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 $15 + 8 + 3 = 26$.

Input

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.

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 $*m*$.

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.