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>
const unsigned long long int M = 1000000007;
using namespace std;
long long power(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = x * res;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
long long power(long long x, long long y, long long mod) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = x * res % mod;
    y = y >> 1;
    x = x * x % mod;
  }
  return res;
}
void nik() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
}
long long vis[100005], a[100005];
std::vector<long long> v[100005];
long long sm[100005];
void dfs(long long s, long long psum) {
  vis[s] = 1;
  if (s != 1) {
    if (sm[s] == -1) {
      long long mini = INT_MAX;
      for (auto i : v[s]) {
        if (!vis[i]) mini = min(mini, sm[i]);
      }
      if (mini == INT_MAX) {
        a[s] = 0;
        sm[s] = psum;
      } else {
        if (mini < psum) {
          cout << -1;
          exit(0);
        }
        a[s] = mini - psum;
        sm[s] = mini;
        psum = mini;
      }
    } else {
      if (sm[s] < psum) {
        cout << -1;
        exit(0);
      }
      a[s] = sm[s] - psum;
      psum = sm[s];
    }
  }
  for (auto i : v[s]) {
    if (!vis[i]) dfs(i, psum);
  }
}
signed main() {
  nik();
  long long test = 1;
  while (test--) {
    long long n;
    cin >> n;
    for (long long i = 2; i <= n; i++) {
      long long x;
      cin >> x;
      v[i].push_back(x);
      v[x].push_back(i);
    }
    for (long long i = 1; i <= n; i++) cin >> sm[i];
    long long ans = 0;
    a[1] = sm[1];
    dfs(1, sm[1]);
    for (long long i = 1; i <= n; i++) {
      ans += a[i];
    }
    cout << ans;
  }
  return 0;
}
