Snuke Numbers

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

inputFormat

Input

Input is given from Standard Input in the following format:

K

outputFormat

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

样例

10

1
2
3
4
5
6
7
8
9
19

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