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>
const int maxn = 1e5 + 10;
const long long inf = 10000000000000ll;
int n, fa[maxn], head[maxn], cnt;
long long a[maxn], s[maxn], ans;
bool flg;
struct edge {
  int t, nxt;
} e[maxn];
void add(int a, int b) {
  e[++cnt] = (edge){b, head[a]};
  head[a] = cnt;
}
long long in() {
  long long re = 0;
  char ch = getchar();
  bool f = 0;
  while (ch < '0' || ch > '9') f |= (ch == '-'), ch = getchar();
  while (ch >= '0' && ch <= '9')
    re = (re << 1) + (re << 3) + (ch ^ '0'), ch = getchar();
  return f ? -re : re;
}
void dfs(int x) {
  long long mins = inf;
  for (int i = head[x]; i; i = e[i].nxt)
    if (e[i].t != fa[x]) {
      dfs(e[i].t);
      mins = std::min(mins, s[e[i].t]);
    }
  if (mins < s[fa[x]]) flg = 1;
  if (s[x] == -1) {
    if (mins == inf)
      s[x] = s[fa[x]];
    else
      s[x] = mins;
  }
}
int main() {
  n = in();
  for (int i = 2; i <= n; ++i) {
    fa[i] = in();
    add(fa[i], i);
  }
  for (int i = 1; i <= n; ++i) s[i] = in();
  dfs(1);
  if (flg)
    puts("-1");
  else {
    for (int i = 1; i <= n; ++i) ans += s[i] - s[fa[i]];
    printf("%lld", ans);
  }
  return 0;
}
