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;
using ll = long long;
vector<char> ReadLine() {
  vector<char> line;
  char c;
  do {
    c = getchar();
  } while (!isalnum(c) && !ispunct(c));
  do {
    line.push_back(c);
    c = getchar();
  } while (isalnum(c) || ispunct(c));
  return line;
}
int n;
vector<vector<int>> adj;
vector<ll> sums;
ll avsum = 0;
bool valid_tree = true;
void Load() {
  scanf("%d", &n);
  adj.resize(n + 1);
  sums.resize(n + 1);
  for (int i = 2; i <= n; ++i) {
    int par;
    scanf("%d", &par);
    adj[i].push_back(par);
    adj[par].push_back(i);
  }
  for (int i = 1; i <= n; ++i) {
    scanf("%lld", &sums[i]);
  }
}
void DfsEven(int v, int parent_v, ll parent_sum);
void DfsOdd(int v, int parent_v) {
  for (int cv : adj[v]) {
    if (cv == parent_v) continue;
    DfsEven(cv, v, sums[v]);
  }
}
void DfsEven(int v, int parent_v, ll parent_sum) {
  if (adj[v].size() == 1) return;
  ll min_child_sum = LLONG_MAX;
  for (int cv : adj[v]) {
    if (cv == parent_v) continue;
    if (sums[cv] < parent_sum) {
      valid_tree = false;
      return;
    }
    min_child_sum = min(min_child_sum, sums[cv]);
  }
  avsum += min_child_sum - parent_sum;
  for (int cv : adj[v]) {
    if (cv == parent_v) continue;
    avsum += sums[cv] - min_child_sum;
    DfsOdd(cv, v);
  }
}
void Solve() {
  avsum += sums[1];
  DfsOdd(1, 0);
  if (valid_tree) {
    printf("%lld\n", avsum);
  } else {
    puts("-1");
  }
}
int main() {
  Load();
  Solve();
}
