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()))
ps = set(p)
s = list(map(int,input().split()))
ok = True
for i in range(1, n + 1):
    if not i in ps:
        if s[i - 1] == -1:
            m = s[p[i - 2] - 1]
        else:
            m = s[i - 1]
        j = i
        while j != 1:
            if m < s[j - 1]:
                ok = False
                break
            if s[j - 1] != -1:
                m = s[j - 1]
            j = p[j - 2]
        if m < s[0]:
            ok = False
    if not ok:
        break
if ok:
    sp = [-1] * n
    for i in range(n - 1):
        if sp[p[i] - 1] == -1:
            sp[p[i] - 1] = [i + 2]
        else:
            sp[p[i] - 1].append(i + 2)
    a = [0] * n
    a[0] = s[0]
    for i in range(1, n + 1):
        if s[i - 1] == -1 and sp[i - 1] != -1:
            m = s[sp[i - 1][0] - 1] - s[p[i - 2] - 1]
            for j in sp[i - 1]:
                m = min(m, s[j - 1] - s[p[i - 2] - 1])
            a[i - 1] = m
    for i in range(2, n + 1):
        if s[i - 1] != -1:
            a[i - 1] = s[i - 1] - s[p[p[i - 2] - 2] - 1] - a[p[i - 2] - 1]
    print(sum(a))
else:
    print(-1)