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 deque
n = int(input())
graph = {i: set() for i in range(1, n + 1)}
P = list(map(int, input().split()))
S = [0] + list(map(int, input().split()))
for i in range(n - 1):
    graph[P[i]].add(i + 2)
Q = deque([1])
used = [0] * (n + 1)
ans = S[1]
kek = {1: S[1]}
used[1] = 1
while Q:
    v = Q.popleft()
    for u in graph[v]:
        if used[u] == 0:
            used[u] = 1
            Q.append(u)
            if S[u] != -1:
                if kek[v] > S[u]:
                    print(-1)
                    exit(0)
                ans += (S[u] - kek[v])
                kek[u] = S[u]
            else:
                sos = set()
                for u2 in graph[u]:
                    sos.add(S[u2])
                if sos:
                    x = min(sos)
                    if kek[v] <= x:
                        ans += (x - kek[v])
                        kek[u] = x
                    else:
                        print(-1)
                        exit(0)
print(ans)