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 bisect import bisect_left as bl, bisect_right as br, insort
import sys
import heapq
#from math import *
from collections import defaultdict as dd, deque
def data(): return sys.stdin.readline().strip()
def mdata(): return map(int, data().split())
#sys.setrecursionlimit(100000)
mod=int(1e9+7)



n=int(data())
t=[{} for i  in range(n)]
P=list(mdata())
for i in range(n-1):
    t[P[i]-1][i+1]=0
A=list(mdata())
flag=True
v=[0]*n
v[0]=max(A[0],0)
ans=v[0]
for i in range(0,n):
    if A[i]==-1 :
        l=[]
        for j in t[i]:
            if A[j]!=-1:
                l.append(A[j])
        m=0
        if len(l)>0:
            m=min(l)
            if m<v[i]:
                print(-1)
                exit()
            ans+=m-v[i]
            v[i]=m
    else:
        v[i]=A[i]
    for j in t[i]:
        if A[j]==-1:
            v[j]=v[i]
        elif A[j]<v[i]:
            print(-1)
            exit()
        else:
            v[j]=A[j]
        ans+=v[j]-v[i]
print(ans)