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
# -*- coding:utf-8 -*-

"""

created by shuangquan.huang at 1/17/19

"""

import collections
import time
import os
import sys
import bisect
import heapq


N = int(input())
P = [0, 0] + [int(x) for x in input().split()]
S = [0] + [int(x) for x in input().split()]


isLeaf = [True] * (N+1)
for p in P:
    isLeaf[p] = False

leafs = [i for i in range(1, N+1) if isLeaf[i]]
for leaf in leafs:
    node = leaf
    x = -1
    while node > 0:
        if x < 0:
            x = S[node]
        elif S[node] > x:
            print(-1)
            exit(0)
        node = P[node]
        



G = collections.defaultdict(list)

for node in range(1, N+1):
    G[P[node]].append(node)
    
V = [0] * (N+1)
V[1] = S[1]


for leaf in leafs:
    node = leaf
    while node > 0:
        if S[node] < 0:
            V[node] = min([S[child]-S[P[node]] for child in G[node]] or [0])
            S[node] = S[P[node]] + V[node]
        node = P[node]
        
q = [1]
while q:
    node = q.pop(0)
    if S[node] >= 0:
        V[node] = S[node] - S[P[node]]
    
    q.extend(G[node])
    
    
    
# print(S)
# print(V)
print(sum(V[1:]))