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, vs[100000 + 9], a, prt[100000 + 9];
vector<vector<int> > ns;
bool st = false;
void DFS(int no, int su, int le) {
  if (le & 1) {
    if (no != 1) {
      vs[no] -= su;
      if (vs[no] < 0) {
        printf("-1\n");
        st = true;
        return;
      }
    }
  } else {
    int mi = 1e9;
    for (int i = 0; i < ns[no].size(); i++) {
      mi = min(vs[ns[no][i]] - su, mi);
    }
    if (mi == 1e9)
      vs[no] = 0;
    else
      vs[no] = mi;
    if (vs[no] < 0) {
      printf("-1\n");
      st = true;
      return;
    }
  }
  for (int i = 0; i < ns[no].size(); i++) {
    DFS(ns[no][i], su + vs[no], le + 1);
  }
}
int main() {
  scanf("%d", &n);
  ns = vector<vector<int> >(n + 1);
  for (int i = 2; i <= n; i++) {
    scanf("%d", &a);
    ns[a].push_back(i);
    prt[i] = a;
  }
  for (int i = 1; i <= n; i++) scanf("%d", &vs[i]);
  DFS(1, 0, 1);
  if (st) return 0;
  long long res = 0;
  for (int i = 1; i <= n; i++) res += vs[i];
  printf("%lld", res);
  return 0;
}
