A10130. 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 $x$ ( $1<=x<=10^{18}$ ) — 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 $m$ .

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.