Spongebob and Squares

Description:

Input:

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.

Output:

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.

Sample Input:

26

Sample Output:

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

Sample Input:

2

Sample Output:

2
1 2
2 1

Sample Input:

8

Sample Output:

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.