#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
template <typename T>
vector<T>& operator--(vector<T>& v) {
  for (auto& i : v) --i;
  return v;
}
template <typename T>
vector<T>& operator++(vector<T>& v) {
  for (auto& i : v) ++i;
  return v;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& i : v) is >> i;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
  for (auto& i : v) os << i << ' ';
  return os;
}
template <typename T, typename U>
pair<T, U>& operator--(pair<T, U>& p) {
  --p.first;
  --p.second;
  return p;
}
template <typename T, typename U>
pair<T, U>& operator++(pair<T, U>& p) {
  ++p.first;
  ++p.second;
  return p;
}
template <typename T, typename U>
istream& operator>>(istream& is, pair<T, U>& p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, pair<T, U> p) {
  os << p.first << ' ' << p.second;
  return os;
}
template <typename T, typename U>
pair<T, U> operator-(pair<T, U> a, pair<T, U> b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
template <typename T, typename U>
pair<T, U> operator+(pair<T, U> a, pair<T, U> b) {
  return make_pair(a.first + b.first, a.second + b.second);
}
template <typename T, typename U>
void umin(T& a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
void umax(T& a, U b) {
  if (a < b) a = b;
}
struct Sieve {
  struct PrimeIterator {
    int prime;
    int count;
    int num;
    const Sieve& sieve;
    PrimeIterator(int num, const Sieve& sieve) : num(num), sieve(sieve) {
      step();
    }
    void step() {
      void(0);
      prime = sieve.mn[num];
      count = 0;
      while (num != 1 && sieve.mn[num] == prime) {
        void(0);
        num /= sieve.mn[num];
        ++count;
      }
    }
    bool operator==(const PrimeIterator& other) const {
      return tie(prime, count, num) == tie(other.prime, other.count, other.num);
    }
    bool operator!=(const PrimeIterator& other) const {
      return !(*this == other);
    }
    PrimeIterator& operator++() {
      step();
      return *this;
    }
    pair<int, int> operator*() const { return {prime, count}; }
  };
  struct PrimeIteratorContainer {
    int num;
    const Sieve& sieve;
    PrimeIteratorContainer(int num, const Sieve& sieve)
        : num(num), sieve(sieve) {}
    PrimeIterator begin() const { return PrimeIterator(num, sieve); }
    PrimeIterator end() const { return PrimeIterator(1, sieve); }
    vector<pair<int, int>> collect() const {
      vector<pair<int, int>> result;
      for (auto p : *this) result.push_back(p);
      return result;
    }
  };
  vector<bool> isp;
  vector<int> primes;
  vector<int> mn;
  Sieve(int n, bool gen_primes = false, bool gen_mn = false) {
    isp.assign(n + 1, true);
    isp[0] = isp[1] = false;
    for (int i = 2; i * i <= n; ++i)
      if (isp[i])
        for (int j = i * i; j <= n; j += i) isp[j] = false;
    if (gen_primes)
      for (int i = 2; i <= n; ++i)
        if (isp[i]) primes.push_back(i);
    if (gen_mn) {
      mn.resize(n + 1);
      for (int i = 2; i <= n; ++i) {
        if (isp[i]) {
          mn[i] = i;
          if ((ll)i * i <= n)
            for (int j = i * i; j <= n; j += i) mn[j] = i;
        }
      }
    }
  }
  bool is_prime(int k) const { return isp[k]; }
  bool operator[](int k) const { return isp[k]; }
  PrimeIteratorContainer get_prime_divs(int k) const {
    return PrimeIteratorContainer(k, *this);
  }
  int phi(int n) const {
    auto v = get_prime_divs(n);
    for (auto [p, c] : v) n = n / p * (p - 1);
    return n;
  }
};
const int N = 1e6 + 19;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  vector<int> a(n);
  cin >> a;
  Sieve sieve(N, true, true);
  string s;
  cin >> s;
  vector<vector<pair<int, int>>> pos(N);
  vector<vector<int>> tor(N);
  for (int i = 0; i < n; ++i) {
    auto res = sieve.get_prime_divs(a[i]);
    int sign = (s[i] == '*' ? 1 : -1);
    for (auto [p, c] : res) {
      c *= sign;
      pos[p].emplace_back(i, c);
    }
  }
  vector<int> st;
  vector<int> good;
  for (int i = 0; i < pos.size(); ++i) {
    if (pos[i].empty()) continue;
    good.push_back(i);
    pos[i].insert(pos[i].begin(), make_pair(-1, 0));
    for (int j = 1; j < pos[i].size(); ++j)
      pos[i][j].second += pos[i][j - 1].second;
    tor[i].assign(pos[i].size(), pos[i].size());
    st.clear();
    for (int j = pos[i].size() - 1; j >= 0; --j) {
      while (!st.empty() && pos[i][st.back()].second >= pos[i][j].second)
        st.pop_back();
      if (!st.empty()) tor[i][j] = st.back();
      st.push_back(j);
    }
    pos[i].emplace_back(n, -1);
  }
  set<pair<int, int>> cur;
  for (int k : good) {
    cur.emplace(pos[k][tor[k][0]].first, k);
  }
  cur.emplace(n, 1e9);
  ll ans = 0;
  vector<int> ind(N, 0);
  for (int l = 0; l < n; ++l) {
    void(0);
    ans += cur.begin()->first - l;
    auto res = sieve.get_prime_divs(a[l]);
    for (auto [k, c] : res) {
      cur.erase({pos[k][tor[k][ind[k]]].first, k});
      ++ind[k];
      if (ind[k] < tor[k].size()) cur.insert({pos[k][tor[k][ind[k]]].first, k});
    }
  }
  cout << ans << '\n';
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

