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;
const long long N = 1e5 + 2;
long long s[N], s12[N];
set<int> s1[N];
int main() {
  int n;
  cin >> n;
  for (int i = 2; i <= n; i++) {
    int p;
    cin >> p;
    s1[p].insert(i);
  }
  for (int i = 1; i <= n; i++) cin >> s[i];
  long long sum = s[1];
  queue<int> file;
  file.push(1);
  while (!file.empty()) {
    int u = file.front();
    long long sum1 = s[u];
    file.pop();
    if (s[u] == -1) {
      if (s1[u].empty())
        ;
      else {
        long long minn = 1e10;
        for (set<int>::iterator it = s1[u].begin(); it != s1[u].end(); it++) {
          file.push(*it);
          if (s[*it] < minn) minn = s[*it];
        }
        if (s12[u] <= minn) {
          sum += minn - s12[u];
          for (set<int>::iterator it = s1[u].begin(); it != s1[u].end(); it++)
            sum += s[*it] - minn;
        } else {
          cout << "-1";
          return 0;
        }
      }
    } else {
      for (set<int>::iterator it = s1[u].begin(); it != s1[u].end(); it++) {
        file.push(*it);
        s12[*it] = s[u];
      }
    }
  }
  cout << sum;
}
