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 <string>
#include <iostream>
#include <cmath>
#include <algorithm>
using namespace std;
int sum(long long n) {
    int r = 0;
    while (n > 0) {
        r += n % 10;
        n /= 10;
    }
    return r;
}
int main(){
    int k;
    cin >> k;
    long long a=1;
    long long p=1;
    for(int i=1;i<=k;i++){
        cout << a<< endl;
        long long c=a+p;
        long long d=a+p*10;
        if(c* sum(d) <= d * sum(c)){
            a=c;
        }
        else {
            a=d;
            p=p*10;
        }
    }


}