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CSES Problem Set

Two Sets


Task | Statistics


CSES - Two Sets

Time limit:1.00 s Memory limit:512 MB

Your task is to divide the numbers $1,2,\ldots,n$ into two sets so that the sums of the sets are equal.

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 how to create the sets. First, print the number of elements in the first set and the elements, and then, print the second set in a similar way.

Constraints
Example 1

Input:
7

Output:
YES
4
1 2 4 7
3
3 5 6


Example 2

Input:
6

Output:
NO