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;
long long int n, a[100004], b[100005], c[100005];
std::vector<long long int> adj[100005];
int vis[100005];
long long int w = 0;
void dfs(long long int node) {
  vis[node] = 1;
  if (node == 1)
    c[node] = b[node];
  else {
    if (b[node] == -1) {
      long long int x = 1000000007;
      if (adj[node].size() - 1 <= 1) {
        c[node] = 0;
      } else {
        for (int i = 0; i < adj[node].size(); i++) {
          if (vis[adj[node][i]] == 0) x = min(x, b[adj[node][i]]);
        }
        x = x - b[a[node]];
        c[node] = x;
        if (c[node] < 0) w = 1;
      }
    } else {
      c[node] = b[node] - b[a[a[node]]] - c[a[node]];
      if (c[node] < 0) {
        w = 1;
      }
    }
  }
  for (auto i : adj[node])
    if (!vis[i]) dfs(i);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int TESTS = 1;
  while (TESTS--) {
    cin >> n;
    for (int i = 2; i <= n; i++) {
      cin >> a[i];
      adj[i].push_back(a[i]);
      adj[a[i]].push_back(i);
    }
    for (int i = 1; i <= n; i++) cin >> b[i];
    dfs(1);
    if (w == 1)
      cout << "-1";
    else {
      long long int s = 0;
      for (int i = 1; i <= n; i++) {
        s += c[i];
      }
      cout << s;
    }
  }
  return 0;
}
