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<long long int> adj[100100];
long long int sum[100100];
long long int a[100100];
long long int minSum[100100];
void dfs1(long long int node, long long int pa, long long int dep) {
  if (dep % 2 == 1)
    minSum[node] = sum[node];
  else
    minSum[node] = 1e18;
  for (auto n : adj[node]) {
    if (n == pa) continue;
    dfs1(n, node, dep + 1);
    if (dep % 2 == 0) {
      minSum[node] = min(minSum[node], minSum[n]);
    }
  }
  if (minSum[node] == 1e18) minSum[node] = minSum[pa];
}
bool dfs2(long long int node, long long int pa, long long int s) {
  if (minSum[node] < s) return false;
  a[node] = minSum[node] - s;
  bool ans = true;
  for (auto n : adj[node]) {
    if (n == pa) continue;
    ans = (ans and dfs2(n, node, minSum[node]));
  }
  return ans;
}
void solve() {
  long long int n;
  cin >> n;
  for (__typeof(n + 1) i = (2) - ((2) > (n + 1));
       i != (n + 1) - ((2) > (n + 1)); i += 1 - 2 * ((2) > (n + 1))) {
    long long int p;
    cin >> p;
    adj[i].emplace_back(p);
    adj[p].emplace_back(i);
  }
  for (__typeof(n + 1) i = (1) - ((1) > (n + 1));
       i != (n + 1) - ((1) > (n + 1)); i += 1 - 2 * ((1) > (n + 1))) {
    cin >> sum[i];
  }
  dfs1(1, -1, 1);
  bool ans = dfs2(1, -1, 0);
  if (!ans) {
    cout << -1 << endl;
    return;
  }
  long long int s = 0;
  for (__typeof(n + 1) i = (1) - ((1) > (n + 1));
       i != (n + 1) - ((1) > (n + 1)); i += 1 - 2 * ((1) > (n + 1))) {
    s += a[i];
  }
  cout << s << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int t;
  t = 1;
  while (t--) {
    solve();
  }
}
