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
def s(n):
  return n / sum(map(int, str(n)))
k = int(input())
p = 1
e = 0
i = 0
while i < k:
  n = (p + 1) * 10**e - 1
  nxt = (p + 2) * 10**e - 1
  if s(n) <= s(nxt):
    print(n)
    p += 1
    i += 1
  else:
    e += 1
    p = (p + 1) // 10
