }
        min_x = min(min_x, s[child] - s[par]);
      }
    }
    if (min_x != INT_MAX) {
      res -= (min_x * (gr[src].size() - 1));
      res += min_x;
    }
  } else {
    for (auto child : gr[src]) {
      if (child != par) {
        res += dfs(child, src, par, ht + 1);
      }
    }
    if (ht == 1) res += s[1];
  }
  return res;
}
int main() {
  fastio();
  long long n;
  cin >> n;
  for (long long i = 2; i <= n; i++) {
    long long p;
    cin >> p;
    gr[p].push_back(i);
    gr[i].push_back(p);
  }
  for (long long i = 1; i <= n; i++) cin >> s[i];
  cout << dfs(1, 0, 0, 1);
  return 0;
}
