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
from math import ceil,sqrt
read=sys.stdin.buffer.readline

mi=lambda:map(int,read().split())
li=lambda:list(mi())
cin=lambda:int(read())

for _ in range(1):
    n=cin()
    p=li()
    s=li()
    child={i:[] for i in range(1,n+1)}
    for i in range(n-1):
        child[p[i]].append(i+2)
    a=[0]*n
    #print(child)
    a[0]=s[0]
    flag=True
    if a[0]==-1:
        flag=False
    stack=[[1,a[0]]]
    while stack:
        node,sm=stack[-1][0],stack[-1][1]
        stack.pop()
        mn=1000000001
        for el in child[node]:
            if s[el-1]==-1:
                a[el-1]=0
                stack.append([el,sm])
            else:
                a[el-1]=s[el-1]-sm
                stack.append([el,s[el-1]])
            if a[el-1]<0:
                flag=False
                break
            mn=min(mn,a[el-1])
        if flag==False:
            break
        if s[node-1]==-1 and child[node]!=[]:
            a[node-1]=mn
            for el in child[node]:
                a[el-1]-=mn
    if flag:
        print(sum(a))
    else:
        print(-1)