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 D{

	static List<Integer>[] adj;
	static long[] s;
	static long[] a;
	static long sum = 0;
	static boolean works = true;
	static void dfs(int i, long think) {
		if (s[i] == -1) {
			// On evens, assign this the minimum of all children.
			if (adj[i].size() == 0) {
				a[i] = 0;
				return;
			}
			
			long min = Long.MAX_VALUE;
			for (int x: adj[i]) {
				min = Long.min(min, s[x]);
			}
			a[i] = min - think; 
			for (int x: adj[i]) {
				dfs(x,min);
			}
		}
		else {
			// On odds, just assign whatever you think.
			a[i] = s[i] - think;
			for (int x: adj[i]) {
				dfs(x, s[i]);
			}
		}
	}
	
	public static void main(String[] args) throws IOException {
		// br = new BufferedReader(new FileReader(".in"));
		// out = new PrintWriter(new FileWriter(".out"));
		//new Thread(null, new (), "peepee", 1<<28).start();
		
		int n =readInt();
		adj = new List[n+2];
		a = new long[n+2];
		Arrays.fill(a, -1);
		for (int i = 0 ; i < adj.length; i++) adj[i] = new ArrayList<Integer>();
		s = new long[n+2];
		for (int i = 2; i <= n; i++) adj[readInt()].add(i);
		for (int i = 1; i <=n; i++) s[i] = readInt();
		dfs(1,0);
		long sum = 0;
		for (int i = 1; i <=n; i++) {
			if (a[i] < 0) works = false;
			sum += a[i];
		}
		if (works) {
			out.println(sum);
		}
		else out.println(-1);
		out.close();
	}
	
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
	static StringTokenizer st = new StringTokenizer("");
	static String read() throws IOException{return st.hasMoreTokens() ? st.nextToken():(st = new StringTokenizer(br.readLine())).nextToken();}
	static int readInt() throws IOException{return Integer.parseInt(read());}
	static long readLong() throws IOException{return Long.parseLong(read());}
	static double readDouble() throws IOException{return Double.parseDouble(read());}
	
}