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
class vertex():
    def __init__(self,v,sv,av=0):
        self.v=v
        self.sv=sv
        self.av=av
        self.child=[]
    def sve(self):
        if self.child==[]: 
            return(t.vert[pa[self.v-2]].sv)
        l=[t.vert[i].sv for i in self.child]
        return(min(l))
        
    
class tree():
    def __init__(self):
        self.vert={}
sum=0
t=tree()
n=int(input())
pa=list(map(int, input().split()))
s=list(map(int, input().split()))
for i in range(1,n+1):
    t.vert[i]=vertex(i,s[i-1])
for i in range(n-1):
    par=pa[i]
    t.vert[par].child.append(i+2)
for i in range(1,n+1):
    if t.vert[i].sv==-1:
        t.vert[i].sv=t.vert[i].sve()
for i in range(2,n+1):
    k=t.vert[i].sv-t.vert[pa[t.vert[i].v-2]].sv
    if k<0:
        sum=-1
        break
    else:t.vert[i].av=k
if sum==-1:print(-1)
else:
    r=s[0]
    for i in range(2,n+1):
        r+=t.vert[i].av
    print(r)