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 sum([ord(x)-ord('0') for x in str(n)])

def r(n):
	return n/s(n)

def f(n):
	d = 10
	m = n
	while d <= n*10:
		n //= d
		n *= d
		n += d-1
		d *= 10
		if(r(n) < r(m)):
			m = n
	return m

n = 1
for _ in range(int(input())):
	print(n)
	n = f(n+1)