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
import sys
try:
    sys.setrecursionlimit(10**6)
    n = int(input())
    connections = [0,0]+list(map(int, input().split()))
    sums = list(map(int, input().split()))
    values = [0 for _ in range(len(sums))]
    unknown = set()
    tree = defaultdict(list)
    for i, (connect, curSum) in enumerate(zip(connections[1:], sums)):
        if curSum == -1:
            sums[i] = sums[connections[connect]]
            unknown.add(i+1)
            values[i] = 0
        else:
            if i == 0:
                values[0] = sums[0]
                continue
            value = sums[i]-sums[connections[connect]-1]
            if value < 0:
                print(-1)
                exit()
            values[i] = value
        tree[connect].append(i+1)

    total = [sum(values)]
    connections = 0
    sums = 0
    for i in range(1,n+1):
        mn = float("inf")
        if i not in tree:
            continue
        if i in unknown:
            for v in tree[i]:
                if values[v-1] < mn:
                    mn = values[v-1]
            total[0] += mn - mn*len(tree[i])

    print(total[0])
except Exception as e:
    print(e)

