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;
using db = double;
ll f(ll n) {
  ll u = 0;
  while (n > 0) {
    u += n % 10;
    n /= 10;
  }
  return u;
}
int main(){
    ll k,s=1,a=1;
    cin>>k;
    for (ll i = 1; i <= k; i++)
    {
        cout<<s<<endl;
        if((db)s/f(s)<(db)(s+a)/f(s+a) && (db)(s+a)/f(s+a) > (db)(s+2*a)/f(s+2*a))a*=10;
        s+=a;
    }
}