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>
using namespace std;
using ll = long long;

ll d(ll n) {
  ll res = 0;
  while (n) {
    res += 1;
    n /= 10;
  }
  return res;
}

ll s(ll n) {
  ll res = 0;
  while (n) {
    res += n % 10;
    n /= 10;
  }
  return res;
}

ll f(ll n) {
  ll x = 1;
  for (int i = 0; i <= d(n); i++) {
    int y = 0;
    while (y < 9 - n / x % 10) {
      if (n * s(n + x) <= (n + x) * s(n)) break;
      y++;
    }
    n += x * y;
    x *= 10;
  }
  return n;
}

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  int K;
  cin >> K;

  ll n = 0;
  while (K--) {
    n = f(n + 1);
    cout << n << "\n";
  }
}