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;
int n;
vector<int> edge[100010];
int s[100010], p[100010];
bool dfsCheck(int u, int b) {
  if ((s[u] < b) && (s[u] != -1)) {
    return false;
  } else if (s[u] > b) {
    b = s[u];
  }
  for (int v : edge[u]) {
    if (!dfsCheck(v, b)) {
      return false;
    }
  }
  return true;
}
void dfsSet(int u) {
  int b = INT_MAX;
  bool has_child = false;
  for (int v : edge[u]) {
    dfsSet(v);
    b = min(s[v], b);
    has_child = true;
  }
  if ((s[u] == -1) && has_child) {
    s[u] = b;
  } else if (s[u] == -1) {
    s[u] = s[p[u]];
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  p[1] = 0;
  s[0] = 0;
  for (int i = 2; i <= n; i++) {
    cin >> p[i];
    edge[p[i]].push_back(i);
  }
  for (int i = 1; i <= n; i++) {
    cin >> s[i];
  }
  if (!dfsCheck(1, 0)) {
    cout << -1 << endl;
    return 0;
  }
  dfsSet(1);
  long long res = 0;
  for (int i = 1; i <= n; i++) {
    res += (long long)(s[i] - s[p[i]]);
  }
  printf("%lld\n", res);
  return 0;
}
