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())

class Tree:
    height = 1
    def __init__(self, parent=None):
        self.nodes = []
        self.s = -1
        self.a = -1
        self.parent = parent
        if parent:
            self.height = parent.height+1
            parent.nodes.append(self)

trs = [Tree()]

for i in map(int, input().split()):
    trs.append(Tree(trs[i-1]))

for i, s in enumerate(map(int, input().split())):
    trs[i].s = s

trs.sort(key=lambda x: x.height)
trs[0].a = trs[0].s
res = trs[0].a

try:
    for t in trs[1:]:
        if t.s == -1:
            t.a = min(map(lambda x: x.s - t.parent.s,t.nodes), default=0)
            t.s = t.a + t.parent.s
        else:
            t.a = t.s - t.parent.s
        if t.a < 0:
            raise
        res += t.a
    print(res)
except:
    print(-1)
