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 main() {
  int n;
  cin >> n;
  vector<vector<int> > graph(n + 1, vector<int>(0, 0));
  for (int i = 2; i <= n; i++) {
    int t;
    cin >> t;
    graph[t].push_back(i);
  }
  vector<int> s(n + 1, 0);
  for (int i = 1; i <= n; i++) cin >> s[i];
  vector<int> news(n + 1, -1);
  vector<int> a(n + 1, -1);
  queue<int> q;
  q.push(1);
  news[1] = 0;
  bool flag = true;
  while (!q.empty() and flag) {
    int i = q.front();
    q.pop();
    if (s[i] == -1) {
      if (graph[i].size() > 0) {
        int minv = INT_MAX;
        for (int j = 0; j < graph[i].size(); j++) {
          minv = min(minv, s[graph[i][j]]);
        }
        if (minv < news[i]) {
          flag = false;
        } else {
          a[i] = minv - news[i];
          news[i] = minv;
          for (int j = 0; j < graph[i].size(); j++) {
            q.push(graph[i][j]);
            news[graph[i][j]] = news[i];
          }
        }
      } else {
        a[i] = 0;
      }
    } else {
      if (news[i] > s[i]) {
        flag = false;
      } else {
        a[i] = s[i] - news[i];
        news[i] = s[i];
        for (int j = 0; j < graph[i].size(); j++) {
          q.push(graph[i][j]);
          news[graph[i][j]] = news[i];
        }
      }
    }
  }
  if (flag) {
    long long sum = 0;
    for (int i = 1; i <= n; i++) sum += a[i];
    cout << sum << "\n";
  } else {
    cout << "-1\n";
  }
  return 0;
}
