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;
signed main() {
  ios_base::sync_with_stdio(false);
  int64_t N;
  cin >> N;
  int64_t par[N + 1];
  vector<int64_t> child[N + 1];
  for (int64_t i = 2; i <= N; i++) {
    cin >> par[i];
    child[par[i]].push_back(i);
  }
  int64_t a[N + 1], s[N + 1];
  for (int64_t i = 1; i <= N; i++) {
    cin >> s[i];
  }
  queue<vector<int64_t> > Q;
  Q.push({1, 1});
  a[1] = s[1];
  while (!Q.empty()) {
    vector<int64_t> c = Q.front();
    Q.pop();
    int64_t dep = c[1], cur = c[0];
    if (dep % 2 == 0) {
      if (child[cur].empty())
        a[cur] = 0;
      else {
        int64_t mini = INT_MAX;
        for (int64_t c : child[cur]) {
          mini = min(s[c] - s[par[cur]], mini);
          Q.push({c, dep + 1});
        }
        if (mini < 0) {
          cout << -1 << "\n";
          return 0;
        }
        a[cur] = mini;
        s[cur] = s[par[cur]] + a[cur];
      }
    } else {
      if (cur != 1) a[cur] = s[cur] - s[par[cur]];
      if (a[cur] < 0) {
        cout << -1 << "\n";
        return 0;
      }
      for (int64_t c : child[cur]) {
        Q.push({c, dep + 1});
      }
    }
  }
  int64_t sum = 0;
  for (int64_t i = 1; i <= N; i++) {
    sum += a[i];
  }
  cout << sum << "\n";
  return 0;
}
