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
#include <bits/stdc++.h>
using namespace std;
template <typename S, typename T>
bool minx(S &a, const T &b) {
  return a < b ? 1 : a = b, 0;
}
template <typename T>
void int_in(T &res) {
  int flag = 1;
  char ch;
  while (isspace(ch = getchar()))
    ;
  res = 0;
  if (ch == '-')
    flag = -1;
  else if (ch >= '0' && ch <= '9')
    res = ch - '0';
  while ((ch = getchar()) >= '0' && ch <= '9') res = res * 10 + ch - '0';
  res *= flag;
}
template <typename T>
void int_out(T a) {
  if (a < 0) {
    putchar('-');
    a = -a;
  }
  if (a > 9) int_out(a / 10);
  putchar(a % 10 + '0');
}
const int INF = 0x3f3f3f3f;
const double tol = 1e-8;
const int N = 1 << 13;
vector<int> g[N];
int ans[N], r[N];
int main() {
  int n;
  int_in(n);
  for (int i = 0; i <= N - 1; ++i) {
    r[i] = N;
    g[i].push_back(0);
  }
  ans[0] = 1;
  for (int i = 1; i <= n; ++i) {
    int u;
    int_in(u);
    for (auto &v : g[u]) {
      int x = u ^ v;
      ans[x] = 1;
      if (r[x] > u) r[x]--;
      while (r[x] > u) {
        g[r[x]].push_back(x);
        r[x]--;
      }
    }
    g[u].clear();
  }
  int_out(accumulate(ans, ans + N, 0)), puts("");
  for (int i = 0; i <= N - 1; ++i) {
    if (ans[i]) int_out(i), putchar(' ');
  }
  puts("");
  return 0;
}
