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
n=input()
lst=map(int,raw_input().split())
w=map(int,raw_input().split())
dp=[]
par=[]
for i in range(n+2):
    dp.append([])
for i in range(n+2):
    par.append(0)
for i in range(0,len(lst)):
    dp[lst[i]].append(i+2)
    par[i+2]=lst[i]
#print dp
from collections import deque
def bfs(x,dp):
    dist=[0]*(n+2)
    dist[x]=0
    q=deque()
    q.append(x)
    while q:
        t=q.popleft()
        for i in dp[t]:
           # print i,"i",dist[t],t
            if dist[i]==0:
                q.append(i)
                dist[i]=dist[t]+1

    return dist
dist=bfs(1,dp)
f=[]
lev=[]
for i in range(1,n+2):
    lev.append([])
for i in range(1,n+1):
    lev[dist[i]+1].append(i)
#print lev
mt=[]
qk=0
for i in range(1,n+1):
    if i%2:
        m=1000000000000000
        for j in range(0,len(lev[i])):
            m=min(m,w[lev[i][j]-1])
    mt.append(m)
tk=[0]*(n+1)
#if sorted(mt)!=mt:
#    print -1
if 1==1:
    #print par
    for i in range(1,n+1):
        if i==1:
            tk[1]=w[0]

        elif i%2:
            for j in range(0,len(lev[i])):
                t=lev[i][j]
                tk[t]=w[t-1]-w[par[t]-1]
        else:
            m = 100000000000000000
            for j in range(0, len(lev[i])):
                fk=lev[i][j]
                #print fk ,i,par[fk]
                m=1000000000000000000
                for k in dp[fk]:
                    m=min(m,w[k-1])
                if len(dp[fk])==0:
                    tk[fk]=0
                    w[fk-1]=0
                else:

                    tk[fk]=m-w[par[fk]-1]
                    w[fk-1]=m
    c=0
    #print tk
    for i in tk:
        if i<0:
            print -1
            exit()
        c=c+i

    print c


