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;
vector<vector<long long int>> grp;
vector<long long int> sum;
long long int dfs(long long int i, long long int p, long long int val) {
  long long int ans = 0;
  if ((sum[i] != -1) && (sum[i] >= val))
    ans += (sum[i] - val);
  else if (sum[i] != -1) {
    cout << -1 << endl;
    exit(0);
  } else {
    long long int mn = INT_MAX;
    for (long long int u : grp[i]) {
      if (u != p) mn = min(mn, sum[u] - val);
    }
    if ((mn >= 0) && (mn < INT_MAX)) {
      ans += mn;
      val += mn;
    }
  }
  for (long long int u : grp[i]) {
    if (u != p) {
      if (sum[i] != -1)
        ans += dfs(u, i, sum[i]);
      else
        ans += dfs(u, i, val);
    }
  }
  return ans;
}
int32_t main() {
  std::ios_base::sync_with_stdio(false);
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int t;
  t = 1;
  while (t--) {
    long long int n;
    cin >> n;
    grp.assign(n + 1, vector<long long int>());
    sum.assign(n + 1, 0);
    for (long long int i = 2; i <= n; i++) {
      long long int u;
      cin >> u;
      grp[u].push_back(i);
      grp[i].push_back(u);
    }
    for (long long int i = 1; i <= n; i++) {
      long long int u;
      cin >> u;
      sum[i] = u;
    }
    cout << dfs(1, 1, 0) << endl;
  }
  return 0;
}
