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>
#include <algorithm>
#include <string>
#include <cmath>
#define int long long
using namespace std;

int digit(int u) {
  int t = 0;
  while(u != 0) {
    t += u % 10;
    u /= 10;
  }
  return t;
}

signed main() {
  int K; cin >> K;
  int ans = 1, r = 1;
  for(int i = 0; i < K; ++i) {
    cout << ans << endl;
    if((ans + 1) % (r*10) == 0 && digit(ans + r) * r <= (ans + r)) r *= 10;
    ans += r;
  }

  return 0;
}
