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>
#define rep(i,n) for (int i = 0; i < n; ++i)
using namespace std;
using ll = long long;
double S(ll n){
	double cnt = 0;
	while(n){
		cnt += n%10;
		n /= 10;
	}
	return cnt;
}
int main() {
	cin.tie(nullptr); ios::sync_with_stdio(false);
	int k; cin >> k;
	ll a = 0, b = 1;
	while(k--){
		a += b;
		cout << a << endl;
		if (b < (a+b)/S(a+b))b *= 10;
	}
}