Hypercubes#4238
Petya and Vasya are playing a game called hyperdice. The rules are straightforward: Petya rolls standard dice, and if the total sum of the points matches the number Vasya has predicted, Vasya wins; otherwise, Petya wins. For a single die, all outcomes are equally likely, but with two dice, the most likely sum is . Your task is to assist Vasya in identifying the most probable sums for any given .
The input consists of a single integer (1 \leq n \leq 10^8).
On the first line of the output, print – the count of the most probable sums when rolling dice. On the second line, list numbers in ascending order, representing the most probable sums of the dice rolls.
Example 1