Spongebob and Squares

Spongebob is already tired trying to reason his weird actions and calculations, so he simply asked you to find all pairs of n and m, such that there are exactly x distinct squares in the table consisting of n rows and m columns. For example, in a 3 × 5 table there are 15 squares with side one, 8 squares with side two and 3 squares with side three. The total number of distinct squares in a 3 × 5 table is 15 + 8 + 3 = 26.

The first line of the input contains a single integer x (1 ≤ x ≤ 10¹⁸) — the number of squares inside the tables Spongebob is interested in.

First print a single integer k — the number of tables with exactly x distinct squares inside.

Then print k pairs of integers describing the tables. Print the pairs in the order of increasing n, and in case of equality — in the order of increasing m.

26

6
1 26
2 9
3 5
5 3
9 2
26 1

2

2
1 2
2 1

8

4
1 8
2 3
3 2
8 1

 Note

In a 1 × 2 table there are 2 1 × 1 squares. So, 2 distinct squares in total.
 
  

In a 2 × 3 table there are 6 1 × 1 squares and 2 2 × 2 squares. That is equal to 8 squares in total.