ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, '$+$' (plus) and '' (square root). Initially, the number $2$ is displayed on the screen. There are $*n* + 1$ levels in the game and ZS the Coder start at the level $1$.

When ZS the Coder is at level $*k*$, 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 '' button. Let the number on the screen be $*x*$. After pressing this button, the number becomes . 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 integer $*m*$.

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 '' 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 '' button $*n*$ times. Help him determine the number of times he should press the '$+$' button before pressing the '' 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.

Input

The first and only line of the input contains a single integer $*n*$ ($1 ≤ *n* ≤ 100 000$), denoting that ZS the Coder wants to reach level $*n* + 1$.

Output

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 '' 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.

Note

In the first sample case:

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 '' button, and the number became .

After that, on the second level, ZS pressed the '$+$' button $16$ times, so the number becomes $4 + 16·2 = 36$. Then, ZS pressed the '' button, levelling up and changing the number into .

After that, on the third level, ZS pressed the '$+$' button $46$ times, so the number becomes $6 + 46·3 = 144$. Then, ZS pressed the '' button, levelling up and changing the number into .

Note that $12$ is indeed divisible by $4$, so ZS the Coder can reach level $4$.

Also, note that pressing the '$+$' button $10$ times on the third level before levelling up does not work, because the number becomes $6 + 10·3 = 36$, and when the '' button is pressed, the number becomes and ZS the Coder is at Level $4$. However, $6$ is not divisible by $4$ now, so this is not a valid solution.

In the second sample case:

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 '' button, and the number became .

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 '' button, levelling up and changing the number into .

Note that $300000$ is a multiple of $3$, so ZS the Coder can reach level $3$.