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
import java.util.*;
import java.lang.*;
import java.io.*;

public class Main
{
	PrintWriter out = new PrintWriter(System.out);
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer tok = new StringTokenizer("");
    String next() throws IOException {
        if (!tok.hasMoreTokens()) { tok = new StringTokenizer(in.readLine()); }
        return tok.nextToken();
    }
    int ni() throws IOException { return Integer.parseInt(next()); }
    long nl() throws IOException { return Long.parseLong(next()); }
    
    ArrayList<Integer>A[];
    int n;
    int[]P,S;
    long ans;
    boolean f;
  
    void solve() throws IOException {
        n=ni();
        A=new ArrayList[n+1];
        for(int x=1;x<=n;x++) A[x]=new ArrayList();
        P=new int[n+1];
        for (int x=2;x<=n;x++) { P[x]=ni(); A[P[x]].add(x); }
        S=new int[n+1];
        for (int x=1;x<=n;x++) S[x]=ni();
        ans=S[1];
        f=true;
        dfs(1,1);
        
        if (f) System.out.println(ans);
        else System.out.println(-1);
    }
    
    void dfs(int u,int d) {
        if (d%2==0 && A[u].size()>0) {
            long min=Long.MAX_VALUE;
            long total=0;
            for (int i=0;i<A[u].size();i++) {
                int v=A[u].get(i);
                min=Math.min(min,S[v]);
                total+=S[v];
            }
            if (min<S[P[u]]) f=false;
            ans=ans+min-S[P[u]];
            min=min*A[u].size();
            ans=ans+total-min;
        }
        for (int i=0;i<A[u].size();i++) dfs(A[u].get(i),d+1);
    }
    
    public static void main(String[] args) throws IOException {
        new Main().solve();
    }
}