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.util.*;
public class D {
	static long sum;
	static boolean b = false;
	static ArrayList<Integer>[] a;
	static int[] s;
	static int[] p;
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		a = new ArrayList[n];
		s = new int[n];
		p = new int[n];
		for(int i=0;i<n;i++) {
			a[i] = new ArrayList<Integer>();
		}
		p[0] = 0;
		for(int i=1;i<n;i++) {
			int x = in.nextInt();
			p[i] = x-1;
			a[x-1].add(i);
		}
		for(int i=0;i<n;i++) {
			s[i] = in.nextInt();
		}
		sum=s[0];
		dfs(0,s[0],0);
		if(b) {
			System.out.println(-1);
		}else {
			System.out.println(sum);			
		}
	}
	static void dfs(int i, int max, int d) {
		if(d%2==0) {
			if(s[i]-s[p[i]]<0) {
				b=true;
			}
			sum+=(s[i]-s[p[i]]);
		}else {
			if(a[i].size()!=0) {
				int min=s[a[i].get(0)];
				for(int j:a[i]) {
					if(s[j]<min) {
						min=s[j];
					}
				}
				if(min-s[p[i]]<0) {
					b=true;
				}
				sum+=min-s[p[i]];
				s[i] = min;
			}
		}
		//System.out.println(i+" "+s[i]+" "+d+" "+sum+" "+b+" "+s[p[i]]);
		for(int j:a[i]) {
			dfs(j,max,d+1);
		}
	}
}
