Appleman has a tree with n vertices. Some of the vertices (at least one) are colored black and other vertices are colored white.

Consider a set consisting of k (0 ≤ k < n) edges of Appleman's tree. If Appleman deletes these edges from the tree, then it will split into (k + 1) parts. Note, that each part will be a tree with colored vertices.

Now Appleman wonders, what is the number of sets splitting the tree in such a way that each resulting part will have exactly one black vertex? Find this number modulo 1000000007 (109 + 7).

Input

The first line contains an integer n (2 ≤ n ≤ 105) — the number of tree vertices. 

The second line contains the description of the tree: n - 1 integers p0, p1, ..., pn - 2 (0 ≤ pi ≤ i). Where pi means that there is an edge connecting vertex (i + 1) of the tree and vertex pi. Consider tree vertices are numbered from 0 to n - 1.

The third line contains the description of the colors of the vertices: n integers x0, x1, ..., xn - 1 (xi is either 0 or 1). If xi is equal to 1, vertex i is colored black. Otherwise, vertex i is colored white.

Output

Output a single integer — the number of ways to split the tree modulo 1000000007 (109 + 7).

Examples

Input

3
0 0
0 1 1


Output

2


Input

6
0 1 1 0 4
1 1 0 0 1 0


Output

1


Input

10
0 1 2 1 4 4 4 0 8
0 0 0 1 0 1 1 0 0 1


Output

27
n = int(raw_input())
p = [0] + map(int, raw_input().split())
color = map(int, raw_input().split())
MODP = int(1e9) + 7

res = []
for i in range(n):
    if color[i] == 1:
        res.append([0, 1])
    else:
        res.append([1, 0]) 

for i in range(n-1, 0, -1):
    if color[p[i]] == 1:
        res[p[i]][1] = ((res[i][0] + res[i][1])* res[p[i]][1]) % MODP
    else:
        res[p[i]][1] = (res[p[i]][0] * res[i][1] + res[p[i]][1] * (res[i][0] + res[i][1])) % MODP
        res[p[i]][0] = (res[p[i]][0] * (res[i][0] + res[i][1])) % MODP

print res[0][1] 
 
