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 maxn = 1e5 + 5;
const long long inf = 0x3f3f3f3f;
vector<int> G[maxn];
long long sum[maxn], a[maxn];
int minson[maxn];
int n;
int getson(int v) {
  int minkey = inf;
  for (int i = 0; i < G[v].size(); ++i) {
    int to = G[v][i];
    if (minkey > getson(to)) {
      minkey = sum[to];
      minson[v] = to;
    }
  }
  return sum[v];
}
void dfs(int v, long long fasum, int deep) {
  if (deep & 1)
    a[v] = sum[v] - fasum;
  else if (!G[v].size()) {
    a[v] = 0;
    return;
  } else
    a[v] = sum[minson[v]] - fasum;
  for (int i = 0; i < G[v].size(); ++i) dfs(G[v][i], fasum + a[v], deep + 1);
}
int main() {
  std::ios::sync_with_stdio(false);
  while (cin >> n) {
    int pa;
    for (int i = 2; i <= n; ++i) {
      cin >> pa;
      G[pa].push_back(i);
    }
    for (int i = 1; i <= n; ++i) cin >> sum[i];
    getson(1);
    dfs(1, 0, 1);
    long long maxsum = 0;
    int flag = 0;
    for (int i = 1; i <= n; ++i) {
      if (a[i] >= 0)
        maxsum += a[i];
      else
        flag = 1;
    }
    if (!flag)
      cout << maxsum << endl;
    else
      cout << -1 << endl;
    for (int i = 0; i <= n; ++i) G[i].clear();
  }
  return 0;
}
