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;
const int mod = 1e9 + 7;
vector<int> G[100010];
int dp[100010][2], color[100010];
inline void addIt(int &x, int val) {
  x += val;
  if (x >= mod) x -= mod;
}
void dfs(int u, int father) {
  dp[u][1] = color[u];
  dp[u][0] = color[u] ^ 1;
  for (vector<int>::iterator e = G[u].begin(); e != G[u].end(); e++) {
    int v = *e;
    if (v == father) continue;
    dfs(v, u);
    int temp[2] = {0, 0};
    addIt(temp[0], dp[u][0] * 1LL * dp[v][0] % mod);
    addIt(temp[0], dp[u][0] * 1LL * dp[v][1] % mod);
    addIt(temp[1], dp[u][1] * 1LL * dp[v][0] % mod);
    addIt(temp[1], dp[u][1] * 1LL * dp[v][1] % mod);
    addIt(temp[1], dp[u][0] * 1LL * dp[v][1] % mod);
    dp[u][0] = temp[0];
    dp[u][1] = temp[1];
  }
}
int main() {
  int N, from, to, u;
  scanf("%d", &N);
  for (int i = 0; i < N - 1; i++) {
    scanf("%d", &from);
    G[from].push_back(i + 1);
    G[i + 1].push_back(from);
  }
  for (int i = 0; i < N; i++) scanf("%d", color + i);
  dfs(0, -1);
  printf("%d\n", dp[0][1]);
  return 0;
}
