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 long long LL_INF = (long long)2e18 + 5;
int N;
vector<int> parent;
vector<long long> sums;
vector<long long> A;
int main() {
  scanf("%d", &N);
  parent.resize(N);
  parent[0] = -1;
  for (int i = 1; i < N; i++) {
    scanf("%d", &parent[i]);
    parent[i]--;
  }
  sums.resize(N);
  for (int i = 0; i < N; i++) scanf("%lld", &sums[i]);
  A.assign(N, LL_INF);
  A[0] = sums[0];
  for (int i = 1; i < N; i++)
    if (sums[i] >= 0) {
      int p = parent[i];
      int gp = parent[p];
      assert(p >= 0 && gp >= 0);
      if (sums[i] < sums[gp]) {
        puts("-1");
        return 0;
      }
      A[p] = min(A[p], sums[i] - sums[gp]);
    }
  for (int i = 1; i < N; i++)
    if (sums[i] < 0) {
      if (A[i] == LL_INF) A[i] = 0;
    } else {
      int p = parent[i];
      int gp = parent[p];
      A[i] = sums[i] - sums[gp] - A[p];
      assert(A[i] >= 0);
    }
  long long total = accumulate(A.begin(), A.end(), 0LL);
  printf("%lld\n", total);
}
