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>> graph;
vector<long long> sum;
vector<long long> a;
vector<bool> visit;
void DFS(long long root) {
  visit[root] = true;
  long long minimum = INT32_MAX;
  long long parent;
  for (auto &x : graph[root]) {
    if (!visit[x] && sum[root] == -1) {
      minimum > sum[x] ? minimum = sum[x] : minimum = minimum;
    } else if (visit[x]) {
      parent = x;
    }
  }
  minimum == INT32_MAX &&root != 1 ? minimum = sum[parent] : minimum = minimum;
  sum[root] == -1 ? sum[root] = minimum : sum[root] = sum[root];
  root == 1 ? a[root] = sum[root] : a[root] = sum[root] - sum[parent];
  for (auto &x : graph[root]) {
    if (!visit[x]) DFS(x);
  }
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long v;
  cin >> v;
  graph.resize(v + 1);
  sum.resize(v + 1);
  a.resize(v + 1);
  visit.resize(v + 1, false);
  for (long long i = 2; i <= v; i++) {
    long long parent;
    cin >> parent;
    graph[i].push_back(parent);
    graph[parent].push_back(i);
  }
  for (long long i = 1; i <= v; i++) {
    long long s;
    cin >> s;
    sum[i] = s;
  }
  a[1] = sum[1];
  DFS(1);
  long long sumOfa = 0;
  for (long long i = 1; i <= v; i++) {
    if (a[i] >= 0)
      sumOfa += a[i];
    else {
      sumOfa = -1;
      break;
    }
  }
  cout << sumOfa << endl;
}
