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;
typedef long long ll;
ll f(ll x){
    ll p=0;
    while(x){
        p+=x%10;
        x/=10;
    }
    return p;
}
int main(void){
    int n;
    cin>>n;
    ll a=0;
    ll b=1;
    for(int i=0;i<n;i++){
        if((a+b)*f(a+b*10)>(a+b*10)*f(a+b)){
            b*=10;
        }
        a+=b;
        cout<<a<<endl;
    }
}
