33371번 - Bit Component 스페셜 저지다국어

문제

Denis really likes binary representation of numbers. Once he wrote down binary representations of numbers from 1ドル$ to 7ドル,ドル 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ドル$ to $n$ for different $n$.

You are given an integer $n$. You should find a good permutation of all integers from 1ドル$ to $n,ドル 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.

입력

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

출력

If there is no good permutation of numbers from 1ドル$ to $n,ドル 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.

제한

노트

Third example