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 SumInTree {
	
	static int[] a;
	public static void main(String[] args) throws Exception{
		BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
		
		int n = Integer.parseInt(f.readLine());
		ArrayList<Integer>[] adj = new ArrayList[n];
		a = new int[n];
		for(int i = 0; i < n; i ++) {
			adj[i] = new ArrayList<Integer>();
		}
		
		StringTokenizer st = new StringTokenizer(f.readLine());
		for(int i = 1; i < n; i ++) {
			int x = Integer.parseInt(st.nextToken());
			adj[x-1].add(i);
		}
		
		long ans = 0;
		int[] s = new int[n];
		st = new StringTokenizer(f.readLine());
		for(int i = 0; i < n; i ++) {
			int x = Integer.parseInt(st.nextToken());
			s[i] = x;
		}
		
		dfs(0,-1,adj,s);
		
		for(int i = 0; i < n; i ++) {
			ans += a[i];
		}
		
		System.out.println(ans);
	}
	
	static void dfs(int i, int p, ArrayList<Integer>[] adj, int[] s) {
		if(p == -1) {
			a[i] = s[i];
			for(int x: adj[i]) {
				dfs(x,i,adj,s);
			}
			return;
		}
		if(s[i] != -1) {
			for(int x: adj[i]) {
				dfs(x,i,adj,s);
			}
			return;
		}
		int min = Integer.MAX_VALUE;
		for(int x: adj[i]) {
			min = Integer.min(min, s[x]);
		}
		
		if(min < s[p]) {
			System.out.println(-1);
			System.exit(0);
		}
		if(min == Integer.MAX_VALUE) {
			a[i] = 0;
		}
		else {
			a[i] = min - s[p];
		}
		for(int x: adj[i]) {
			a[x] = s[x] - min;
			dfs(x,i,adj,s);
		}
	}

}
