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 N = 1e5;
vector<int> graph[N];
int a[N];
int s[N];
void DFS(int u, int p) {
  if (s[u] == -1) {
    int best = INT_MAX;
    for (int v : graph[u]) {
      if (v != p) {
        best = min(best, s[v]);
      }
    }
    if (best == INT_MAX) {
      best = s[p];
    }
    s[u] = best;
    if (s[u] < s[p]) {
      cout << -1;
      exit(0);
    }
    a[u] = s[u] - s[p];
  } else {
    if (p == -1) {
      a[u] = s[u];
    } else {
      a[u] = s[u] - s[p];
    }
  }
  for (int v : graph[u]) {
    if (v != p) {
      DFS(v, u);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    graph[i].push_back(p - 1);
    graph[p - 1].push_back(i);
  }
  for (int i = 0; i < n; i++) {
    cin >> s[i];
  }
  DFS(0, -1);
  cout << accumulate(a, a + n, 0LL);
  return 0;
}
