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 <bits/stdc++.h>
using namespace std;
using ll = long long;

ll sum(ll n) {
  ll sum = 0;
  while (n > 0) {
    sum += n % 10;
    n /= 10;
  }
  return sum;
}

int main() {
  int k;
  cin >> k;
  ll ans = 1, add = 1;
  for (int i = 0; i < k; ++i) {
    cout << ans << endl;
    if (sum(ans + add) * (ans + add * 10) < sum(ans + add * 10) * (ans + add))
      add *= 10;
    ans += add;
  }
}
