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())

def S(n):
    return sum(map(int, list(str(n))))

def norm(n):
    return n/S(n)

snk = 1
order = 0
for i in range(K):
    print(snk)
    nxt1 = snk + 10 ** order
    nxt2 = snk + 10 ** (order + 1)
    if norm(nxt2) < norm(nxt1):
        order += 1
        snk = nxt2
    else:
        snk = nxt1
