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 nmax = 1e5 + 42, inf = 1e9 + 42;
int n;
vector<int> adj[nmax];
int sum[nmax];
int depth[nmax];
int parent[nmax];
int main() {
  scanf("%i", &n);
  int x;
  for (int i = 2; i <= n; i++) {
    scanf("%i", &x);
    depth[i] = depth[x] + 1;
    parent[i] = x;
    adj[i].push_back(x);
    adj[x].push_back(i);
  }
  for (int i = 1; i <= n; i++) scanf("%i", &sum[i]);
  for (int i = 1; i <= n; i++)
    if (sum[i] == -1) {
      int mini = inf, maxi = 0;
      for (auto k : adj[i])
        if (depth[k] == depth[i] + 1)
          mini = min(mini, sum[k]);
        else
          maxi = sum[k];
      if (mini == inf) mini = maxi;
      if (mini < maxi) {
        printf("%i\n", -1);
        return 0;
      }
      sum[i] = mini;
    }
  long long ans = 0;
  for (int i = 1; i <= n; i++) ans = ans + sum[i] - sum[parent[i]];
  printf("%lld\n", ans);
  return 0;
}
