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
#include <iostream>
#include <cstdio>

using namespace std;

typedef long long ll;

ll k;
ll ans, now = 1;

ll s(ll p)
{
    ll re = 0;
    while(p != 0)
    {
        re += p % 10;
        p /= 10;
    }
    return re;
}

int main()
{
    scanf("%lld", &k);
    while(k--)
    {
        ans += now;
        if(s(ans) * (ans + now) < s(ans + now) * ans) ans -= now, now *= 10, ans += now;
        printf("%lld\n", ans);
    }
    return 0;
}
