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 = [-1] + [int(a)-1 for a in input().split()]
S = [int(a) for a in input().split()]
T = [s for s in S]

for i in range(1, n):
    if S[P[i]] < 0:
        if T[P[i]] < 0:
            T[P[i]] = S[i]
        else:
            T[P[i]] = min(T[P[i]], S[i])

for i in range(1, n):
    if T[i] < 0:
        T[i] = T[P[i]]

S = [t for t in T]

ans = S[0]
for i in range(1, n):
    if S[i] < S[P[i]]:
        print(-1)
        break
    else:
        ans += S[i] - S[P[i]]
else:
    print(ans)
