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())
p = list(map(int, input().split()))
p = [-1] + [i - 1 for i in p]
s = list(map(int, input().split()))
g = {}
for i in range(n):
    g[i] = []
for i in range(1, len(p)):
    g[p[i]].append(i)

d = {}
md = 1
q = [(0, 1)]
while len(q) > 0:
    v = q[0]
    del q[0]
    nd = v[1] + 1
    if nd not in d:
        d[nd] = []
    for nv in g[v[0]]:
        q.append((nv, nd))
        d[nd].append(nv)
        md = max(md, nd)
sh = [0 for i in range(n)]
a = [0 for i in range(n)]
a[0] = s[0]
for dp in range(md, 0, -1):
    if dp % 2 == 0 or dp == 1:
        continue
    dc = {}
    for v in d[dp]:
        sv = s[v]
        gp = p[p[v]]
        gpv = s[gp]
        if sv < gpv:
            print(-1)
            exit()
        a[v] = sv - gpv
        pr = p[v]
        if pr not in dc:
            dc[pr] = 10**15
        dc[pr] = min(dc[pr], a[v])
    for v in d[dp]:
        pr = p[v]
        a[v] -= dc[pr]
    for pr in dc:
        a[pr] = dc[pr]

print(sum(a))