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 <algorithm>
#include <cmath>
#include <iostream>
#include <numeric>
#include <utility>
#include <vector>

using namespace std;

// rec
long s(long n) {
    int sn = 0;
    while (n > 0) {
        sn += n % 10;
        n /= 10;
    }
    return sn;
}

bool smls(long x, long y) {
    return x * s(y) <= y * s(x);
}

int main() {
    long n;
    cin >> n;

    long nmax = 1000000000000000;
    vector<long> chl;
    long diff = nmax / 10;
    long next = nmax + nmax / 10;
    while (next - 2 > 0) {
        if (next <= diff) {
            diff /= 10;
        } else if (diff > 1 && smls(next - diff / 10 - 1, next - 1)) {
            diff /= 10;
        }
        next -= diff;
        chl.push_back(next - 1);
    }
    for (int i = 1; i <= n; i++) {
        cout << chl[chl.size() - i] << endl;
    }
}
