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 __future__ import division
from sys import stdin, stdout
# from fractions import gcd
# from math import *
# from operator import mul
# from functools import reduce
# from copy import copy
from collections import deque, defaultdict, Counter

rstr = lambda: stdin.readline().strip()
rstrs = lambda: [str(x) for x in stdin.readline().split()]
rint = lambda: int(stdin.readline())
rints = lambda: [int(x) for x in stdin.readline().split()]
rstr_2d = lambda n: [rstr() for _ in range(n)]
rint_2d = lambda n: [rint() for _ in range(n)]
rints_2d = lambda n: [rints() for _ in range(n)]
pr = lambda args, sep: stdout.write(sep.join(map(str, args)) + '\n')
out = []


class graph:
    # initialize graph
    def __init__(self, gdict=None):
        if gdict is None:
            gdict = defaultdict(list)
        self.gdict, self.edges, self.l = gdict, defaultdict(int), defaultdict(int)

    # add edge
    def addEdge(self, node1, node2, w=None):
        self.gdict[node1].append(node2)
        self.gdict[node2].append(node1)

    def bfs_util(self, i):
        self.visit = [0] * (n + 1)
        queue, self.visit[i], ans = deque([[i, a[0]]]), 1, a[0]

        while queue:
            # dequeue parent vertix
            s, cur = queue.popleft()
            mi, que = float('inf'), []

            # enqueue child vertices
            for i in self.gdict[s]:
                if self.visit[i] == 0:
                    self.visit[i] = 1
                    if a[i - 1] == -1:
                        queue.append([i, cur])
                    elif a[i - 1] < cur:
                        print(-1)
                        exit()
                    else:
                        mi = min(mi, a[i - 1] - cur)
                        queue.append([i, a[i - 1]])
                        que.append(i)

            while que:
                ans += a[que.pop() - 1] - (mi + cur)

            if mi != float('inf'):
                ans += mi

        print(ans)


n, par, a = int(input()), rints(), rints()
g = graph()
for i in range(n - 1):
    g.addEdge(par[i], i + 2)
g.bfs_util(1)
