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
from sys import stdin
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,factorial,gcd
from collections import deque
n=int(input())
l=list(map(int,input().split()))
s=list(map(int,input().split()))
graph={i:set() for i in range(1,n+1)}
for i in range(n-1):
	graph[l[i]].add(i+2)
level=[[] for i in range(n+2)]
stack=[[1,1]]
flag=1
while stack:
	x,y=stack.pop()
	level[y].append(x)
	for i in graph[x]:
		stack.append([i,y+1])
# print(level)
ans=[0 for i in range(n+2)]
ans[1]=s[0]
for i in range(1,n+1):
	if i%2==0:
		for j in level[i]:
			papa=s[l[j-2]-1]
			if len(graph[j])==0:
				s[j-1]=papa
				ans[j]=0
			else:
				mi=float("infinity")
				for k in graph[j]:
					mi=min(mi,s[k-1])
					if s[k-1]<papa:
						flag=0
						break
				ans[j]=mi-papa
				s[j-1]=papa+ans[j]
	else:
		if i>1:
			for j in level[i]:
				papa=s[l[j-2]-1]
				# print(papa)
				ans[j]=s[j-1]-papa
# print(ans)
if flag==0:
	print(-1)
else:
	print(sum(ans))
