Roads of Potokolandiya#189
In Potokoland, there are cities and two-way roads. The -th road connects cities and (i+i) (if i+i>n, then i+i-n).
For example, if n=5, the roads will be , , , , and .
Determine if it is possible to travel from any city to any other city using the roads. If not, find a pair of cities that are not connected.
The first line contains one integer (1 \leq n \leq 10^6).
Output YES if it is possible to travel from any city to any other city.
Otherwise, output NO on the first line. On the second line, output any two cities and (1 \leq a, b \leq n; a \neq b) such that it is impossible to travel from to using the roads.
Example 1
Example 2
Example 3
Example 4