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 bool debug = 0;
int n;
int p[100005], a[100005], s[100005];
vector<int> c[100005];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n;
  p[0] = -1;
  for (int i = (1); i < (n); ++i) {
    cin >> p[i];
    p[i]--;
    c[p[i]].push_back(i);
  }
  stack<int> odds;
  stack<int> evens;
  for (int i = (0); i < (n); ++i) {
    a[i] = -1;
    cin >> s[i];
    if (s[i] == -1)
      evens.push(i);
    else
      odds.push(i);
  }
  long long ret = 0;
  while (!evens.empty()) {
    int tmp = evens.top();
    evens.pop();
    int ps = s[p[tmp]];
    int mch = -1;
    for (auto ch : c[tmp]) {
      if (s[ch] < ps) {
        cout << -1 << endl;
        exit(0);
      } else {
        if (mch == -1)
          mch = s[ch];
        else
          mch = min(mch, s[ch]);
      }
    }
    if (mch == -1) mch = ps;
    s[tmp] = mch;
    a[tmp] = mch - ps;
    ret += a[tmp];
    if (debug) cout << tmp << " " << a[tmp] << endl;
  }
  if (debug) cout << "end of even" << endl;
  while (!odds.empty()) {
    int tmp = odds.top();
    odds.pop();
    if (p[tmp] == -1)
      a[tmp] = s[tmp];
    else {
      a[tmp] = s[tmp] - s[p[tmp]];
    }
    if (a[tmp] < 0) {
      cout << -1 << endl;
      exit(0);
    }
    ret += a[tmp];
    if (debug) cout << tmp << " " << a[tmp] << endl;
  }
  cout << ret << endl;
  return 0;
}
