Problem: There are n cities in the Kingdom of Autumn, numbered from 1 to n. People can travel between any two cities using n-1 two-directional roads.

This year, the government decides to separate the kingdom. There will be regions of different levels. The whole kingdom will be the region of level 1. Each region of i-th level should be separated into several (at least two) regions of i+1-th level, unless i-th level is the last level. Each city should belong to exactly one region of each level and for any two cities in the same region, it should be possible to travel between them passing the cities in the same region only.

According to research, for each city i, there is a value a_i, which describes the importance of this city. All regions of the same level should have an equal sum of city importances.

Your task is to find how many plans there are to determine the separation of the regions that all the conditions are satisfied. Two plans are considered different if and only if their numbers of levels are different or there exist two cities in the same region of one level in one plan but in different regions of this level in the other plan. Since the answer may be very large, output it modulo 10^9+7.

Input

The first line contains one integer n (1 ≤ n ≤ 10^6) — the number of the cities.

The second line contains n integers, the i-th of which is a_i (1 ≤ a_i ≤ 10^9) — the value of each city.

The third line contains n-1 integers, p_1, p_2, …, p_{n-1}; p_i (p_i ≤ i) describes a road between cities p_i and i+1.

Output

Print one integer — the number of different plans modulo 10^9+7.

Examples

Input

4
1 1 1 1
1 2 3


Output

4

Input

4
1 1 1 1
1 2 2


Output

2

Input

4
1 2 1 2
1 1 3


Output

3

Note

For the first example, there are 4 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}.

Plan 3: Level-1: \{1,2,3,4\}, Level-2: \{1\},\{2\},\{3\},\{4\}.

Plan 4: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}, Level-3: \{1\},\{2\},\{3\},\{4\}.

For the second example, there are 2 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1\},\{2\},\{3\},\{4\}.

For the third example, there are 3 different plans:

Plan 1: Level-1: \{1,2,3,4\}.

Plan 2: Level-1: \{1,2,3,4\}, Level-2: \{1,2\},\{3,4\}.

