#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
#include <cstdint>

int main() {
  constexpr int K = 9 * 2;
  int N;
  std::cin >> N;
  std::vector<std::vector<int>> counts(K + 1, std::vector<int>(K + 1));
  std::int64_t count = 0;
  for (int i = 0; i < N; ++i) {
    double a;
    std::cin >> a;
    auto value = static_cast<std::int64_t>(std::round(a * 1.0e9));
    int count2 = 0, count5 = 0;
    while (value % 2 == 0) {
      value /= 2;
      ++count2;
    }
    while (value % 5 == 0) {
      value /= 5;
      ++count5;
    }
    count2 = std::min(count2, K);
    count5 = std::min(count5, K);
    for (int i = K - count2; i <= K; ++i) {
      for (int j = K - count5; j <= K; ++j) {
        count += counts[i][j];
      }
    }
    ++counts[count2][count5];
  }
  std::cout << count << std::endl;
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.

Constraints

* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.


N
A_1
A_2
\vdots
A_N


Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Examples

Input

5
7.5
2.4
17.000000001
17
16.000000000


Output

3


Input

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001


Output

8

### Response

```cpp
#include <algorithm>
#include <iostream>
#include <vector>
#include <cmath>
#include <cstdint>

int main() {
  constexpr int K = 9 * 2;
  int N;
  std::cin >> N;
  std::vector<std::vector<int>> counts(K + 1, std::vector<int>(K + 1));
  std::int64_t count = 0;
  for (int i = 0; i < N; ++i) {
    double a;
    std::cin >> a;
    auto value = static_cast<std::int64_t>(std::round(a * 1.0e9));
    int count2 = 0, count5 = 0;
    while (value % 2 == 0) {
      value /= 2;
      ++count2;
    }
    while (value % 5 == 0) {
      value /= 5;
      ++count5;
    }
    count2 = std::min(count2, K);
    count5 = std::min(count5, K);
    for (int i = K - count2; i <= K; ++i) {
      for (int j = K - count5; j <= K; ++j) {
        count += counts[i][j];
      }
    }
    ++counts[count2][count5];
  }
  std::cout << count << std::endl;
  return 0;
}

```