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 <algorithm>
#include <vector>
#include <cmath>
#include <string>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
const int mod = 1000000007;

int main() {
    ios::sync_with_stdio(false);
    int k;
    ll a = 1, d = 1;
    cin >> k;
    while (k--) {
        string s = to_string(a + d), t = to_string(a + d * 10);
        double m = 0, n = 0;
        for (char i : s) m += i - '0';
        for (char i : t) n += i - '0';
        double b = (a + d) / m, c = (a + d * 10) / n;
        cout << a << '\n';
        if (b < c + 1e-9) a += d;
        else d *= 10, a += d;
    }
}
