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;
using ll = long long;
int const MAXN = 1e5 + 99;
int s[MAXN];
int val[MAXN];
int v;
vector<vector<int>> adj;
bool pos = true;
void dfs(int u, int p, int cur_sum) {
  bool leaf = true;
  if (s[u] == -1) {
    val[u] = 0;
  } else {
    val[u] = s[u] - cur_sum;
    if (val[u] < 0) pos = false;
  }
  for (auto v : adj[u]) {
    if (v == p) continue;
    leaf = false;
    dfs(v, u, cur_sum + val[u]);
  }
  if (!leaf && s[u] == -1) {
    int common = MAXN;
    for (auto v : adj[u]) {
      if (v == p) continue;
      common = min(common, val[v]);
    }
    val[u] += common;
    for (auto v : adj[u]) {
      if (v == p) continue;
      val[v] -= common;
    }
  }
}
int main() {
  int n;
  cin >> n;
  adj = vector<vector<int>>(n);
  for (int u = 1; u < n; u++) {
    cin >> v;
    v--;
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  for (int i = 0; i < n; i++) cin >> s[i];
  val[0] = (s[0] == -1 ? 0 : s[0]);
  dfs(0, -1, 0);
  if (pos) {
    ll res = 0;
    for (int i = 0; i < n; i++) res += val[i];
    cout << res;
  } else {
    cout << -1;
  }
  return 0;
}
