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
from math import log, floor
from itertools import islice

k = int(input())

def s(n):
    return n / sum(map(int, str(n)))

def f(n):
    ds = range(int(log(n+1, 10))+2)
    xs = [(10**(d+1))*floor(n/(10**(d+1)) + 1) - 1 for d in ds]
    return min(xs, key=s)

def g():
    for n in range(1, 10):
        yield n
    while True:
        n = f(n+1)
        yield n

for x in islice(g(), k):
    print(x)