Kuzya started going to school. He was given math homework in which he was given an array a of length n and an array of symbols b of length n, consisting of symbols '*' and '/'.

Let's denote a path of calculations for a segment [l; r] (1 ≤ l ≤ r ≤ n) in the following way: 

  * Let x=1 initially. For every i from l to r we will consequently do the following: if b_i= '*', x=x*a_i, and if b_i= '/', then x=(x)/(a_i). Let's call a path of calculations for the segment [l; r] a list of all x that we got during the calculations (the number of them is exactly r - l + 1). 



For example, let a=[7, 12, 3, 5, 4, 10, 9], b=[/, *, /, /, /, *, *], l=2, r=6, then the path of calculations for that segment is [12, 4, 0.8, 0.2, 2].

Let's call a segment [l;r] simple if the path of calculations for it contains only integer numbers. 

Kuzya needs to find the number of simple segments [l;r] (1 ≤ l ≤ r ≤ n). Since he obviously has no time and no interest to do the calculations for each option, he asked you to write a program to get to find that number!

Input

The first line contains a single integer n (2 ≤ n ≤ 10^6).

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^6).

The third line contains n symbols without spaces between them — the array b_1, b_2 … b_n (b_i= '/' or b_i= '*' for every 1 ≤ i ≤ n).

Output

Print a single integer — the number of simple segments [l;r].

