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 int Max = 1e5 + 5;
const long long Mod = 1e9 + 7;
int fa[Max];
long long sum[Max], ans = 0;
vector<int> son[Max];
bool flag = 0;
void dfs(int now) {
  if (sum[now] == -1) {
    long long temp = 1e9 + 5;
    for (auto to : son[now]) {
      temp = min(temp, sum[to]);
    }
    if (temp != 1e9 + 5)
      sum[now] = temp;
    else
      sum[now] = sum[fa[now]];
  }
  for (auto to : son[now]) dfs(to);
}
void dfs_sum(int now) {
  if (flag) return;
  for (auto to : son[now]) {
    long long temp = sum[to] - sum[now];
    if (temp < 0) flag = 1;
    ans += temp;
    dfs_sum(to);
  }
}
int main() {
  std::ios::sync_with_stdio(false);
  int n;
  cin >> n;
  for (int i = 2; i <= n; i++) {
    int x;
    cin >> x;
    son[x].push_back(i);
    fa[i] = x;
  }
  for (int i = 1; i <= n; i++) cin >> sum[i];
  dfs(1);
  dfs_sum(1);
  ans += sum[1];
  if (flag)
    cout << -1 << '\n';
  else
    cout << ans << '\n';
}
