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 Main {
	public static void main(String[] arg) {
		new Main().solve();
	}
	
	StringTokenizer ST;
	BufferedReader BR;
	PrintWriter PW;
	
	String next() {
		while(ST == null || !ST.hasMoreTokens()) {
			try {
				ST = new StringTokenizer(BR.readLine());
			}catch (Exception e) {
				// TODO: handle exception
				throw new RuntimeException(e);
			}
		}
		return ST.nextToken();
	}
	
	int nextInt() {
		return Integer.parseInt(next());
	}
	
	long nextLong() {
		return Long.parseLong(next());
	}
	
	ArrayList<Integer> G[];
	int a[], b[];
	
	void solve() {
		BR = new BufferedReader(new InputStreamReader(System.in));
		PW = new PrintWriter(System.out);
		
		int n = nextInt();
		a = new int[n+1];
		b = new int[n+1];
		G = new ArrayList[n+1];
		for(int i = 1; i <= n; i++) G[i] = new ArrayList<>();
		
		for(int i = 2; i <= n; i++) {
			int j = nextInt();
			G[j].add(i);
		}
		
		for(int i = 1; i <= n; i++)
			a[i] = nextInt();
		
		b[1] = a[1];
		if(dfs(1, 0)) {
			long ans = 0;
			for(int i = 1; i <= n; i++) {
				if(b[i] > 0) ans += b[i];
//				PW.print(b[i] + " ");
			}
//			PW.println();
				
			PW.println(ans);
		} else {
			PW.println(-1);
		}
		
		PW.close();
	}
	
	boolean dfs(int u, int p) {
		if(G[u].size() == 0) {
			if(a[u] == -1) b[u] = 0;
			return true;
		}
		if(a[u] == -1) {
			int mn = (int)1e9;
			for(int v : G[u]) mn = Math.min(mn, a[v]);
			if(mn < a[p]) return false;
			b[u] = mn - a[p];
			for(int v : G[u]) b[v] = a[v] - mn;
		}
		
		for(int v : G[u]) if(!dfs(v, u)) return false;
		return true;
	}
	
}