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()))
sv = list(map(int, input().split()))
av = [0 for _ in range(n)]
visited = [False for _ in range(n)]


def addEdge( v, w):
    adj[v].append(w)
    adj[w].append(v)

INF=1e18
adj = [[] for i in range(n)]
for i in range(0, len(p)):
    addEdge(i + 1, p[i] - 1)

for i in range(0,n):
    visited[i]=True
    if sv[i]==-1:
        temp=INF
        for j in adj[i]:
            if visited[j]==False:
                temp=min(temp,sv[j])
        if temp==INF:
            sv[i]=sv[p[i-1]-1]
        else:
            sv[i]=temp
# print(sv)


av[0]=sv[0]
for i in range(1,n):
    av[i]=sv[i]-sv[p[i-1]-1]
if min(av)<0:
    print(-1)
else:
    print(sum(av))
