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 solution {
	
    public static void main (String[] args) throws IOException{
    	FastReader f=new FastReader();
    	int n = f.nextInt();
    	
    	tn[] tree = new tn[n+1];
    	for (int i=1;i<=n;i++) tree[i] = new tn();
    	
    	for (int i=2;i<=n;i++) {
    		int p = f.nextInt();
    		tree[p].cn.add(i);
    		tree[i].p = p;
    	}
    	
    	for (int i=1;i<=n;i++) tree[i].s = f.nextInt();
    	
    	Queue<Integer> q = new LinkedList<>();
    	q.add(1);
    	
    	long sums = 0;
    	
    	while(!q.isEmpty()) {
    		Queue<Integer> q2 = new LinkedList<>();
    		while(!q.isEmpty()) {
    			int pos = q.remove();
    			for (int child: tree[pos].cn) q2.add(child);
    			if (tree[pos].s==-1) {
    	    		int min = Integer.MAX_VALUE;
    	    		for (int child: tree[pos].cn) {
    	    			if (tree[child].s<min) min = tree[child].s;
    	    		}
    	    		if (min==Integer.MAX_VALUE) min = tree[tree[pos].p].s;
    	    		tree[pos].s = min;
    	    		tree[pos].a = tree[pos].s - tree[tree[pos].p].s;
    	    		if (tree[pos].a<0) {
    	    			System.out.println(-1);
    	    			return;
    	    		}
    	    		sums+=tree[pos].a;
    	    		continue;
    	    	}
    			int ps=0;
    			if (tree[pos].p!=0) ps = tree[tree[pos].p].s;
    			tree[pos].a = tree[pos].s - ps;
    			sums+=tree[pos].a;
    			if (tree[pos].a<0) {
	    			System.out.println(-1);
	    			return;
	    		}
    		}
    		q=q2;
    	}
    	
    	System.out.println(sums);
    	
    }

    
    static class tn{
    	int a;
    	int s;
    	int p;
    	ArrayList<Integer> cn;
    	tn() { cn = new ArrayList<>(); }
    }
    
    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; 
        } 
    } 
  
}
