When ZS the Coder is at levelk, he can :

1. Press the '+' button. This increases the number on the screen by exactly $k$. So, if the number on the screen was $x$, it becomes $x+k$.
2. Press the '$\sqrt{}$' button. Let the number on the screen bex. After pressing this button, the number becomes $\sqrt x$. After that, ZS the Coder levels up, so his current level becomes $k+1$. This button can only be pressed when $x$ is a perfect square, i.e. $x=m^2$ for some positive integerm.

Additionally, after each move, if ZS the Coder is at level $k$, and the number on the screen is $m$, then $m$ must be a multiple of $k$. Note that this condition is only checked after performing the press. For example, if ZS the Coder is at level $4$ and current number is $100$, he presses the '$\sqrt{}$' button and the number turns into $10$. Note that at this moment, $10$ is not divisible by $4$, but this press is still valid, because after it, ZS the Coder is at level $5$, and $10$ is divisible by $5$.
ZS the Coder needs your help in beating the game − he wants to reach level $n+1$. In other words, he needs to press the '$\sqrt{}$' button $n$ times. Help him determine the number of times he should press the '+' button before pressing the '$\sqrt{}$' button at each level.
Please note that ZS the Coder wants to find just any sequence of presses allowing him to reach level $n+1$, but not necessarily a sequence minimizing the number of presses.

The first and only line of the input contains a single integer $n\ (1≤n≤100000)$, denoting that ZS the Coder wants to reach level $n+1$.

Print $n$ non-negative integers, one per line. $i$-th of them should be equal to the number of times that ZS the Coder needs to press the '+' button before pressing the '$\sqrt{}$' button at level $i$.

Each number in the output should not exceed $10^{18}$. However, the number on the screen can be greater than $10^{18}$.

It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.

14
16
46

On the first level, ZS the Coder pressed the '+' button $14$ times (and the number on screen is initially $2$), so the number became $2+14·1=16$. Then, ZS the Coder pressed the '$\sqrt{}$' button, and the number became $\sqrt 16=4$.
After that, on the second level, ZS pressed the '+' button $16$ times, so the number becomes $4+16·2=36$. Then, ZS pressed the '$\sqrt{}$' button, levelling up and changing the number into $\sqrt 36=6$.
After that, on the third level, ZS pressed the '+' button $46$ times, so the number becomes $6+46·3=144$. Then, ZS pressed the '$\sqrt{}$' button, levelling up and changing the number into $\sqrt 144=12$.
Note that $12$ is indeed divisible by $4$, so ZS the Coder can reach level $4$.
Also, note that pressing the '+' button10times on the third level before levelling up does not work, because the number becomes $6+10·3=36$, and when the '$\sqrt{}$' button is pressed, the number becomes $\sqrt 36=6$ and ZS the Coder is at Level $4$. However, $6$ is not divisible by $4$ now, so this isnot a valid solution.

999999999999999998
44500000000

On the first level, ZS the Coder pressed the '+' button $999999999999999998$ times (and the number on screen is initially $2$), so the number became $2+999999999999999998·1=10^{18}$. Then, ZS the Coder pressed the '$\sqrt{}$' button, and the number became $\sqrt 10^{18}=10^9$.
After that, on the second level, ZS pressed the '+' button $44500000000$ times, so the number becomes $10^9+44500000000·2=9·10^{10}$. Then, ZS pressed the '$\sqrt{}$' button, levelling up and changing the number into $\sqrt {9\times 10^{10}}=300000$.
Note that $300000$ is a multiple of $3$, so ZS the Coder can reach level $3$.