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())
parents = [None]+[int(x)-1 for x in input().split()]
s = list(map(int, input().split()))
children = [[] for _ in range(n)]
a = [None for _ in range(n)]

for v, parent in enumerate(parents):
    if parent is not None:
        children[parent] += [v]

broken = False
stack = []
stack.append((0, 1))
a[0] = s[0]
while len(stack) > 0:
    v, depth = stack.pop()
    # assert (s[v]==-1) == (depth%2==0)
    if depth % 2 == 0:
        if len(children[v]) > 0:
            s[v] = s[min(children[v], key=lambda child: s[child])]
        else:
            s[v] = s[parents[v]]
        if s[v] < s[parents[v]]:
            broken = True
            break
    if depth>1:
        a[v] = s[v] - s[parents[v]]
    for child in children[v]:
        stack.append((child, depth+1))

if not broken:
    print(sum(a))
else:
    print(-1)

