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 maxn = 100000;
const long long inf = 10000000000;
long long n;
long long t[maxn + 2], v[maxn + 2], s[maxn + 2], sum;
vector<long long> G[maxn + 2];
void dfs(long long nod, long long nivel) {
  if (nivel % 2) {
    v[nod] = s[nod] - s[t[nod]];
  } else {
    if (G[nod].size() > 1) {
      long long minim = inf;
      for (auto it : G[nod]) {
        minim = min(minim, s[it] - s[t[nod]]);
      }
      v[nod] = minim;
      s[nod] = s[t[nod]] + minim;
    } else {
      v[nod] = 0;
      s[nod] = s[t[nod]];
    }
  }
  if (G[nod].size()) {
    for (auto it : G[nod]) {
      dfs(it, nivel + 1);
    }
  }
}
int main() {
  cin >> n;
  for (int i = 2; i <= n; i++) {
    cin >> t[i];
    G[t[i]].push_back(i);
  }
  for (int i = 1; i <= n; i++) {
    cin >> s[i];
  }
  for (int i = 2; i <= n; i++) {
    if (s[i] != -1) {
      if (s[i] < s[t[t[i]]]) {
        cout << "-1";
        return 0;
      }
    }
  }
  v[1] = s[1];
  dfs(1, 1);
  for (int i = 1; i <= n; i++) {
    sum = sum + v[i];
  }
  cout << sum;
  return 0;
}