Plan 3: Level-1: \{1,2,3,4\}, Level-2: \{1,3\},\{2\},\{4\}.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target( \
    "sse,sse2,sse3,ssse3,sse4,sse4.1,sse4.2,popcnt,mmx,avx,tune=native")
using namespace std;
const int MOD = 1000000007;
const int UNDEF = -1;
const int INF = 1 << 30;
template <typename T>
inline bool chkmax(T &aa, T bb) {
  return aa < bb ? aa = bb, true : false;
}
template <typename T>
inline bool chkmin(T &aa, T bb) {
  return aa > bb ? aa = bb, true : false;
}
int rint();
char rch();
long long rlong();
const int mn = 1e6 + 4;
long long a[mn];
int oa[mn];
unsigned int b[mn];
int p[mn];
int n;
unsigned int hia = 0;
bool fint(unsigned int t) {
  if ((unsigned int)hia > (unsigned int)t) return false;
  for (int x = 1; x < n; x++) b[x] = oa[x];
  for (int x = 0; x <= n - 2; x++) {
    int par = p[x];
    if (b[x] < t) {
      b[par] += b[x];
      if (b[par] > t) return false;
    }
  }
  return (b[n - 1] == t);
}
bool f(long long t) {
  if (t + hia < UINT_MAX) return fint(t);
  for (int x = 1; x < n; x++) a[x] = oa[x];
  for (int x = 0; x <= n - 2; x++) {
    int par = p[x];
    if (a[x] < t) {
      a[par] += a[x];
      if (a[par] > t) return false;
    }
  }
  return (a[n - 1] == t);
}
vector<pair<long long, int> > pliv;
void compress(vector<long long> &v) {
  sort(v.begin(), v.end());
  int cnt = 1;
  for (int i = 1; i < v.size(); i++) {
    if (v[i] != v[i - 1]) {
      pliv.push_back(make_pair(v[i - 1], cnt));
      cnt = 1;
    } else
      cnt++;
  }
  if (cnt) pliv.push_back(make_pair(v.back(), cnt));
}
long long gt;
int gocc;
void countOcc(int vl, int vr, int kl, int kr) {
  if (vl > vr || kl > kr) return;
  if (vl == vr) {
    if ((pliv[vl].first == kl * gt) || (0 == pliv[vl].first % gt))
      gocc += pliv[vl].second;
    return;
  }
  int vmid = (vl + vr) / 2;
  int kmid = pliv[vmid].first / gt;
  countOcc(vl, vmid, kl, kmid);
  countOcc(vmid + 1, vr, kmid + 1, kr);
}
bool can(int g, long long d) {
  gt = d;
  gocc = 0;
  countOcc(0, pliv.size() - 1, 1, g);
  return gocc == g;
}
const int slim = 1e6 / 200;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  n = rint();
  long long suma = 0;
  for (int y = 1; y <= n; y++) {
    unsigned int got = rint();
    chkmax(hia, got);
    oa[n - y] = got;
    suma += got;
  }
  a[0] = b[0] = oa[0];
  for (int y = 2; y <= n; y++) {
    p[n - y] = n - rint();
  }
  map<long long, int, greater<long long> > h;
  {
    long long d = hia;
    if (f(d)) h[d] = 0;
  };
  for (int g = n / 2; g >= slim; g--) {
    if (suma % g == 0) {
      long long d = suma / g;
      if (f(d)) h[d] = 0;
    }
  }
  vector<long long> sumsubtree(n);
  for (int x = 0; x < n; x++) sumsubtree[x] = oa[x];
  for (int x = 0; x <= n - 2; x++) sumsubtree[p[x]] += sumsubtree[x];
  compress(sumsubtree);
  for (int g = slim - 1; g >= 2; g--) {
    if (suma % g == 0) {
      long long d = suma / g;
      if (can(g, d)) h[d] = 0;
    }
  }
  h[suma] = 1;
  int final = 0;
  for (auto it = h.begin(); it != h.end(); ++it) {
    int add = it->second;
    final += add;
    if (final >= MOD) final -= MOD;
    auto jt = it;
    ++jt;
    for (; jt != h.end(); ++jt) {
      if (it->first % (jt->first) != 0) continue;
      int ans = jt->second + add;
      if (ans >= MOD) ans -= MOD;
      jt->second = ans;
    }
  }
  printf("%d\n", final);
}
static char stdinBuffer[1024];
static char *stdinDataEnd = stdinBuffer + sizeof(stdinBuffer);
static const char *stdinPos = stdinDataEnd;
void readAhead(size_t amount) {
  size_t remaining = stdinDataEnd - stdinPos;
  if (remaining < amount) {
    memmove(stdinBuffer, stdinPos, remaining);
    size_t sz = fread(stdinBuffer + remaining, 1,
                      sizeof(stdinBuffer) - remaining, stdin);
    stdinPos = stdinBuffer;
    stdinDataEnd = stdinBuffer + remaining + sz;
    if (stdinDataEnd != stdinBuffer + sizeof(stdinBuffer)) *stdinDataEnd = 0;
  }
}
int rint() {
  readAhead(16);
  int x = 0;
  bool neg = false;
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  if (*stdinPos == '-') {
    ++stdinPos;
    neg = true;
  }
  while (*stdinPos >= '0' && *stdinPos <= '9') {
    x *= 10;
    x += *stdinPos - '0';
    ++stdinPos;
  }
  return neg ? -x : x;
}
char rch() {
  readAhead(16);
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  char ans = *stdinPos;
  ++stdinPos;
  return ans;
}
long long rlong() {
  readAhead(32);
  long long x = 0;
  bool neg = false;
  while (*stdinPos == ' ' || *stdinPos == '\n') ++stdinPos;
  if (*stdinPos == '-') {
    ++stdinPos;
    neg = true;
  }
  while (*stdinPos >= '0' && *stdinPos <= '9') {
    x *= 10;
    x += *stdinPos - '0';
    ++stdinPos;
  }
  return neg ? -x : x;
}