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.*;
import java.math.*;

public class Main {
	InputReader in = new InputReader(System.in);
	PrintWriter out = new PrintWriter(System.out);
	class InputReader {
    	BufferedReader reader;
    	StringTokenizer tokenizer;
    	InputReader(InputStream stream) {
    		reader = new BufferedReader(new InputStreamReader(stream), 32768);
    		tokenizer = null;
    	}
    	String next() {
    		while(tokenizer==null || !tokenizer.hasMoreTokens()) {
    			try { tokenizer = new StringTokenizer(reader.readLine()); }
    			catch(IOException e) { throw new RuntimeException(e); }
    		}
    		return tokenizer.nextToken();
    	}
    	int nextInt() { return Integer.parseInt(next()); }
    	long nextLong() { return Long.parseLong(next()); }
    }
    
	final int N = (int)(1e5+10);
	final int INF = 0x3f3f3f3f;
	
	boolean flag = true;
	int[] s = new int[N];
	long sum = 0;
    ArrayList<Integer> G[] = new ArrayList[N];
    
    int dfs(int u, int fa) {
    	int mn = INF;
    	for(int v:G[u]) mn = Math.min(dfs(v, u), mn);
    	if(s[u] == -1) {
    		if(mn == INF) mn = s[fa];
    		s[u] = mn;
    	}
    	for(int v:G[u]) {
    		int t = s[v]-s[u];
    		if(t < 0) flag = false;
    		sum += t;
    	}
//    	out.println(mn);
    	return Math.min(mn, s[u]);
    }
    
	void work() {
		int n = in.nextInt();
		for(int i = 1; i <= n; i++) G[i] = new ArrayList<>();
		for(int i = 2; i <= n; i++) G[in.nextInt()].add(i);
		for(int i = 1; i <= n; i++) s[i] = in.nextInt();
		dfs(1, 0);
		sum += s[1];
		if(!flag) sum = -1;
		out.println(sum);
		
		out.close();
	}
	
	public static void main(String[] args) { new Main().work(); }
}