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, fa[210001], son[210001], bro[210001], v[210001], sum[210001],
    Min[210001];
void addt(int a, int b) {
  bro[b] = son[a];
  fa[b] = a;
  son[a] = b;
}
void read() {
  int ls1;
  scanf("%d", &n);
  for (int i = 2; i <= n; ++i) scanf("%d", &ls1), addt(ls1, i);
  for (int i = 1; i <= n; ++i) scanf("%d", sum + i), Min[i] = 1e9 + 1;
  return;
}
void dfs(int a) {
  if (sum[a] != -1) Min[a] = sum[a];
  for (int b = son[a]; b; b = bro[b]) {
    dfs(b);
    if (Min[b] < sum[a]) printf("-1\n"), exit(0);
    Min[a] = min(Min[a], Min[b]);
  }
}
void dfs2(int a) {
  v[a] = Min[a] - Min[fa[a]];
  if (Min[a] == 1e9 + 1) v[a] = 0;
  for (int b = son[a]; b; b = bro[b]) {
    dfs2(b);
  }
}
int main() {
  read();
  dfs(1);
  dfs2(1);
  long long Ans = 0;
  for (int i = 1; i <= n; ++i) {
    if (Min[i] < sum[i]) printf("-1\n"), exit(0);
  }
  for (int i = 1; i <= n; ++i) Ans += v[i];
  cout << Ans << endl;
  return 0;
}
