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>
const int MAX_N = 2e5 + 5;
const int MODULO = 1000000007;
int N;
std::vector<int> children[MAX_N];
std::bitset<MAX_N> isBlack;
long long memo[MAX_N][2];
long long f(int vertex, bool blackAbove);
int gcdExtended(int a, int b, int *x, int *y) {
  if (a == 0) {
    *x = 0, *y = 1;
    return b;
  }
  int x1, y1;
  int gcd = gcdExtended(b % a, a, &x1, &y1);
  *x = y1 - (b / a) * x1;
  *y = x1;
  return gcd;
}
int modInverse(int b, int m) {
  int x, y;
  int g = gcdExtended(b, m, &x, &y);
  if (g != 1) return -1;
  return (x % m + m) % m;
}
long long blackBlackAbove(int vertex) { return 0; }
long long blackWhiteAbove(int vertex) {
  long long result = 1;
  for (int child : children[vertex]) {
    result *=
        (f(child, false) + (isBlack[child] ? 0 : f(child, true))) % MODULO;
    result %= MODULO;
  }
  return result;
}
long long whiteBlackAbove(int vertex) {
  long long result = 1;
  for (int child : children[vertex]) {
    result *= f(child, false) + (isBlack[child] ? 0 : f(child, true));
    result %= MODULO;
  }
  return result;
}
long long whiteWhiteAbove(int vertex) {
  long long productChildren = 1;
  for (int child : children[vertex]) {
    productChildren *=
        (f(child, false) + (isBlack[child] ? 0 : f(child, true))) % MODULO;
    productChildren %= MODULO;
  }
  long long result = 0;
  for (int child : children[vertex]) {
    int fChild =
        (f(child, false) + (isBlack[child] ? 0 : f(child, true))) % MODULO;
    fChild = modInverse(fChild, MODULO);
    result += ((productChildren * fChild) % MODULO) * f(child, false);
    result %= MODULO;
  }
  return result;
}
long long f(int vertex, bool blackAbove) {
  if (isBlack[vertex]) {
    if (blackAbove) {
      if (memo[vertex][1] != -1) return memo[vertex][1];
      return memo[vertex][1] = blackBlackAbove(vertex);
    } else {
      if (memo[vertex][0] != -1) return memo[vertex][0];
      return memo[vertex][0] = blackWhiteAbove(vertex);
    }
  } else {
    if (blackAbove) {
      if (memo[vertex][1] != -1) return memo[vertex][1];
      return memo[vertex][1] = whiteBlackAbove(vertex);
    } else {
      if (memo[vertex][0] != -1) return memo[vertex][0];
      return memo[vertex][0] = whiteWhiteAbove(vertex);
    }
  }
}
int main() {
  std::cin >> N;
  for (int i = 1; i < N; i++) {
    int tmp;
    std::cin >> tmp;
    children[tmp].push_back(i);
  }
  for (int i = 0; i < N; i++) {
    int tmp;
    std::cin >> tmp;
    isBlack[i] = tmp ? true : false;
  }
  for (int i = 0; i < MAX_N; i++) memo[i][0] = memo[i][1] = -1;
  std::cout << f(0, false) << std::endl;
  return 0;
}
