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;
int n;
string s;
vector<vector<int>> G;
vector<int> Cost, RealCost, Par;
void dfs(int v, int par, int h) {
  if (h) {
    int mi = 2e9;
    if ((long long)(G[v]).size() == 1) {
      mi = Cost[par];
    }
    for (auto u : G[v]) {
      if (u == par) {
        continue;
      }
      mi = min(Cost[u], mi);
    }
    if (mi < Cost[par]) {
      cout << -1;
      exit(0);
    } else {
      RealCost[v] = mi - Cost[par];
    }
    for (auto u : G[v]) {
      if (u == par) {
        continue;
      }
      dfs(u, v, h ^ 1);
    }
    return;
  } else {
    if (v == 0) {
      RealCost[v] = Cost[v];
      for (auto u : G[v]) {
        dfs(u, v, h ^ 1);
      }
      return;
    }
    RealCost[v] = Cost[v] - Cost[Par[par]] - RealCost[par];
    for (auto u : G[v]) {
      if (u == par) {
        continue;
      }
      dfs(u, v, h ^ 1);
    }
    return;
  }
}
int main() {
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cin >> n;
  G.resize(n);
  Cost.resize(n);
  RealCost.resize(n);
  Par.resize(n);
  for (int i = 1; i < n; i++) {
    int v;
    cin >> v;
    v--;
    G[i].push_back(v);
    G[v].push_back(i);
    Par[i] = v;
  }
  for (int i = 0; i < n; i++) {
    cin >> Cost[i];
  }
  dfs(0, -1, 0);
  long long ans = 0;
  for (int i = 0; i < n; i++) {
    ans += RealCost[i];
  }
  cout << ans;
}
