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;
struct elem {
  int parent;
  vector<int> next;
  int sum;
  int val;
  elem() {
    parent = 0;
    sum = -2;
    val = -2;
  }
};
elem arr[100000 + 7];
int bfs(int index, long long int sTillNow) {
  if (arr[index].val < 0 && arr[index].sum < 0) {
    bool flag = false;
    int temp = INT_MAX;
    for (int i = 0; i < arr[index].next.size(); i++) {
      if (arr[arr[index].next[i]].sum >= 0) {
        flag = true;
        temp = min(temp, arr[arr[index].next[i]].sum);
      }
    }
    if (!flag)
      arr[index].val = 0;
    else if (temp < sTillNow)
      return -1;
    else
      arr[index].val = temp - sTillNow;
  } else if (arr[index].val < 0 && arr[index].sum >= 0) {
    if (arr[index].sum < sTillNow) return -1;
    arr[index].val = arr[index].sum - sTillNow;
  }
  sTillNow += arr[index].val;
  for (int i = 0; i < arr[index].next.size(); i++) {
    if (bfs(arr[index].next[i], 1LL * sTillNow) == -1) return -1;
  }
  return sTillNow;
}
int main() {
  ios_base::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 2; i < n + 1; i++) {
    cin >> arr[i].parent;
    arr[arr[i].parent].next.push_back(i);
  }
  for (int i = 1; i < n + 1; i++) {
    cin >> arr[i].sum;
  }
  arr[1].val = arr[1].sum;
  for (int i = 0; i < arr[1].next.size(); i++) {
    if (bfs(arr[1].next[i], 1LL * arr[1].val) == -1) {
      cout << -1;
      return 0;
    }
  }
  long long int sum = 0;
  for (int i = 1; i < n + 1; i++) {
    sum += arr[i].val;
  }
  cout << sum << endl;
  return 0;
}
