Practice Coding with the exercise "Sum of odd"

Statement

In this puzzle, you have to find out if it is possible to compute the number in input by summing at least two consecutive positive odd numbers.

Input

A single number n.

Output

Line 1: the number of valid solutions.
Line 2: first and last values of the longest sequence of consecutive odd numbers.

Constraints

n < 2^32

Example

Input

Output

1
3 7

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