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
from collections import defaultdict

def solve(tree, sum_dict):
    return solve_helper(1, tree, sum_dict, sum_dict[1], sum_dict[1])


def solve_helper(curr_node, tree, sum_dict, curr_sum, total):
    if len(tree[curr_node]) != 0:
        tree_totals = []
        for child in tree[curr_node]:
            if sum_dict[child] != -1:
                if curr_sum > sum_dict[child]:
                    return -1
                else:
                    tree_totals.append(solve_helper(child, tree, sum_dict, sum_dict[child], total+(sum_dict[child]-curr_sum)))
            else:
                tree_totals.append(solve_helper(child, tree, sum_dict, curr_sum, total))
        return sum(tree_totals)
    else:
        return sum_dict[curr_node] - curr_sum + total

n = int(input())
parents = list(map(int, input().split()))
sum_vals = list(map(int, input().split()))

tree = defaultdict(list)
sum_dict = defaultdict(int)

tree[1] = list()

for i in range(2, len(parents) + 2):
    tree[parents[i-2]].append(i)

for i in range(1, n+1):
    sum_dict[i] = sum_vals[i-1]

values = [-1] * n
values[0] = sum_dict[1]

flag = True

for i in range(1, n+1):
    if sum_dict[i] == -1:
        if len(tree[i]) != 0:
            children_vals = []
            parent_val = sum_vals[parents[i-2] - 1]
            for child in tree[i]:
                if sum_dict[child] < parent_val:

                    flag = False
                children_vals.append(sum_dict[child])
            min_children = min(children_vals)
            for child in tree[i]:
                values[child - 1] = sum_dict[child] - min_children
            values[i-1] = min_children - parent_val

        else:
            values[i - 1] = 0

"""for i in range(2, n+1):
    if sum_dict[i] != -1:
        values[i-1] = sum_dict[i] - values[parents[i-2] - 1]"""

"""print(sum_dict)
print(tree)
print(values)"""
print(sum(values) if flag else -1)