Examples

Input


3
1 2 3
*/*


Output


2


Input


7
6 4 10 1 2 15 1
*/*/*//


Output


8

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
template <typename T>
vector<T>& operator--(vector<T>& v) {
  for (auto& i : v) --i;
  return v;
}
template <typename T>
vector<T>& operator++(vector<T>& v) {
  for (auto& i : v) ++i;
  return v;
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (auto& i : v) is >> i;
  return is;
}
template <typename T>
ostream& operator<<(ostream& os, vector<T> v) {
  for (auto& i : v) os << i << ' ';
  return os;
}
template <typename T, typename U>
pair<T, U>& operator--(pair<T, U>& p) {
  --p.first;
  --p.second;
  return p;
}
template <typename T, typename U>
pair<T, U>& operator++(pair<T, U>& p) {
  ++p.first;
  ++p.second;
  return p;
}
template <typename T, typename U>
istream& operator>>(istream& is, pair<T, U>& p) {
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
ostream& operator<<(ostream& os, pair<T, U> p) {
  os << p.first << ' ' << p.second;
  return os;
}
template <typename T, typename U>
pair<T, U> operator-(pair<T, U> a, pair<T, U> b) {
  return make_pair(a.first - b.first, a.second - b.second);
}
template <typename T, typename U>
pair<T, U> operator+(pair<T, U> a, pair<T, U> b) {
  return make_pair(a.first + b.first, a.second + b.second);
}
template <typename T, typename U>
void umin(T& a, U b) {
  if (a > b) a = b;
}
template <typename T, typename U>
void umax(T& a, U b) {
  if (a < b) a = b;
}
struct Sieve {
  struct PrimeIterator {
    int prime;
    int count;
    int num;
    const Sieve& sieve;
    PrimeIterator(int num, const Sieve& sieve) : num(num), sieve(sieve) {
      step();
    }
    void step() {
      void(0);
      prime = sieve.mn[num];
      count = 0;
      while (num != 1 && sieve.mn[num] == prime) {
        void(0);
        num /= sieve.mn[num];
        ++count;
      }
    }
    bool operator==(const PrimeIterator& other) const {
      return tie(prime, count, num) == tie(other.prime, other.count, other.num);
    }
    bool operator!=(const PrimeIterator& other) const {
      return !(*this == other);
    }
    PrimeIterator& operator++() {
      step();
      return *this;
    }
    pair<int, int> operator*() const { return {prime, count}; }
  };
  struct PrimeIteratorContainer {
    int num;
    const Sieve& sieve;
    PrimeIteratorContainer(int num, const Sieve& sieve)
        : num(num), sieve(sieve) {}
    PrimeIterator begin() const { return PrimeIterator(num, sieve); }
    PrimeIterator end() const { return PrimeIterator(1, sieve); }
    vector<pair<int, int>> collect() const {
      vector<pair<int, int>> result;
      for (auto p : *this) result.push_back(p);
      return result;
    }
  };
  vector<bool> isp;
  vector<int> primes;
  vector<int> mn;
  Sieve(int n, bool gen_primes = false, bool gen_mn = false) {
    isp.assign(n + 1, true);
    isp[0] = isp[1] = false;
    for (int i = 2; i * i <= n; ++i)
      if (isp[i])
        for (int j = i * i; j <= n; j += i) isp[j] = false;
    if (gen_primes)
      for (int i = 2; i <= n; ++i)
        if (isp[i]) primes.push_back(i);
    if (gen_mn) {
      mn.resize(n + 1);
      for (int i = 2; i <= n; ++i) {
        if (isp[i]) {
          mn[i] = i;
          if ((ll)i * i <= n)
            for (int j = i * i; j <= n; j += i) mn[j] = i;
        }
      }
    }
  }
  bool is_prime(int k) const { return isp[k]; }
  bool operator[](int k) const { return isp[k]; }
  PrimeIteratorContainer get_prime_divs(int k) const {
    return PrimeIteratorContainer(k, *this);
  }
  int phi(int n) const {
    auto v = get_prime_divs(n);
    for (auto [p, c] : v) n = n / p * (p - 1);
    return n;
  }
};
const int N = 1e6 + 19;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int n;
  cin >> n;
  vector<int> a(n);
  cin >> a;
  Sieve sieve(N, true, true);
  string s;
  cin >> s;
  vector<vector<pair<int, int>>> pos(N);
  vector<vector<int>> tor(N);
  for (int i = 0; i < n; ++i) {
    auto res = sieve.get_prime_divs(a[i]);
    int sign = (s[i] == '*' ? 1 : -1);
    for (auto [p, c] : res) {
      c *= sign;
      pos[p].emplace_back(i, c);
    }
  }
  vector<int> st;
  vector<int> good;
  for (int i = 0; i < pos.size(); ++i) {
    if (pos[i].empty()) continue;
    good.push_back(i);
    pos[i].insert(pos[i].begin(), make_pair(-1, 0));
    for (int j = 1; j < pos[i].size(); ++j)
      pos[i][j].second += pos[i][j - 1].second;
    tor[i].assign(pos[i].size(), pos[i].size());
    st.clear();
    for (int j = pos[i].size() - 1; j >= 0; --j) {
      while (!st.empty() && pos[i][st.back()].second >= pos[i][j].second)
        st.pop_back();
      if (!st.empty()) tor[i][j] = st.back();
      st.push_back(j);
    }
    pos[i].emplace_back(n, -1);
  }
  set<pair<int, int>> cur;
  for (int k : good) {
    cur.emplace(pos[k][tor[k][0]].first, k);
  }
  cur.emplace(n, 1e9);
  ll ans = 0;
  vector<int> ind(N, 0);
  for (int l = 0; l < n; ++l) {
    void(0);
    ans += cur.begin()->first - l;
    auto res = sieve.get_prime_divs(a[l]);
    for (auto [k, c] : res) {
      cur.erase({pos[k][tor[k][ind[k]]].first, k});
      ++ind[k];
      if (ind[k] < tor[k].size()) cur.insert({pos[k][tor[k][ind[k]]].first, k});
    }
  }
  cout << ans << '\n';
  return 0;
}

```