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 int INF = 2147483647;
const unsigned int UINF = 0xffffffff;
void print_array(int v[], int n) {
  for (int i = int(0); i < int(n); i++) cout << v[i] << ' ';
  cout << endl;
}
void print_vector(vector<int> V) {
  vector<int>::iterator it;
  for (it = V.begin(); it != V.end(); it++) cout << *it << ' ';
  cout << endl;
}
void print_array_pairs(pair<int, int> v[], int n) {
  for (int i = int(0); i < int(n); i++)
    cout << '(' << v[i].first << ", " << v[i].second << ") ";
  cout << endl;
}
void print_vector_pairs(vector<pair<int, int> > P) {
  vector<pair<int, int> >::iterator it;
  for (it = P.begin(); it != P.end(); it++)
    cout << '(' << it->first << ", " << it->second << ") ";
  cout << endl;
}
const int MOD = 1e9 + 7;
long long int sum[100100], answer = 0;
vector<int> adj[100100];
void dfs(int me, int parent = 0) {
  long long int value;
  if (sum[me] == -1) {
    long long int mn = INF;
    for (auto v : adj[me]) mn = min(mn, sum[v]);
    if (adj[me].empty()) {
      value = 0;
      sum[me] = sum[parent];
    } else {
      if (sum[parent] > mn) {
        cout << "-1\n";
        exit(0);
      }
      value = mn - sum[parent];
      sum[me] = mn;
    }
  } else
    value = sum[me] - sum[parent];
  answer += value;
  for (auto v : adj[me]) dfs(v, me);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n, x;
  cin >> n;
  for (int i = int(0); i < int(n - 1); i++) {
    cin >> x;
    adj[x].push_back(i + 2);
  }
  for (int i = int(1); i <= int(n); i++) cin >> sum[i];
  dfs(1, 0);
  cout << answer << "\n";
  return 0;
}
