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<cstdio>

long k;

int main() {
    scanf("%ld", &k);
    
    long ans = 0;
    for (long i = 0, j = 1; i < k; i++) {
        long x = ans + j;
        int y = 0;
        while (x > 0) {
            y += (x % 10);
            x /= 10;
        }
        if (y * j < ans + j) j *= 10;
        ans += j;
        printf("%ld\n", ans);
    }

    return 0;
}
