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.io.*;
import java.lang.reflect.Array;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;
import java.math.RoundingMode;
 
public class WCS {
	
	public static void solve(int curr, int depth, long[] s, ArrayList <Integer>[] tree, int[] parent) {
		if(depth % 2 == 0) {
			if(tree[curr].size() == 0) {
				s[curr] = s[parent[curr]];
				return;
			}
			long min = s[tree[curr].get(0)];
			for(int i = 1; i < tree[curr].size(); i ++)
				min = Math.min(min, s[tree[curr].get(i)]);
			s[curr] = min >= s[parent[curr]] ? min : -1;
		}
		for(int i = 0; i < tree[curr].size(); i ++)
			solve(tree[curr].get(i), depth + 1, s, tree, parent);
	}
	
	public static void main(String[] args) throws IOException {
		int n = in.nextInt();
		int[] parent = new int[n];
		for(int i = 1; i < n; i ++)
			parent[i] = in.nextInt() - 1;
		ArrayList <Integer>[] tree = new ArrayList[n];
		for(int i = 0; i < n; i ++)
			tree[i] = new ArrayList <> ();
		for(int i = 1; i < n; i ++)
			tree[parent[i]].add(i);
		//for(int i = 0; i < n; i ++)
		//	System.out.println(i + ": " + tree[i]);
		long[] s = new long[n];
		for(int i = 0; i < n; i ++)
			s[i] = in.nextLong();
		solve(0, 1, s, tree, parent);
		long ans = s[0];
		for(int i = 1; i < n; i ++) {
			if(s[i] == -1) {
				ans = -1;
				break;
			}
			ans += s[i] - s[parent[i]];
		}
		System.out.println(ans);
	}
    
    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();
        }
 
        BigInteger nextBigInteger() {
        	return new BigInteger(in.next());
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        char nextChar() {
            return in.next().charAt(0);
        }
 
        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;
        }
    }
    
    static FastReader in = new FastReader();
    static OutputStream out = new BufferedOutputStream(System.out);
    
    public static byte[] toByte(Object o) {
        return String.valueOf(o).getBytes();
    }
    
    public static void sop(Object o) {
        System.out.print(o);
    }
}