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;
const int MAXN = 1e5;
long long s[MAXN + 2];
long long a[MAXN + 2];
long long respuesta;
int p[MAXN + 2];
int nivel[MAXN + 2];
vector<int> hijos[MAXN + 2];
void matate() {
  cout << "-1" << '\n';
  exit(0);
}
void dfs(int nodo) {
  if (nivel[nodo] & 1) {
    if (s[nodo] == -1) matate();
  } else {
    if (s[nodo] != -1) matate();
  }
  int padre = p[nodo];
  if (s[nodo] == -1) {
    a[nodo] = 0;
    s[nodo] = s[padre];
    long long menor = -1;
    for (const auto& sig : hijos[nodo]) {
      if (s[sig] < s[nodo]) matate();
      if (menor == -1 || s[sig] < menor) menor = s[sig];
    }
    if (menor == -1) menor = s[nodo];
    a[nodo] = menor - s[nodo];
    s[nodo] = menor;
    respuesta += a[nodo];
  } else {
    if (nodo == 0) {
      a[nodo] = s[nodo];
    } else {
      a[nodo] = s[nodo] - s[padre];
    }
    if (a[nodo] < 0) matate();
    respuesta += a[nodo];
  }
  for (const auto& sig : hijos[nodo]) {
    nivel[sig] = nivel[nodo] + 1;
    dfs(sig);
  }
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i < n; ++i) {
    cin >> p[i];
    p[i]--;
    hijos[p[i]].push_back(i);
  }
  for (int i = 0; i < n; ++i) cin >> s[i];
  respuesta = 0;
  nivel[0] = 1;
  dfs(0);
  cout << respuesta << '\n';
  return 0;
}
