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(x) :
    ret = 0
    while x :
        ret += x % 10
        x //= 10
    return ret

L = set()
nine = ''
for i in range(16) :
    for j in range(1, 1000) :
        x = int(str(j) + nine)
        L.add(x)
    nine += '9'
    
L = list(L)
L.sort()

v = [1]
n = [1]

for l in L[1:] :
    x = l / S(l)
    while v[-1] > x :
        v.pop()
        n.pop()
    v.append(x)
    n.append(l)

for i in range(K) :
    print(n[i])
