Problem C. Confections ≡

Statement

Today is Grisha's birthday! Each of his n friends brought a box of favorite sweets as a gift to the birthday boy. Since Grisha is not a greedy boy, he took all the sweets out of the boxes and put them on n + 1 plates and placed them in front of each guest (including himself). To everyone's delight, this was done without a remainder. Immediately after that, his mother returned from work and it was decided to put all the sweets on n + 2 plates. To everyone's surprise, this division was completed without a remainder.

Given the known number of sweets in one box k, determine the possible number of guests at the party.

Input format

The only line of the input contains a natural number k.

Output format

In the first line output single natural number g — the number of possible answers to the problem's question. In the second line print g natural numbers — possible number of guests in ascending order, separated by a space. It is guaranteed that there is at least one suitable answer.

Constraints

1 ≤ k ≤ 10⁹

Notes on sample

In the sample, the number of candies in one box is 6.

If one guest came to Grisha, then the total number of sweets is also 6. It is easy to divide them equally without a remainder both into two and three plates.

If two guests came to Grisha, then the total number of sweets is 12. It is easy to divide them equally without a remainder both into three and four plates

There are no other solutions.

Sample tests

6

2
1 2