The magician shuffles a small pack of cards, holds it face down and performs the following procedure:
- One card is moved from the top of the pack to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
- Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
- Three cards are moved ...
- This goes on until the $n$-th and last card turns out to be the $n$ of Spades.
This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards, $n$.
Input
The input contains integer $n$, the number of cards.
Output
Output a line with the correct permutation of the values $1 \ldots n$, space separated. The first number showing the top card of the pack.
Constraints
Examples
Input:
4
Output:
2 1 4 3
Input:
5
Output:
3 1 4 5 2