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
'''input
3
1 2
2 -1 1
'''
from sys import stdin
import math
import queue
class Graph():
	def __init__(self, mydict=None):
		if mydict == None:
			self.gdict = dict() # for adjacency list
			self.nodes = set()	# for nodes
		else:
			self.gdict = mydict

	def addEdge(self, u, v, weight = 0, bidir = True):
		self.nodes.add(u) 	# adds the node u in self.nodes. O(1) on average.
		self.nodes.add(v)	# adds the node v in self.nodes

		if u in self.gdict:
			self.gdict[u].append(v)
		else:
			self.gdict[u] = [v]

		if bidir == True:
				if v in self.gdict:
					self.gdict[v].append(u)
				else:
					self.gdict[v] = [u]

	def display_graph(self):
		print(self.gdict)


def get_min(g, node, visited, sumi, current_sum):
	mini = float('inf')
	for i in g.gdict[node]:
		if visited[i] == False:
			mini = min(mini, sumi[i])
	if mini == float('inf'):
		return current_sum
	return mini


def bfs(g, sumi):
	weight = dict()
	visited= dict()
	for i in range(n):
		visited[i + 1] = False
		weight[i + 1] = 0

	weight[1] = sumi[1]
	mq = queue.Queue()
	mq.put(1)
	

	while mq.qsize() > 0:
		node = mq.get()
		current_sum = sumi[node]
		visited[node] = True
		for i in g.gdict[node]:
			if visited[i] == False:
				mq.put(i)
				if sumi[i] == -1:
					minimum = get_min(g, i, visited, sumi, current_sum)
					#print(minimum, current_sum)
					if minimum < current_sum:
						print("-1")
						return
					else:
						weight[i] = minimum - current_sum
						sumi[i] = current_sum + weight[i]
				else:
					weight[i] = sumi[i] - sumi[node]
			#print("weight is ", weight)
			#print("sumi is ", sumi)
	total = 0
	for i in weight:
		total += weight[i]
	print(total)


				



# main starts
n = int(stdin.readline().strip())
g = Graph()
edge = list(map(int, stdin.readline().split()))

for i in range(2, n + 1):
	g.addEdge(edge[i - 2], i)

sumi = dict()

sum_val = list(map(int, stdin.readline().split()))
for i in range(n):
	sumi[i + 1] = sum_val[i]
bfs(g, sumi)


