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 : 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 . 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 ≤ 100 000 ), 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