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;
map<int, int> book;
const int Maxn = 2e5 + 10;
int a[Maxn], b[Maxn], flag = 0;
long long sum;
vector<int> vec[Maxn];
void dfs1(int u, int v) {
  for (int i = 0; i < vec[u].size(); i++) {
    int t = vec[u][i];
    if (t != v) {
      if (a[t] < a[u]) flag = 1;
      sum += a[t] - a[u];
      dfs1(t, u);
    }
  }
}
int dfs(int x, int v) {
  if (v != -1 && vec[x].size() == 1) {
    if (a[x] == -1) a[x] = a[v];
  }
  for (int i = 0; i < vec[x].size(); i++) {
    int t = vec[x][i];
    if (t == v) continue;
    int sum = dfs(t, x);
    if (b[x] == 1) {
      if (a[x] != -1)
        a[x] = min(sum, a[x]);
      else
        a[x] = sum;
    }
  }
  return a[x];
}
int main() {
  int n, maxn = 0;
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) {
    int u;
    scanf("%d", &u);
    vec[u].push_back(i);
    vec[i].push_back(u);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    if (a[i] == -1) b[i] = 1;
  }
  sum = a[1];
  dfs(1, -1);
  dfs1(1, -1);
  if (flag == 1)
    printf("-1\n");
  else
    printf("%I64d\n", sum);
  return 0;
}
