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 <bits/stdc++.h>

int s(int64_t x) {
    int result = 0;
    for (; x != 0; x /= 10)
        result += x % 10;
    return result;
}

double f(int64_t x) {
    return 1.0 * x / s(x);
}

int main() {
    int n;
    scanf("%d", &n);
    int64_t last = 1, high_bit = 1;
    for (int i = 0; i < n; i++) {
        printf("%lld\n", last);
        if (f(last + high_bit * 10) < f(last + high_bit))
            high_bit *= 10;
        last += high_bit;
    }
    return 0;
}
