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
import math
K=int(input())
k=2
m=0
def D(x):
  s=str(x)
  array=list(map(int,list(s)))
  return sum(array)
N=1
S=1
a=0
print(1)
while k<=K:
  N+=10**a
  S=D(N)
  if a<math.log10(N/S):
    a+=1
    N=(N//10**a+1)*10**a-1
  S=D(N)
  print(N)
  k+=1
    
    
