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 1018. However, the number on the screen **can be greater** than 1018.
It is guaranteed that at least one solution exists. If there are multiple solutions, print any of them.
[samples]
## 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 = 1018. 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 109 + 44500000000·2 = 9·1010. 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.
**Definitions**
Let $ n \in \mathbb{Z} $, $ 1 \leq n \leq 100{,}000 $.
Let $ x_0 = 2 $ be the initial number on the screen.
For each level $ k \in \{1, 2, \dots, n\} $, let $ a_k \in \mathbb{Z}_{\geq 0} $ be the number of times the '+' button is pressed before pressing the '√' button at level $ k $.
Let $ x_k $ denote the number on the screen after completing level $ k $ (i.e., after $ a_k $ additions and one square root).
**Constraints**
For each $ k \in \{1, \dots, n\} $:
1. Before pressing '√' at level $ k $, the number is $ x_{k-1} + a_k \cdot k $.
2. After pressing '√', the number becomes $ x_k = \sqrt{x_{k-1} + a_k \cdot k} $.
3. After the press at level $ k $, $ x_k $ must be an integer, and $ x_k \equiv 0 \pmod{k+1} $.
**Objective**
Find any sequence $ (a_1, a_2, \dots, a_n) $ of non-negative integers such that:
$$
x_k = \sqrt{x_{k-1} + a_k \cdot k} \in \mathbb{Z}, \quad \text{and} \quad x_k \equiv 0 \pmod{k+1}, \quad \forall k \in \{1, \dots, n\}
$$
with $ x_0 = 2 $.