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;
long long digits(long long n){
  int mon=0;
  while(n){
    mon+=n%10;
    n/=10;
  }
  return mon;
}
int main(){
  int n;
  cin>>n;
  long long a=0,b=1;
  for(int i=0;i<n;++i){
    if((a+b)*digits(a+b*10)>(a+b*10)*digits(a+b)) b*=10;
    a+=b;
    cout<<a<<endl;
  }
}
