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 sum_digit(n):
    n_str = str(n)
    ans = 0
    for dig in n_str:
        ans += int(dig)
    return ans

def snuke(n):
    return n / sum_digit(n)

K = int(input())

ans = 1
print(ans)
for i in range(K - 1):
    s = len(str(ans))
    x = snuke(ans)
    L = [[ans + 10 ** k, snuke(ans + 10 ** k)] for k in range(s+1)]
    L.sort(key = lambda x: x[1])
    ans = L[0][0]
    print(ans)
