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):
    ret = 0
    while n > 0:
        ret += n % 10
        n //= 10
    return ret
numbers = [999999999999999999]
while numbers[-1] > 1:
    for d in range(0, 100):
        n = numbers[-1]
        m = n - 10 ** d
        if n * s(m) >= m * s(n):
            numbers.append(m)
            break
numbers = list(reversed(numbers))

n = int(input())
for i in range(n):
    print(numbers[i])
