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
#!/usr/bin/env python3

def main():
    K = int(input())

    l = []
    for i in range(1, 1000):
        l.append(i)
    for k in range(1, 13):
        n0 = 10 ** k
        for i in range(100, 1000):
            l.append(i * n0 + n0 - 1)

    r = []
    for n in l:
        sn = 0
        d = n
        while 0 < d:
            d, m = int(d / 10), d % 10
            sn += m
        r.append(n / sn)

    min_r = r[-1]
    for i in range(len(r) - 2, -1, -1):
        if min_r < r[i]:
            r.pop(i)
            l.pop(i)
        else:
            min_r = r[i]

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


if __name__ == '__main__':
    main()

