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=int(input())
p=list(map(int,input().split()))
s=list(map(int,input().split()))
tr=[[] for i in range(n+1)]
for i in range(n-1):
    tr[p[i]].append(i+2)
st=[(1,1)]
vis=[0]*(n+1)
a=[0]*(n+1)
a[1]=s[0]
vis[1]=1
while st:
    x,h=st.pop()
    for i in tr[x]:
        if vis[i]==0:
            if h%2==0 and s[i-1]==-1:
                exit(print(-1))
            elif h%2==0:
                st.append((i,h+1))
                a[i]=s[i-1]-s[p[i-2]-1]
                if a[i]<0:
                    exit(print(-1))
            else:
                st.append((i,h+1))
                m=10e9
                for j in tr[i]:
                    m=min(m,s[j-1])
                if len(tr[i])==0:
                    m=s[p[i-2]-1]
                a[i]=m-s[p[i-2]-1]
                if a[i]<0:
                    exit(print(-1))
                s[i-1]=s[p[i-2]-1]+a[i]
            vis[i]=1
print(sum(a))
                
    