I. Line pinball
time limit per test
0.25 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Line pinball is played with $$$n$$$ metal balls having weights of $$$1, 2, 3, ..., n$$$ grams. Along a straight line, there are $$$n + 1$$$ holes equipped with plungers. The holes are numbered from left to right with numbers from $$$0$$$ to $$$n$$$.

Each plunger is inclined to the right and has its impact force $$$p_i$$$, where $$$i$$$ is the number of the hole. The design and inclination of the plunger are such that if it hits a ball with a mass of $$$x$$$ grams with force $$$p_i$$$, then the ball will move into the hole numbered $$$i + \lfloor p_i / x \rfloor$$$, where $$$\lfloor ... \rfloor$$$ means round down to a lower integer.

The game begins with one of the balls being placed in the starting hole numbered $$$0$$$. Next, the plungers of all the holes into which the ball falls are used sequentially. The game ends and is considered successful when the ball hits the hole number $$$n$$$. The game is considered lost if, at some point, the force of the plunger is too small to throw the ball into another hole or too strong and throws it further than the hole number $$$n$$$.

Write a program that selects the impact force $$$p_i$$$ for all $$$n$$$ plungers so that any ball with a mass from $$$1$$$ to $$$n$$$, starting from hole $$$0$$$, ends up in hole $$$n$$$.

Input

The only line contains the integer $$$n$$$ ($$$1 \leq n \leq 50$$$).

Output

In a single line print $$$n$$$ integers separated by spaces – the impact forces of the plungers $$$p_0, p_1, ..., p_{n-1}$$$ ($$$1 \leq p_i \leq 10^6$$$). The $$$n$$$-th hole plunger is never used, and its parameter must not be printed. It is guaranteed that a solution exists.

If there are multiple solutions print any of them.

Examples
Input
2
Output
2 2
Input
3
Output
3 5 3