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 bfs(node):

    bool[node] = True
    queue = [node]

    ans = l[0]
    while queue!=[]:

        z = queue.pop(0)

        mini = 10**18
        go = []
        go1 = []
        for i in hash[z]:
            if bool[i] == False:

                bool[i] = True
                queue.append(i)
                if l[i-1] == -1:
                    continue
                if l[par[i-1]-1] == -1:

                    z1 = l[i-1]-l[par[par[i-1]-1]-1]
                    # if i == 3:
                    #     print(l[i-1],par[par[i-1]-1])
                    mini = min(z1,mini)
                    go.append(z1)
                    if z1<0:
                        # print(i,z1,l[par[i-1]])
                        print(-1)
                        exit()
                elif l[i-1]!=-1:
                    z1 = l[i-1]-l[z-1]

                    if z1<0:
                        print(-1)
                        exit()
                    else:
                        go1.append(z1)

        for i in go1:
            ans+=i
        for i in go:
            ans+=i-mini

        if go!=[]:

            ans+=mini

    return ans










hash = defaultdict(list)



n = int(input())

par = [1]+list(map(int,input().split()))

l = list(map(int,input().split()))

bool = [False]*(n+1)
a = [-1]*(n+1)

for i in range(1,n):

    hash[i+1].append(par[i])
    hash[par[i]].append(i+1)

ans = 0

print(bfs(1))
