A10468. Plus and Square Root

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.

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 '' 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.

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 $3$ .