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 = input()
pi = map(int,raw_input().split(" "))
si = map(int,raw_input().split(" "))


sons = [ []for i in range(n+1)]

for i in range(n-1):
    sons[pi[i]].append(i+2)

root = 1
dp = [0]*(1+n)
dp[root] = si[root-1]
flag = True
q = [root]
i = 0
deg = 0


for i in range(1,n+1):
    if si[i-1]!=-1:
        dp[i] = si[i-1]

for i in range(1,n+1):
    if si[i-1] == -1:
        dp[i] = 1e18
        for son in sons[i]:
            dp[i] = min(dp[i],dp[son])
        if len(sons[i]) == 0:
            dp[i] = dp[pi[i-2]]
s = dp[1]
for i in range(2,n+1):
    v = dp[i]-dp[pi[i-2]]
    if v<0:
        flag = False
    s += v

if flag:
    print s
else:
    print -1

	 	   			   			 			  	 	 				