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

public class Main {
    static int flag=0;
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=1;
        while(T-->0)
        {
            int n=input.nextInt();
            ArrayList<Integer> adj[]=new ArrayList[n+1];
            Vertex V[]=new Vertex[n+1];
            for(int i=1;i<=n;i++)
            {
                adj[i]=new ArrayList<>();
            }
            for(int i=2;i<=n;i++)
            {
                int p=input.nextInt();
                adj[p].add(i);
                adj[i].add(p);
            }
            for(int i=1;i<=n;i++)
            {
                int s=input.nextInt();
                V[i]=new Vertex(i,s,0);
            }
            bfs(adj,V,1);
            V[1].a=V[1].s;
            if(flag==1)
            {
                out.println(-1);
            }
            else
            {
                for(int i=2;i<=n;i++)
                {
                    if(V[i].s!=-1)
                    {
                        int s=V[i].parent.a+V[i].parent.parent.s;
                        V[i].a=V[i].s-s;
                    }
                }
                long ans=0;
                for(int i=1;i<=n;i++)
                {
                    ans+=V[i].a;
                }
                out.println(ans);
            }
        }
        out.close();
    }
    public static void bfs(ArrayList<Integer> adj[],Vertex V[],int s)
    {
        V[s].color="gray";
        V[s].d=0;
        V[s].parent=null;
        Queue<Integer> q=new LinkedList<>();
        q.add(s);
        while(!q.isEmpty())
        {
            int k=q.poll();
            Vertex u=V[k];
            int min=Integer.MAX_VALUE;
            for(int i=0;i<adj[k].size();i++)
            {
                int key=adj[k].get(i);
                Vertex v=V[key];
                if(v.color=="white")
                {
                    min=Math.min(min,v.s);
                    q.add(key);
                    v.color="gray";
                    v.d=u.d+1;
                    v.parent=u;
                }
            }
            if(u.s==-1)
            {
                if(min==Integer.MAX_VALUE)
                {
                    u.a=0;
                }
                else
                {
                    u.a=min-u.parent.s;
                    if(u.a<0)
                    {
                        flag=1;
                    }
                }
            }
            u.color="black";
        }
    }
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}
class Vertex
{
    int key;
    int d,f,s,a;
    String color;
    Vertex parent;
    Vertex(int key,int s,int a)
    {
        this.s=s;
        this.a=a;
        this.key=key;
        this.d=0;
        this.f=0;
        this.color="white";
        this.parent=null;
    }
}