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
res = []
for digit in range(1,16):
    if digit<=3:
        for i in range(2,11):
            res.append(10**(digit-1)*i-1)
    elif 4<=digit<=12:
        for i in range(11,(digit-2)*10):
            res.append(i*10**(digit-2)-1)
        for i in range(digit-2,11):
            res.append(i*10**(digit-1)-1)
    elif digit==15:
        for i in range(101,110):
            res.append(i*10**(digit-3)-1)
        for i in range(11,101):
            res.append(i*10**(digit-2)-1)
    else:
        for i in range(11,101):
            res.append(i*10**(digit-2)-1)
for i in range(int(input())):
    print(res[i])
