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>
#define ll long long
#define ull unsigned long long
using namespace std;

ull s(ull arg) {
    ull ret = 0;
    while(arg > 0) {
        ret += arg % 10;
        arg /= 10;
    }
    return ret;
}

int main(){
    ull k;
    cin >> k;

    ull base = 1;
    ull diff = 1;
    while(k > 0) {
        if(((double)base / s(base)) <= ((double)(base + diff) / s(base + diff))) {
            cout << base << endl;
            base += diff;
            k--;
        } 
        else {
            base -= diff;
            diff *= 10;
            base += diff;
        }
    }
}