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 <bits/stdc++.h>

using namespace std;

using ll = long long;

ll sum(ll n) {
    ll sum = 0;
    while (n) {
        sum += (n % 10);
        n /= 10;
    }
    return sum;
}

bool compare(ll x, ll y) {
    if (x * sum(y) <= y * sum(x)) return false;
    return true;
}

int main() {
    cin.tie(0); ios::sync_with_stdio(false);

    ll K;
    cin >> K;

    ll cur = 0, add = 1;
    for (int i = 0; i < K; ++i) {
        if (compare(cur + add, cur + 10 * add)) add *= 10;
        cur += add;
        cout << cur << '\n';
    }

    return 0;
}
