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>
#include <cstdio>
using namespace std;

typedef long long ll;
ll k, a = 1;

ll f(ll p) {
	ll re = 0;
	while (p) {
		re += p % 10;
		p /= 10;
	}
	return re;
}

int main()
{
	ll i = 1, t;
	cin >> k;
	while (k--) {
		t = i + a;
        if (t * f(i) < i * f(t)) i -= a, a *= 10, i += a;
		printf("%lld\n", i);
		i += a;
	}
    return 0;
}