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 collections
from collections import defaultdict
n=int(input())
par=[ int(i) for i in input().split() if i!='\n']
suma=[int(i) for i in input().split() if i!='\n']
graph=defaultdict(list)
for i in range(n-1):
    graph[i+2].append(par[i])
    graph[par[i]].append(i+2)
weight=[0]*(n+1)
weight[1]=suma[0]
queue=collections.deque([1])
visited=set()
visited.add(1)
ok=True
while queue:
    vertex=queue.popleft()
    for child in graph[vertex]:
        if child not in visited: 
            if suma[child-1]==-1:
                mina=[]
                if len(graph[child])==1:
                    mina=[0]
                else:   
                    for j in graph[child]:
                        if j!=vertex:
                            mina.append(suma[j-1]-suma[vertex-1])
                ans=suma[vertex-1]+min(mina)
                suma[child-1]=ans
                if suma[child-1]<suma[vertex-1]:
                    ok=False
                else:
                    weight[child]=(suma[child-1]-suma[vertex-1])
            else:
                if suma[child-1]<suma[vertex-1]:
                    ok=False
                else:
                    weight[child]=(suma[child-1]-suma[vertex-1])
            queue.append(child)
            visited.add(child)
if ok==True:
    print(sum(weight))
else:
    print(-1)
