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;
typedef struct node_t {
  long long s, a;
  vector<struct node_t *> children;
  struct node_t *parent;
} Node;
long long n;
vector<long long> p, s, a;
vector<Node *> nodes;
bool error = false;
void FillValues(Node *root) {
  if (!root) {
    return;
  }
  if (root->s == -1) {
    if (root->children.empty()) {
      root->a = 0;
      root->s = root->parent->s;
    } else {
      long long mins = LLONG_MAX;
      for (auto c : root->children) {
        if (c->s < mins) {
          mins = c->s;
        }
      }
      root->s = mins;
      root->a = root->s - root->parent->s;
      if (root->a < 0) {
        cout << -1 << endl;
        exit(0);
      }
    }
  } else if (root->parent && root->parent->parent) {
    root->a = root->s - root->parent->s;
    if (root->a < 0) {
      cout << -1 << endl;
      exit(0);
    }
  }
  for (auto c : root->children) {
    FillValues(c);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n;
  cin >> n;
  s.push_back(0);
  p.push_back(0);
  a.push_back(0);
  p.push_back(0);
  for (long long i = 2; i <= n; i++) {
    long long t;
    cin >> t;
    p.push_back(t);
  }
  for (long long i = 1; i <= n; i++) {
    long long t;
    cin >> t;
    s.push_back(t);
  }
  a.push_back(s[1]);
  nodes.push_back(nullptr);
  for (long long i = 1; i <= n; i++) {
    Node *node = new Node;
    nodes.push_back(node);
  }
  for (long long i = 1; i <= n; i++) {
    nodes[i]->s = s[i];
    nodes[i]->parent = nodes[p[i]];
    if (nodes[i]->parent) {
      nodes[i]->parent->children.push_back(nodes[i]);
    }
  }
  nodes[1]->a = s[1];
  FillValues(nodes[1]);
  long long sum = 0;
  for (Node *n : nodes) {
    if (n) sum += n->a;
  }
  cout << sum << endl;
  for (auto n : nodes) {
    delete n;
  }
  return 0;
}
