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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class D {
    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;
        }
    }
    public static FastReader scn = new FastReader();

    public static void main(String[] args) {
        int t = 1;
        while(t-- > 0) run();
    }


    static class node{
        long a ;
        long s ;

        ArrayList<node> children = new ArrayList<>();

        public node(long aa, long ss){
            a = aa;
            s = ss;
        }
    }

    public static node root;
    public static long sum;

    public static void run(){
        int n = scn.nextInt();
        sum = 0;

        node[] arr = new node[n+1];

        for(int i = 1; i<=n; i++) arr[i] = new node(-1,-1);
        for(int i = 2; i<=n; i++) arr[scn.nextInt()].children.add(arr[i]);

        for(int i = 1; i<=n; i++) arr[i].s = scn.nextInt();
        root = arr[1];
        root.a = root.s;

        helper(root,null);
        if(sum == -1){
            System.out.println(sum);
            return;
        }
        calcSum(root);
        System.out.println(sum);
    }

    public static void helper(node nn, node parent){

        if(nn.a == -1){
            if(nn.children.size()==0){
                nn.a = 0;
            }else {
                long min = Integer.MAX_VALUE;
                for (node i : nn.children) min = Math.min(min, i.s);
                if (min < parent.s) {
                    sum = -1;
                    return;
                }
                nn.a = min - parent.s;

                for (node i : nn.children) i.a = i.s - min;
            }
        }

        for(node i : nn.children){
            helper(i,nn);
        }

    }

    public static void calcSum(node nn){
        sum += nn.a;
        for(node i : nn.children) calcSum(i);
    }
}