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>
using namespace std;

typedef long long ll;
ll res[10000], a[20];

inline int S(ll k) {
	int res = 0;
	while(k) res += k % 10, k /= 10;
	return res;
}

int main() {
	int cnt = 0;
	ll val = 1;
	do {
		res[cnt++] = val;
		val++;
		long long tmp = val, t = 1, c = 0;
		for(c = 0; tmp; c++, tmp /= 10, t *= 10) {
			a[c] = tmp * t + t - 1;
		}
		val = a[0];
		for(int i = 0; i < c; i++)
			if(val * S(a[i]) > a[i] * S(val)) val = a[i];
	} while(val < 10000000000000000ll);
int k; scanf("%d", &k);
for(int i = 0; i< k; i++) printf("%lld\n", res[i]);
	return 0;
}