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
//package com.company;
import java.util.*;
import java.io.IOException;

public class Main {

    public static void main(String args[]) throws IOException {
        Scanner in  = new Scanner(System.in);
//        int t = in.nextInt();
        int t=1;
        for (int jay = 0; jay < t; jay++) {
            int n = in.nextInt();
            graph g =  new graph(n);

            for(int i=1;i<n;i++){
                g.addE(i,in.nextInt()-1);
            }

            for(int i=0;i<n;i++)
            {
                g.sms[i] = in.nextInt();
            }
            g.cost[0] = g.sms[0];

            long ans = g.dfs(0,-1);
            if(ans!=-1){
                for(int x:g.cost){
                    ans+=x;
                }
            }
            System.out.println(ans);
        }
    }

    static class graph{
        int N;
        int[] cost;
        int[] sms;
        int[] visit;
        List<Integer>[] Edges;

        graph(int n){
            N = n;
            Edges = new ArrayList[n];
            visit = new int[n];
            cost = new int[n];
            sms = new int[n];
            for(int i=0;i<n;i++){
                Edges[i] = new ArrayList<>();
            }
        }
        public void addE(int u,int v){
            Edges[u].add(v);
            Edges[v].add(u);
        }

        public int dfs(int x,int parent){
            visit[x] = 1;

            if(sms[x]==-1){
                int flag = 0;
                int mini = Integer.MAX_VALUE;
                for(int i=0;i<Edges[x].size();i++){
                    int cur = Edges[x].get(i);
                    if(visit[cur]==0){
                        flag=1;
                        int tmp = sms[cur]-sms[parent];
                        if(tmp<0) return -1;
                        mini = Math.min(tmp,mini);
                        }
                    }
                if(flag==0) mini = 0;
                cost[x] = mini;
                for(int i=0;i<Edges[x].size();i++){
                    int cur = Edges[x].get(i);
                    if(visit[cur]==0){
                        cost[cur] = sms[cur] - (sms[parent]) - (cost[x]);
                        if(dfs(cur,x)==-1) return -1;
                    }
                }
            } else{
                for(int i=0;i<Edges[x].size();i++){
                    int cur = Edges[x].get(i);
                    if(visit[cur]==0){
                        if(dfs(cur,x)==-1) return -1;
                    }
                }
            }

            if(false){
                System.out.print("\t");
                for(int it=0;it<N;it++)System.out.print(cost[it]+" ");
                System.out.println("\t");
            }

            return 0;
        }

    }
    private static String rev(String s){
        return new StringBuffer(s).reverse().toString();
    }

    private static boolean isPrime(double n) {
//        no two power
        double x  = Math.sqrt(n);
        int i=3;
        int c=0;

        while(i<=x){
            if(n%i==0) c+=1;
            if(c>=1) return false;
            i+=2;
        }
        if(c==0) return true;
        return false;
    }
    public static void showArr(int[] arr){
        int n=arr.length;
        for(int i=0;i<n;i++){
            System.out.print(arr[i]+" ");
        }
    }
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        return gcd(y % x, x);
    }
    public static boolean twoPow (long n)
    {
        return n!=0 && ((n&(n-1)) == 0);
    }
}