Let S(n) denote the sum of the digits in the decimal notation of n. For example, S(123) = 1 + 2 + 3 = 6.

We will call an integer n a Snuke number when, for all positive integers m such that m > n, \frac{n}{S(n)} \leq \frac{m}{S(m)} holds.

Given an integer K, list the K smallest Snuke numbers.

Constraints

* 1 \leq K
* The K-th smallest Snuke number is not greater than 10^{15}.

Input

Input is given from Standard Input in the following format:


K


Output

Print K lines. The i-th line should contain the i-th smallest Snuke number.

Example

Input

10


Output

1
2
3
4
5
6
7
8
9
19
#include <iostream>

long long int S(long long int N) {
  int s = 0;

  for (long long int n = N; n > 0; n /= 10) {
    s += n % 10;
  }

  return s;
}

int main() {
  long long int K;
  std::cin >> K;

  long long int s = 1, d = 1;

  for (int i = 0; i < K; i++) {
    std::cout << s << std::endl;

    while (1.0 * (s + d) / S(s + d) > 1.0 * (s + 2 * d) / S(s + 2 * d)) {
      d *= 10;
    }

    s += d;
  }
}
