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;

long long s(long long n) {
    long long ans = 0;

    while (n) {
        ans += n % 10;
        n /= 10;
    }

    return ans;
}

int main() {
    int k;
    cin >> k;

    long long n = 1, d = 1;
    cout << 1 << endl;

    for (int i = 1; i < k; i++) {
        if (s(n+d) * (n+d*10) < s(n+d*10) * (n+d)) {
            d *= 10;
        }
        n += d;
        cout << n << endl;
    }
}
