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 fastMax(int x, int y) { return (((y - x) >> (32 - 1)) & (x ^ y)) ^ y; }
int fastMin(int x, int y) { return (((y - x) >> (32 - 1)) & (x ^ y)) ^ x; }
const long long int MAXN = 1e5 + 1;
vector<long long int> graph[MAXN];
long long int sum[MAXN];
long long int a[MAXN];
long long int pre[MAXN];
void dfs_(long long int u, long long int p) {
  if (sum[u] == -1) {
    pre[u] = sum[p];
  } else {
    pre[u] = sum[u];
  }
  if (pre[u] < pre[p]) {
    cout << -1 << endl;
    exit(0);
  }
  for (long long int v : graph[u]) {
    if (v == p) continue;
    dfs_(v, u);
  }
}
void dfs(long long int u, long long int p) {
  bool flag = false;
  if (sum[u] == -1) flag = true;
  if (sum[u] == -1) sum[u] = LLONG_MAX;
  if (graph[u].size() == 1 && u != 1) {
    sum[u] = pre[u];
  }
  for (long long int v : graph[u]) {
    if (v == p) continue;
    dfs(v, u);
    if (flag) sum[u] = min(sum[v], sum[u]);
  }
}
void dfs2(long long int u, long long int p) {
  a[u] = sum[u] - sum[p];
  for (long long int v : graph[u]) {
    if (v == p) continue;
    dfs2(v, u);
  }
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ;
  long long int n;
  cin >> n;
  for (int i = (2); i <= (n); ++i) {
    long long int p;
    cin >> p;
    graph[p].push_back(i);
    graph[i].push_back(p);
  }
  for (int i = (1); i <= (n); ++i) cin >> sum[i];
  dfs_(1, 0);
  dfs(1, 0);
  dfs2(1, 0);
  long long int ans = 0;
  for (int i = (1); i <= (n); ++i) ans += a[i];
  cout << ans << endl;
}
