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;
inline long long in() {
  int32_t x;
  scanf("%d", &x);
  return x;
}
inline string getStr() {
  char ch[1000000];
  scanf("%s", ch);
  return ch;
}
inline char getCh() {
  char ch;
  scanf(" %c", &ch);
  return ch;
}
const long long INF = 1e18;
const long long MOD = 1e9 + 7;
const long long MAX_N = 1e5 + 5;
struct edge {
  long long v, u, w;
  edge() {}
  edge(long long v, long long u, long long w) : v(v), u(u), w(w) {}
};
edge e[MAX_N];
bool b[MAX_N];
vector<long long> graph[MAX_N];
long long dp[2][MAX_N];
inline void dfs(long long node, long long pr) {
  dp[1][node] = b[node], dp[0][node] = b[node] ^ 1;
  for (long long i = 0; i < (long long)graph[node].size(); i++) {
    long long D0 = dp[0][node], D1 = dp[1][node];
    long long u = graph[node][i];
    if (u == pr) continue;
    dp[0][node] = dp[1][node] = 0;
    dfs(u, node);
    dp[0][node] += (1LL * dp[0][u] * D0 + 1LL * dp[1][u] * D0) % MOD;
    dp[1][node] +=
        (1LL * dp[1][u] * D0 + 1LL * dp[1][u] * D1 + 1LL * dp[0][u] * D1) % MOD;
  }
}
int32_t main() {
  long long n = in();
  for (long long i = 0; i < n - 1; i++) {
    e[i].v = in(), e[i].u = i + 1;
    graph[e[i].v].push_back(e[i].u);
    graph[e[i].u].push_back(e[i].v);
  }
  for (long long i = 0; i < n; i++) {
    b[i] = in();
  }
  dfs(1, -1);
  cout << dp[1][1] << endl;
}
