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
import sys
input = sys.stdin.readline

n=int(input())
P=[0,0]+list(map(int,input().split()))
S=[0]+list(map(int,input().split()))

SONS=[[] for i in range(n+1)]

for i in range(n+1):
    SONS[P[i]].append(i)


from collections import deque


height=0
SCORE=[0]*(n+1)
SCORESUM=[0]*(n+1)

SCORE[1]=S[1]
SCORESUM[1]=S[1]

QUE = deque(SONS[1])


while QUE:
    x=QUE.pop()
    #print(x,QUE,SCORE,SCORESUM)

    if S[x]>=0:
        SCORE[x]=S[x]-SCORESUM[P[x]]
        SCORESUM[x]=S[x]
        for to in SONS[x]:
            QUE.append(to)

        continue
    
    elif S[x]==-1:
        MINSCORE=float("inf")

        for to in SONS[x]:
            QUE.append(to)
            if MINSCORE>S[to]:
                MINSCORE=S[to]

        if MINSCORE==float("inf"):
            SCORE[x]=0
            SCORESUM[x]=SCORESUM[P[x]]

        else:
            SCORE[x]=MINSCORE-SCORESUM[P[x]]
            SCORESUM[x]=SCORESUM[P[x]]+SCORE[x]

#print(SCORE)
#print(SCORESUM)
if min(SCORE)<0:
    print(-1)
else:
    print(sum(SCORE))
            
    
