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 M = 1e5 + 10;
const long long inf = 1e18 + 7;
long long head[M], cnt, flag;
long long ans, a[M], b[M];
vector<long long> g[M];
void dfs(long long u, long long fa, long long dep) {
  long long mn = inf;
  if (dep % 2 == 0) {
    for (long long i = 0; i < g[u].size(); i++) {
      long long v = g[u][i];
      mn = min(mn, a[v]);
    }
    if (mn != inf)
      a[u] = mn, b[u] = a[u] - a[fa];
    else
      a[u] = a[fa], b[u] = 0;
  } else {
    b[u] = a[u] - a[fa];
  }
  for (long long i = 0; i < g[u].size(); i++) {
    long long v = g[u][i];
    dfs(v, u, dep + 1);
  }
}
int main() {
  long long n, x;
  scanf("%lld", &n);
  for (long long i = 2; i <= n; i++) {
    scanf("%lld", &x);
    g[x].push_back(i);
  }
  for (long long i = 1; i <= n; i++) {
    scanf("%lld", &a[i]);
  }
  dfs(1, 0, 1);
  for (long long i = 1; i <= n; i++) {
    ans += b[i];
    if (b[i] < 0) flag = 1;
  }
  if (!flag)
    printf("%lld\n", ans);
  else
    printf("-1\n");
}
