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>
using namespace std;
using Int = long long;
int S(Int n)
{
    int s = 0;
    while (n) {
        s += n % 10;
        n /= 10;
    }
    return s;
}
Int P[16] = {1};
int main()
{
    for (int i = 1; i <= 15; i++) {
        P[i] = P[i-1] * 10;
    }
    int K;
    cin >> K;
    Int n = 1;
    for (int i = 0; i < K; i++) {
        for (int k = 0; n - S(n) * P[k] > 0; k++) {
            n += 9 * P[k];
        }
        cout << n << endl;
        n++;
    }
    return 0;
}
