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
K = int(input())
 
res = [(0, 0)]
mm = 0
cands = []
for i in range(1, 1000):
  v = i
  for j in range(16):
    cands.append(v)
    v = 10 * v + 9

cands = list(sorted(set(cands)))

for x in cands:
  i = sum(ord(c) - ord('0') for c in str(x))
  while x / i < res[-1][0]:
    res = res[:-1]
  res.append((x / i, x))
 
for i in range(1, K + 1):
  print(res[i][1])