Alice and Bob are playing a game.
Alice has a positive integer y between 1 to n. Bob doesn't know this number.
In each round of the game, Bob chooses a positive integer x, and asks Alice: Is y greater than or equal to x? Then Alice has to answer yes or no.
Alice can lie at most once. Bob wants to use as few rounds as possible to determine y, and Alice wants Bob to use as many rounds as possible.
Assume that both Alice and Bob are using the optimal strategy except for the first round.
As a Goodeat, you are neither Alice nor Bob.
But you need to ask, for each x = 1, 2, ..., n, when Bob asks whether y is greater than or equal to x in the first round and Alice answers yes in the first round, how many more rounds Bob needs to determine y.
(Alice may lie in the first round.)

First line contains an integer n. 

Output n numbers in a line, the i-th of which denotes the number of rounds Bob still need to determine y when Bob guesses i in the first round and Alice answers yes. 

4

5 5 4 3