description: 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
solution: #include <bits/stdc++.h>
  using namespace std;
  const long long mod = 1000000007;
  const unsigned gen_seed =
      std::chrono::system_clock::now().time_since_epoch().count();
  std::mt19937_64 gen(gen_seed);
  const int N = 1000500;
  int mindiv[N + 1];
  struct sega {
    sega(){};
    sega(int v) { add(v); };
    map<int, int> deg;
    int numbad = 0;
    void add(int v) {
      while (v > 1) {
        deg[mindiv[v]]++;
        if (deg[mindiv[v]] == 0) numbad--;
        v /= mindiv[v];
      }
    }
    void rem(int v) {
      while (v > 1) {
        deg[mindiv[v]]--;
        if (deg[mindiv[v]] == -1) numbad++;
        v /= mindiv[v];
      }
    }
    void killjoin(sega& f) {
      if (f.deg.size() > deg.size()) {
        swap(f.deg, deg);
        swap(numbad, f.numbad);
      }
      for (auto x : f.deg) {
        if (deg[x.first] < 0) numbad--;
        deg[x.first] += x.second;
        if (deg[x.first] < 0) numbad++;
      }
    }
    bool isbad() { return numbad > 0; }
  };
  int main() {
    vector<long long> pr;
    std::vector<int> isp(N + 1, 0);
    for (int i = 2; i <= N; ++i) {
      if (mindiv[i] == 0) {
        mindiv[i] = i;
        pr.push_back(i);
        isp[i] = 1;
      }
      for (int j = 0; j < (int)pr.size() && pr[j] <= mindiv[i] && i * pr[j] <= N;
           ++j)
        mindiv[i * pr[j]] = pr[j];
    }
    int n;
    scanf("%d", &n);
    std::vector<int> a(n);
    char c[1000500];
    for (int i = 0; i < n; i++) {
      if (i < n - 1)
        scanf("%d", &a[i]);
      else
        scanf("%d\n", &a[i]);
    }
    scanf("%s", c);
    string s(c);
    vector<sega> q;
    long long ans = 0;
    for (int i = 0; i < n; i++) {
      sega cur;
      if (s[i] == '*')
        cur.add(a[i]);
      else
        cur.rem(a[i]);
      while (cur.isbad()) {
        if (q.empty()) break;
        cur.killjoin(q.back());
        q.pop_back();
      }
      if (cur.isbad() == false) {
        q.emplace_back(std::move(cur));
      }
      ans += q.size();
    }
    cout << ans;
  }
  