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
import sys,bisect
input = sys.stdin.buffer.readline


n = int(input())

par = [-1] + list(map(int,input().split()))
ch = [[] for i in range(n)]
for i in range(1,n):
    par[i] -= 1
    ch[par[i]].append(i)

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

val = [0]*n
val[0] = s[0]
eve = [False]*n

tank = [0]
while tank:
    v = tank.pop()

    if s[v] == -1:
        eve[v] = True
        s[v] = s[par[v]]
    else:
        if v != 0:
            val[v] = s[v] - s[par[v]]
            if val[v] < 0:
                print(-1)
                exit()
    for e in ch[v]:
        tank.append(e)
    
for i in range(n):
    if eve[i] and len(ch[i]) > 0:
        mi = val[ch[i][0]]
        for e in ch[i]:
            if mi > val[e]:
                mi = val[e]
        val[i] = mi
        for e in ch[i]:
            val[e] -= mi

print(sum(val))