33371번 - Bit Component 스페셜 저지다국어

Denis really likes binary representation of numbers. Once he wrote down binary representations of numbers from $1$ to $7$, in some order, one under the other, so that their rightmost digits were aligned. Then he realized that the ones in these numbers form a single connected region: if we consider the places for digits as squares on a grid, all squares containing ones are connected by sides. Now he wonders if the same thing can be done for numbers from $1$ to $n$ for different $n$.

You are given an integer $n$. You should find a good permutation of all integers from $1$ to $n$, or determine that there is no such permutation. A permutation is good if, when we write the numbers down as described above, the ones form a single connected region.

The only line contains a single integer $n$ ($1 \leq n \leq 2 \cdot 10^5$).

If there is no good permutation of numbers from $1$ to $n$, print a single line with the word "NO" (uppercase). Otherwise, print a line with the word "YES" (uppercase), and then another line containing the good permutation you found. If there are several possible answers, print any one of them.

Third example