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())
root = list(map(int, input().split()))
sums = list(map(int, input().split()))

direct = []
for i in range(n):
    direct.append([])
for i in range(n-1):
    direct[root[i]-1].append(i+2)

#print(direct)

stack = [1]
s = sums[0]
work = True
while(len(stack) > 0 and work):
    v = stack.pop()
    #v is odd height
    for u in direct[v-1]:
        if len(direct[u-1]) == 0:
            sums[u-1] = sums[v-1]
        else:
            minval = -1
            for w in direct[u-1]:
                if minval == -1 or minval > sums[w-1]:
                    minval = sums[w-1]
                s+=sums[w-1]
                stack.append(w)
            s-=minval*len(direct[u-1])
            sums[u-1] = minval
        if sums[u-1] < sums[v-1]:
            work = False
            break;
        s+=sums[u-1] - sums[v-1]

if work:
    print(s)
else:
    print(-1)


