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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
const int maxdig = 16;
int sum(long long x) {
	int ret = 0;
	while (x > 0) {
		ret += x % 10;
		x /= 10;
	}
	return ret;
}
int main() {
	int n;
	cin >> n;
	long long cur = 1;
	for (int i = 0; i < n; ++i) {
		cout << cur << '\n';
		string s = to_string(cur);
		s = string(maxdig - s.size(), '0') + s;
		vector<long long> vl;
		for (int j = maxdig - 1; j >= 0; --j) {
			while (s[j] < '9') {
				++s[j];
				for (int k = maxdig - 1; k > j; --k) {
					s[k] = '0';
				}
				vl.push_back(stoll(s));
				for (int k = maxdig - 1; k > j; --k) {
					while (s[k] < '9') {
						++s[k];
						vl.push_back(stoll(s));
					}
				}
			}
		}
		cur = *min_element(vl.begin(), vl.end(), [](long long x, long long y) { return x * sum(y) < y * sum(x); });
	}
	return 0;
}