Practice Coding with the exercise "Sum of odd"

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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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