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
#include <bits/stdc++.h>
using namespace std;
struct listNode {
  long long int n;
  listNode *next;
  listNode(long long int n = 0LL) : n(n), next(NULL) {}
};
long long int num;
listNode *edge[100100], *tail[100100];
long long int color[100100];
void insertEdge(long long int a, long long int b) {
  if (!edge[a]) {
    edge[a] = new listNode(b);
    tail[a] = edge[a];
  } else {
    tail[a]->next = new listNode(b);
    tail[a] = tail[a]->next;
  }
}
void dfs(long long int node, long long int parent, long long int &res0,
         long long int &res1) {
  long long int a, b, temp;
  if (color[node]) {
    res0 = 0LL;
    res1 = 1LL;
  } else {
    res0 = 1LL;
    res1 = 0LL;
  }
  for (listNode *ptr = edge[node]; ptr; ptr = ptr->next) {
    if (ptr->n == parent) continue;
    dfs(ptr->n, node, a, b);
    if (color[node]) {
      res1 *= (a + b);
      if (res1 >= 1000000007) res1 %= 1000000007;
    } else {
      res1 *= (a + b);
      if (res1 >= 1000000007) res1 %= 1000000007;
      temp = res0 * b;
      if (temp >= 1000000007) temp %= 1000000007;
      res1 += temp;
      if (res1 >= 1000000007) res1 %= 1000000007;
      res0 *= (a + b);
      if (res0 >= 1000000007) res0 %= 1000000007;
    }
  }
}
int main() {
  long long int i, a, b;
  scanf("%I64d", &num);
  for (i = 1; i <= num - 1; i++) {
    scanf("%I64d", &a);
    insertEdge(i, a);
    insertEdge(a, i);
  }
  for (i = 0; i < num; i++) scanf("%I64d", color + i);
  dfs(0, 0, a, b);
  printf("%I64d\n", b);
  return 0;
}
