Problem Description

Just indulge in your own fantasy!

In this problem, please construct a general formula for the sequence $a_x$ such that

$$a_1=1, a_2=1, a_3=4, a_4=5, a_5=1, a_6=4$$

To test the correctness of the construction, this problem requires you to input a number $n$ and output the first $n$ terms of the function you construct. Regardless of how you construct it, as long as the first $6$ terms of your output are the sequence $[1,1,4,5,1,4]$.

Input

One integer $n$ satisfying $6\leqslant n\leqslant 2\times 10^5$ is given on one line.

Output

Output a sequence of $n$ integers separated by spaces, representing the sequence you have constructed. Ensure that the output numbers are within the range of $[-1\times 10^9,1\times 10^9]$.

Samples

10

1 1 4 5 1 4 54 232 673 1579

Note

Note that when

$$f(x)=\frac{13 x^{5}}{120} - \frac{37 x^{4}}{24} + \frac{181 x^{3}}{24} - \frac{359 x^{2}}{24} + \frac{237 x}{20} - 2,$$

the sequence generated by $a_i$ when $i\in [1,10]$ is $[1,1,4,5,1,4,54,232,673,1579]$.

Please note the data range of $n$ in this problem. The aforementioned construction scheme may not necessarily work for this problem.