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())

L = [int(x)-1 for x in input().split()]

V = [int(x) for x in input().split()]

G = []
DG = []
VD = []
VU = []
for i in range(n):
    G.append([])
    DG.append([])
    VD.append([])
    VU.append([])


for i in range(n-1):
    DG[L[i]].append(i+1)
    G[i+1].append(L[i])
    G[L[i]].append(i+1)

for i in range(n):
    for j in DG[i]:
        if V[j] != -1:
            VD[i].append(V[j])

for i in range(1,n):
    if V[L[i-1]] != -1:
        VU[i].append(V[L[i-1]])


depth = [0]*n
values = [0]*n
s = V[0]
depth[0] = 1
q = DG[0][:]
values[0] = V[0]
bad = False
while q:
    v = q.pop()
    q.extend(DG[v])
    depth[v] = 1-depth[L[v-1]]
    if depth[v] == 1:
        values[v] = V[v]
        s += values[v]-values[L[v-1]]
        if values[v]-values[L[v-1]] < 0:
            bad = True
    else:
        if len(DG[v]) == 0:
            values[v] = 0
        else:
            values[v] = min(V[i] for i in DG[v])
            s += values[v]-values[L[v-1]]
            if values[v]-values[L[v-1]] <0:
                bad = True
if bad:
    print(-1)
else:
    print(s)