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;
unordered_map<int, vector<int> > g;
int sum[1000001];
int vertex[100001];
int mini[100001];
bool check = 1;
int minfill(int parent, int cur) {
  if (g[cur].size() == 0) {
    if (sum[cur] == -1) {
      mini[cur] = INT_MAX;
      return INT_MAX;
    } else {
      mini[cur] = sum[cur];
      return sum[cur];
    }
  }
  if (mini[cur] != -1) {
    return mini[cur];
  }
  int minsum = INT_MAX;
  for (int i = 0; i < g[cur].size(); i++) {
    int ans = minfill(cur, g[cur][i]);
    if (ans < minsum) {
      minsum = ans;
    }
  }
  if (sum[cur] == -1) {
    mini[cur] = minsum;
    return mini[cur];
  } else {
    mini[cur] = sum[cur];
    return sum[cur];
  }
}
void fill(int parent, int cur) {
  if (g[cur].size() == 0) {
    int val = 0;
    if (mini[cur] != INT_MAX) {
      sum[cur] = mini[cur];
      val = sum[cur] - sum[parent];
      vertex[cur] = val;
    } else {
      sum[cur] = sum[parent];
      val = 0;
      vertex[cur] = 0;
    }
  }
  if (sum[cur] == -1) {
    if (mini[cur] == INT_MAX) {
      sum[cur] = sum[parent];
      vertex[cur] = 0;
    } else {
      sum[cur] = mini[cur];
      int val = sum[cur] - sum[parent];
      vertex[cur] = val;
    }
    for (int i = 0; i < g[cur].size(); i++) {
      fill(cur, g[cur][i]);
    }
  } else {
    int val = sum[cur] - sum[parent];
    vertex[cur] = val;
    for (int i = 0; i < g[cur].size(); i++) {
      fill(cur, g[cur][i]);
    }
  }
}
int main() {
  std::ios_base::sync_with_stdio(false);
  memset(sum, -1, sizeof(sum));
  memset(vertex, 0, sizeof(vertex));
  memset(mini, -1, sizeof(mini));
  int n;
  cin >> n;
  for (int i = 2; i <= n; i++) {
    int par;
    cin >> par;
    g[par].push_back(i);
  }
  sum[0] = 0;
  for (int i = 1; i <= n; i++) {
    int a;
    cin >> a;
    sum[i] = a;
  }
  int waste = minfill(0, 1);
  fill(0, 1);
  long long int ans = 0;
  for (int i = 1; i <= n; i++) {
    if (vertex[i] < 0) {
      cout << "-1";
      return 0;
    }
    ans += vertex[i];
  }
  cout << ans;
}
