Your task is to divide the numbers ~1, 2, \ldots, n~ into two sets of equal sum.

Input

• The only input line contains an integer ~n~.

Output

• Print YES, if the division is possible, and NO otherwise.
• After this, if the division is possible, print an example of how to create the sets. First, print the number of elements in the first set followed by the elements themselves in a separate line, and then, print the second set in a similar way.

Giới hạn

• ~1 \le n \le 10^6~

Example

Sample input 1

7

Sample output 1

YES
4
1 2 4 7
3
3 5 6

Sample input 2

6

Sample output 2

NO