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
a = input()
parents = list(map(int, raw_input().strip().split()))
vals = list(map(int, raw_input().strip().split()))
erased = []
can = True
parents.insert(0,0)
c = [[] for i in range(len(parents))]
for i in range(1,len(parents)):
    c[parents[i]-1].append(i)
for i in range(len(vals)):
    if vals[i] == -1:
        erased.append(i)
for i in range(len(erased)):
    par = parents[erased[i]] - 1
    s = vals[par]
    m = 20000000000000
    for j in c[erased[i]]:
        m = min(vals[j],m)
    if len(c[erased[i]]) == 0:
        m = s
    vals[erased[i]] = m
    if m < s:
        can = False

ans = [0 for i in range(len(vals))]
ans[0] = vals[0]
for i in range(1,len(vals)):
    ans[i] = vals[i] - vals[parents[i]-1]
s = 0
for i in ans:
    s += i
if can:
    print s
else:
    print -1