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
#!/usr/bin/env python3
from fractions import Fraction
import sys


def g():
    i = 1
    while True:
        si = str(i)
        ni = min({
            int(si[:j] + "9" * (len(si) - j))
            for j in range(len(si) + 1)
        }, key=lambda a: (Fraction(a, sum(int(x) for x in str(a))), a))
        yield ni
        i = ni + 1


def solve(K: int):
    it = g()
    for i in range(K):
        print(next(it))


def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    K = int(next(tokens))  # type: int
    solve(K)


if __name__ == '__main__':
    main()
